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overflow: hidden; text-overflow: ellipsis; -webkit-line-clamp: 3; -webkit-box-orient: vertical; }</style><div class="col-xs-12 clearfix"><div class="u-floatLeft"><h1 class="PageHeader-title u-m0x u-fs30">Mathematical Knowledge for Teaching</h1><div class="u-tcGrayDark">420 Followers</div><div class="u-tcGrayDark u-mt2x">Recent papers in <b>Mathematical Knowledge for Teaching</b></div></div></div></div></div></div><div class="TabbedNavigation"><div class="container"><div class="row"><div class="col-xs-12 clearfix"><ul class="nav u-m0x u-p0x list-inline u-displayFlex"><li class="active"><a href="https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching">Top Papers</a></li><li><a href="https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching/MostCited">Most Cited Papers</a></li><li><a href="https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching/MostDownloaded">Most Downloaded Papers</a></li><li><a href="https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching/MostRecent">Newest Papers</a></li><li><a class="" href="https://www.academia.edu/People/Mathematical_Knowledge_for_Teaching">People</a></li></ul></div><style type="text/css">ul.nav{flex-direction:row}@media(max-width: 567px){ul.nav{flex-direction:column}.TabbedNavigation li{max-width:100%}.TabbedNavigation li.active{background-color:var(--background-grey, #dddde2)}.TabbedNavigation li.active:before,.TabbedNavigation li.active:after{display:none}}</style></div></div></div><div class="container"><div class="row"><div class="col-xs-12"><div class="u-displayFlex"><div class="u-flexGrow1"><div class="works"><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_43099612" data-work_id="43099612" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/43099612/2021_35_1_El_conocimiento_matem%C3%A1tico_del_profesor_acerca_de_la_par%C3%A1bola_dise%C3%B1o_de_un_instrumento_para_investigaci%C3%B3n">2021, 35(1) - El conocimiento matemático del profesor acerca de la parábola: diseño de un instrumento para investigación</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">La investigación en Educación Matemática suele centrarse en compartir los resultados de la aplicación de instrumentos de obtención de información. Si bien dichos instrumentos suelen describirse en la sección de metodología, el proceso de... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_43099612" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">La investigación en Educación Matemática suele centrarse en compartir los resultados de la aplicación de instrumentos de obtención de información. Si bien dichos instrumentos suelen describirse en la sección de metodología, el proceso de su desarrollo no suele ser muy transparente para el lector. En esta investigación el objetivo es abordar dicha problemática y describir con todo detalle el proceso de generación de un cuestionario, basado en el modelo MTSK, para la exploración del conocimiento del profesor acerca de la parábola, entendida como cónica. Se presenta el diseño de un instrumento de carácter cualitativo que permite hacer una aproximación al conocimiento matemático del profesor acerca de la parábola, poniendo énfasis tanto en el uso de la teoría, como de la triangulación, interna y externa, como elementos clave en el diseño metodológico. El principal aporte fue determinar pautas para el diseño de cuestionarios basados en el modelo MTSK, las cuales pueden ser tomadas en cuenta al margen de los contenidos matemáticos.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/43099612" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="63ffb20a2cb44b842e400cc77a4d8dc0" rel="nofollow" data-download="{"attachment_id":64353999,"asset_id":43099612,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/64353999/download_file?st=MTczMzAyOTA0OCw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="28483274" href="https://una-cr.academia.edu/RevistaUniciencia">Revista Uniciencia</a><script data-card-contents-for-user="28483274" type="text/json">{"id":28483274,"first_name":"Revista","last_name":"Uniciencia","domain_name":"una-cr","page_name":"RevistaUniciencia","display_name":"Revista Uniciencia","profile_url":"https://una-cr.academia.edu/RevistaUniciencia?f_ri=66102","photo":"https://0.academia-photos.com/28483274/8049897/10096681/s65_revista.uniciencia.jpg"}</script></span></span></li><li class="js-paper-rank-work_43099612 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="43099612"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 43099612, container: ".js-paper-rank-work_43099612", }); 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$(".js-view-count[data-work-id=43099612]").text(description); $(".js-view-count-work_43099612").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_43099612").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="43099612"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">19</a>  </div><span class="InlineList-item-text u-textTruncate u-pl10x"><a class="InlineList-item-text" data-has-card-for-ri="2731" href="https://www.academia.edu/Documents/in/Mathematics_Education">Mathematics Education</a>, <script data-card-contents-for-ri="2731" type="text/json">{"id":2731,"name":"Mathematics Education","url":"https://www.academia.edu/Documents/in/Mathematics_Education?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="27801" href="https://www.academia.edu/Documents/in/Mathematics_Teacher_Education">Mathematics Teacher Education</a>, <script data-card-contents-for-ri="27801" type="text/json">{"id":27801,"name":"Mathematics Teacher Education","url":"https://www.academia.edu/Documents/in/Mathematics_Teacher_Education?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="46722" href="https://www.academia.edu/Documents/in/Elementary_Mathematics_Education">Elementary Mathematics Education</a>, <script data-card-contents-for-ri="46722" type="text/json">{"id":46722,"name":"Elementary Mathematics Education","url":"https://www.academia.edu/Documents/in/Elementary_Mathematics_Education?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="66102" href="https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching">Mathematical Knowledge for Teaching</a><script data-card-contents-for-ri="66102" type="text/json">{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=43099612]'), work: {"id":43099612,"title":"2021, 35(1) - El conocimiento matemático del profesor acerca de la parábola: diseño de un instrumento para investigación","created_at":"2020-05-18T17:17:19.117-07:00","url":"https://www.academia.edu/43099612/2021_35_1_El_conocimiento_matem%C3%A1tico_del_profesor_acerca_de_la_par%C3%A1bola_dise%C3%B1o_de_un_instrumento_para_investigaci%C3%B3n?f_ri=66102","dom_id":"work_43099612","summary":"La investigación en Educación Matemática suele centrarse en compartir los resultados de la aplicación de instrumentos de obtención de información. Si bien dichos instrumentos suelen describirse en la sección de metodología, el proceso de su desarrollo no suele ser muy transparente para el lector. En esta investigación el objetivo es abordar dicha problemática y describir con todo detalle el proceso de generación de un cuestionario, basado en el modelo MTSK, para la exploración del conocimiento del profesor acerca de la parábola, entendida como cónica. Se presenta el diseño de un instrumento de carácter cualitativo que permite hacer una aproximación al conocimiento matemático del profesor acerca de la parábola, poniendo énfasis tanto en el uso de la teoría, como de la triangulación, interna y externa, como elementos clave en el diseño metodológico. El principal aporte fue determinar pautas para el diseño de cuestionarios basados en el modelo MTSK, las cuales pueden ser tomadas en cuenta al margen de los contenidos matemáticos.","downloadable_attachments":[{"id":64353999,"asset_id":43099612,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":28483274,"first_name":"Revista","last_name":"Uniciencia","domain_name":"una-cr","page_name":"RevistaUniciencia","display_name":"Revista Uniciencia","profile_url":"https://una-cr.academia.edu/RevistaUniciencia?f_ri=66102","photo":"https://0.academia-photos.com/28483274/8049897/10096681/s65_revista.uniciencia.jpg"}],"research_interests":[{"id":2731,"name":"Mathematics Education","url":"https://www.academia.edu/Documents/in/Mathematics_Education?f_ri=66102","nofollow":false},{"id":27801,"name":"Mathematics Teacher Education","url":"https://www.academia.edu/Documents/in/Mathematics_Teacher_Education?f_ri=66102","nofollow":false},{"id":46722,"name":"Elementary Mathematics Education","url":"https://www.academia.edu/Documents/in/Elementary_Mathematics_Education?f_ri=66102","nofollow":false},{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102","nofollow":false},{"id":72555,"name":"Didáctica de las matemáticas en Educación Básica","url":"https://www.academia.edu/Documents/in/Didactica_de_las_matematicas_en_Educacion_Basica?f_ri=66102"},{"id":88878,"name":"Questionnaire","url":"https://www.academia.edu/Documents/in/Questionnaire?f_ri=66102"},{"id":145280,"name":"Educação Matemática","url":"https://www.academia.edu/Documents/in/Educa%C3%A7%C3%A3o_Matem%C3%A1tica?f_ri=66102"},{"id":182978,"name":"Educación Matemática","url":"https://www.academia.edu/Documents/in/Educaci%C3%B3n_Matem%C3%A1tica?f_ri=66102"},{"id":325323,"name":"Functions","url":"https://www.academia.edu/Documents/in/Functions?f_ri=66102"},{"id":327850,"name":"Questionnaires","url":"https://www.academia.edu/Documents/in/Questionnaires?f_ri=66102"},{"id":332569,"name":"Funciones","url":"https://www.academia.edu/Documents/in/Funciones?f_ri=66102"},{"id":356017,"name":"Secondary and Primary Mathematics Education","url":"https://www.academia.edu/Documents/in/Secondary_and_Primary_Mathematics_Education?f_ri=66102"},{"id":388984,"name":"Cuestionarios","url":"https://www.academia.edu/Documents/in/Cuestionarios?f_ri=66102"},{"id":725264,"name":"MTSK","url":"https://www.academia.edu/Documents/in/MTSK?f_ri=66102"},{"id":901174,"name":"Questionário","url":"https://www.academia.edu/Documents/in/Question%C3%A1rio?f_ri=66102"},{"id":1259256,"name":"Parabola","url":"https://www.academia.edu/Documents/in/Parabola?f_ri=66102"},{"id":2005517,"name":"Conocimiento matemático","url":"https://www.academia.edu/Documents/in/Conocimiento_matem%C3%A1tico?f_ri=66102"},{"id":2582347,"name":"Conocimiento profesional del profesor - Matemática en contexto","url":"https://www.academia.edu/Documents/in/Conocimiento_profesional_del_profesor_-_Matem%C3%A1tica_en_contexto?f_ri=66102"},{"id":3065386,"name":"Conhecimento matemático para o ensino","url":"https://www.academia.edu/Documents/in/Conhecimento_matem%C3%A1tico_para_o_ensino?f_ri=66102"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_197801" data-work_id="197801" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/197801/The_Nature_of_Knowing_A_Resource_Manual_for_the_International_Baccalaureate_Ibid_Press_Melbourne_2006_">The Nature of Knowing: A Resource Manual for the International Baccalaureate. Ibid Press: Melbourne (2006)</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">One important aim of Theory of Knowledge in the International Baccalaureate is to teach students how to think for themselves. The student is encouraged to reflect on what they are learning and to reflect on themselves as learners. Theory... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_197801" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">One important aim of Theory of Knowledge in the International Baccalaureate is to teach students how to think for themselves. The student is encouraged to reflect on what they are learning and to reflect on themselves as learners. Theory of Knowledge is different from other areas in the International Baccalaureate because there are few hard facts to be learned. The Theory of Knowledge program aims to develop a certain attitude of questioning and the skills needed to ask these questions and find answers to them. Another aim of Theory of Knowledge is to ask students to look at the whole of what they are learning and relate their knowledge to themselves as individuals and to life as they know it outside of the classroom. This book is an attempt to achieve both of these aims. <br /> <br />Theory of Knowledge or TOK is a holistic endeavour: it aims to make connections between the ways of knowing and various areas of knowledge studied during the International Baccalaureate. In conventional philosophical terms, it might be termed practical epistemology (“epistemology” = study of knowledge). In contrast to the dry debates with which philosophers of knowledge concern themselves, TOK attempts to understand knowledge as an organic process involving situated knowers in a world of facts and information, which require interpretation. The knower begins to interpret this information by means of various ways of knowing and drawing upon, and influencing, a number of areas of knowledge. <br />The four ways of knowing are emotion, reason, language, and sense perception. It is taken for granted in TOK that each of these facets of knowing is crucial for determining our knowledge and knowledge claims. Knowledge is more than rationality, though reason too is a vital part of knowing. Quite often we base our judgements on things other than reason, as this book will make plain. The means by which each of these ways of knowing contribute to what we take to be knowledge is a matter of considerable importance to both individual human life and civilization. An understanding of these processes, and the role they play in knowledge, is part of what it means to be an “educated person”. Hence the importance of TOK for the International Baccalaureate.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/197801" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="2aa68dd8694145e9d2ff623f0be7fd17" rel="nofollow" data-download="{"attachment_id":64632808,"asset_id":197801,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/64632808/download_file?st=MTczMzAyOTA0OCw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="86006" href="https://unimelb.academia.edu/MartinDavies">Martin Davies</a><script data-card-contents-for-user="86006" type="text/json">{"id":86006,"first_name":"Martin","last_name":"Davies","domain_name":"unimelb","page_name":"MartinDavies","display_name":"Martin Davies","profile_url":"https://unimelb.academia.edu/MartinDavies?f_ri=66102","photo":"https://0.academia-photos.com/86006/23998/151125862/s65_martin.davies.jpeg"}</script></span></span></li><li class="js-paper-rank-work_197801 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="197801"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 197801, container: ".js-paper-rank-work_197801", }); });</script></li><li class="js-percentile-work_197801 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 197801; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_197801"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_197801 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="197801"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 197801; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=197801]").text(description); $(".js-view-count-work_197801").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_197801").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="197801"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">7</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="815" href="https://www.academia.edu/Documents/in/Epistemology">Epistemology</a>, <script data-card-contents-for-ri="815" type="text/json">{"id":815,"name":"Epistemology","url":"https://www.academia.edu/Documents/in/Epistemology?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="18779" href="https://www.academia.edu/Documents/in/International_Baccalaureate">International Baccalaureate</a>, <script data-card-contents-for-ri="18779" type="text/json">{"id":18779,"name":"International Baccalaureate","url":"https://www.academia.edu/Documents/in/International_Baccalaureate?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="22913" href="https://www.academia.edu/Documents/in/Science_Epistemology">Science Epistemology</a>, <script data-card-contents-for-ri="22913" type="text/json">{"id":22913,"name":"Science Epistemology","url":"https://www.academia.edu/Documents/in/Science_Epistemology?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="23925" href="https://www.academia.edu/Documents/in/Philosophy_of_Science_History_of_the_Philosophy_of_Science_Epistemology_of_Experimentation_Histor">Philosophy of Science, History of the Philosophy of Science, Epistemology of Experimentation, History of the Human sciences</a><script data-card-contents-for-ri="23925" type="text/json">{"id":23925,"name":"Philosophy of Science, History of the Philosophy of Science, Epistemology of Experimentation, History of the Human sciences","url":"https://www.academia.edu/Documents/in/Philosophy_of_Science_History_of_the_Philosophy_of_Science_Epistemology_of_Experimentation_Histor?f_ri=66102","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=197801]'), work: {"id":197801,"title":"The Nature of Knowing: A Resource Manual for the International Baccalaureate. Ibid Press: Melbourne (2006)","created_at":"2009-11-19T06:17:08.726-08:00","url":"https://www.academia.edu/197801/The_Nature_of_Knowing_A_Resource_Manual_for_the_International_Baccalaureate_Ibid_Press_Melbourne_2006_?f_ri=66102","dom_id":"work_197801","summary":"One important aim of Theory of Knowledge in the International Baccalaureate is to teach students how to think for themselves. The student is encouraged to reflect on what they are learning and to reflect on themselves as learners. Theory of Knowledge is different from other areas in the International Baccalaureate because there are few hard facts to be learned. The Theory of Knowledge program aims to develop a certain attitude of questioning and the skills needed to ask these questions and find answers to them. Another aim of Theory of Knowledge is to ask students to look at the whole of what they are learning and relate their knowledge to themselves as individuals and to life as they know it outside of the classroom. This book is an attempt to achieve both of these aims.\r\n\r\nTheory of Knowledge or TOK is a holistic endeavour: it aims to make connections between the ways of knowing and various areas of knowledge studied during the International Baccalaureate. In conventional philosophical terms, it might be termed practical epistemology (“epistemology” = study of knowledge). In contrast to the dry debates with which philosophers of knowledge concern themselves, TOK attempts to understand knowledge as an organic process involving situated knowers in a world of facts and information, which require interpretation. The knower begins to interpret this information by means of various ways of knowing and drawing upon, and influencing, a number of areas of knowledge.\r\nThe four ways of knowing are emotion, reason, language, and sense perception. It is taken for granted in TOK that each of these facets of knowing is crucial for determining our knowledge and knowledge claims. Knowledge is more than rationality, though reason too is a vital part of knowing. Quite often we base our judgements on things other than reason, as this book will make plain. The means by which each of these ways of knowing contribute to what we take to be knowledge is a matter of considerable importance to both individual human life and civilization. An understanding of these processes, and the role they play in knowledge, is part of what it means to be an “educated person”. Hence the importance of TOK for the International Baccalaureate.","downloadable_attachments":[{"id":64632808,"asset_id":197801,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":86006,"first_name":"Martin","last_name":"Davies","domain_name":"unimelb","page_name":"MartinDavies","display_name":"Martin Davies","profile_url":"https://unimelb.academia.edu/MartinDavies?f_ri=66102","photo":"https://0.academia-photos.com/86006/23998/151125862/s65_martin.davies.jpeg"}],"research_interests":[{"id":815,"name":"Epistemology","url":"https://www.academia.edu/Documents/in/Epistemology?f_ri=66102","nofollow":false},{"id":18779,"name":"International Baccalaureate","url":"https://www.academia.edu/Documents/in/International_Baccalaureate?f_ri=66102","nofollow":false},{"id":22913,"name":"Science Epistemology","url":"https://www.academia.edu/Documents/in/Science_Epistemology?f_ri=66102","nofollow":false},{"id":23925,"name":"Philosophy of Science, History of the Philosophy of Science, Epistemology of Experimentation, History of the Human sciences","url":"https://www.academia.edu/Documents/in/Philosophy_of_Science_History_of_the_Philosophy_of_Science_Epistemology_of_Experimentation_Histor?f_ri=66102","nofollow":false},{"id":47614,"name":"Theory of Knowledge","url":"https://www.academia.edu/Documents/in/Theory_of_Knowledge?f_ri=66102"},{"id":48712,"name":"Alternative ways of knowing","url":"https://www.academia.edu/Documents/in/Alternative_ways_of_knowing?f_ri=66102"},{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_74323147" data-work_id="74323147" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/74323147/El_conocimiento_del_profesorado_de_Educaci%C3%B3n_Primaria_para_ense%C3%B1ar_estad%C3%ADstica_y_probabilidad_una_revisi%C3%B3n_sistem%C3%A1tica">El conocimiento del profesorado de Educación Primaria para enseñar estadística y probabilidad: una revisión sistemática.</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">Se presenta una revisión sistemática de estudios de los últimos 25 años (1997-2021) que analizan, desde distintos modelos, el conocimiento del profesorado de Educación Primaria para enseñar estadística y probabilidad. A partir de una... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_74323147" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">Se presenta una revisión sistemática de estudios de los últimos 25 años (1997-2021) que analizan, desde distintos modelos, el conocimiento del profesorado de Educación Primaria para enseñar estadística y probabilidad. A partir de una revisión en JCR/SSCI, Scopus, Eric, Google Académico, Science Direct, World Scientific, Springer y Wiley Online library, se han identificado 34 estudios que se han analizado con base en dos objetivos: 1) identificar los participantes, el conocimiento matemático y el modelo de conocimiento utilizado; 2) identificar, en los estudios con profesorado en activo, los instrumentos de obtención de datos y los resultados obtenidos. Los datos del primer objetivo muestran: un predominio de las investigaciones con futuros docentes; un mayor número de estudios sobre el conocimiento para enseñar probabilidad; y los modelos más usados son el Mathematical Knowledge for Teaching (MKT) y el Modelo de Conocimientos y Competencias Didáctico-Matemáticas (CCDM). En relación con el segundo objetivo, el instrumento más utilizado es el cuestionario y los estudios reportan bajos conocimientos. Palabras Clave: estadística, probabilidad, conocimiento del profesorado, revisión sistemática, Educación Primaria.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/74323147" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="5a2d2de0cb2ef0d68e95c0a7c026f639" rel="nofollow" data-download="{"attachment_id":82515686,"asset_id":74323147,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/82515686/download_file?st=MTczMzAyOTA0OCw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="542378" href="https://ugirona.academia.edu/AngelAlsina">Angel Alsina</a><script data-card-contents-for-user="542378" type="text/json">{"id":542378,"first_name":"Angel","last_name":"Alsina","domain_name":"ugirona","page_name":"AngelAlsina","display_name":"Angel Alsina","profile_url":"https://ugirona.academia.edu/AngelAlsina?f_ri=66102","photo":"https://0.academia-photos.com/542378/9879688/15244312/s65_angel.alsina.jpg"}</script></span></span></li><li class="js-paper-rank-work_74323147 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="74323147"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 74323147, container: ".js-paper-rank-work_74323147", }); 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$(".js-view-count[data-work-id=74323147]").text(description); $(".js-view-count-work_74323147").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_74323147").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="74323147"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">15</a>  </div><span class="InlineList-item-text u-textTruncate u-pl10x"><a class="InlineList-item-text" data-has-card-for-ri="892" href="https://www.academia.edu/Documents/in/Statistics">Statistics</a>, <script data-card-contents-for-ri="892" type="text/json">{"id":892,"name":"Statistics","url":"https://www.academia.edu/Documents/in/Statistics?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="4840" href="https://www.academia.edu/Documents/in/Statistics_Education">Statistics Education</a>, <script data-card-contents-for-ri="4840" type="text/json">{"id":4840,"name":"Statistics Education","url":"https://www.academia.edu/Documents/in/Statistics_Education?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="6482" href="https://www.academia.edu/Documents/in/Meta-Analysis_and_Systematic_Review">Meta-Analysis and Systematic Review</a>, <script data-card-contents-for-ri="6482" type="text/json">{"id":6482,"name":"Meta-Analysis and Systematic Review","url":"https://www.academia.edu/Documents/in/Meta-Analysis_and_Systematic_Review?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="22613" href="https://www.academia.edu/Documents/in/Probability_and_statistics">Probability and statistics</a><script data-card-contents-for-ri="22613" type="text/json">{"id":22613,"name":"Probability and statistics","url":"https://www.academia.edu/Documents/in/Probability_and_statistics?f_ri=66102","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=74323147]'), work: {"id":74323147,"title":"El conocimiento del profesorado de Educación Primaria para enseñar estadística y probabilidad: una revisión sistemática.","created_at":"2022-03-22T11:51:09.614-07:00","url":"https://www.academia.edu/74323147/El_conocimiento_del_profesorado_de_Educaci%C3%B3n_Primaria_para_ense%C3%B1ar_estad%C3%ADstica_y_probabilidad_una_revisi%C3%B3n_sistem%C3%A1tica?f_ri=66102","dom_id":"work_74323147","summary":"Se presenta una revisión sistemática de estudios de los últimos 25 años (1997-2021) que analizan, desde distintos modelos, el conocimiento del profesorado de Educación Primaria para enseñar estadística y probabilidad. A partir de una revisión en JCR/SSCI, Scopus, Eric, Google Académico, Science Direct, World Scientific, Springer y Wiley Online library, se han identificado 34 estudios que se han analizado con base en dos objetivos: 1) identificar los participantes, el conocimiento matemático y el modelo de conocimiento utilizado; 2) identificar, en los estudios con profesorado en activo, los instrumentos de obtención de datos y los resultados obtenidos. Los datos del primer objetivo muestran: un predominio de las investigaciones con futuros docentes; un mayor número de estudios sobre el conocimiento para enseñar probabilidad; y los modelos más usados son el Mathematical Knowledge for Teaching (MKT) y el Modelo de Conocimientos y Competencias Didáctico-Matemáticas (CCDM). En relación con el segundo objetivo, el instrumento más utilizado es el cuestionario y los estudios reportan bajos conocimientos. Palabras Clave: estadística, probabilidad, conocimiento del profesorado, revisión sistemática, Educación Primaria. ","downloadable_attachments":[{"id":82515686,"asset_id":74323147,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":542378,"first_name":"Angel","last_name":"Alsina","domain_name":"ugirona","page_name":"AngelAlsina","display_name":"Angel Alsina","profile_url":"https://ugirona.academia.edu/AngelAlsina?f_ri=66102","photo":"https://0.academia-photos.com/542378/9879688/15244312/s65_angel.alsina.jpg"}],"research_interests":[{"id":892,"name":"Statistics","url":"https://www.academia.edu/Documents/in/Statistics?f_ri=66102","nofollow":false},{"id":4840,"name":"Statistics Education","url":"https://www.academia.edu/Documents/in/Statistics_Education?f_ri=66102","nofollow":false},{"id":6482,"name":"Meta-Analysis and Systematic Review","url":"https://www.academia.edu/Documents/in/Meta-Analysis_and_Systematic_Review?f_ri=66102","nofollow":false},{"id":22613,"name":"Probability and statistics","url":"https://www.academia.edu/Documents/in/Probability_and_statistics?f_ri=66102","nofollow":false},{"id":23876,"name":"Mathematics Education at Primary Schools","url":"https://www.academia.edu/Documents/in/Mathematics_Education_at_Primary_Schools?f_ri=66102"},{"id":33069,"name":"Probability","url":"https://www.academia.edu/Documents/in/Probability?f_ri=66102"},{"id":44293,"name":"Literature Review","url":"https://www.academia.edu/Documents/in/Literature_Review?f_ri=66102"},{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102"},{"id":72555,"name":"Didáctica de las matemáticas en Educación Básica","url":"https://www.academia.edu/Documents/in/Didactica_de_las_matematicas_en_Educacion_Basica?f_ri=66102"},{"id":109652,"name":"Teacher knowledge","url":"https://www.academia.edu/Documents/in/Teacher_knowledge?f_ri=66102"},{"id":402504,"name":"Mathematical Knowledge for Teaching, Mathematics Teacher Education","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching_Mathematics_Teacher_Education?f_ri=66102"},{"id":531896,"name":"Estadística","url":"https://www.academia.edu/Documents/in/Estad%C3%ADstica?f_ri=66102"},{"id":830901,"name":"Educación Primaria","url":"https://www.academia.edu/Documents/in/Educaci%C3%B3n_Primaria?f_ri=66102"},{"id":849389,"name":"Probabilidad","url":"https://www.academia.edu/Documents/in/Probabilidad?f_ri=66102"},{"id":1352060,"name":"REVISIÓN BIBLIOGRÁFICA","url":"https://www.academia.edu/Documents/in/REVISI%C3%93N_BIBLIOGR%C3%81FICA?f_ri=66102"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_650177" data-work_id="650177" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/650177/Mathematical_knowledge_and_practices_resulting_from_access_to_digital_technologies">Mathematical knowledge and practices resulting from access to digital technologies</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">Through an extensive review of the literature we indicate how technol-ogy has influenced the contexts for learning mathematics, and the emergence of a new learning ecology that results from the integration of technology into these... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_650177" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">Through an extensive review of the literature we indicate how technol-ogy has influenced the contexts for learning mathematics, and the emergence of a new learning ecology that results from the integration of technology into these learning contexts. Conversely, we argue that the mathematics on which the tech-nologies are based influences their design, especially the affordances and con-straints for learning of the specific design. The literature indicates that interactions among students, teachers, tasks, and technologies can bring about a shift in em-powerment from teacher or external authority to the students as generators of ma-thematical knowledge and practices; and that feedback provided through the use of different technologies can contribute to students‘ learning. Recent develop-ments in dynamic technologies have the potential to promote new mathematical practices in different contexts: for example, dynamic geometry, statistical educa-tion, robotics and digital games. We propose a transformation of the traditional di-dactic triangle into a didactic tetrahedron through the introduction of technology and conclude by restructuring this model so as to redefine the space in which new mathematical knowledge and practices can emerge.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/650177" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="5ae81b0dfa560c0c7728c9fce99f37cc" rel="nofollow" data-download="{"attachment_id":3578321,"asset_id":650177,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/3578321/download_file?st=MTczMzAyOTA0OCw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="131727" href="https://uq.academia.edu/KatieMakar">Katie Makar</a><script data-card-contents-for-user="131727" type="text/json">{"id":131727,"first_name":"Katie","last_name":"Makar","domain_name":"uq","page_name":"KatieMakar","display_name":"Katie Makar","profile_url":"https://uq.academia.edu/KatieMakar?f_ri=66102","photo":"https://0.academia-photos.com/131727/35108/528465/s65_katie.makar.jpg"}</script></span></span></li><li class="js-paper-rank-work_650177 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="650177"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 650177, container: ".js-paper-rank-work_650177", }); 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$(".js-view-count[data-work-id=650177]").text(description); $(".js-view-count-work_650177").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_650177").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="650177"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">3</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="19592" href="https://www.academia.edu/Documents/in/Mathematical_Practice">Mathematical Practice</a>, <script data-card-contents-for-ri="19592" type="text/json">{"id":19592,"name":"Mathematical Practice","url":"https://www.academia.edu/Documents/in/Mathematical_Practice?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="20216" href="https://www.academia.edu/Documents/in/Context_Based_Learning">Context Based Learning</a>, <script data-card-contents-for-ri="20216" type="text/json">{"id":20216,"name":"Context Based Learning","url":"https://www.academia.edu/Documents/in/Context_Based_Learning?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="66102" href="https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching">Mathematical Knowledge for Teaching</a><script data-card-contents-for-ri="66102" type="text/json">{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=650177]'), work: {"id":650177,"title":"Mathematical knowledge and practices resulting from access to digital technologies","created_at":"2011-06-07T11:11:41.608-07:00","url":"https://www.academia.edu/650177/Mathematical_knowledge_and_practices_resulting_from_access_to_digital_technologies?f_ri=66102","dom_id":"work_650177","summary":"Through an extensive review of the literature we indicate how technol-ogy has influenced the contexts for learning mathematics, and the emergence of a new learning ecology that results from the integration of technology into these learning contexts. Conversely, we argue that the mathematics on which the tech-nologies are based influences their design, especially the affordances and con-straints for learning of the specific design. The literature indicates that interactions among students, teachers, tasks, and technologies can bring about a shift in em-powerment from teacher or external authority to the students as generators of ma-thematical knowledge and practices; and that feedback provided through the use of different technologies can contribute to students‘ learning. Recent develop-ments in dynamic technologies have the potential to promote new mathematical practices in different contexts: for example, dynamic geometry, statistical educa-tion, robotics and digital games. We propose a transformation of the traditional di-dactic triangle into a didactic tetrahedron through the introduction of technology and conclude by restructuring this model so as to redefine the space in which new mathematical knowledge and practices can emerge.","downloadable_attachments":[{"id":3578321,"asset_id":650177,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":131727,"first_name":"Katie","last_name":"Makar","domain_name":"uq","page_name":"KatieMakar","display_name":"Katie Makar","profile_url":"https://uq.academia.edu/KatieMakar?f_ri=66102","photo":"https://0.academia-photos.com/131727/35108/528465/s65_katie.makar.jpg"}],"research_interests":[{"id":19592,"name":"Mathematical Practice","url":"https://www.academia.edu/Documents/in/Mathematical_Practice?f_ri=66102","nofollow":false},{"id":20216,"name":"Context Based Learning","url":"https://www.academia.edu/Documents/in/Context_Based_Learning?f_ri=66102","nofollow":false},{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102","nofollow":false}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_42948511 coauthored" data-work_id="42948511" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/42948511/Assessing_Factors_Influencing_Pre_Service_Teachers_Mathematical_Knowledge_for_Teaching_MKT_Mathematics_in_Ghanaian_Basic_Schools">Assessing Factors Influencing Pre-Service Teachers' Mathematical Knowledge for Teaching (MKT) Mathematics in Ghanaian Basic Schools</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">Introduction: Knowledge about teaching mathematics remains a contentious issue in the preparation of pre-service teachers. This study assessed factors influencing pre-service teachers' mathematical knowledge for teaching (MKT) mathematics... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_42948511" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">Introduction: Knowledge about teaching mathematics remains a contentious issue in the preparation of pre-service teachers. This study assessed factors influencing pre-service teachers' mathematical knowledge for teaching (MKT) mathematics in Ghanaian basic schools. Methods: The cross-sectional survey design was adopted for this study. A total of 998 pre-service teachers from ten (10) public colleges of education were sampled via multi-stage sampling technique for the study. Structured questionnaire and unstructured observation schedule were used to conduct the survey. Secondary data was also collected in the form of mathematics test results. The Statistical Package for Social Sciences version 22 was used to analyse the data using descriptive statistics (frequency count, percentage) and inferential statistics (Pearson's correlation, multiple regression, exploratory factor analysis). Results: The study revealed that many pre-service teachers in Ghanaian public colleges of education had weak mathematics content knowledge. The following factors influenced MKT of the pre-service teachers: gender, ways of imparting mathematics knowledge, perception about mathematics as a subject, perception about mathematics teaching and learning and attitudes towards mathematics (p < .05). Conclusions: This study exploring the factors that influence pre-service teachers' MKT suggests that, to be able to build effective mathematics teacher base in any basic school, there must be effective training on factors like gender, perception, and attitude. There is therefore the need for the National Council for Tertiary Education to emphasis on factors that influence MKT besides the content of the college of education mathematics curriculum.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/42948511" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="9f8dffdca4cf6b20888da54676fc7222" rel="nofollow" data-download="{"attachment_id":63203457,"asset_id":42948511,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/63203457/download_file?st=MTczMzAyOTA0OCw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="37769006" href="https://texilaconnect.academia.edu/TexilaInternationalJournal">Texila International Journal</a><script data-card-contents-for-user="37769006" type="text/json">{"id":37769006,"first_name":"Texila International","last_name":"Journal","domain_name":"texilaconnect","page_name":"TexilaInternationalJournal","display_name":"Texila International Journal","profile_url":"https://texilaconnect.academia.edu/TexilaInternationalJournal?f_ri=66102","photo":"https://0.academia-photos.com/37769006/15581072/16233473/s65_texila_international.journal.png"}</script></span></span><span class="u-displayInlineBlock InlineList-item-text"> and <span class="u-textDecorationUnderline u-clickable InlineList-item-text js-work-more-authors-42948511">+1</span><div class="hidden js-additional-users-42948511"><div><span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a href="https://ugh.academia.edu/MillicentNarhKert">Millicent Narh-Kert</a></span></div></div></span><script>(function(){ var popoverSettings = { el: $('.js-work-more-authors-42948511'), placement: 'bottom', hide_delay: 200, html: true, content: function(){ return $('.js-additional-users-42948511').html(); } } new HoverPopover(popoverSettings); })();</script></li><li class="js-paper-rank-work_42948511 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="42948511"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 42948511, container: ".js-paper-rank-work_42948511", }); });</script></li><li class="js-percentile-work_42948511 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 42948511; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_42948511"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_42948511 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="42948511"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 42948511; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=42948511]").text(description); $(".js-view-count-work_42948511").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_42948511").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="42948511"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">4</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="66102" href="https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching">Mathematical Knowledge for Teaching</a>, <script data-card-contents-for-ri="66102" type="text/json">{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="82717" href="https://www.academia.edu/Documents/in/Pre-service_teachers">Pre-service teachers</a>, <script data-card-contents-for-ri="82717" type="text/json">{"id":82717,"name":"Pre-service teachers","url":"https://www.academia.edu/Documents/in/Pre-service_teachers?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="90962" href="https://www.academia.edu/Documents/in/Academic_research">Academic research</a>, <script data-card-contents-for-ri="90962" type="text/json">{"id":90962,"name":"Academic research","url":"https://www.academia.edu/Documents/in/Academic_research?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="1741385" href="https://www.academia.edu/Documents/in/Colleges_of_Education">Colleges of Education</a><script data-card-contents-for-ri="1741385" type="text/json">{"id":1741385,"name":"Colleges of Education","url":"https://www.academia.edu/Documents/in/Colleges_of_Education?f_ri=66102","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=42948511]'), work: {"id":42948511,"title":"Assessing Factors Influencing Pre-Service Teachers' Mathematical Knowledge for Teaching (MKT) Mathematics in Ghanaian Basic Schools","created_at":"2020-05-05T05:01:46.302-07:00","url":"https://www.academia.edu/42948511/Assessing_Factors_Influencing_Pre_Service_Teachers_Mathematical_Knowledge_for_Teaching_MKT_Mathematics_in_Ghanaian_Basic_Schools?f_ri=66102","dom_id":"work_42948511","summary":"Introduction: Knowledge about teaching mathematics remains a contentious issue in the preparation of pre-service teachers. This study assessed factors influencing pre-service teachers' mathematical knowledge for teaching (MKT) mathematics in Ghanaian basic schools. Methods: The cross-sectional survey design was adopted for this study. A total of 998 pre-service teachers from ten (10) public colleges of education were sampled via multi-stage sampling technique for the study. Structured questionnaire and unstructured observation schedule were used to conduct the survey. Secondary data was also collected in the form of mathematics test results. The Statistical Package for Social Sciences version 22 was used to analyse the data using descriptive statistics (frequency count, percentage) and inferential statistics (Pearson's correlation, multiple regression, exploratory factor analysis). Results: The study revealed that many pre-service teachers in Ghanaian public colleges of education had weak mathematics content knowledge. The following factors influenced MKT of the pre-service teachers: gender, ways of imparting mathematics knowledge, perception about mathematics as a subject, perception about mathematics teaching and learning and attitudes towards mathematics (p \u003c .05). Conclusions: This study exploring the factors that influence pre-service teachers' MKT suggests that, to be able to build effective mathematics teacher base in any basic school, there must be effective training on factors like gender, perception, and attitude. There is therefore the need for the National Council for Tertiary Education to emphasis on factors that influence MKT besides the content of the college of education mathematics curriculum.","downloadable_attachments":[{"id":63203457,"asset_id":42948511,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":37769006,"first_name":"Texila International","last_name":"Journal","domain_name":"texilaconnect","page_name":"TexilaInternationalJournal","display_name":"Texila International Journal","profile_url":"https://texilaconnect.academia.edu/TexilaInternationalJournal?f_ri=66102","photo":"https://0.academia-photos.com/37769006/15581072/16233473/s65_texila_international.journal.png"},{"id":158008486,"first_name":"Millicent","last_name":"Narh-Kert","domain_name":"ugh","page_name":"MillicentNarhKert","display_name":"Millicent Narh-Kert","profile_url":"https://ugh.academia.edu/MillicentNarhKert?f_ri=66102","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102","nofollow":false},{"id":82717,"name":"Pre-service teachers","url":"https://www.academia.edu/Documents/in/Pre-service_teachers?f_ri=66102","nofollow":false},{"id":90962,"name":"Academic research","url":"https://www.academia.edu/Documents/in/Academic_research?f_ri=66102","nofollow":false},{"id":1741385,"name":"Colleges of Education","url":"https://www.academia.edu/Documents/in/Colleges_of_Education?f_ri=66102","nofollow":false}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_42347551 coauthored" data-work_id="42347551" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/42347551/2021_35_1_Conocimiento_de_profesores_de_matem%C3%A1ticas_en_formaci%C3%B3n_sobre_los_productos_notables">2021, 35(1) - Conocimiento de profesores de matemáticas en formación sobre los productos notables</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">La presente investigación indaga sobre el conocimiento de futuros profesores de matemáticas en relación con los productos notables. El estudio de corte cualitativo y descriptivo se desarrolla con estudiantes universitarios que cursan un... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_42347551" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">La presente investigación indaga sobre el conocimiento de futuros profesores de matemáticas en relación con los productos notables. El estudio de corte cualitativo y descriptivo se desarrolla con estudiantes universitarios que cursan un programa de formación de profesores de matemáticas para el nivel bachillerato. Se utilizaron criterios de análisis relativos al Conocimiento Matemático para la Enseñanza como elementos teóricos que permitieron, a partir de la aplicación de un cuestionario, analizar los conocimientos manifestados por los profesores en formación. Se proporciona evidencia de la actividad matemática que realizan los estudiantes para profesor, al resolver tareas que involucran a los productos notables y su enseñanza. Los resultados informan de las inconsistencias en los conocimientos de los futuros docentes y sobre las fortalezas que manifiestan en los subdominios del Conocimiento Matemático para la Enseñanza, lo que permite establecer áreas de desarrollo en su formación.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/42347551" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="37791991cc5833b17c5b6cc0238e80fa" rel="nofollow" data-download="{"attachment_id":64241487,"asset_id":42347551,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/64241487/download_file?st=MTczMzAyOTA0OCw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="28483274" href="https://una-cr.academia.edu/RevistaUniciencia">Revista Uniciencia</a><script data-card-contents-for-user="28483274" type="text/json">{"id":28483274,"first_name":"Revista","last_name":"Uniciencia","domain_name":"una-cr","page_name":"RevistaUniciencia","display_name":"Revista Uniciencia","profile_url":"https://una-cr.academia.edu/RevistaUniciencia?f_ri=66102","photo":"https://0.academia-photos.com/28483274/8049897/10096681/s65_revista.uniciencia.jpg"}</script></span></span><span class="u-displayInlineBlock InlineList-item-text"> and <span class="u-textDecorationUnderline u-clickable InlineList-item-text js-work-more-authors-42347551">+1</span><div class="hidden js-additional-users-42347551"><div><span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a href="https://uaq.academia.edu/LiliaPAke">Lilia P. Aké</a></span></div></div></span><script>(function(){ var popoverSettings = { el: $('.js-work-more-authors-42347551'), placement: 'bottom', hide_delay: 200, html: true, content: function(){ return $('.js-additional-users-42347551').html(); } } new HoverPopover(popoverSettings); })();</script></li><li class="js-paper-rank-work_42347551 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="42347551"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 42347551, container: ".js-paper-rank-work_42347551", }); });</script></li><li class="js-percentile-work_42347551 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 42347551; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_42347551"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_42347551 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="42347551"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 42347551; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=42347551]").text(description); $(".js-view-count-work_42347551").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_42347551").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="42347551"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">19</a>  </div><span class="InlineList-item-text u-textTruncate u-pl10x"><a class="InlineList-item-text" data-has-card-for-ri="2731" href="https://www.academia.edu/Documents/in/Mathematics_Education">Mathematics Education</a>, <script data-card-contents-for-ri="2731" type="text/json">{"id":2731,"name":"Mathematics Education","url":"https://www.academia.edu/Documents/in/Mathematics_Education?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="13545" href="https://www.academia.edu/Documents/in/Teacher_Training">Teacher Training</a>, <script data-card-contents-for-ri="13545" type="text/json">{"id":13545,"name":"Teacher Training","url":"https://www.academia.edu/Documents/in/Teacher_Training?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="21093" href="https://www.academia.edu/Documents/in/Education_Mathematics_">Education (Mathematics)</a>, <script data-card-contents-for-ri="21093" type="text/json">{"id":21093,"name":"Education (Mathematics)","url":"https://www.academia.edu/Documents/in/Education_Mathematics_?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="27801" href="https://www.academia.edu/Documents/in/Mathematics_Teacher_Education">Mathematics Teacher Education</a><script data-card-contents-for-ri="27801" type="text/json">{"id":27801,"name":"Mathematics Teacher Education","url":"https://www.academia.edu/Documents/in/Mathematics_Teacher_Education?f_ri=66102","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=42347551]'), work: {"id":42347551,"title":"2021, 35(1) - Conocimiento de profesores de matemáticas en formación sobre los productos notables","created_at":"2020-03-27T19:29:37.623-07:00","url":"https://www.academia.edu/42347551/2021_35_1_Conocimiento_de_profesores_de_matem%C3%A1ticas_en_formaci%C3%B3n_sobre_los_productos_notables?f_ri=66102","dom_id":"work_42347551","summary":"La presente investigación indaga sobre el conocimiento de futuros profesores de matemáticas en relación con los productos notables. El estudio de corte cualitativo y descriptivo se desarrolla con estudiantes universitarios que cursan un programa de formación de profesores de matemáticas para el nivel bachillerato. Se utilizaron criterios de análisis relativos al Conocimiento Matemático para la Enseñanza como elementos teóricos que permitieron, a partir de la aplicación de un cuestionario, analizar los conocimientos manifestados por los profesores en formación. Se proporciona evidencia de la actividad matemática que realizan los estudiantes para profesor, al resolver tareas que involucran a los productos notables y su enseñanza. Los resultados informan de las inconsistencias en los conocimientos de los futuros docentes y sobre las fortalezas que manifiestan en los subdominios del Conocimiento Matemático para la Enseñanza, lo que permite establecer áreas de desarrollo en su formación.","downloadable_attachments":[{"id":64241487,"asset_id":42347551,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":28483274,"first_name":"Revista","last_name":"Uniciencia","domain_name":"una-cr","page_name":"RevistaUniciencia","display_name":"Revista Uniciencia","profile_url":"https://una-cr.academia.edu/RevistaUniciencia?f_ri=66102","photo":"https://0.academia-photos.com/28483274/8049897/10096681/s65_revista.uniciencia.jpg"},{"id":35497067,"first_name":"Lilia P.","last_name":"Aké","domain_name":"uaq","page_name":"LiliaPAke","display_name":"Lilia P. Aké","profile_url":"https://uaq.academia.edu/LiliaPAke?f_ri=66102","photo":"https://0.academia-photos.com/35497067/10308012/91817677/s65_lilia_p..ake.jpg"}],"research_interests":[{"id":2731,"name":"Mathematics Education","url":"https://www.academia.edu/Documents/in/Mathematics_Education?f_ri=66102","nofollow":false},{"id":13545,"name":"Teacher Training","url":"https://www.academia.edu/Documents/in/Teacher_Training?f_ri=66102","nofollow":false},{"id":21093,"name":"Education (Mathematics)","url":"https://www.academia.edu/Documents/in/Education_Mathematics_?f_ri=66102","nofollow":false},{"id":27801,"name":"Mathematics Teacher Education","url":"https://www.academia.edu/Documents/in/Mathematics_Teacher_Education?f_ri=66102","nofollow":false},{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102"},{"id":102651,"name":"Formação De Professores","url":"https://www.academia.edu/Documents/in/Forma%C3%A7%C3%A3o_De_Professores?f_ri=66102"},{"id":126353,"name":"EDUCACION MATEMÁTICA","url":"https://www.academia.edu/Documents/in/EDUCACION_MATEMATICA?f_ri=66102"},{"id":145280,"name":"Educação Matemática","url":"https://www.academia.edu/Documents/in/Educa%C3%A7%C3%A3o_Matem%C3%A1tica?f_ri=66102"},{"id":149995,"name":"Preservice Teachers","url":"https://www.academia.edu/Documents/in/Preservice_Teachers?f_ri=66102"},{"id":182978,"name":"Educación Matemática","url":"https://www.academia.edu/Documents/in/Educaci%C3%B3n_Matem%C3%A1tica?f_ri=66102"},{"id":193171,"name":"FORMACION DE PROFESORES","url":"https://www.academia.edu/Documents/in/FORMACION_DE_PROFESORES?f_ri=66102"},{"id":322707,"name":"Prospective Teachers","url":"https://www.academia.edu/Documents/in/Prospective_Teachers?f_ri=66102"},{"id":405367,"name":"Formación De Profesores De Matemática","url":"https://www.academia.edu/Documents/in/Formacion_De_Profesores_De_Matematica?f_ri=66102"},{"id":482595,"name":"Teacher Training and Education","url":"https://www.academia.edu/Documents/in/Teacher_Training_and_Education?f_ri=66102"},{"id":499816,"name":"Educação Matematica","url":"https://www.academia.edu/Documents/in/Educa%C3%A7%C3%A3o_Matematica?f_ri=66102"},{"id":2005517,"name":"Conocimiento matemático","url":"https://www.academia.edu/Documents/in/Conocimiento_matem%C3%A1tico?f_ri=66102"},{"id":2107048,"name":"Productos Notables","url":"https://www.academia.edu/Documents/in/Productos_Notables?f_ri=66102"},{"id":2857577,"name":"futuros docentes","url":"https://www.academia.edu/Documents/in/futuros_docentes?f_ri=66102"},{"id":3600830,"name":"conocimiento matemático para la enseñanza","url":"https://www.academia.edu/Documents/in/conocimiento_matem%C3%A1tico_para_la_ense%C3%B1anza?f_ri=66102"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_74983930" data-work_id="74983930" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/74983930/_Qu%C3%A9_conocimientos_necesita_el_profesorado_de_Educaci%C3%B3n_Infantil_para_ense%C3%B1ar_matem%C3%A1ticas">¿Qué conocimientos necesita el profesorado de Educación Infantil para enseñar matemáticas?</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">Se concretan los conocimientos para enseñar matemáticas en Educación Infantil a partir de la revisión de: a) las finalidades, las prácticas y la organización de la enseñanza; b) la literatura previa sobre el conocimiento del profesorado... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_74983930" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">Se concretan los conocimientos para enseñar matemáticas en Educación Infantil a partir de la revisión de: a) las finalidades, las prácticas y la organización de la enseñanza; b) la literatura previa sobre el conocimiento del profesorado de infantil para enseñar matemáticas. Considerando estos antecedentes, se describen y ejemplifican dos tipos de conocimiento: Conocimiento Matemático en Educación Infantil y Conocimiento Didáctico de las Matemáticas en Educación Infantil, junto con sus respectivos subtipos. Se concluye que la concreción de estos conocimientos puede contribuir al desarrollo profesional del profesorado de infantil y, adicionalmente, pueden usarse como herramienta de análisis.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/74983930" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="fa97c783c4e8aa95bb24e77301b1f01f" rel="nofollow" data-download="{"attachment_id":82937300,"asset_id":74983930,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/82937300/download_file?st=MTczMzAyOTA0OCw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="542378" href="https://ugirona.academia.edu/AngelAlsina">Angel Alsina</a><script data-card-contents-for-user="542378" type="text/json">{"id":542378,"first_name":"Angel","last_name":"Alsina","domain_name":"ugirona","page_name":"AngelAlsina","display_name":"Angel Alsina","profile_url":"https://ugirona.academia.edu/AngelAlsina?f_ri=66102","photo":"https://0.academia-photos.com/542378/9879688/15244312/s65_angel.alsina.jpg"}</script></span></span></li><li class="js-paper-rank-work_74983930 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="74983930"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 74983930, container: ".js-paper-rank-work_74983930", }); });</script></li><li class="js-percentile-work_74983930 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 74983930; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_74983930"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_74983930 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="74983930"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 74983930; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=74983930]").text(description); $(".js-view-count-work_74983930").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_74983930").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="74983930"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">11</a>  </div><span class="InlineList-item-text u-textTruncate u-pl10x"><a class="InlineList-item-text" data-has-card-for-ri="3753" href="https://www.academia.edu/Documents/in/Early_Childhood_Education">Early Childhood Education</a>, <script data-card-contents-for-ri="3753" type="text/json">{"id":3753,"name":"Early Childhood Education","url":"https://www.academia.edu/Documents/in/Early_Childhood_Education?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="22277" href="https://www.academia.edu/Documents/in/Math_Education_in_Early_Childhood_Education">Math Education in Early Childhood Education</a>, <script data-card-contents-for-ri="22277" type="text/json">{"id":22277,"name":"Math Education in Early Childhood Education","url":"https://www.academia.edu/Documents/in/Math_Education_in_Early_Childhood_Education?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="66102" href="https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching">Mathematical Knowledge for Teaching</a>, <script data-card-contents-for-ri="66102" type="text/json">{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="79368" href="https://www.academia.edu/Documents/in/Educaci%C3%B3n_Infantil">Educación Infantil</a><script data-card-contents-for-ri="79368" type="text/json">{"id":79368,"name":"Educación Infantil","url":"https://www.academia.edu/Documents/in/Educaci%C3%B3n_Infantil?f_ri=66102","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=74983930]'), work: {"id":74983930,"title":"¿Qué conocimientos necesita el profesorado de Educación Infantil para enseñar matemáticas?","created_at":"2022-03-30T08:15:45.761-07:00","url":"https://www.academia.edu/74983930/_Qu%C3%A9_conocimientos_necesita_el_profesorado_de_Educaci%C3%B3n_Infantil_para_ense%C3%B1ar_matem%C3%A1ticas?f_ri=66102","dom_id":"work_74983930","summary":"Se concretan los conocimientos para enseñar matemáticas en Educación Infantil a partir de la revisión de: a) las finalidades, las prácticas y la organización de la enseñanza; b) la literatura previa sobre el conocimiento del profesorado de infantil para enseñar matemáticas. Considerando estos antecedentes, se describen y ejemplifican dos tipos de conocimiento: Conocimiento Matemático en Educación Infantil y Conocimiento Didáctico de las Matemáticas en Educación Infantil, junto con sus respectivos subtipos. Se concluye que la concreción de estos conocimientos puede contribuir al desarrollo profesional del profesorado de infantil y, adicionalmente, pueden usarse como herramienta de análisis.","downloadable_attachments":[{"id":82937300,"asset_id":74983930,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":542378,"first_name":"Angel","last_name":"Alsina","domain_name":"ugirona","page_name":"AngelAlsina","display_name":"Angel Alsina","profile_url":"https://ugirona.academia.edu/AngelAlsina?f_ri=66102","photo":"https://0.academia-photos.com/542378/9879688/15244312/s65_angel.alsina.jpg"}],"research_interests":[{"id":3753,"name":"Early Childhood Education","url":"https://www.academia.edu/Documents/in/Early_Childhood_Education?f_ri=66102","nofollow":false},{"id":22277,"name":"Math Education in Early Childhood Education","url":"https://www.academia.edu/Documents/in/Math_Education_in_Early_Childhood_Education?f_ri=66102","nofollow":false},{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102","nofollow":false},{"id":79368,"name":"Educación Infantil","url":"https://www.academia.edu/Documents/in/Educaci%C3%B3n_Infantil?f_ri=66102","nofollow":false},{"id":109652,"name":"Teacher knowledge","url":"https://www.academia.edu/Documents/in/Teacher_knowledge?f_ri=66102"},{"id":150410,"name":"Teaching practice","url":"https://www.academia.edu/Documents/in/Teaching_practice?f_ri=66102"},{"id":399102,"name":"Early Childhood Teacher Education","url":"https://www.academia.edu/Documents/in/Early_Childhood_Teacher_Education?f_ri=66102"},{"id":402504,"name":"Mathematical Knowledge for Teaching, Mathematics Teacher Education","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching_Mathematics_Teacher_Education?f_ri=66102"},{"id":521730,"name":"Mathematics Knowledge","url":"https://www.academia.edu/Documents/in/Mathematics_Knowledge?f_ri=66102"},{"id":955887,"name":"Enseñanza De Las Matemáticas","url":"https://www.academia.edu/Documents/in/Ense%C3%B1anza_De_Las_Matem%C3%A1ticas?f_ri=66102"},{"id":2582347,"name":"Conocimiento profesional del profesor - Matemática en contexto","url":"https://www.academia.edu/Documents/in/Conocimiento_profesional_del_profesor_-_Matem%C3%A1tica_en_contexto?f_ri=66102"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_8172977" data-work_id="8172977" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/8172977/Conceptualising_Teachers_Mathematical_Knowledge_in_Teaching">Conceptualising Teachers’ Mathematical Knowledge in Teaching</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/8172977" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="23bc95d7b6cfa7ce0481cef985fbabd3" rel="nofollow" data-download="{"attachment_id":34608216,"asset_id":8172977,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/34608216/download_file?st=MTczMzAyOTA0OCw4LjIyMi4yMDguMTQ2&s=work_strip"><i 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class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="8172977"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 8172977, container: ".js-paper-rank-work_8172977", }); });</script></li><li class="js-percentile-work_8172977 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 8172977; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_8172977"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_8172977 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="8172977"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 8172977; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=8172977]").text(description); $(".js-view-count-work_8172977").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_8172977").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="8172977"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">2</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="66102" href="https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching">Mathematical Knowledge for Teaching</a>, <script data-card-contents-for-ri="66102" type="text/json">{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="413300" href="https://www.academia.edu/Documents/in/Analytical_Model">Analytical Model</a><script data-card-contents-for-ri="413300" type="text/json">{"id":413300,"name":"Analytical Model","url":"https://www.academia.edu/Documents/in/Analytical_Model?f_ri=66102","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=8172977]'), work: {"id":8172977,"title":"Conceptualising Teachers’ Mathematical Knowledge in Teaching","created_at":"2014-09-02T11:58:17.723-07:00","url":"https://www.academia.edu/8172977/Conceptualising_Teachers_Mathematical_Knowledge_in_Teaching?f_ri=66102","dom_id":"work_8172977","summary":null,"downloadable_attachments":[{"id":34608216,"asset_id":8172977,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":15977234,"first_name":"Marilena","last_name":"Petrou","domain_name":"independent","page_name":"MarilenaPetrou","display_name":"Marilena Petrou","profile_url":"https://independent.academia.edu/MarilenaPetrou?f_ri=66102","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102","nofollow":false},{"id":413300,"name":"Analytical Model","url":"https://www.academia.edu/Documents/in/Analytical_Model?f_ri=66102","nofollow":false}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_62899875" data-work_id="62899875" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/62899875/Conocimientos_matem%C3%A1ticos_del_profesorado_de_la_Escuela_Infantil_0_3_a%C3%B1os_efecto_en_el_dise%C3%B1o_de_espacios_para_desarrollar_las_matem%C3%A1ticas_informales">Conocimientos matemáticos del profesorado de la Escuela Infantil (0-3 años): efecto en el diseño de espacios para desarrollar las matemáticas informales.</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">En este estudio se analizan los conocimientos matemáticos del profesorado de la Escuela Infantil para favorecer el desarrollo de los primeros conocimientos matemáticos intuitivos e informales de los niños y niñas de 0 a 3 años, a través... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_62899875" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">En este estudio se analizan los conocimientos matemáticos del profesorado de la Escuela Infantil para favorecer el desarrollo de los primeros conocimientos matemáticos intuitivos e informales de los niños y niñas de 0 a 3 años, a través del diseño de los espacios y materiales. Se ha diseñado un estudio cuasi-experimental (Pre-Post) en el que, antes y después de una actividad de formación, se ha administrado el Cuestionario "Conocimientos Didáctico-Matemáticos en la Escuela Infantil" (CDM 0-3) a 28 profesionales. Los resultados obtenidos muestran cambios significativos en los conocimientos matemáticos y, por consiguiente, en el diseño de los espacios y materiales que se ofrecen a los niños y las niñas de 0 a 3 años, incrementando el contenido y sentido matemático. Se concluye que es imprescindible una formación inicial y continua de calidad que garantice que los profesionales de la Escuela Infantil tengan los conocimientos matemáticos necesarios para diseñar espacios ricos desde un punto de vista matemático.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/62899875" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="1a9fa9be53ea2367703ac673a10b8a4d" rel="nofollow" data-download="{"attachment_id":75515447,"asset_id":62899875,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/75515447/download_file?st=MTczMzAyOTA0OCw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="542378" href="https://ugirona.academia.edu/AngelAlsina">Angel Alsina</a><script data-card-contents-for-user="542378" type="text/json">{"id":542378,"first_name":"Angel","last_name":"Alsina","domain_name":"ugirona","page_name":"AngelAlsina","display_name":"Angel Alsina","profile_url":"https://ugirona.academia.edu/AngelAlsina?f_ri=66102","photo":"https://0.academia-photos.com/542378/9879688/15244312/s65_angel.alsina.jpg"}</script></span></span></li><li class="js-paper-rank-work_62899875 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="62899875"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 62899875, container: ".js-paper-rank-work_62899875", }); });</script></li><li class="js-percentile-work_62899875 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 62899875; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_62899875"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_62899875 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="62899875"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 62899875; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=62899875]").text(description); $(".js-view-count-work_62899875").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_62899875").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="62899875"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">13</a>  </div><span class="InlineList-item-text u-textTruncate u-pl10x"><a class="InlineList-item-text" data-has-card-for-ri="2731" href="https://www.academia.edu/Documents/in/Mathematics_Education">Mathematics Education</a>, <script data-card-contents-for-ri="2731" type="text/json">{"id":2731,"name":"Mathematics Education","url":"https://www.academia.edu/Documents/in/Mathematics_Education?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="17773" href="https://www.academia.edu/Documents/in/Teachers_professional_development-1">Teachers' professional development</a>, <script data-card-contents-for-ri="17773" type="text/json">{"id":17773,"name":"Teachers' professional development","url":"https://www.academia.edu/Documents/in/Teachers_professional_development-1?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="22277" href="https://www.academia.edu/Documents/in/Math_Education_in_Early_Childhood_Education">Math Education in Early Childhood Education</a>, <script data-card-contents-for-ri="22277" type="text/json">{"id":22277,"name":"Math Education in Early Childhood Education","url":"https://www.academia.edu/Documents/in/Math_Education_in_Early_Childhood_Education?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="57305" href="https://www.academia.edu/Documents/in/Teaching_Mathematics">Teaching Mathematics</a><script data-card-contents-for-ri="57305" type="text/json">{"id":57305,"name":"Teaching Mathematics","url":"https://www.academia.edu/Documents/in/Teaching_Mathematics?f_ri=66102","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=62899875]'), work: {"id":62899875,"title":"Conocimientos matemáticos del profesorado de la Escuela Infantil (0-3 años): efecto en el diseño de espacios para desarrollar las matemáticas informales.","created_at":"2021-12-01T14:14:23.352-08:00","url":"https://www.academia.edu/62899875/Conocimientos_matem%C3%A1ticos_del_profesorado_de_la_Escuela_Infantil_0_3_a%C3%B1os_efecto_en_el_dise%C3%B1o_de_espacios_para_desarrollar_las_matem%C3%A1ticas_informales?f_ri=66102","dom_id":"work_62899875","summary":"En este estudio se analizan los conocimientos matemáticos del profesorado de la Escuela Infantil para favorecer el desarrollo de los primeros conocimientos matemáticos intuitivos e informales de los niños y niñas de 0 a 3 años, a través del diseño de los espacios y materiales. Se ha diseñado un estudio cuasi-experimental (Pre-Post) en el que, antes y después de una actividad de formación, se ha administrado el Cuestionario \"Conocimientos Didáctico-Matemáticos en la Escuela Infantil\" (CDM 0-3) a 28 profesionales. Los resultados obtenidos muestran cambios significativos en los conocimientos matemáticos y, por consiguiente, en el diseño de los espacios y materiales que se ofrecen a los niños y las niñas de 0 a 3 años, incrementando el contenido y sentido matemático. Se concluye que es imprescindible una formación inicial y continua de calidad que garantice que los profesionales de la Escuela Infantil tengan los conocimientos matemáticos necesarios para diseñar espacios ricos desde un punto de vista matemático.","downloadable_attachments":[{"id":75515447,"asset_id":62899875,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":542378,"first_name":"Angel","last_name":"Alsina","domain_name":"ugirona","page_name":"AngelAlsina","display_name":"Angel Alsina","profile_url":"https://ugirona.academia.edu/AngelAlsina?f_ri=66102","photo":"https://0.academia-photos.com/542378/9879688/15244312/s65_angel.alsina.jpg"}],"research_interests":[{"id":2731,"name":"Mathematics Education","url":"https://www.academia.edu/Documents/in/Mathematics_Education?f_ri=66102","nofollow":false},{"id":17773,"name":"Teachers' professional development","url":"https://www.academia.edu/Documents/in/Teachers_professional_development-1?f_ri=66102","nofollow":false},{"id":22277,"name":"Math Education in Early Childhood Education","url":"https://www.academia.edu/Documents/in/Math_Education_in_Early_Childhood_Education?f_ri=66102","nofollow":false},{"id":57305,"name":"Teaching Mathematics","url":"https://www.academia.edu/Documents/in/Teaching_Mathematics?f_ri=66102","nofollow":false},{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102"},{"id":79368,"name":"Educación Infantil","url":"https://www.academia.edu/Documents/in/Educaci%C3%B3n_Infantil?f_ri=66102"},{"id":122049,"name":"Manipulatives","url":"https://www.academia.edu/Documents/in/Manipulatives?f_ri=66102"},{"id":182978,"name":"Educación Matemática","url":"https://www.academia.edu/Documents/in/Educaci%C3%B3n_Matem%C3%A1tica?f_ri=66102"},{"id":1188839,"name":"Nursery School","url":"https://www.academia.edu/Documents/in/Nursery_School?f_ri=66102"},{"id":1458454,"name":"Teachers' Mathematical Content Knowledge","url":"https://www.academia.edu/Documents/in/Teachers_Mathematical_Content_Knowledge?f_ri=66102"},{"id":1532113,"name":"Conocimiento Del Profesor","url":"https://www.academia.edu/Documents/in/Conocimiento_Del_Profesor?f_ri=66102"},{"id":2626681,"name":"Infant school","url":"https://www.academia.edu/Documents/in/Infant_school?f_ri=66102"},{"id":2789660,"name":"Escuela Infantil","url":"https://www.academia.edu/Documents/in/Escuela_Infantil?f_ri=66102"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_60757486" data-work_id="60757486" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/60757486/When_pre_service_teachers_learn_to_function_using_spreadsheet_based_algebraic_approaches">When pre-service teachers learn to function using spreadsheet-based algebraic approaches</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">In this report we present a conceptualisation of our work with pre-service mathematics teachers, wherein we exploit spreadsheets as a particular example of Information Communication Technology through which to reform school algebra. We... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_60757486" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">In this report we present a conceptualisation of our work with pre-service mathematics teachers, wherein we exploit spreadsheets as a particular example of Information Communication Technology through which to reform school algebra. We start by describing the working space between spreadsheets and school algebra (and vice versa), and what it means to make spreadsheets a &#x27;mathematical instrument.&#x27;These we connect with two of the &#x27;central tasks&#x27; in pre-service teacher preparation, namely, building a &#x27;beginning repertoire&#x27; ...</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/60757486" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="5e6a2f0b9ad9fa883eec4c9416b8b993" rel="nofollow" data-download="{"attachment_id":74058362,"asset_id":60757486,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/74058362/download_file?st=MTczMzAyOTA0OCw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="871926" href="https://sun.academia.edu/AOlivier">Alwyn Olivier</a><script data-card-contents-for-user="871926" type="text/json">{"id":871926,"first_name":"Alwyn","last_name":"Olivier","domain_name":"sun","page_name":"AOlivier","display_name":"Alwyn Olivier","profile_url":"https://sun.academia.edu/AOlivier?f_ri=66102","photo":"https://0.academia-photos.com/871926/314340/38064255/s65_alwyn.olivier.jpg"}</script></span></span></li><li class="js-paper-rank-work_60757486 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="60757486"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 60757486, container: ".js-paper-rank-work_60757486", }); });</script></li><li class="js-percentile-work_60757486 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 60757486; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_60757486"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_60757486 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="60757486"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 60757486; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=60757486]").text(description); $(".js-view-count-work_60757486").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_60757486").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="60757486"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i></div><span class="InlineList-item-text u-textTruncate u-pl6x"><a class="InlineList-item-text" data-has-card-for-ri="66102" href="https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching">Mathematical Knowledge for Teaching</a><script data-card-contents-for-ri="66102" type="text/json">{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102","nofollow":false}</script></span></li><script>(function(){ if (false) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=60757486]'), work: {"id":60757486,"title":"When pre-service teachers learn to function using spreadsheet-based algebraic approaches","created_at":"2021-11-01T19:28:10.657-07:00","url":"https://www.academia.edu/60757486/When_pre_service_teachers_learn_to_function_using_spreadsheet_based_algebraic_approaches?f_ri=66102","dom_id":"work_60757486","summary":"In this report we present a conceptualisation of our work with pre-service mathematics teachers, wherein we exploit spreadsheets as a particular example of Information Communication Technology through which to reform school algebra. We start by describing the working space between spreadsheets and school algebra (and vice versa), and what it means to make spreadsheets a \u0026#x27;mathematical instrument.\u0026#x27;These we connect with two of the \u0026#x27;central tasks\u0026#x27; in pre-service teacher preparation, namely, building a \u0026#x27;beginning repertoire\u0026#x27; ...","downloadable_attachments":[{"id":74058362,"asset_id":60757486,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":871926,"first_name":"Alwyn","last_name":"Olivier","domain_name":"sun","page_name":"AOlivier","display_name":"Alwyn Olivier","profile_url":"https://sun.academia.edu/AOlivier?f_ri=66102","photo":"https://0.academia-photos.com/871926/314340/38064255/s65_alwyn.olivier.jpg"}],"research_interests":[{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102","nofollow":false}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_49619394 coauthored" data-work_id="49619394" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/49619394/Identificando_los_conocimientos_para_ense%C3%B1ar_matem%C3%A1ticas_en_educaci%C3%B3n_infantil_un_primer_paso_para_el_desarrollo_profesional">Identificando los conocimientos para enseñar matemáticas en educación infantil: un primer paso para el desarrollo profesional.</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">En este estudio se indaga en las prácticas de enseñanza de las matemáticas del profesorado de Educación Infantil, asumiendo que la identificación de los componentes de dicha práctica es el punto de partida necesario para promover el... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_49619394" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">En este estudio se indaga en las prácticas de enseñanza de las matemáticas del profesorado de Educación Infantil, asumiendo que la identificación de los componentes de dicha práctica es el punto de partida necesario para promover el desarrollo profesional. En este sentido, se han identificado los conocimientos para enseñar matemáticas que pone en juego una maestra durante una sesión de clases, a partir de los dominios y subdominios que componen el modelo de Conocimientos para Enseñar Matemáticas en Educación Infantil (CEM-EI). El análisis ha permitido identificar evidencias de los tres subdominios del Conocimiento Matemático en Educación Infantil (CM-EI): Conocimientos matemáticos Intuitivos e Informales (C-IeI); Conocimiento de los contenidos matemáticos (C-CM) y Conocimiento de los procesos matemáticos (C-PM), y dos de los tres subdominios del Conocimiento Didáctico de las Matemáticas en Educación Infantil (CDM-EI): Conocimiento sobre las formas de aprendizaje de las matemáticas en la infancia (C-FAM) y Conocimiento sobre la planificación y gestión de actividades de enseñanza de las matemáticas (C-PGA). Se concluye que serán necesarios nuevos estudios que permitan afinar y consolidar estos primeros resultados.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/49619394" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="fde496bc5d9027c33a73be99a07be214" rel="nofollow" data-download="{"attachment_id":67929260,"asset_id":49619394,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/67929260/download_file?st=MTczMzAyOTA0OCw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="542378" href="https://ugirona.academia.edu/AngelAlsina">Angel Alsina</a><script data-card-contents-for-user="542378" type="text/json">{"id":542378,"first_name":"Angel","last_name":"Alsina","domain_name":"ugirona","page_name":"AngelAlsina","display_name":"Angel Alsina","profile_url":"https://ugirona.academia.edu/AngelAlsina?f_ri=66102","photo":"https://0.academia-photos.com/542378/9879688/15244312/s65_angel.alsina.jpg"}</script></span></span><span class="u-displayInlineBlock InlineList-item-text"> and <span class="u-textDecorationUnderline u-clickable InlineList-item-text js-work-more-authors-49619394">+1</span><div class="hidden js-additional-users-49619394"><div><span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a href="https://independent.academia.edu/RosaDelgadoRebolledo">Rosa Delgado Rebolledo</a></span></div></div></span><script>(function(){ var popoverSettings = { el: $('.js-work-more-authors-49619394'), placement: 'bottom', hide_delay: 200, html: true, content: function(){ return $('.js-additional-users-49619394').html(); } } new HoverPopover(popoverSettings); })();</script></li><li class="js-paper-rank-work_49619394 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="49619394"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 49619394, container: ".js-paper-rank-work_49619394", }); });</script></li><li class="js-percentile-work_49619394 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 49619394; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_49619394"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_49619394 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="49619394"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 49619394; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=49619394]").text(description); $(".js-view-count-work_49619394").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_49619394").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="49619394"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">14</a>  </div><span class="InlineList-item-text u-textTruncate u-pl10x"><a class="InlineList-item-text" data-has-card-for-ri="2731" href="https://www.academia.edu/Documents/in/Mathematics_Education">Mathematics Education</a>, <script data-card-contents-for-ri="2731" type="text/json">{"id":2731,"name":"Mathematics Education","url":"https://www.academia.edu/Documents/in/Mathematics_Education?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="3753" href="https://www.academia.edu/Documents/in/Early_Childhood_Education">Early Childhood Education</a>, <script data-card-contents-for-ri="3753" type="text/json">{"id":3753,"name":"Early Childhood Education","url":"https://www.academia.edu/Documents/in/Early_Childhood_Education?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="17773" href="https://www.academia.edu/Documents/in/Teachers_professional_development-1">Teachers' professional development</a>, <script data-card-contents-for-ri="17773" type="text/json">{"id":17773,"name":"Teachers' professional development","url":"https://www.academia.edu/Documents/in/Teachers_professional_development-1?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="22277" href="https://www.academia.edu/Documents/in/Math_Education_in_Early_Childhood_Education">Math Education in Early Childhood Education</a><script data-card-contents-for-ri="22277" type="text/json">{"id":22277,"name":"Math Education in Early Childhood Education","url":"https://www.academia.edu/Documents/in/Math_Education_in_Early_Childhood_Education?f_ri=66102","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=49619394]'), work: {"id":49619394,"title":"Identificando los conocimientos para enseñar matemáticas en educación infantil: un primer paso para el desarrollo profesional.","created_at":"2021-07-08T14:19:29.601-07:00","url":"https://www.academia.edu/49619394/Identificando_los_conocimientos_para_ense%C3%B1ar_matem%C3%A1ticas_en_educaci%C3%B3n_infantil_un_primer_paso_para_el_desarrollo_profesional?f_ri=66102","dom_id":"work_49619394","summary":"En este estudio se indaga en las prácticas de enseñanza de las matemáticas del profesorado de Educación Infantil, asumiendo que la identificación de los componentes de dicha práctica es el punto de partida necesario para promover el desarrollo profesional. En este sentido, se han identificado los conocimientos para enseñar matemáticas que pone en juego una maestra durante una sesión de clases, a partir de los dominios y subdominios que componen el modelo de Conocimientos para Enseñar Matemáticas en Educación Infantil (CEM-EI). El análisis ha permitido identificar evidencias de los tres subdominios del Conocimiento Matemático en Educación Infantil (CM-EI): Conocimientos matemáticos Intuitivos e Informales (C-IeI); Conocimiento de los contenidos matemáticos (C-CM) y Conocimiento de los procesos matemáticos (C-PM), y dos de los tres subdominios del Conocimiento Didáctico de las Matemáticas en Educación Infantil (CDM-EI): Conocimiento sobre las formas de aprendizaje de las matemáticas en la infancia (C-FAM) y Conocimiento sobre la planificación y gestión de actividades de enseñanza de las matemáticas (C-PGA). Se concluye que serán necesarios nuevos estudios que permitan afinar y consolidar estos primeros resultados. ","downloadable_attachments":[{"id":67929260,"asset_id":49619394,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":542378,"first_name":"Angel","last_name":"Alsina","domain_name":"ugirona","page_name":"AngelAlsina","display_name":"Angel Alsina","profile_url":"https://ugirona.academia.edu/AngelAlsina?f_ri=66102","photo":"https://0.academia-photos.com/542378/9879688/15244312/s65_angel.alsina.jpg"},{"id":134113893,"first_name":"Rosa","last_name":"Delgado Rebolledo","domain_name":"independent","page_name":"RosaDelgadoRebolledo","display_name":"Rosa Delgado Rebolledo","profile_url":"https://independent.academia.edu/RosaDelgadoRebolledo?f_ri=66102","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":2731,"name":"Mathematics Education","url":"https://www.academia.edu/Documents/in/Mathematics_Education?f_ri=66102","nofollow":false},{"id":3753,"name":"Early Childhood Education","url":"https://www.academia.edu/Documents/in/Early_Childhood_Education?f_ri=66102","nofollow":false},{"id":17773,"name":"Teachers' professional development","url":"https://www.academia.edu/Documents/in/Teachers_professional_development-1?f_ri=66102","nofollow":false},{"id":22277,"name":"Math Education in Early Childhood Education","url":"https://www.academia.edu/Documents/in/Math_Education_in_Early_Childhood_Education?f_ri=66102","nofollow":false},{"id":34229,"name":"Teacher professional development","url":"https://www.academia.edu/Documents/in/Teacher_professional_development?f_ri=66102"},{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102"},{"id":79368,"name":"Educación Infantil","url":"https://www.academia.edu/Documents/in/Educaci%C3%B3n_Infantil?f_ri=66102"},{"id":96413,"name":"Desarrollo profesional docente","url":"https://www.academia.edu/Documents/in/Desarrollo_profesional_docente?f_ri=66102"},{"id":109652,"name":"Teacher knowledge","url":"https://www.academia.edu/Documents/in/Teacher_knowledge?f_ri=66102"},{"id":126354,"name":"Didáctica de las matemáticas","url":"https://www.academia.edu/Documents/in/Did%C3%A1ctica_de_las_matem%C3%A1ticas?f_ri=66102"},{"id":150410,"name":"Teaching practice","url":"https://www.academia.edu/Documents/in/Teaching_practice?f_ri=66102"},{"id":182978,"name":"Educación Matemática","url":"https://www.academia.edu/Documents/in/Educaci%C3%B3n_Matem%C3%A1tica?f_ri=66102"},{"id":521730,"name":"Mathematics Knowledge","url":"https://www.academia.edu/Documents/in/Mathematics_Knowledge?f_ri=66102"},{"id":2582331,"name":"Conocimiento profesional del profesor ","url":"https://www.academia.edu/Documents/in/Conocimiento_profesional_del_profesor?f_ri=66102"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_44391743 coauthored" data-work_id="44391743" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/44391743/Deficits_in_the_Statistical_and_Probabilistic_Literacy_of_Citizens_Effects_in_a_World_in_Crisis">Deficits in the Statistical and Probabilistic Literacy of Citizens: Effects in a World in Crisis</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">The emergency caused by coronavirus disease 2019 (COVID-19) has revealed significant deficiencies in citizens' statistical and probabilistic knowledge and in people's understanding of mathematical and, particularly, stochastic models,... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_44391743" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">The emergency caused by coronavirus disease 2019 (COVID-19) has revealed significant deficiencies in citizens' statistical and probabilistic knowledge and in people's understanding of mathematical and, particularly, stochastic models, which may lead to wrong personal or institutional choices, with critical consequences for the entire population. Mathematics teachers play an essential role in ensuring citizens' statistical and probabilistic literacy. This study aimed at analyzing the pedagogical content knowledge that teachers utilized to teach statistics and probability through considering contextualized situations. In order to accomplish this purpose, fourteen secondary mathematics teachers participated in a formative and evaluative activity that was designed using the transformational professional competence model. During each evaluative phase, a group discussion was conducted. Participants were asked to reflect on their actions when promoting statistical and probabilistic literacy by considering a range of topics (data science, didactic resources, and methodological approaches) that were addressed during the training phase. A mixed, quantitative-qualitative methodological design was used for the data collection and analysis, which involved open-ended, multiple-choice, or scale-type questions that were moderated by the Metaplan ® approach and the Mentimeter ® software. The main ideas that emerged from the results indicated the need to reinforce the use of real data, technological resources to handle the visualization of information, the elaboration of different types of graphs besides the classical ones, and the formulation of hypotheses. The initial diagnosis will continue within a research and practice community made up of teachers and researchers. Therefore, a working proposal based on examples and models contextualized within the COVID-19 crisis is presented in order to enhance secondary mathematics teachers' pedagogical content knowledge.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/44391743" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="787bdb2a062fcfe172ddb54f547b5909" rel="nofollow" data-download="{"attachment_id":64797360,"asset_id":44391743,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/64797360/download_file?st=MTczMzAyOTA0OCw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="542378" href="https://ugirona.academia.edu/AngelAlsina">Angel Alsina</a><script data-card-contents-for-user="542378" type="text/json">{"id":542378,"first_name":"Angel","last_name":"Alsina","domain_name":"ugirona","page_name":"AngelAlsina","display_name":"Angel Alsina","profile_url":"https://ugirona.academia.edu/AngelAlsina?f_ri=66102","photo":"https://0.academia-photos.com/542378/9879688/15244312/s65_angel.alsina.jpg"}</script></span></span><span class="u-displayInlineBlock InlineList-item-text"> and <span class="u-textDecorationUnderline u-clickable InlineList-item-text js-work-more-authors-44391743">+2</span><div class="hidden js-additional-users-44391743"><div><span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a href="https://independent.academia.edu/LuisJoseRodriguezMu%C3%91iz">Luis Jose Rodriguez MuÑiz</a></span></div><div><span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a href="https://uniovi.academia.edu/LauraMu%C3%B1izRodriguez">Laura Muñiz Rodriguez</a></span></div></div></span><script>(function(){ var popoverSettings = { el: $('.js-work-more-authors-44391743'), placement: 'bottom', hide_delay: 200, html: true, content: function(){ return $('.js-additional-users-44391743').html(); 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container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_44391743 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="44391743"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 44391743; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=44391743]").text(description); $(".js-view-count-work_44391743").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_44391743").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="44391743"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">15</a>  </div><span class="InlineList-item-text u-textTruncate u-pl10x"><a class="InlineList-item-text" data-has-card-for-ri="300" href="https://www.academia.edu/Documents/in/Mathematics">Mathematics</a>, <script data-card-contents-for-ri="300" type="text/json">{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="2731" href="https://www.academia.edu/Documents/in/Mathematics_Education">Mathematics Education</a>, <script data-card-contents-for-ri="2731" type="text/json">{"id":2731,"name":"Mathematics Education","url":"https://www.academia.edu/Documents/in/Mathematics_Education?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="9490" href="https://www.academia.edu/Documents/in/Education_for_Citizenship">Education for Citizenship</a>, <script data-card-contents-for-ri="9490" type="text/json">{"id":9490,"name":"Education for Citizenship","url":"https://www.academia.edu/Documents/in/Education_for_Citizenship?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="13545" href="https://www.academia.edu/Documents/in/Teacher_Training">Teacher Training</a><script data-card-contents-for-ri="13545" type="text/json">{"id":13545,"name":"Teacher Training","url":"https://www.academia.edu/Documents/in/Teacher_Training?f_ri=66102","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=44391743]'), work: {"id":44391743,"title":"Deficits in the Statistical and Probabilistic Literacy of Citizens: Effects in a World in Crisis","created_at":"2020-10-29T00:35:57.806-07:00","url":"https://www.academia.edu/44391743/Deficits_in_the_Statistical_and_Probabilistic_Literacy_of_Citizens_Effects_in_a_World_in_Crisis?f_ri=66102","dom_id":"work_44391743","summary":"The emergency caused by coronavirus disease 2019 (COVID-19) has revealed significant deficiencies in citizens' statistical and probabilistic knowledge and in people's understanding of mathematical and, particularly, stochastic models, which may lead to wrong personal or institutional choices, with critical consequences for the entire population. Mathematics teachers play an essential role in ensuring citizens' statistical and probabilistic literacy. This study aimed at analyzing the pedagogical content knowledge that teachers utilized to teach statistics and probability through considering contextualized situations. In order to accomplish this purpose, fourteen secondary mathematics teachers participated in a formative and evaluative activity that was designed using the transformational professional competence model. During each evaluative phase, a group discussion was conducted. Participants were asked to reflect on their actions when promoting statistical and probabilistic literacy by considering a range of topics (data science, didactic resources, and methodological approaches) that were addressed during the training phase. A mixed, quantitative-qualitative methodological design was used for the data collection and analysis, which involved open-ended, multiple-choice, or scale-type questions that were moderated by the Metaplan ® approach and the Mentimeter ® software. The main ideas that emerged from the results indicated the need to reinforce the use of real data, technological resources to handle the visualization of information, the elaboration of different types of graphs besides the classical ones, and the formulation of hypotheses. The initial diagnosis will continue within a research and practice community made up of teachers and researchers. Therefore, a working proposal based on examples and models contextualized within the COVID-19 crisis is presented in order to enhance secondary mathematics teachers' pedagogical content knowledge.","downloadable_attachments":[{"id":64797360,"asset_id":44391743,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":542378,"first_name":"Angel","last_name":"Alsina","domain_name":"ugirona","page_name":"AngelAlsina","display_name":"Angel Alsina","profile_url":"https://ugirona.academia.edu/AngelAlsina?f_ri=66102","photo":"https://0.academia-photos.com/542378/9879688/15244312/s65_angel.alsina.jpg"},{"id":33508068,"first_name":"Luis Jose Rodriguez","last_name":"MuÑiz","domain_name":"independent","page_name":"LuisJoseRodriguezMuÑiz","display_name":"Luis Jose Rodriguez MuÑiz","profile_url":"https://independent.academia.edu/LuisJoseRodriguezMu%C3%91iz?f_ri=66102","photo":"/images/s65_no_pic.png"},{"id":27139736,"first_name":"Laura","last_name":"Muñiz Rodriguez","domain_name":"uniovi","page_name":"LauraMuñizRodriguez","display_name":"Laura Muñiz Rodriguez","profile_url":"https://uniovi.academia.edu/LauraMu%C3%B1izRodriguez?f_ri=66102","photo":"https://0.academia-photos.com/27139736/17562672/18050307/s65_laura.mu_iz_rodriguez.jpg"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics?f_ri=66102","nofollow":false},{"id":2731,"name":"Mathematics Education","url":"https://www.academia.edu/Documents/in/Mathematics_Education?f_ri=66102","nofollow":false},{"id":9490,"name":"Education for Citizenship","url":"https://www.academia.edu/Documents/in/Education_for_Citizenship?f_ri=66102","nofollow":false},{"id":13545,"name":"Teacher Training","url":"https://www.academia.edu/Documents/in/Teacher_Training?f_ri=66102","nofollow":false},{"id":17773,"name":"Teachers' professional development","url":"https://www.academia.edu/Documents/in/Teachers_professional_development-1?f_ri=66102"},{"id":22613,"name":"Probability and statistics","url":"https://www.academia.edu/Documents/in/Probability_and_statistics?f_ri=66102"},{"id":31412,"name":"Probability and Mathematical Statistics","url":"https://www.academia.edu/Documents/in/Probability_and_Mathematical_Statistics?f_ri=66102"},{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102"},{"id":126354,"name":"Didáctica de las matemáticas","url":"https://www.academia.edu/Documents/in/Did%C3%A1ctica_de_las_matem%C3%A1ticas?f_ri=66102"},{"id":126749,"name":"Ciudadanía","url":"https://www.academia.edu/Documents/in/Ciudadan%C3%ADa?f_ri=66102"},{"id":182978,"name":"Educación Matemática","url":"https://www.academia.edu/Documents/in/Educaci%C3%B3n_Matem%C3%A1tica?f_ri=66102"},{"id":407776,"name":"Formación docente","url":"https://www.academia.edu/Documents/in/Formaci%C3%B3n_docente?f_ri=66102"},{"id":531896,"name":"Estadística","url":"https://www.academia.edu/Documents/in/Estad%C3%ADstica?f_ri=66102"},{"id":849389,"name":"Probabilidad","url":"https://www.academia.edu/Documents/in/Probabilidad?f_ri=66102"},{"id":975026,"name":"FORMACIÓN DE DOCENTES","url":"https://www.academia.edu/Documents/in/FORMACI%C3%93N_DE_DOCENTES?f_ri=66102"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_60288789" data-work_id="60288789" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/60288789/Teachers_Mathematics_Knowledge_for_Teaching_Early_Algebra_A_Systematic_Review_from_the_MKT_Perspective">Teachers' Mathematics Knowledge for Teaching Early Algebra: A Systematic Review from the MKT Perspective</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">The mathematical knowledge for teaching (MKT) model emerged from the advances proposed by Shulman in 1986 and 1987 as part of the teacher’s professional knowledge model, and refers to the mathematical knowledge that the teacher employs to... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_60288789" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">The mathematical knowledge for teaching (MKT) model emerged from the advances proposed by Shulman in 1986 and 1987 as part of the teacher’s professional knowledge model, and refers to the mathematical knowledge that the teacher employs to carry out the instruction process in the classroom. MKT has become an international benchmark for research into mathematics education and boasts a great scope and impact to date. The objective of this study is to conduct a systematic review of the way in which the MKT of early algebra teachers has been conceptualized and empirically studied in the scientific literature from 2010 to 2021. A systematic search in the Web of Science and Scopus databases led to a review of 17 papers. The results show great advances in the conceptualization of mathematical knowledge for teaching early algebra, focusing mainly on primary education teachers and on specialized knowledge of the content. In turn, there is a predominance of studies that address functional thin...</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/60288789" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="69c1f985f16942fca387b0c62addb4cd" rel="nofollow" data-download="{"attachment_id":73801993,"asset_id":60288789,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/73801993/download_file?st=MTczMzAyOTA0OCw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="24392923" href="https://independent.academia.edu/natalypincheira">nataly pincheira</a><script data-card-contents-for-user="24392923" type="text/json">{"id":24392923,"first_name":"nataly","last_name":"pincheira","domain_name":"independent","page_name":"natalypincheira","display_name":"nataly pincheira","profile_url":"https://independent.academia.edu/natalypincheira?f_ri=66102","photo":"https://0.academia-photos.com/24392923/9893410/11029499/s65_nataly.pincheira.jpg"}</script></span></span></li><li class="js-paper-rank-work_60288789 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="60288789"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 60288789, container: ".js-paper-rank-work_60288789", }); });</script></li><li class="js-percentile-work_60288789 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 60288789; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_60288789"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_60288789 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="60288789"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 60288789; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=60288789]").text(description); $(".js-view-count-work_60288789").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_60288789").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="60288789"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">17</a>  </div><span class="InlineList-item-text u-textTruncate u-pl10x"><a class="InlineList-item-text" data-has-card-for-ri="300" href="https://www.academia.edu/Documents/in/Mathematics">Mathematics</a>, <script data-card-contents-for-ri="300" type="text/json">{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="329" href="https://www.academia.edu/Documents/in/Algebra">Algebra</a>, <script data-card-contents-for-ri="329" type="text/json">{"id":329,"name":"Algebra","url":"https://www.academia.edu/Documents/in/Algebra?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="2731" href="https://www.academia.edu/Documents/in/Mathematics_Education">Mathematics Education</a>, <script data-card-contents-for-ri="2731" type="text/json">{"id":2731,"name":"Mathematics Education","url":"https://www.academia.edu/Documents/in/Mathematics_Education?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="3753" href="https://www.academia.edu/Documents/in/Early_Childhood_Education">Early Childhood Education</a><script data-card-contents-for-ri="3753" type="text/json">{"id":3753,"name":"Early Childhood Education","url":"https://www.academia.edu/Documents/in/Early_Childhood_Education?f_ri=66102","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=60288789]'), work: {"id":60288789,"title":"Teachers' Mathematics Knowledge for Teaching Early Algebra: A Systematic Review from the MKT Perspective","created_at":"2021-10-29T03:17:43.637-07:00","url":"https://www.academia.edu/60288789/Teachers_Mathematics_Knowledge_for_Teaching_Early_Algebra_A_Systematic_Review_from_the_MKT_Perspective?f_ri=66102","dom_id":"work_60288789","summary":"The mathematical knowledge for teaching (MKT) model emerged from the advances proposed by Shulman in 1986 and 1987 as part of the teacher’s professional knowledge model, and refers to the mathematical knowledge that the teacher employs to carry out the instruction process in the classroom. MKT has become an international benchmark for research into mathematics education and boasts a great scope and impact to date. The objective of this study is to conduct a systematic review of the way in which the MKT of early algebra teachers has been conceptualized and empirically studied in the scientific literature from 2010 to 2021. A systematic search in the Web of Science and Scopus databases led to a review of 17 papers. The results show great advances in the conceptualization of mathematical knowledge for teaching early algebra, focusing mainly on primary education teachers and on specialized knowledge of the content. In turn, there is a predominance of studies that address functional thin...","downloadable_attachments":[{"id":73801993,"asset_id":60288789,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":24392923,"first_name":"nataly","last_name":"pincheira","domain_name":"independent","page_name":"natalypincheira","display_name":"nataly pincheira","profile_url":"https://independent.academia.edu/natalypincheira?f_ri=66102","photo":"https://0.academia-photos.com/24392923/9893410/11029499/s65_nataly.pincheira.jpg"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics?f_ri=66102","nofollow":false},{"id":329,"name":"Algebra","url":"https://www.academia.edu/Documents/in/Algebra?f_ri=66102","nofollow":false},{"id":2731,"name":"Mathematics Education","url":"https://www.academia.edu/Documents/in/Mathematics_Education?f_ri=66102","nofollow":false},{"id":3753,"name":"Early Childhood Education","url":"https://www.academia.edu/Documents/in/Early_Childhood_Education?f_ri=66102","nofollow":false},{"id":22277,"name":"Math Education in Early Childhood Education","url":"https://www.academia.edu/Documents/in/Math_Education_in_Early_Childhood_Education?f_ri=66102"},{"id":44348,"name":"Systematic Reviews","url":"https://www.academia.edu/Documents/in/Systematic_Reviews?f_ri=66102"},{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102"},{"id":72555,"name":"Didáctica de las matemáticas en Educación Básica","url":"https://www.academia.edu/Documents/in/Didactica_de_las_matematicas_en_Educacion_Basica?f_ri=66102"},{"id":79368,"name":"Educación Infantil","url":"https://www.academia.edu/Documents/in/Educaci%C3%B3n_Infantil?f_ri=66102"},{"id":88382,"name":"Primary Education","url":"https://www.academia.edu/Documents/in/Primary_Education?f_ri=66102"},{"id":109652,"name":"Teacher knowledge","url":"https://www.academia.edu/Documents/in/Teacher_knowledge?f_ri=66102"},{"id":182978,"name":"Educación Matemática","url":"https://www.academia.edu/Documents/in/Educaci%C3%B3n_Matem%C3%A1tica?f_ri=66102"},{"id":298842,"name":"Early Algebra","url":"https://www.academia.edu/Documents/in/Early_Algebra?f_ri=66102"},{"id":382119,"name":"Álgebra","url":"https://www.academia.edu/Documents/in/%C3%81lgebra?f_ri=66102"},{"id":830901,"name":"Educación Primaria","url":"https://www.academia.edu/Documents/in/Educaci%C3%B3n_Primaria?f_ri=66102"},{"id":3186213,"name":"revisión sistemática","url":"https://www.academia.edu/Documents/in/revisi%C3%B3n_sistem%C3%A1tica?f_ri=66102"},{"id":3334382,"name":"álgebra temprana","url":"https://www.academia.edu/Documents/in/%C3%A1lgebra_temprana?f_ri=66102"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_38175402" data-work_id="38175402" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/38175402/Secondary_mathematics_student_teachers_types_of_noticing_while_teaching">Secondary mathematics student teachers’ types of noticing while teaching</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">The purpose of this paper is to describe secondary mathematics student teachers’ types of noticing while teaching. We discuss the importance of focusing on the interrelatedness of the noticing skills rather than reporting on individual... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_38175402" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">The purpose of this paper is to describe secondary mathematics student teachers’ types of noticing while teaching. We discuss the importance of focusing on the interrelatedness of the noticing skills rather than reporting on individual skills separately. We apply the types of noticing to videos of student teachers to identify their ability to elicit and interpret student mathematical thinking in-the-moment while teaching. Results suggest that our student teachers did elicit and attend to student mathematical thinking while teaching, but how they interpreted the elicited student thinking varied. We hypothesize three reasons for why student teachers may have interpreted student mathematical thinking at a general level.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/38175402" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="77c84dd2bd5bb44a225a77c739d5baea" rel="nofollow" data-download="{"attachment_id":58211074,"asset_id":38175402,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/58211074/download_file?st=MTczMzAyOTA0OCw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="5465520" href="https://tcu.academia.edu/MattSwitzer">Matt Switzer</a><script data-card-contents-for-user="5465520" type="text/json">{"id":5465520,"first_name":"Matt","last_name":"Switzer","domain_name":"tcu","page_name":"MattSwitzer","display_name":"Matt Switzer","profile_url":"https://tcu.academia.edu/MattSwitzer?f_ri=66102","photo":"https://0.academia-photos.com/5465520/2399908/3032558/s65_matt.switzer.jpg"}</script></span></span></li><li class="js-paper-rank-work_38175402 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="38175402"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 38175402, container: ".js-paper-rank-work_38175402", }); });</script></li><li class="js-percentile-work_38175402 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 38175402; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_38175402"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_38175402 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="38175402"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 38175402; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=38175402]").text(description); $(".js-view-count-work_38175402").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_38175402").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="38175402"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">5</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="1601" href="https://www.academia.edu/Documents/in/Teacher_Education">Teacher Education</a>, <script data-card-contents-for-ri="1601" type="text/json">{"id":1601,"name":"Teacher Education","url":"https://www.academia.edu/Documents/in/Teacher_Education?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="66102" href="https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching">Mathematical Knowledge for Teaching</a>, <script data-card-contents-for-ri="66102" type="text/json">{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="81911" href="https://www.academia.edu/Documents/in/Preservice_Teacher_Education">Preservice Teacher Education</a>, <script data-card-contents-for-ri="81911" type="text/json">{"id":81911,"name":"Preservice Teacher Education","url":"https://www.academia.edu/Documents/in/Preservice_Teacher_Education?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="109652" href="https://www.academia.edu/Documents/in/Teacher_knowledge">Teacher knowledge</a><script data-card-contents-for-ri="109652" type="text/json">{"id":109652,"name":"Teacher knowledge","url":"https://www.academia.edu/Documents/in/Teacher_knowledge?f_ri=66102","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=38175402]'), work: {"id":38175402,"title":"Secondary mathematics student teachers’ types of noticing while teaching","created_at":"2019-01-18T08:25:14.414-08:00","url":"https://www.academia.edu/38175402/Secondary_mathematics_student_teachers_types_of_noticing_while_teaching?f_ri=66102","dom_id":"work_38175402","summary":"The purpose of this paper is to describe secondary mathematics student teachers’ types of noticing while teaching. We discuss the importance of focusing on the interrelatedness of the noticing skills rather than reporting on individual skills separately. We apply the types of noticing to videos of student teachers to identify their ability to elicit and interpret student mathematical thinking in-the-moment while teaching. Results suggest that our student teachers did elicit and attend to student mathematical thinking while teaching, but how they interpreted the elicited student thinking varied. We hypothesize three reasons for why student teachers may have interpreted student mathematical thinking at a general level.","downloadable_attachments":[{"id":58211074,"asset_id":38175402,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":5465520,"first_name":"Matt","last_name":"Switzer","domain_name":"tcu","page_name":"MattSwitzer","display_name":"Matt Switzer","profile_url":"https://tcu.academia.edu/MattSwitzer?f_ri=66102","photo":"https://0.academia-photos.com/5465520/2399908/3032558/s65_matt.switzer.jpg"}],"research_interests":[{"id":1601,"name":"Teacher Education","url":"https://www.academia.edu/Documents/in/Teacher_Education?f_ri=66102","nofollow":false},{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102","nofollow":false},{"id":81911,"name":"Preservice Teacher Education","url":"https://www.academia.edu/Documents/in/Preservice_Teacher_Education?f_ri=66102","nofollow":false},{"id":109652,"name":"Teacher knowledge","url":"https://www.academia.edu/Documents/in/Teacher_knowledge?f_ri=66102","nofollow":false},{"id":816081,"name":"Mathematics Teacher Noticing","url":"https://www.academia.edu/Documents/in/Mathematics_Teacher_Noticing?f_ri=66102"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_50785624" data-work_id="50785624" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/50785624/_Mis_alignment_between_noticing_and_instructional_quality_The_role_of_psychological_and_cognitive_constructs">(Mis) alignment between noticing and instructional quality: The role of psychological and cognitive constructs</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">In this study, we investigated the relationship between teachers’ post-instruction noticing (PIN) and the quality of their mathematics instruction. We analyzed the conversations of elementary teachers around five coached lessons and... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_50785624" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">In this study, we investigated the relationship between teachers’ post-instruction noticing (PIN) and the quality of their mathematics instruction. We analyzed the conversations of elementary teachers around five coached lessons and scored their level of post-instruction noticing and the mathematical quality of the instruction of the lesson. We compared teachers’ PIN levels with their instructional quality, using scores from the Mathematical Quality of Instruction (MQI) rubric, for each coached lesson. There was both alignment and discrepancies between the level of PIN and MQI scores. Explorations of the cognitive and psychological constructs that seemed to influence teacher’s noticing showed that mathematical knowledge for teaching (MKT), efficacy, beliefs, emotions, and identity was influential on teachers’ PIN although they seemed to influence teachers differently. In some cases, the constructs appeared to support attentiveness to students’ thinking and in other cases they did not. We discuss implications for professional development and future research on teachers’ noticing.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/50785624" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="3596c58b32f233a35ea5c64da042de14" rel="nofollow" data-download="{"attachment_id":68653148,"asset_id":50785624,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/68653148/download_file?st=MTczMzAyOTA0OCw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="108999422" href="https://scranton.academia.edu/JinqingLiu">Jinqing Liu</a><script data-card-contents-for-user="108999422" type="text/json">{"id":108999422,"first_name":"Jinqing","last_name":"Liu","domain_name":"scranton","page_name":"JinqingLiu","display_name":"Jinqing Liu","profile_url":"https://scranton.academia.edu/JinqingLiu?f_ri=66102","photo":"https://0.academia-photos.com/108999422/44319626/52081559/s65_jinqing.liu.jpg"}</script></span></span></li><li class="js-paper-rank-work_50785624 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="50785624"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 50785624, container: ".js-paper-rank-work_50785624", }); });</script></li><li class="js-percentile-work_50785624 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 50785624; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_50785624"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_50785624 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="50785624"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 50785624; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=50785624]").text(description); $(".js-view-count-work_50785624").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_50785624").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="50785624"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">8</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="17773" href="https://www.academia.edu/Documents/in/Teachers_professional_development-1">Teachers' professional development</a>, <script data-card-contents-for-ri="17773" type="text/json">{"id":17773,"name":"Teachers' professional development","url":"https://www.academia.edu/Documents/in/Teachers_professional_development-1?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="21804" href="https://www.academia.edu/Documents/in/Teachers_Motivation_And_Emotions_For_Professional_Development">Teachers' Motivation And Emotions For Professional Development</a>, <script data-card-contents-for-ri="21804" type="text/json">{"id":21804,"name":"Teachers' Motivation And Emotions For Professional Development","url":"https://www.academia.edu/Documents/in/Teachers_Motivation_And_Emotions_For_Professional_Development?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="50025" href="https://www.academia.edu/Documents/in/Teacher_Identity">Teacher Identity</a>, <script data-card-contents-for-ri="50025" type="text/json">{"id":50025,"name":"Teacher Identity","url":"https://www.academia.edu/Documents/in/Teacher_Identity?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="50581" href="https://www.academia.edu/Documents/in/Self_Efficacy">Self Efficacy</a><script data-card-contents-for-ri="50581" type="text/json">{"id":50581,"name":"Self Efficacy","url":"https://www.academia.edu/Documents/in/Self_Efficacy?f_ri=66102","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=50785624]'), work: {"id":50785624,"title":"(Mis) alignment between noticing and instructional quality: The role of psychological and cognitive constructs","created_at":"2021-08-07T21:41:35.714-07:00","url":"https://www.academia.edu/50785624/_Mis_alignment_between_noticing_and_instructional_quality_The_role_of_psychological_and_cognitive_constructs?f_ri=66102","dom_id":"work_50785624","summary":"In this study, we investigated the relationship between teachers’ post-instruction noticing (PIN) and the quality of their mathematics instruction. We analyzed the conversations of elementary teachers around five coached lessons and scored their level of post-instruction noticing and the mathematical quality of the instruction of the lesson. We compared teachers’ PIN levels with their instructional quality, using scores from the Mathematical Quality of Instruction (MQI) rubric, for each coached lesson. There was both alignment and discrepancies between the level of PIN and MQI scores. Explorations of the cognitive and psychological constructs that seemed to influence teacher’s noticing showed that mathematical knowledge for teaching (MKT), efficacy, beliefs, emotions, and identity was influential on teachers’ PIN although they seemed to influence teachers differently. In some cases, the constructs appeared to support attentiveness to students’ thinking and in other cases they did not. We discuss implications for professional development and future research on teachers’ noticing.","downloadable_attachments":[{"id":68653148,"asset_id":50785624,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":108999422,"first_name":"Jinqing","last_name":"Liu","domain_name":"scranton","page_name":"JinqingLiu","display_name":"Jinqing Liu","profile_url":"https://scranton.academia.edu/JinqingLiu?f_ri=66102","photo":"https://0.academia-photos.com/108999422/44319626/52081559/s65_jinqing.liu.jpg"}],"research_interests":[{"id":17773,"name":"Teachers' professional development","url":"https://www.academia.edu/Documents/in/Teachers_professional_development-1?f_ri=66102","nofollow":false},{"id":21804,"name":"Teachers' Motivation And Emotions For Professional Development","url":"https://www.academia.edu/Documents/in/Teachers_Motivation_And_Emotions_For_Professional_Development?f_ri=66102","nofollow":false},{"id":50025,"name":"Teacher Identity","url":"https://www.academia.edu/Documents/in/Teacher_Identity?f_ri=66102","nofollow":false},{"id":50581,"name":"Self Efficacy","url":"https://www.academia.edu/Documents/in/Self_Efficacy?f_ri=66102","nofollow":false},{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102"},{"id":240653,"name":"Teachers Beliefs","url":"https://www.academia.edu/Documents/in/Teachers_Beliefs?f_ri=66102"},{"id":1286528,"name":"Professional Noticing","url":"https://www.academia.edu/Documents/in/Professional_Noticing?f_ri=66102"},{"id":4037789,"name":"mathematical quality of instruction","url":"https://www.academia.edu/Documents/in/mathematical_quality_of_instruction?f_ri=66102"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_2040761" data-work_id="2040761" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/2040761/Clivaz_S_2012_Connaissances_math%C3%A9matiques_des_enseignants_et_enseignement_de_l_algorithme_de_la_multiplication_In_J_L_Dorier_and_C_Sylvia_Eds_Enseignement_des_math%C3%A9matiques_et_contrat_social_enjeux_et_d%C3%A9fis_pour_le_21e_si%C3%A8cle_Actes_du_colloque_EMF2012_pp_GT1_pp_172_182_Gen%C3%A8ve">Clivaz, S. (2012). Connaissances mathématiques des enseignants et enseignement de l’algorithme de la multiplication. In J.-L. Dorier & C. Sylvia (Eds.), Enseignement des mathématiques et contrat social : enjeux et défis pour le 21e siècle – Actes du colloque EMF2012 (pp. GT1, pp. 172–182). Genève.</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">In order to describe the influence of primary school teachers’ mathematical knowledge on their didactical management of classroom mathematical tasks, four teachers have been observed while teaching multidigit multiplication algorithm. The... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_2040761" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">In order to describe the influence of primary school teachers’ mathematical knowledge on their didactical management of classroom mathematical tasks, four teachers have been observed while teaching multidigit multiplication algorithm. The sequences were analyzed using three frames: categories of mathematical knowledge for teaching, the criteria for mathematical pertinence of the teacher and the structure of the milieu. The results are taken into account from a general perspective and then focused on a finer grained analysis. The analysis shows the links between mathematical knowledge, pertinence and teachers’ didactical choices. <br /> <br /> <br />Afin de décrire l’influence des connaissances mathématiques des enseignants primaires sur leur gestion didactique de tâches mathématiques, quatre enseignants ont été observés durant leur enseignement de l’algorithme de la multiplication par un nombre à plusieurs chiffres. Les séquences sont analysées à l’aide de trois cadres : les catégories de connaissances mathématiques pour l’enseignement, les critères de pertinence mathématique du professeur et la structuration du milieu. Les résultats sont considérés à partir d’un niveau d’observation général et se focalisent ensuite sur un grain d’analyse plus fin. Ils font apparaître des liens entre connaissances mathématiques, pertinence et choix didactiques des enseignants.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/2040761" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="01b8025f31c9fb7114a5fcea8e410fba" rel="nofollow" data-download="{"attachment_id":30871423,"asset_id":2040761,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/30871423/download_file?st=MTczMzAyOTA0OCw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="515022" href="https://hepl.academia.edu/stephaneclivaz">Clivaz Stéphane</a><script data-card-contents-for-user="515022" type="text/json">{"id":515022,"first_name":"Clivaz","last_name":"Stéphane","domain_name":"hepl","page_name":"stephaneclivaz","display_name":"Clivaz Stéphane","profile_url":"https://hepl.academia.edu/stephaneclivaz?f_ri=66102","photo":"https://0.academia-photos.com/515022/180027/73742387/s65_clivaz.st_phane.jpg"}</script></span></span></li><li class="js-paper-rank-work_2040761 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="2040761"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 2040761, container: ".js-paper-rank-work_2040761", }); 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$(".js-view-count[data-work-id=2040761]").text(description); $(".js-view-count-work_2040761").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_2040761").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="2040761"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">3</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="27801" href="https://www.academia.edu/Documents/in/Mathematics_Teacher_Education">Mathematics Teacher Education</a>, <script data-card-contents-for-ri="27801" type="text/json">{"id":27801,"name":"Mathematics Teacher Education","url":"https://www.academia.edu/Documents/in/Mathematics_Teacher_Education?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="66102" href="https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching">Mathematical Knowledge for Teaching</a>, <script data-card-contents-for-ri="66102" type="text/json">{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="152051" href="https://www.academia.edu/Documents/in/Didactique_des_mathematiques">Didactique des mathématiques</a><script data-card-contents-for-ri="152051" type="text/json">{"id":152051,"name":"Didactique des mathématiques","url":"https://www.academia.edu/Documents/in/Didactique_des_mathematiques?f_ri=66102","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=2040761]'), work: {"id":2040761,"title":"Clivaz, S. (2012). Connaissances mathématiques des enseignants et enseignement de l’algorithme de la multiplication. In J.-L. Dorier \u0026 C. Sylvia (Eds.), Enseignement des mathématiques et contrat social : enjeux et défis pour le 21e siècle – Actes du colloque EMF2012 (pp. GT1, pp. 172–182). Genève.","created_at":"2012-10-18T19:49:38.806-07:00","url":"https://www.academia.edu/2040761/Clivaz_S_2012_Connaissances_math%C3%A9matiques_des_enseignants_et_enseignement_de_l_algorithme_de_la_multiplication_In_J_L_Dorier_and_C_Sylvia_Eds_Enseignement_des_math%C3%A9matiques_et_contrat_social_enjeux_et_d%C3%A9fis_pour_le_21e_si%C3%A8cle_Actes_du_colloque_EMF2012_pp_GT1_pp_172_182_Gen%C3%A8ve?f_ri=66102","dom_id":"work_2040761","summary":"In order to describe the influence of primary school teachers’ mathematical knowledge on their didactical management of classroom mathematical tasks, four teachers have been observed while teaching multidigit multiplication algorithm. The sequences were analyzed using three frames: categories of mathematical knowledge for teaching, the criteria for mathematical pertinence of the teacher and the structure of the milieu. The results are taken into account from a general perspective and then focused on a finer grained analysis. The analysis shows the links between mathematical knowledge, pertinence and teachers’ didactical choices.\r\n\r\n\r\nAfin de décrire l’influence des connaissances mathématiques des enseignants primaires sur leur gestion didactique de tâches mathématiques, quatre enseignants ont été observés durant leur enseignement de l’algorithme de la multiplication par un nombre à plusieurs chiffres. Les séquences sont analysées à l’aide de trois cadres : les catégories de connaissances mathématiques pour l’enseignement, les critères de pertinence mathématique du professeur et la structuration du milieu. Les résultats sont considérés à partir d’un niveau d’observation général et se focalisent ensuite sur un grain d’analyse plus fin. Ils font apparaître des liens entre connaissances mathématiques, pertinence et choix didactiques des enseignants.","downloadable_attachments":[{"id":30871423,"asset_id":2040761,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":515022,"first_name":"Clivaz","last_name":"Stéphane","domain_name":"hepl","page_name":"stephaneclivaz","display_name":"Clivaz Stéphane","profile_url":"https://hepl.academia.edu/stephaneclivaz?f_ri=66102","photo":"https://0.academia-photos.com/515022/180027/73742387/s65_clivaz.st_phane.jpg"}],"research_interests":[{"id":27801,"name":"Mathematics Teacher Education","url":"https://www.academia.edu/Documents/in/Mathematics_Teacher_Education?f_ri=66102","nofollow":false},{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102","nofollow":false},{"id":152051,"name":"Didactique des mathématiques","url":"https://www.academia.edu/Documents/in/Didactique_des_mathematiques?f_ri=66102","nofollow":false}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_58054252" data-work_id="58054252" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/58054252/Teachers_Mathematics_Knowledge_for_Teaching_Early_Algebra_A_Systematic_Review_from_the_MKT_Perspective">Teachers' Mathematics Knowledge for Teaching Early Algebra: A Systematic Review from the MKT Perspective</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">The mathematical knowledge for teaching (MKT) model emerged from the advances proposed by Shulman in 1986 and 1987 as part of the teacher’s professional knowledge model, and refers to the mathematical knowledge that the teacher employs to... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_58054252" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">The mathematical knowledge for teaching (MKT) model emerged from the advances proposed by Shulman in 1986 and 1987 as part of the teacher’s professional knowledge model, and refers to the mathematical knowledge that the teacher employs to carry out the instruction process in the classroom. MKT has become an international benchmark for research into mathematics education and boasts a great scope and impact to date. The objective of this study is to conduct a<br />systematic review of the way in which the MKT of early algebra teachers has been conceptualized and empirically studied in the scientific literature from 2010 to 2021. A systematic search in the Web<br />of Science and Scopus databases led to a review of 17 papers. The results show great advances in the conceptualization of mathematical knowledge for teaching early algebra, focusing mainly on primary<br />education teachers and on specialized knowledge of the content. In turn, there is a predominance of studies that address functional thinking as a content area. We conclude that more empirical studies are needed that address the mathematical knowledge that childhood and primary education teachers have of early algebra.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/58054252" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="af15b4c63abf6b12d93958196c4c4a26" rel="nofollow" data-download="{"attachment_id":72650678,"asset_id":58054252,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/72650678/download_file?st=MTczMzAyOTA0OCw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="542378" href="https://ugirona.academia.edu/AngelAlsina">Angel Alsina</a><script data-card-contents-for-user="542378" type="text/json">{"id":542378,"first_name":"Angel","last_name":"Alsina","domain_name":"ugirona","page_name":"AngelAlsina","display_name":"Angel Alsina","profile_url":"https://ugirona.academia.edu/AngelAlsina?f_ri=66102","photo":"https://0.academia-photos.com/542378/9879688/15244312/s65_angel.alsina.jpg"}</script></span></span></li><li class="js-paper-rank-work_58054252 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="58054252"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 58054252, container: ".js-paper-rank-work_58054252", }); 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$(".js-view-count[data-work-id=58054252]").text(description); $(".js-view-count-work_58054252").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_58054252").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="58054252"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">17</a>  </div><span class="InlineList-item-text u-textTruncate u-pl10x"><a class="InlineList-item-text" data-has-card-for-ri="329" href="https://www.academia.edu/Documents/in/Algebra">Algebra</a>, <script data-card-contents-for-ri="329" type="text/json">{"id":329,"name":"Algebra","url":"https://www.academia.edu/Documents/in/Algebra?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="2731" href="https://www.academia.edu/Documents/in/Mathematics_Education">Mathematics Education</a>, <script data-card-contents-for-ri="2731" type="text/json">{"id":2731,"name":"Mathematics Education","url":"https://www.academia.edu/Documents/in/Mathematics_Education?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="3753" href="https://www.academia.edu/Documents/in/Early_Childhood_Education">Early Childhood Education</a>, <script data-card-contents-for-ri="3753" type="text/json">{"id":3753,"name":"Early Childhood Education","url":"https://www.academia.edu/Documents/in/Early_Childhood_Education?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="22277" href="https://www.academia.edu/Documents/in/Math_Education_in_Early_Childhood_Education">Math Education in Early Childhood Education</a><script data-card-contents-for-ri="22277" type="text/json">{"id":22277,"name":"Math Education in Early Childhood Education","url":"https://www.academia.edu/Documents/in/Math_Education_in_Early_Childhood_Education?f_ri=66102","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=58054252]'), work: {"id":58054252,"title":"Teachers' Mathematics Knowledge for Teaching Early Algebra: A Systematic Review from the MKT Perspective","created_at":"2021-10-15T02:28:38.427-07:00","url":"https://www.academia.edu/58054252/Teachers_Mathematics_Knowledge_for_Teaching_Early_Algebra_A_Systematic_Review_from_the_MKT_Perspective?f_ri=66102","dom_id":"work_58054252","summary":"The mathematical knowledge for teaching (MKT) model emerged from the advances proposed by Shulman in 1986 and 1987 as part of the teacher’s professional knowledge model, and refers to the mathematical knowledge that the teacher employs to carry out the instruction process in the classroom. MKT has become an international benchmark for research into mathematics education and boasts a great scope and impact to date. The objective of this study is to conduct a\nsystematic review of the way in which the MKT of early algebra teachers has been conceptualized and empirically studied in the scientific literature from 2010 to 2021. A systematic search in the Web\nof Science and Scopus databases led to a review of 17 papers. The results show great advances in the conceptualization of mathematical knowledge for teaching early algebra, focusing mainly on primary\neducation teachers and on specialized knowledge of the content. In turn, there is a predominance of studies that address functional thinking as a content area. We conclude that more empirical studies are needed that address the mathematical knowledge that childhood and primary education teachers have of early algebra.","downloadable_attachments":[{"id":72650678,"asset_id":58054252,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":542378,"first_name":"Angel","last_name":"Alsina","domain_name":"ugirona","page_name":"AngelAlsina","display_name":"Angel Alsina","profile_url":"https://ugirona.academia.edu/AngelAlsina?f_ri=66102","photo":"https://0.academia-photos.com/542378/9879688/15244312/s65_angel.alsina.jpg"}],"research_interests":[{"id":329,"name":"Algebra","url":"https://www.academia.edu/Documents/in/Algebra?f_ri=66102","nofollow":false},{"id":2731,"name":"Mathematics Education","url":"https://www.academia.edu/Documents/in/Mathematics_Education?f_ri=66102","nofollow":false},{"id":3753,"name":"Early Childhood Education","url":"https://www.academia.edu/Documents/in/Early_Childhood_Education?f_ri=66102","nofollow":false},{"id":22277,"name":"Math Education in Early Childhood Education","url":"https://www.academia.edu/Documents/in/Math_Education_in_Early_Childhood_Education?f_ri=66102","nofollow":false},{"id":44348,"name":"Systematic Reviews","url":"https://www.academia.edu/Documents/in/Systematic_Reviews?f_ri=66102"},{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102"},{"id":72555,"name":"Didáctica de las matemáticas en Educación Básica","url":"https://www.academia.edu/Documents/in/Didactica_de_las_matematicas_en_Educacion_Basica?f_ri=66102"},{"id":79368,"name":"Educación Infantil","url":"https://www.academia.edu/Documents/in/Educaci%C3%B3n_Infantil?f_ri=66102"},{"id":88382,"name":"Primary Education","url":"https://www.academia.edu/Documents/in/Primary_Education?f_ri=66102"},{"id":109652,"name":"Teacher knowledge","url":"https://www.academia.edu/Documents/in/Teacher_knowledge?f_ri=66102"},{"id":182978,"name":"Educación Matemática","url":"https://www.academia.edu/Documents/in/Educaci%C3%B3n_Matem%C3%A1tica?f_ri=66102"},{"id":298842,"name":"Early Algebra","url":"https://www.academia.edu/Documents/in/Early_Algebra?f_ri=66102"},{"id":382119,"name":"Álgebra","url":"https://www.academia.edu/Documents/in/%C3%81lgebra?f_ri=66102"},{"id":402504,"name":"Mathematical Knowledge for Teaching, Mathematics Teacher Education","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching_Mathematics_Teacher_Education?f_ri=66102"},{"id":830901,"name":"Educación Primaria","url":"https://www.academia.edu/Documents/in/Educaci%C3%B3n_Primaria?f_ri=66102"},{"id":3186213,"name":"revisión sistemática","url":"https://www.academia.edu/Documents/in/revisi%C3%B3n_sistem%C3%A1tica?f_ri=66102"},{"id":3334382,"name":"álgebra temprana","url":"https://www.academia.edu/Documents/in/%C3%A1lgebra_temprana?f_ri=66102"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_36271128 coauthored" data-work_id="36271128" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/36271128/Complementing_Mathematics_Teachers_Horizon_Content_Knowledge_with_an_Elementary_on_Advanced_Aspect_Pedagogical_Research_Vol_3_Issue_1">Complementing Mathematics Teachers' Horizon Content Knowledge with an Elementary-on-Advanced Aspect - Pedagogical Research, Vol 3 Issue 1</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">Although Ball and her colleagues provided empirical evidence to support the existence of the six sub-domains in mathematical knowledge for teaching (MKT) and further explained or defined the majority of these sub-domains, there were few... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_36271128" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">Although Ball and her colleagues provided empirical evidence to support the existence of the six sub-domains in mathematical knowledge for teaching (MKT) and further explained or defined the majority of these sub-domains, there were few explanations of what horizon content knowledge (HCK) embedded in MKT meant and they merely provided ideas about HCK. Many researchers attempted to provide some teaching incidents and exemplification to interpret the construct of HCK. Moreover, they thought teachers' studies of tertiary mathematics are useful for classroom teaching practice. Their discourse and instantiation of HCK was correspondent with a higher perspective on elementary mathematics mentioned by Felix Klein (1924), but was not entirely coincide with a kind of elementary perspective on advanced knowledge introduced by Ball and Bass (2009). This study lasted 1 years, and data collection included in-depth interviews, classroom observation and video analysis. We provide a shared classroom teaching incidence and illustrations to explain and to describe the construct of HCK. HCK not only is a kind of elementary perspective on advanced mathematical knowledge, but also complements to a higher perspective on elementary mathematics. Furthermore, HCK could be seen as a reciprocal pathway between the elementary and advanced mathematical knowledge.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/36271128" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="4a4c74fec9058da24808e5c309924a37" rel="nofollow" data-download="{"attachment_id":56176172,"asset_id":36271128,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/56176172/download_file?st=MTczMzAyOTA0OCw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="39496068" href="https://independent.academia.edu/LectitoJournals">Lectito Journals</a><script data-card-contents-for-user="39496068" type="text/json">{"id":39496068,"first_name":"Lectito","last_name":"Journals","domain_name":"independent","page_name":"LectitoJournals","display_name":"Lectito Journals","profile_url":"https://independent.academia.edu/LectitoJournals?f_ri=66102","photo":"https://0.academia-photos.com/39496068/10873067/12134370/s65_lectito.journals.jpg"}</script></span></span><span class="u-displayInlineBlock InlineList-item-text"> and <span class="u-textDecorationUnderline u-clickable InlineList-item-text js-work-more-authors-36271128">+1</span><div class="hidden js-additional-users-36271128"><div><span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a href="https://independent.academia.edu/YiAnCho">Yi-An Cho</a></span></div></div></span><script>(function(){ var popoverSettings = { el: $('.js-work-more-authors-36271128'), placement: 'bottom', hide_delay: 200, html: true, content: function(){ return $('.js-additional-users-36271128').html(); 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Many researchers attempted to provide some teaching incidents and exemplification to interpret the construct of HCK. Moreover, they thought teachers' studies of tertiary mathematics are useful for classroom teaching practice. Their discourse and instantiation of HCK was correspondent with a higher perspective on elementary mathematics mentioned by Felix Klein (1924), but was not entirely coincide with a kind of elementary perspective on advanced knowledge introduced by Ball and Bass (2009). This study lasted 1 years, and data collection included in-depth interviews, classroom observation and video analysis. We provide a shared classroom teaching incidence and illustrations to explain and to describe the construct of HCK. HCK not only is a kind of elementary perspective on advanced mathematical knowledge, but also complements to a higher perspective on elementary mathematics. Furthermore, HCK could be seen as a reciprocal pathway between the elementary and advanced mathematical knowledge.","downloadable_attachments":[{"id":56176172,"asset_id":36271128,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":39496068,"first_name":"Lectito","last_name":"Journals","domain_name":"independent","page_name":"LectitoJournals","display_name":"Lectito Journals","profile_url":"https://independent.academia.edu/LectitoJournals?f_ri=66102","photo":"https://0.academia-photos.com/39496068/10873067/12134370/s65_lectito.journals.jpg"},{"id":80005682,"first_name":"Yi-An","last_name":"Cho","domain_name":"independent","page_name":"YiAnCho","display_name":"Yi-An Cho","profile_url":"https://independent.academia.edu/YiAnCho?f_ri=66102","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":2731,"name":"Mathematics Education","url":"https://www.academia.edu/Documents/in/Mathematics_Education?f_ri=66102","nofollow":false},{"id":28493,"name":"STEM Education","url":"https://www.academia.edu/Documents/in/STEM_Education?f_ri=66102","nofollow":false},{"id":54727,"name":"Educational Sciences","url":"https://www.academia.edu/Documents/in/Educational_Sciences?f_ri=66102","nofollow":false},{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102","nofollow":false},{"id":98999,"name":"Pedagogical Content Knowledge (PCK)","url":"https://www.academia.edu/Documents/in/Pedagogical_Content_Knowledge_PCK_?f_ri=66102"},{"id":150410,"name":"Teaching practice","url":"https://www.academia.edu/Documents/in/Teaching_practice?f_ri=66102"},{"id":1002486,"name":"Advanced Mathematics and Science Courses","url":"https://www.academia.edu/Documents/in/Advanced_Mathematics_and_Science_Courses?f_ri=66102"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_10746839 coauthored" data-work_id="10746839" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/10746839/Mathematical_Knowledge_and_Practices_Resulting_from_Access_to_Digital_Technologies">Mathematical Knowledge and Practices Resulting from Access to Digital Technologies</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">Through an extensive review o f the literature we indicate how technology has influenced the contexts for learning mathematics, and the emergence of a new learning ecology that results from the integration of technology into these... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_10746839" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">Through an extensive review o f the literature we indicate how technology has influenced the contexts for learning mathematics, and the emergence of a new learning ecology that results from the integration of technology into these learning contexts. Conversely, we argue that the mathematics on which the technologies are based influences their design, especially the affordances and constraints for learning of the specific design. The literature indicates that interactions among students, teachers, tasks, and technologies can bring about a shift in empowerment from teacher or external authority to the students as generators of mathematical knowledge and practices; and that feedback provided through the use of different technologies can contribute to students' learning. Recent developments in dynamic technologies have the potential to promote new mathematical practices in different contexts: for example, dynamic geometry, statistical education, robotics and digital games. We propose a transformation of the traditional didactic triangle into a didactic tetrahedron through the introduction of technology and conclude by restructuring this model so as to redefine the space in which new mathematical knowledge and practices can emerge.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/10746839" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="ae675d49d106e2f128faa9484d25dbb0" rel="nofollow" data-download="{"attachment_id":47157993,"asset_id":10746839,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/47157993/download_file?st=MTczMzAyOTA0OCw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="131727" href="https://uq.academia.edu/KatieMakar">Katie Makar</a><script data-card-contents-for-user="131727" type="text/json">{"id":131727,"first_name":"Katie","last_name":"Makar","domain_name":"uq","page_name":"KatieMakar","display_name":"Katie Makar","profile_url":"https://uq.academia.edu/KatieMakar?f_ri=66102","photo":"https://0.academia-photos.com/131727/35108/528465/s65_katie.makar.jpg"}</script></span></span><span class="u-displayInlineBlock InlineList-item-text"> and <span class="u-textDecorationUnderline u-clickable InlineList-item-text js-work-more-authors-10746839">+1</span><div class="hidden js-additional-users-10746839"><div><span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a href="https://upn.academia.edu/VHoyos">Veronica Hoyos</a></span></div></div></span><script>(function(){ var popoverSettings = { el: $('.js-work-more-authors-10746839'), placement: 'bottom', hide_delay: 200, html: true, content: function(){ return $('.js-additional-users-10746839').html(); 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container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_10746839 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="10746839"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 10746839; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=10746839]").text(description); $(".js-view-count-work_10746839").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_10746839").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="10746839"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">8</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="4840" href="https://www.academia.edu/Documents/in/Statistics_Education">Statistics Education</a>, <script data-card-contents-for-ri="4840" type="text/json">{"id":4840,"name":"Statistics Education","url":"https://www.academia.edu/Documents/in/Statistics_Education?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="15076" href="https://www.academia.edu/Documents/in/Digital_Games">Digital Games</a>, <script data-card-contents-for-ri="15076" type="text/json">{"id":15076,"name":"Digital Games","url":"https://www.academia.edu/Documents/in/Digital_Games?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="19592" href="https://www.academia.edu/Documents/in/Mathematical_Practice">Mathematical Practice</a>, <script data-card-contents-for-ri="19592" type="text/json">{"id":19592,"name":"Mathematical Practice","url":"https://www.academia.edu/Documents/in/Mathematical_Practice?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="20216" href="https://www.academia.edu/Documents/in/Context_Based_Learning">Context Based Learning</a><script data-card-contents-for-ri="20216" type="text/json">{"id":20216,"name":"Context Based Learning","url":"https://www.academia.edu/Documents/in/Context_Based_Learning?f_ri=66102","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=10746839]'), work: {"id":10746839,"title":"Mathematical Knowledge and Practices Resulting from Access to Digital Technologies","created_at":"2015-02-12T14:00:25.267-08:00","url":"https://www.academia.edu/10746839/Mathematical_Knowledge_and_Practices_Resulting_from_Access_to_Digital_Technologies?f_ri=66102","dom_id":"work_10746839","summary":"Through an extensive review o f the literature we indicate how technology has influenced the contexts for learning mathematics, and the emergence of a new learning ecology that results from the integration of technology into these learning contexts. Conversely, we argue that the mathematics on which the technologies are based influences their design, especially the affordances and constraints for learning of the specific design. The literature indicates that interactions among students, teachers, tasks, and technologies can bring about a shift in empowerment from teacher or external authority to the students as generators of mathematical knowledge and practices; and that feedback provided through the use of different technologies can contribute to students' learning. Recent developments in dynamic technologies have the potential to promote new mathematical practices in different contexts: for example, dynamic geometry, statistical education, robotics and digital games. We propose a transformation of the traditional didactic triangle into a didactic tetrahedron through the introduction of technology and conclude by restructuring this model so as to redefine the space in which new mathematical knowledge and practices can emerge.","downloadable_attachments":[{"id":47157993,"asset_id":10746839,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":131727,"first_name":"Katie","last_name":"Makar","domain_name":"uq","page_name":"KatieMakar","display_name":"Katie Makar","profile_url":"https://uq.academia.edu/KatieMakar?f_ri=66102","photo":"https://0.academia-photos.com/131727/35108/528465/s65_katie.makar.jpg"},{"id":26187699,"first_name":"Veronica","last_name":"Hoyos","domain_name":"upn","page_name":"VHoyos","display_name":"Veronica Hoyos","profile_url":"https://upn.academia.edu/VHoyos?f_ri=66102","photo":"https://0.academia-photos.com/26187699/10540032/29569105/s65_veronica.hoyos.jpg"}],"research_interests":[{"id":4840,"name":"Statistics Education","url":"https://www.academia.edu/Documents/in/Statistics_Education?f_ri=66102","nofollow":false},{"id":15076,"name":"Digital Games","url":"https://www.academia.edu/Documents/in/Digital_Games?f_ri=66102","nofollow":false},{"id":19592,"name":"Mathematical Practice","url":"https://www.academia.edu/Documents/in/Mathematical_Practice?f_ri=66102","nofollow":false},{"id":20216,"name":"Context Based Learning","url":"https://www.academia.edu/Documents/in/Context_Based_Learning?f_ri=66102","nofollow":false},{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102"},{"id":173288,"name":"Student-Teacher Relationships","url":"https://www.academia.edu/Documents/in/Student-Teacher_Relationships?f_ri=66102"},{"id":487702,"name":"Dynamic Geometry","url":"https://www.academia.edu/Documents/in/Dynamic_Geometry?f_ri=66102"},{"id":911182,"name":"Use of digital technologies in mathematics classrooms","url":"https://www.academia.edu/Documents/in/Use_of_digital_technologies_in_mathematics_classrooms?f_ri=66102"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_26197831 coauthored" data-work_id="26197831" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/26197831/Elementary_school_mathematics_teachers_perception_of_their_professional_needs">Elementary school mathematics teachers' perception of their professional needs</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">This study explored Israeli elementary school mathematics teachers’ perceptions of their professional needs, with the purpose of developing in-service training courses which cater to these needs. Eighty-four teachers responded to the... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_26197831" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">This study explored Israeli elementary school mathematics teachers’ perceptions of their professional needs, with the purpose of developing in-service training courses which cater to these needs. <br />Eighty-four teachers responded to the questionnaire and were interviewed. The results indicate that the respondents’ main needs are associated with strengthening their didactic knowledge capability of dealing with emotional aspects that relate to pupils’ learning of mathematics.<br />Although most of the respondents lack formal mathematics education, they attribute less importance to their need to enhance knowledge in the field. <br />In light of Israeli pupils’ relatively low attainments in mathematics, the authors believe that the education system should require teachers to expand their mathematics knowledge and that only teachers with appropriate knowledge will be permitted to teach the discipline.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/26197831" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="6e3021513fd47eb999879b49b61e17cb" rel="nofollow" data-download="{"attachment_id":46519170,"asset_id":26197831,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/46519170/download_file?st=MTczMzAyOTA0OCw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="6405428" href="https://smkb.academia.edu/AtaraShriki">Atara Shriki</a><script data-card-contents-for-user="6405428" type="text/json">{"id":6405428,"first_name":"Atara","last_name":"Shriki","domain_name":"smkb","page_name":"AtaraShriki","display_name":"Atara Shriki","profile_url":"https://smkb.academia.edu/AtaraShriki?f_ri=66102","photo":"https://0.academia-photos.com/6405428/10665204/11906293/s65_atara.shriki.jpg"}</script></span></span><span class="u-displayInlineBlock InlineList-item-text"> and <span class="u-textDecorationUnderline u-clickable InlineList-item-text js-work-more-authors-26197831">+1</span><div class="hidden js-additional-users-26197831"><div><span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a href="https://smkb.academia.edu/DoritPatkin">Dorit Patkin</a></span></div></div></span><script>(function(){ var popoverSettings = { el: $('.js-work-more-authors-26197831'), placement: 'bottom', hide_delay: 200, html: true, content: function(){ return $('.js-additional-users-26197831').html(); } } new HoverPopover(popoverSettings); })();</script></li><li class="js-paper-rank-work_26197831 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="26197831"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 26197831, container: ".js-paper-rank-work_26197831", }); });</script></li><li class="js-percentile-work_26197831 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 26197831; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_26197831"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_26197831 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="26197831"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 26197831; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=26197831]").text(description); $(".js-view-count-work_26197831").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_26197831").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="26197831"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">3</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="34229" href="https://www.academia.edu/Documents/in/Teacher_professional_development">Teacher professional development</a>, <script data-card-contents-for-ri="34229" type="text/json">{"id":34229,"name":"Teacher professional development","url":"https://www.academia.edu/Documents/in/Teacher_professional_development?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="66102" href="https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching">Mathematical Knowledge for Teaching</a>, <script data-card-contents-for-ri="66102" type="text/json">{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="1164350" href="https://www.academia.edu/Documents/in/Teachers_Professional_Needs">Teachers Professional Needs</a><script data-card-contents-for-ri="1164350" type="text/json">{"id":1164350,"name":"Teachers Professional Needs","url":"https://www.academia.edu/Documents/in/Teachers_Professional_Needs?f_ri=66102","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=26197831]'), work: {"id":26197831,"title":"Elementary school mathematics teachers' perception of their professional needs","created_at":"2016-06-15T14:05:19.635-07:00","url":"https://www.academia.edu/26197831/Elementary_school_mathematics_teachers_perception_of_their_professional_needs?f_ri=66102","dom_id":"work_26197831","summary":"This study explored Israeli elementary school mathematics teachers’ perceptions of their professional needs, with the purpose of developing in-service training courses which cater to these needs. \nEighty-four teachers responded to the questionnaire and were interviewed. The results indicate that the respondents’ main needs are associated with strengthening their didactic knowledge capability of dealing with emotional aspects that relate to pupils’ learning of mathematics.\nAlthough most of the respondents lack formal mathematics education, they attribute less importance to their need to enhance knowledge in the field. \nIn light of Israeli pupils’ relatively low attainments in mathematics, the authors believe that the education system should require teachers to expand their mathematics knowledge and that only teachers with appropriate knowledge will be permitted to teach the discipline.","downloadable_attachments":[{"id":46519170,"asset_id":26197831,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":6405428,"first_name":"Atara","last_name":"Shriki","domain_name":"smkb","page_name":"AtaraShriki","display_name":"Atara Shriki","profile_url":"https://smkb.academia.edu/AtaraShriki?f_ri=66102","photo":"https://0.academia-photos.com/6405428/10665204/11906293/s65_atara.shriki.jpg"},{"id":34154566,"first_name":"Dorit","last_name":"Patkin","domain_name":"smkb","page_name":"DoritPatkin","display_name":"Dorit Patkin","profile_url":"https://smkb.academia.edu/DoritPatkin?f_ri=66102","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":34229,"name":"Teacher professional development","url":"https://www.academia.edu/Documents/in/Teacher_professional_development?f_ri=66102","nofollow":false},{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102","nofollow":false},{"id":1164350,"name":"Teachers Professional Needs","url":"https://www.academia.edu/Documents/in/Teachers_Professional_Needs?f_ri=66102","nofollow":false}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_9420105" data-work_id="9420105" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/9420105/Pre_service_teachers_problem_posing_in_combinatorics">Pre-service teachers' problem posing in combinatorics</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">Combinatorics is seen as one of the more difficult areas of mathematics to teach and to learn. Mathematical knowledge for teaching combinatorics of 14 pre-service teachers for primary school developed during session integrating... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_9420105" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">Combinatorics is seen as one of the more difficult areas of mathematics to teach and to learn. Mathematical knowledge for teaching combinatorics of 14 pre-service teachers for primary school developed during session integrating mathematical and pedagogical activities was assessed through the problem posing. Knowledge of combinatorics of some was enhanced but not in satisfactory extend. Lack of subject matter knowledge influenced students’ ability to pose and subsequently solve combinatorial problems.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/9420105" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="02fe5a9b5836f67e611166535f74b2cd" rel="nofollow" data-download="{"attachment_id":35664140,"asset_id":9420105,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/35664140/download_file?st=MTczMzAyOTA0OCw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="170296" href="https://ukf.academia.edu/JankaMedova">Janka Medova (Melusova)</a><script data-card-contents-for-user="170296" type="text/json">{"id":170296,"first_name":"Janka","last_name":"Medova (Melusova)","domain_name":"ukf","page_name":"JankaMedova","display_name":"Janka Medova (Melusova)","profile_url":"https://ukf.academia.edu/JankaMedova?f_ri=66102","photo":"https://0.academia-photos.com/170296/6005501/6814458/s65_janka.melusova.jpg"}</script></span></span></li><li class="js-paper-rank-work_9420105 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="9420105"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 9420105, container: ".js-paper-rank-work_9420105", }); });</script></li><li class="js-percentile-work_9420105 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 9420105; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_9420105"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_9420105 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="9420105"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 9420105; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=9420105]").text(description); $(".js-view-count-work_9420105").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_9420105").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="9420105"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">4</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="2731" href="https://www.academia.edu/Documents/in/Mathematics_Education">Mathematics Education</a>, <script data-card-contents-for-ri="2731" type="text/json">{"id":2731,"name":"Mathematics Education","url":"https://www.academia.edu/Documents/in/Mathematics_Education?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="27801" href="https://www.academia.edu/Documents/in/Mathematics_Teacher_Education">Mathematics Teacher Education</a>, <script data-card-contents-for-ri="27801" type="text/json">{"id":27801,"name":"Mathematics Teacher Education","url":"https://www.academia.edu/Documents/in/Mathematics_Teacher_Education?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="66102" href="https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching">Mathematical Knowledge for Teaching</a>, <script data-card-contents-for-ri="66102" type="text/json">{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="402504" href="https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching_Mathematics_Teacher_Education">Mathematical Knowledge for Teaching, Mathematics Teacher Education</a><script data-card-contents-for-ri="402504" type="text/json">{"id":402504,"name":"Mathematical Knowledge for Teaching, Mathematics Teacher Education","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching_Mathematics_Teacher_Education?f_ri=66102","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=9420105]'), work: {"id":9420105,"title":"Pre-service teachers' problem posing in combinatorics","created_at":"2014-11-20T16:31:54.487-08:00","url":"https://www.academia.edu/9420105/Pre_service_teachers_problem_posing_in_combinatorics?f_ri=66102","dom_id":"work_9420105","summary":"Combinatorics is seen as one of the more difficult areas of mathematics to teach and to learn. Mathematical knowledge for teaching combinatorics of 14 pre-service teachers for primary school developed during session integrating mathematical and pedagogical activities was assessed through the problem posing. Knowledge of combinatorics of some was enhanced but not in satisfactory extend. Lack of subject matter knowledge influenced students’ ability to pose and subsequently solve combinatorial problems. ","downloadable_attachments":[{"id":35664140,"asset_id":9420105,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":170296,"first_name":"Janka","last_name":"Medova (Melusova)","domain_name":"ukf","page_name":"JankaMedova","display_name":"Janka Medova (Melusova)","profile_url":"https://ukf.academia.edu/JankaMedova?f_ri=66102","photo":"https://0.academia-photos.com/170296/6005501/6814458/s65_janka.melusova.jpg"}],"research_interests":[{"id":2731,"name":"Mathematics Education","url":"https://www.academia.edu/Documents/in/Mathematics_Education?f_ri=66102","nofollow":false},{"id":27801,"name":"Mathematics Teacher Education","url":"https://www.academia.edu/Documents/in/Mathematics_Teacher_Education?f_ri=66102","nofollow":false},{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102","nofollow":false},{"id":402504,"name":"Mathematical Knowledge for Teaching, Mathematics 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data-has-card-for-ri="66102" href="https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching">Mathematical Knowledge for Teaching</a>, <script data-card-contents-for-ri="66102" type="text/json">{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="402504" href="https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching_Mathematics_Teacher_Education">Mathematical Knowledge for Teaching, Mathematics Teacher Education</a><script data-card-contents-for-ri="402504" type="text/json">{"id":402504,"name":"Mathematical Knowledge for Teaching, Mathematics Teacher Education","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching_Mathematics_Teacher_Education?f_ri=66102","nofollow":false}</script></span></li><script>(function(){ if (true) { new 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Primaria","url":"https://www.academia.edu/Documents/in/Educaci%C3%B3n_Primaria?f_ri=66102"},{"id":849389,"name":"Probabilidad","url":"https://www.academia.edu/Documents/in/Probabilidad?f_ri=66102"},{"id":1352060,"name":"REVISIÓN BIBLIOGRÁFICA","url":"https://www.academia.edu/Documents/in/REVISI%C3%93N_BIBLIOGR%C3%81FICA?f_ri=66102"},{"id":1861148,"name":"Meta Analysis and Systematic Review","url":"https://www.academia.edu/Documents/in/Meta_Analysis_and_Systematic_Review?f_ri=66102"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_74559434" data-work_id="74559434" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/74559434/Elementary_school_mathematics_teachers_perception_of_their_professional_needs">Elementary school mathematics teachers’ perception of their professional needs</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">This study explored Israeli elementary school mathematics teachers’ perceptions of their professional needs, with the purpose of developing in-service training courses which cater to these needs. Eighty-four teachers responded to the... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_74559434" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">This study explored Israeli elementary school mathematics teachers’ perceptions of their professional needs, with the purpose of developing in-service training courses which cater to these needs. Eighty-four teachers responded to the questionnaire and were interviewed. The results indicate that the respondents’ main needs are associated with strengthening their didactical knowledge capability of dealing with emotional aspects that relate to pupils’ learning of mathematics. Although most of the respondents lack formal mathematics education, they attribute less importance to their need to enhance knowledge in the field. In light of Israeli pupils’ relatively low attainments in mathematics, the authors believe that the education system should require teachers to expand their mathematics knowledge and that only teachers with appropriate knowledge will be permitted to teach the discipline.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/74559434" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="96595162" href="https://levinsky.academia.edu/DoritPatkin">Dorit Patkin</a><script data-card-contents-for-user="96595162" type="text/json">{"id":96595162,"first_name":"Dorit","last_name":"Patkin","domain_name":"levinsky","page_name":"DoritPatkin","display_name":"Dorit Patkin","profile_url":"https://levinsky.academia.edu/DoritPatkin?f_ri=66102","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_74559434 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="74559434"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 74559434, container: ".js-paper-rank-work_74559434", }); 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$(".js-view-count[data-work-id=74559434]").text(description); $(".js-view-count-work_74559434").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_74559434").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="74559434"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">6</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="221" href="https://www.academia.edu/Documents/in/Psychology">Psychology</a>, <script data-card-contents-for-ri="221" type="text/json">{"id":221,"name":"Psychology","url":"https://www.academia.edu/Documents/in/Psychology?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="33897" href="https://www.academia.edu/Documents/in/Teacher_Development">Teacher Development</a>, <script data-card-contents-for-ri="33897" type="text/json">{"id":33897,"name":"Teacher Development","url":"https://www.academia.edu/Documents/in/Teacher_Development?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="34229" href="https://www.academia.edu/Documents/in/Teacher_professional_development">Teacher professional development</a>, <script data-card-contents-for-ri="34229" type="text/json">{"id":34229,"name":"Teacher professional development","url":"https://www.academia.edu/Documents/in/Teacher_professional_development?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="66102" href="https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching">Mathematical Knowledge for Teaching</a><script data-card-contents-for-ri="66102" type="text/json">{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=74559434]'), work: {"id":74559434,"title":"Elementary school mathematics teachers’ perception of their professional needs","created_at":"2022-03-25T10:18:07.091-07:00","url":"https://www.academia.edu/74559434/Elementary_school_mathematics_teachers_perception_of_their_professional_needs?f_ri=66102","dom_id":"work_74559434","summary":"This study explored Israeli elementary school mathematics teachers’ perceptions of their professional needs, with the purpose of developing in-service training courses which cater to these needs. Eighty-four teachers responded to the questionnaire and were interviewed. The results indicate that the respondents’ main needs are associated with strengthening their didactical knowledge capability of dealing with emotional aspects that relate to pupils’ learning of mathematics. Although most of the respondents lack formal mathematics education, they attribute less importance to their need to enhance knowledge in the field. In light of Israeli pupils’ relatively low attainments in mathematics, the authors believe that the education system should require teachers to expand their mathematics knowledge and that only teachers with appropriate knowledge will be permitted to teach the discipline.","downloadable_attachments":[],"ordered_authors":[{"id":96595162,"first_name":"Dorit","last_name":"Patkin","domain_name":"levinsky","page_name":"DoritPatkin","display_name":"Dorit Patkin","profile_url":"https://levinsky.academia.edu/DoritPatkin?f_ri=66102","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":221,"name":"Psychology","url":"https://www.academia.edu/Documents/in/Psychology?f_ri=66102","nofollow":false},{"id":33897,"name":"Teacher Development","url":"https://www.academia.edu/Documents/in/Teacher_Development?f_ri=66102","nofollow":false},{"id":34229,"name":"Teacher professional development","url":"https://www.academia.edu/Documents/in/Teacher_professional_development?f_ri=66102","nofollow":false},{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102","nofollow":false},{"id":1107057,"name":"Pedagogical Content Knowledge of Science Teachers","url":"https://www.academia.edu/Documents/in/Pedagogical_Content_Knowledge_of_Science_Teachers?f_ri=66102"},{"id":1164350,"name":"Teachers Professional Needs","url":"https://www.academia.edu/Documents/in/Teachers_Professional_Needs?f_ri=66102"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_73295155" data-work_id="73295155" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/73295155/Transcriptions_mathematical_cognition_and_epistemology">Transcriptions, mathematical cognition, and epistemology</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">The epistemologies researchers bring to their studies mediate not only their theories but also their methods, including what they select from their data sources to present the findings on which claims are based. Most articles reduce... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_73295155" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">The epistemologies researchers bring to their studies mediate not only their<br />theories but also their methods, including what they select from their data sources to present the findings on which claims are based. Most articles reduce mathematical knowing to linguistic/mathematical structures, which, in the case of embodiment/enactivist theories, undermines the very argument about the special nature of mathematical knowing. The purpose of this study is to illustrate how different transcriptions of mathematics lessons are generally used to support different epistemologies of mathematical knowing/competence. As part of our third illustration, we provide embodiment/enactivist researchers with an innovative means of representing classroom interactions that are more consistent with their theoretical claims. We offer a comprehensive transcription, which, when treated by readers in the way musicians treat their scores, allow them to enact and feel the knowledge that the article is about.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/73295155" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="00f36cda6f9c98799759811cf1a11322" rel="nofollow" data-download="{"attachment_id":81870501,"asset_id":73295155,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/81870501/download_file?st=MTczMzAyOTA0OCw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="216666343" href="https://ied.academia.edu/AlfredoBautista">Alfredo Bautista</a><script data-card-contents-for-user="216666343" type="text/json">{"id":216666343,"first_name":"Alfredo","last_name":"Bautista","domain_name":"ied","page_name":"AlfredoBautista","display_name":"Alfredo Bautista","profile_url":"https://ied.academia.edu/AlfredoBautista?f_ri=66102","photo":"https://0.academia-photos.com/216666343/75058710/63564449/s65_alfredo.bautista.jpg"}</script></span></span></li><li class="js-paper-rank-work_73295155 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="73295155"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 73295155, container: ".js-paper-rank-work_73295155", }); });</script></li><li class="js-percentile-work_73295155 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 73295155; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_73295155"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_73295155 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="73295155"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 73295155; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=73295155]").text(description); $(".js-view-count-work_73295155").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_73295155").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="73295155"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">11</a>  </div><span class="InlineList-item-text u-textTruncate u-pl10x"><a class="InlineList-item-text" data-has-card-for-ri="300" href="https://www.academia.edu/Documents/in/Mathematics">Mathematics</a>, <script data-card-contents-for-ri="300" type="text/json">{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="815" href="https://www.academia.edu/Documents/in/Epistemology">Epistemology</a>, <script data-card-contents-for-ri="815" type="text/json">{"id":815,"name":"Epistemology","url":"https://www.academia.edu/Documents/in/Epistemology?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="922" href="https://www.academia.edu/Documents/in/Education">Education</a>, <script data-card-contents-for-ri="922" type="text/json">{"id":922,"name":"Education","url":"https://www.academia.edu/Documents/in/Education?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="2731" href="https://www.academia.edu/Documents/in/Mathematics_Education">Mathematics Education</a><script data-card-contents-for-ri="2731" type="text/json">{"id":2731,"name":"Mathematics Education","url":"https://www.academia.edu/Documents/in/Mathematics_Education?f_ri=66102","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=73295155]'), work: {"id":73295155,"title":"Transcriptions, mathematical cognition, and epistemology","created_at":"2022-03-07T23:58:20.102-08:00","url":"https://www.academia.edu/73295155/Transcriptions_mathematical_cognition_and_epistemology?f_ri=66102","dom_id":"work_73295155","summary":"The epistemologies researchers bring to their studies mediate not only their\ntheories but also their methods, including what they select from their data sources to present the findings on which claims are based. Most articles reduce mathematical knowing to linguistic/mathematical structures, which, in the case of embodiment/enactivist theories, undermines the very argument about the special nature of mathematical knowing. The purpose of this study is to illustrate how different transcriptions of mathematics lessons are generally used to support different epistemologies of mathematical knowing/competence. As part of our third illustration, we provide embodiment/enactivist researchers with an innovative means of representing classroom interactions that are more consistent with their theoretical claims. We offer a comprehensive transcription, which, when treated by readers in the way musicians treat their scores, allow them to enact and feel the knowledge that the article is about.","downloadable_attachments":[{"id":81870501,"asset_id":73295155,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":216666343,"first_name":"Alfredo","last_name":"Bautista","domain_name":"ied","page_name":"AlfredoBautista","display_name":"Alfredo Bautista","profile_url":"https://ied.academia.edu/AlfredoBautista?f_ri=66102","photo":"https://0.academia-photos.com/216666343/75058710/63564449/s65_alfredo.bautista.jpg"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics?f_ri=66102","nofollow":false},{"id":815,"name":"Epistemology","url":"https://www.academia.edu/Documents/in/Epistemology?f_ri=66102","nofollow":false},{"id":922,"name":"Education","url":"https://www.academia.edu/Documents/in/Education?f_ri=66102","nofollow":false},{"id":2731,"name":"Mathematics Education","url":"https://www.academia.edu/Documents/in/Mathematics_Education?f_ri=66102","nofollow":false},{"id":27785,"name":"Enactivism","url":"https://www.academia.edu/Documents/in/Enactivism?f_ri=66102"},{"id":42132,"name":"Transcription","url":"https://www.academia.edu/Documents/in/Transcription?f_ri=66102"},{"id":54418,"name":"Geometry","url":"https://www.academia.edu/Documents/in/Geometry?f_ri=66102"},{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102"},{"id":321840,"name":"Early Mathematics","url":"https://www.academia.edu/Documents/in/Early_Mathematics?f_ri=66102"},{"id":377879,"name":"Mathematics Curriculum","url":"https://www.academia.edu/Documents/in/Mathematics_Curriculum?f_ri=66102"},{"id":643054,"name":"Epistemology of Mathematics","url":"https://www.academia.edu/Documents/in/Epistemology_of_Mathematics?f_ri=66102"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_43908159" data-work_id="43908159" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/43908159/FORMA%C3%87%C3%83O_MATEM%C3%81TICA_NA_LICENCIATURA_E_PR%C3%81TICA_DOCENTE_NA_ESCOLA_O_CASO_DA_UNICIDADE_DA_DECOMPOSI%C3%87%C3%83O_EM_PRIMOS_Prospective_Teacher_Education_and_school_teaching_practice_the_case_of_the_uniqueness_of_prime_decomposition">FORMAÇÃO MATEMÁTICA NA LICENCIATURA E PRÁTICA DOCENTE NA ESCOLA: O CASO DA UNICIDADE DA DECOMPOSIÇÃO EM PRIMOS Prospective Teacher Education and school teaching practice: the case of the uniqueness of prime decomposition</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">RESUMO Neste texto discutimos o Teorema Fundamental da Aritmética, tomando como referência as formas como o tema é trabalhado na Educação Básica e nos cursos de Licenciatura em Matemática. Defendemos uma discussão desse tópico, situada no... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_43908159" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">RESUMO Neste texto discutimos o Teorema Fundamental da Aritmética, tomando como referência as formas como o tema é trabalhado na Educação Básica e nos cursos de Licenciatura em Matemática. Defendemos uma discussão desse tópico, situada no contexto específico do ensino escolar, em ambas as instâncias de trabalho de educação matemática, mas principalmente nos processos de formação inicial do professor. Como contribuição nesse sentido, apresentamos uma demonstração "escolar" da unicidade da decomposição em primos, contrastando a viabilidade de seu ajustamento ao trabalho docente sobre o tema no sexto ano do Ensino Fundamental, com as (im)possibilidades de adaptação de duas demonstrações acadêmicas desse mesmo fato, as quais aparecem frequentemente em livros-texto utilizados em cursos de formação de professores de matemática para a Educação Básica. Palavras-chave: Educação Matemática. Prática docente escolar. Formação de professores. Saber docente. Teorema Fundamental da Aritmética. ABSTRACT We discuss the way the Fundamental Theorem of Arithmetic is dealt with in school teaching as compared to the correspondent way this topic is examined in (Brazilian) Math Teacher Education. We argue that it is viable, as well as manageable, to develop a situated (in the school teaching context) discussion of the uniqueness of prime decomposition of natural numbers, both in Mathematics Teacher Education Programs and in the school itself, where this issue is essentially ignored. As a contribution, we present a "school" proof of the uniqueness of prime decomposition in the set of natural numbers, contrasting the possibilities of adapting it to the teaching of mathematics in sixth-grade classes, with the (im)possibilities of adjusting two academic proofs, often presented in textbooks used in Math Teacher Education courses in Brazil.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/43908159" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="f46c915a5d808a5c6c46a96c6a42897b" rel="nofollow" data-download="{"attachment_id":64232366,"asset_id":43908159,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/64232366/download_file?st=MTczMzAyOTA0OCw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="161768233" href="https://ufop.academia.edu/PlinioCMoreira">Plinio C A V A L C A N T I Moreira</a><script data-card-contents-for-user="161768233" type="text/json">{"id":161768233,"first_name":"Plinio","last_name":"Moreira","domain_name":"ufop","page_name":"PlinioCMoreira","display_name":"Plinio C A V A L C A N T I Moreira","profile_url":"https://ufop.academia.edu/PlinioCMoreira?f_ri=66102","photo":"https://0.academia-photos.com/161768233/51894097/39985485/s65_plinio.moreira.jpg"}</script></span></span></li><li class="js-paper-rank-work_43908159 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="43908159"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 43908159, container: ".js-paper-rank-work_43908159", }); });</script></li><li class="js-percentile-work_43908159 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 43908159; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_43908159"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_43908159 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="43908159"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 43908159; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=43908159]").text(description); $(".js-view-count-work_43908159").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_43908159").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="43908159"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">7</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="1601" href="https://www.academia.edu/Documents/in/Teacher_Education">Teacher Education</a>, <script data-card-contents-for-ri="1601" type="text/json">{"id":1601,"name":"Teacher Education","url":"https://www.academia.edu/Documents/in/Teacher_Education?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="2731" href="https://www.academia.edu/Documents/in/Mathematics_Education">Mathematics Education</a>, <script data-card-contents-for-ri="2731" type="text/json">{"id":2731,"name":"Mathematics Education","url":"https://www.academia.edu/Documents/in/Mathematics_Education?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="66102" href="https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching">Mathematical Knowledge for Teaching</a>, <script data-card-contents-for-ri="66102" type="text/json">{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="109652" href="https://www.academia.edu/Documents/in/Teacher_knowledge">Teacher knowledge</a><script data-card-contents-for-ri="109652" type="text/json">{"id":109652,"name":"Teacher knowledge","url":"https://www.academia.edu/Documents/in/Teacher_knowledge?f_ri=66102","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=43908159]'), work: {"id":43908159,"title":"FORMAÇÃO MATEMÁTICA NA LICENCIATURA E PRÁTICA DOCENTE NA ESCOLA: O CASO DA UNICIDADE DA DECOMPOSIÇÃO EM PRIMOS Prospective Teacher Education and school teaching practice: the case of the uniqueness of prime decomposition","created_at":"2020-08-20T15:49:33.242-07:00","url":"https://www.academia.edu/43908159/FORMA%C3%87%C3%83O_MATEM%C3%81TICA_NA_LICENCIATURA_E_PR%C3%81TICA_DOCENTE_NA_ESCOLA_O_CASO_DA_UNICIDADE_DA_DECOMPOSI%C3%87%C3%83O_EM_PRIMOS_Prospective_Teacher_Education_and_school_teaching_practice_the_case_of_the_uniqueness_of_prime_decomposition?f_ri=66102","dom_id":"work_43908159","summary":"RESUMO Neste texto discutimos o Teorema Fundamental da Aritmética, tomando como referência as formas como o tema é trabalhado na Educação Básica e nos cursos de Licenciatura em Matemática. Defendemos uma discussão desse tópico, situada no contexto específico do ensino escolar, em ambas as instâncias de trabalho de educação matemática, mas principalmente nos processos de formação inicial do professor. Como contribuição nesse sentido, apresentamos uma demonstração \"escolar\" da unicidade da decomposição em primos, contrastando a viabilidade de seu ajustamento ao trabalho docente sobre o tema no sexto ano do Ensino Fundamental, com as (im)possibilidades de adaptação de duas demonstrações acadêmicas desse mesmo fato, as quais aparecem frequentemente em livros-texto utilizados em cursos de formação de professores de matemática para a Educação Básica. Palavras-chave: Educação Matemática. Prática docente escolar. Formação de professores. Saber docente. Teorema Fundamental da Aritmética. ABSTRACT We discuss the way the Fundamental Theorem of Arithmetic is dealt with in school teaching as compared to the correspondent way this topic is examined in (Brazilian) Math Teacher Education. We argue that it is viable, as well as manageable, to develop a situated (in the school teaching context) discussion of the uniqueness of prime decomposition of natural numbers, both in Mathematics Teacher Education Programs and in the school itself, where this issue is essentially ignored. As a contribution, we present a \"school\" proof of the uniqueness of prime decomposition in the set of natural numbers, contrasting the possibilities of adapting it to the teaching of mathematics in sixth-grade classes, with the (im)possibilities of adjusting two academic proofs, often presented in textbooks used in Math Teacher Education courses in Brazil.","downloadable_attachments":[{"id":64232366,"asset_id":43908159,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":161768233,"first_name":"Plinio","last_name":"Moreira","domain_name":"ufop","page_name":"PlinioCMoreira","display_name":"Plinio C A V A L C A N T I Moreira","profile_url":"https://ufop.academia.edu/PlinioCMoreira?f_ri=66102","photo":"https://0.academia-photos.com/161768233/51894097/39985485/s65_plinio.moreira.jpg"}],"research_interests":[{"id":1601,"name":"Teacher Education","url":"https://www.academia.edu/Documents/in/Teacher_Education?f_ri=66102","nofollow":false},{"id":2731,"name":"Mathematics Education","url":"https://www.academia.edu/Documents/in/Mathematics_Education?f_ri=66102","nofollow":false},{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102","nofollow":false},{"id":109652,"name":"Teacher knowledge","url":"https://www.academia.edu/Documents/in/Teacher_knowledge?f_ri=66102","nofollow":false},{"id":145280,"name":"Educação Matemática","url":"https://www.academia.edu/Documents/in/Educa%C3%A7%C3%A3o_Matem%C3%A1tica?f_ri=66102"},{"id":2729895,"name":"Formação de Professores de Matemática","url":"https://www.academia.edu/Documents/in/Forma%C3%A7%C3%A3o_de_Professores_de_Matem%C3%A1tica?f_ri=66102"},{"id":3263905,"name":"Saberes profissionais Docentes","url":"https://www.academia.edu/Documents/in/Saberes_profissionais_Docentes?f_ri=66102"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_78845782" data-work_id="78845782" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/78845782/El_conocimiento_del_profesorado_de_Educaci%C3%B3n_Primaria_para_ense%C3%B1ar_estad%C3%ADstica_y_probabilidad_una_revisi%C3%B3n_sistem%C3%A1tica">El conocimiento del profesorado de Educación Primaria para enseñar estadística y probabilidad: una revisión sistemática</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/78845782" data-share-source="work_strip" 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itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="217970434" href="https://independent.academia.edu/JoanFrancoSegu%C3%AD">Joan Franco Seguí</a><script data-card-contents-for-user="217970434" type="text/json">{"id":217970434,"first_name":"Joan","last_name":"Franco Seguí","domain_name":"independent","page_name":"JoanFrancoSeguí","display_name":"Joan Franco Seguí","profile_url":"https://independent.academia.edu/JoanFrancoSegu%C3%AD?f_ri=66102","photo":"https://0.academia-photos.com/217970434/76208709/64729783/s65_joan.franco_segu_.png"}</script></span></span></li><li class="js-paper-rank-work_78845782 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="78845782"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 78845782, container: 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type="text/json">{"id":892,"name":"Statistics","url":"https://www.academia.edu/Documents/in/Statistics?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="951" href="https://www.academia.edu/Documents/in/Humanities">Humanities</a>, <script data-card-contents-for-ri="951" type="text/json">{"id":951,"name":"Humanities","url":"https://www.academia.edu/Documents/in/Humanities?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="4840" href="https://www.academia.edu/Documents/in/Statistics_Education">Statistics Education</a>, <script data-card-contents-for-ri="4840" type="text/json">{"id":4840,"name":"Statistics Education","url":"https://www.academia.edu/Documents/in/Statistics_Education?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="22613" href="https://www.academia.edu/Documents/in/Probability_and_statistics">Probability and statistics</a><script data-card-contents-for-ri="22613" type="text/json">{"id":22613,"name":"Probability and statistics","url":"https://www.academia.edu/Documents/in/Probability_and_statistics?f_ri=66102","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=78845782]'), work: {"id":78845782,"title":"El conocimiento del profesorado de Educación Primaria para enseñar estadística y probabilidad: una revisión sistemática","created_at":"2022-05-09T05:02:35.133-07:00","url":"https://www.academia.edu/78845782/El_conocimiento_del_profesorado_de_Educaci%C3%B3n_Primaria_para_ense%C3%B1ar_estad%C3%ADstica_y_probabilidad_una_revisi%C3%B3n_sistem%C3%A1tica?f_ri=66102","dom_id":"work_78845782","summary":null,"downloadable_attachments":[{"id":85745291,"asset_id":78845782,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":217970434,"first_name":"Joan","last_name":"Franco Seguí","domain_name":"independent","page_name":"JoanFrancoSeguí","display_name":"Joan Franco Seguí","profile_url":"https://independent.academia.edu/JoanFrancoSegu%C3%AD?f_ri=66102","photo":"https://0.academia-photos.com/217970434/76208709/64729783/s65_joan.franco_segu_.png"}],"research_interests":[{"id":892,"name":"Statistics","url":"https://www.academia.edu/Documents/in/Statistics?f_ri=66102","nofollow":false},{"id":951,"name":"Humanities","url":"https://www.academia.edu/Documents/in/Humanities?f_ri=66102","nofollow":false},{"id":4840,"name":"Statistics Education","url":"https://www.academia.edu/Documents/in/Statistics_Education?f_ri=66102","nofollow":false},{"id":22613,"name":"Probability and statistics","url":"https://www.academia.edu/Documents/in/Probability_and_statistics?f_ri=66102","nofollow":false},{"id":23876,"name":"Mathematics Education at Primary Schools","url":"https://www.academia.edu/Documents/in/Mathematics_Education_at_Primary_Schools?f_ri=66102"},{"id":33069,"name":"Probability","url":"https://www.academia.edu/Documents/in/Probability?f_ri=66102"},{"id":44293,"name":"Literature Review","url":"https://www.academia.edu/Documents/in/Literature_Review?f_ri=66102"},{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102"},{"id":72555,"name":"Didáctica de las matemáticas en Educación Básica","url":"https://www.academia.edu/Documents/in/Didactica_de_las_matematicas_en_Educacion_Basica?f_ri=66102"},{"id":109652,"name":"Teacher knowledge","url":"https://www.academia.edu/Documents/in/Teacher_knowledge?f_ri=66102"},{"id":531896,"name":"Estadística","url":"https://www.academia.edu/Documents/in/Estad%C3%ADstica?f_ri=66102"},{"id":830901,"name":"Educación Primaria","url":"https://www.academia.edu/Documents/in/Educaci%C3%B3n_Primaria?f_ri=66102"},{"id":849389,"name":"Probabilidad","url":"https://www.academia.edu/Documents/in/Probabilidad?f_ri=66102"},{"id":1352060,"name":"REVISIÓN BIBLIOGRÁFICA","url":"https://www.academia.edu/Documents/in/REVISI%C3%93N_BIBLIOGR%C3%81FICA?f_ri=66102"},{"id":1861148,"name":"Meta Analysis and Systematic Review","url":"https://www.academia.edu/Documents/in/Meta_Analysis_and_Systematic_Review?f_ri=66102"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_78617953" data-work_id="78617953" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/78617953/Reshaping_Teachers_Mathematical_Perceptions_Analysis_of_a_Professional_Development_Task">Reshaping Teachers' Mathematical Perceptions: Analysis of a Professional Development Task</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">As the focus of mathematics education moves from memorization toward reasoning and problem solving, professional development for in-service teachers must model these activities while simultaneously increasing participants&#39;... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_78617953" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">As the focus of mathematics education moves from memorization toward reasoning and problem solving, professional development for in-service teachers must model these activities while simultaneously increasing participants&#39; mathematical knowledge. We examine a representative task from a mathematics professional development course that uses rational number operation as an opportunity for problem solving and modeling. Transcripts exemplify the growth teachers make in deeply understanding the content–division of fractions–while engaging in guided reinvention and classroom discourse. We propose 4 interconnected qualities of this task that allow participants to engage in and reflect on the process of guided reinvention: (1) authentic context with multiple solution methods, including visual; (2) cognitive dissonance; (3) deep engagement; and (4) impact on mathematical knowledge for teaching.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/78617953" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="37790901" href="https://boisestate.academia.edu/MicheleCarney">Michele Carney</a><script data-card-contents-for-user="37790901" type="text/json">{"id":37790901,"first_name":"Michele","last_name":"Carney","domain_name":"boisestate","page_name":"MicheleCarney","display_name":"Michele Carney","profile_url":"https://boisestate.academia.edu/MicheleCarney?f_ri=66102","photo":"https://0.academia-photos.com/37790901/11192629/12489511/s65_michele.carney"}</script></span></span></li><li class="js-paper-rank-work_78617953 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="78617953"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 78617953, container: ".js-paper-rank-work_78617953", }); });</script></li><li class="js-percentile-work_78617953 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 78617953; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_78617953"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_78617953 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="78617953"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 78617953; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=78617953]").text(description); $(".js-view-count-work_78617953").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_78617953").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="78617953"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">6</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="17769" href="https://www.academia.edu/Documents/in/Professional_Development">Professional Development</a>, <script data-card-contents-for-ri="17769" type="text/json">{"id":17769,"name":"Professional Development","url":"https://www.academia.edu/Documents/in/Professional_Development?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="31686" href="https://www.academia.edu/Documents/in/Curriculum_and_Instruction">Curriculum and Instruction</a>, <script data-card-contents-for-ri="31686" type="text/json">{"id":31686,"name":"Curriculum and Instruction","url":"https://www.academia.edu/Documents/in/Curriculum_and_Instruction?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="66102" href="https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching">Mathematical Knowledge for Teaching</a>, <script data-card-contents-for-ri="66102" type="text/json">{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="345107" href="https://www.academia.edu/Documents/in/Teacher_education_and_professional_development">Teacher education and professional development</a><script data-card-contents-for-ri="345107" type="text/json">{"id":345107,"name":"Teacher education and professional development","url":"https://www.academia.edu/Documents/in/Teacher_education_and_professional_development?f_ri=66102","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=78617953]'), work: {"id":78617953,"title":"Reshaping Teachers' Mathematical Perceptions: Analysis of a Professional Development Task","created_at":"2022-05-06T09:44:37.781-07:00","url":"https://www.academia.edu/78617953/Reshaping_Teachers_Mathematical_Perceptions_Analysis_of_a_Professional_Development_Task?f_ri=66102","dom_id":"work_78617953","summary":"As the focus of mathematics education moves from memorization toward reasoning and problem solving, professional development for in-service teachers must model these activities while simultaneously increasing participants\u0026#39; mathematical knowledge. We examine a representative task from a mathematics professional development course that uses rational number operation as an opportunity for problem solving and modeling. Transcripts exemplify the growth teachers make in deeply understanding the content–division of fractions–while engaging in guided reinvention and classroom discourse. We propose 4 interconnected qualities of this task that allow participants to engage in and reflect on the process of guided reinvention: (1) authentic context with multiple solution methods, including visual; (2) cognitive dissonance; (3) deep engagement; and (4) impact on mathematical knowledge for teaching.","downloadable_attachments":[],"ordered_authors":[{"id":37790901,"first_name":"Michele","last_name":"Carney","domain_name":"boisestate","page_name":"MicheleCarney","display_name":"Michele Carney","profile_url":"https://boisestate.academia.edu/MicheleCarney?f_ri=66102","photo":"https://0.academia-photos.com/37790901/11192629/12489511/s65_michele.carney"}],"research_interests":[{"id":17769,"name":"Professional Development","url":"https://www.academia.edu/Documents/in/Professional_Development?f_ri=66102","nofollow":false},{"id":31686,"name":"Curriculum and Instruction","url":"https://www.academia.edu/Documents/in/Curriculum_and_Instruction?f_ri=66102","nofollow":false},{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102","nofollow":false},{"id":345107,"name":"Teacher education and professional development","url":"https://www.academia.edu/Documents/in/Teacher_education_and_professional_development?f_ri=66102","nofollow":false},{"id":1251652,"name":"Content Knowledge","url":"https://www.academia.edu/Documents/in/Content_Knowledge?f_ri=66102"},{"id":2652577,"name":"Fraction division","url":"https://www.academia.edu/Documents/in/Fraction_division?f_ri=66102"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_73991064" data-work_id="73991064" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/73991064/_Mis_alignment_between_noticing_and_instructional_quality_the_role_of_psychological_and_cognitive_constructs">(Mis)alignment between noticing and instructional quality: the role of psychological and cognitive constructs</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">In this study, we investigated the relationship between teachers’ post-instruction noticing (PIN) and the quality of their mathematics instruction. We analyzed the conversations of elementary teachers around five coached lessons and... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_73991064" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">In this study, we investigated the relationship between teachers’ post-instruction noticing (PIN) and the quality of their mathematics instruction. We analyzed the conversations of elementary teachers around five coached lessons and scored their level of post-instruction noticing and the mathematical quality of the instruction of the lesson. We compared teachers’ PIN levels with their instructional quality, using scores from the Mathematical Quality of Instruction (MQI) rubric, for each coached lesson. There was both alignment and discrepancies between the level of PIN and MQI scores. Explorations of the cognitive and psychological constructs that seemed to influence teacher’s noticing showed that mathematical knowledge for teaching (MKT), efficacy, beliefs, emotions, and identity was influential on teachers’ PIN although they seemed to influence teachers differently. In some cases, the constructs appeared to support attentiveness to students’ thinking and in other cases they did not. We discuss implications for professional development and future research on teachers’ noticing.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/73991064" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="21451553" href="https://independent.academia.edu/AyferEker">Ayfer Eker</a><script data-card-contents-for-user="21451553" type="text/json">{"id":21451553,"first_name":"Ayfer","last_name":"Eker","domain_name":"independent","page_name":"AyferEker","display_name":"Ayfer Eker","profile_url":"https://independent.academia.edu/AyferEker?f_ri=66102","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_73991064 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="73991064"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 73991064, container: ".js-paper-rank-work_73991064", }); });</script></li><li class="js-percentile-work_73991064 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 73991064; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_73991064"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_73991064 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="73991064"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 73991064; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=73991064]").text(description); $(".js-view-count-work_73991064").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_73991064").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="73991064"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">15</a>  </div><span class="InlineList-item-text u-textTruncate u-pl10x"><a class="InlineList-item-text" data-has-card-for-ri="221" href="https://www.academia.edu/Documents/in/Psychology">Psychology</a>, <script data-card-contents-for-ri="221" type="text/json">{"id":221,"name":"Psychology","url":"https://www.academia.edu/Documents/in/Psychology?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="18866" href="https://www.academia.edu/Documents/in/Beliefs">Beliefs</a>, <script data-card-contents-for-ri="18866" type="text/json">{"id":18866,"name":"Beliefs","url":"https://www.academia.edu/Documents/in/Beliefs?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="27801" href="https://www.academia.edu/Documents/in/Mathematics_Teacher_Education">Mathematics Teacher Education</a>, <script data-card-contents-for-ri="27801" type="text/json">{"id":27801,"name":"Mathematics Teacher Education","url":"https://www.academia.edu/Documents/in/Mathematics_Teacher_Education?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="42162" href="https://www.academia.edu/Documents/in/Emotions">Emotions</a><script data-card-contents-for-ri="42162" type="text/json">{"id":42162,"name":"Emotions","url":"https://www.academia.edu/Documents/in/Emotions?f_ri=66102","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=73991064]'), work: {"id":73991064,"title":"(Mis)alignment between noticing and instructional quality: the role of psychological and cognitive constructs","created_at":"2022-03-18T00:48:21.708-07:00","url":"https://www.academia.edu/73991064/_Mis_alignment_between_noticing_and_instructional_quality_the_role_of_psychological_and_cognitive_constructs?f_ri=66102","dom_id":"work_73991064","summary":"In this study, we investigated the relationship between teachers’ post-instruction noticing (PIN) and the quality of their mathematics instruction. We analyzed the conversations of elementary teachers around five coached lessons and scored their level of post-instruction noticing and the mathematical quality of the instruction of the lesson. We compared teachers’ PIN levels with their instructional quality, using scores from the Mathematical Quality of Instruction (MQI) rubric, for each coached lesson. There was both alignment and discrepancies between the level of PIN and MQI scores. Explorations of the cognitive and psychological constructs that seemed to influence teacher’s noticing showed that mathematical knowledge for teaching (MKT), efficacy, beliefs, emotions, and identity was influential on teachers’ PIN although they seemed to influence teachers differently. In some cases, the constructs appeared to support attentiveness to students’ thinking and in other cases they did not. We discuss implications for professional development and future research on teachers’ noticing.","downloadable_attachments":[],"ordered_authors":[{"id":21451553,"first_name":"Ayfer","last_name":"Eker","domain_name":"independent","page_name":"AyferEker","display_name":"Ayfer Eker","profile_url":"https://independent.academia.edu/AyferEker?f_ri=66102","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":221,"name":"Psychology","url":"https://www.academia.edu/Documents/in/Psychology?f_ri=66102","nofollow":false},{"id":18866,"name":"Beliefs","url":"https://www.academia.edu/Documents/in/Beliefs?f_ri=66102","nofollow":false},{"id":27801,"name":"Mathematics Teacher Education","url":"https://www.academia.edu/Documents/in/Mathematics_Teacher_Education?f_ri=66102","nofollow":false},{"id":42162,"name":"Emotions","url":"https://www.academia.edu/Documents/in/Emotions?f_ri=66102","nofollow":false},{"id":42968,"name":"Coaching","url":"https://www.academia.edu/Documents/in/Coaching?f_ri=66102"},{"id":50025,"name":"Teacher Identity","url":"https://www.academia.edu/Documents/in/Teacher_Identity?f_ri=66102"},{"id":50581,"name":"Self Efficacy","url":"https://www.academia.edu/Documents/in/Self_Efficacy?f_ri=66102"},{"id":55490,"name":"Mathematical Thinking","url":"https://www.academia.edu/Documents/in/Mathematical_Thinking?f_ri=66102"},{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102"},{"id":240653,"name":"Teachers Beliefs","url":"https://www.academia.edu/Documents/in/Teachers_Beliefs?f_ri=66102"},{"id":508371,"name":"Curriculum and Pedagogy","url":"https://www.academia.edu/Documents/in/Curriculum_and_Pedagogy?f_ri=66102"},{"id":1266753,"name":"Teachers Motivation and Emotions for Professional Development","url":"https://www.academia.edu/Documents/in/Teachers_Motivation_and_Emotions_for_Professional_Development-1?f_ri=66102"},{"id":1268087,"name":"Teachers Professional Development","url":"https://www.academia.edu/Documents/in/Teachers_Professional_Development-4?f_ri=66102"},{"id":1286528,"name":"Professional Noticing","url":"https://www.academia.edu/Documents/in/Professional_Noticing?f_ri=66102"},{"id":4037789,"name":"mathematical quality of instruction","url":"https://www.academia.edu/Documents/in/mathematical_quality_of_instruction?f_ri=66102"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_73991003" data-work_id="73991003" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/73991003/_Mis_alignment_between_noticing_and_instructional_quality_The_role_of_psychological_and_cognitive_constructs">(Mis) alignment between noticing and instructional quality: The role of psychological and cognitive constructs</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">In this study, we investigated the relationship between teachers’ post-instruction noticing (PIN) and the quality of their mathematics instruction. We analyzed the conversations of elementary teachers around five coached lessons and... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_73991003" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">In this study, we investigated the relationship between teachers’ post-instruction noticing (PIN) and the quality of their mathematics instruction. We analyzed the conversations of elementary teachers around five coached lessons and scored their level of post-instruction noticing and the mathematical quality of the instruction of the lesson. We compared teachers’ PIN levels with their instructional quality, using scores from the Mathematical Quality of Instruction (MQI) rubric, for each coached lesson. There was both alignment and discrepancies between the level of PIN and MQI scores. Explorations of the cognitive and psychological constructs that seemed to influence teacher’s noticing showed that mathematical knowledge for teaching (MKT), efficacy, beliefs, emotions, and identity were influential on teachers’ PIN although they seemed to influence teachers differently. In some cases, the constructs appeared to support attentiveness to students’ thinking and in other cases they did n...</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/73991003" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="21451553" href="https://independent.academia.edu/AyferEker">Ayfer Eker</a><script data-card-contents-for-user="21451553" type="text/json">{"id":21451553,"first_name":"Ayfer","last_name":"Eker","domain_name":"independent","page_name":"AyferEker","display_name":"Ayfer Eker","profile_url":"https://independent.academia.edu/AyferEker?f_ri=66102","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_73991003 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="73991003"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 73991003, container: ".js-paper-rank-work_73991003", }); });</script></li><li class="js-percentile-work_73991003 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 73991003; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_73991003"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_73991003 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="73991003"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 73991003; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=73991003]").text(description); $(".js-view-count-work_73991003").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_73991003").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="73991003"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">15</a>  </div><span class="InlineList-item-text u-textTruncate u-pl10x"><a class="InlineList-item-text" data-has-card-for-ri="221" href="https://www.academia.edu/Documents/in/Psychology">Psychology</a>, <script data-card-contents-for-ri="221" type="text/json">{"id":221,"name":"Psychology","url":"https://www.academia.edu/Documents/in/Psychology?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="18866" href="https://www.academia.edu/Documents/in/Beliefs">Beliefs</a>, <script data-card-contents-for-ri="18866" type="text/json">{"id":18866,"name":"Beliefs","url":"https://www.academia.edu/Documents/in/Beliefs?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="27801" href="https://www.academia.edu/Documents/in/Mathematics_Teacher_Education">Mathematics Teacher Education</a>, <script data-card-contents-for-ri="27801" type="text/json">{"id":27801,"name":"Mathematics Teacher Education","url":"https://www.academia.edu/Documents/in/Mathematics_Teacher_Education?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="42162" href="https://www.academia.edu/Documents/in/Emotions">Emotions</a><script data-card-contents-for-ri="42162" type="text/json">{"id":42162,"name":"Emotions","url":"https://www.academia.edu/Documents/in/Emotions?f_ri=66102","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=73991003]'), work: {"id":73991003,"title":"(Mis) alignment between noticing and instructional quality: The role of psychological and cognitive constructs","created_at":"2022-03-18T00:47:48.802-07:00","url":"https://www.academia.edu/73991003/_Mis_alignment_between_noticing_and_instructional_quality_The_role_of_psychological_and_cognitive_constructs?f_ri=66102","dom_id":"work_73991003","summary":"In this study, we investigated the relationship between teachers’ post-instruction noticing (PIN) and the quality of their mathematics instruction. We analyzed the conversations of elementary teachers around five coached lessons and scored their level of post-instruction noticing and the mathematical quality of the instruction of the lesson. We compared teachers’ PIN levels with their instructional quality, using scores from the Mathematical Quality of Instruction (MQI) rubric, for each coached lesson. There was both alignment and discrepancies between the level of PIN and MQI scores. Explorations of the cognitive and psychological constructs that seemed to influence teacher’s noticing showed that mathematical knowledge for teaching (MKT), efficacy, beliefs, emotions, and identity were influential on teachers’ PIN although they seemed to influence teachers differently. In some cases, the constructs appeared to support attentiveness to students’ thinking and in other cases they did n...","downloadable_attachments":[],"ordered_authors":[{"id":21451553,"first_name":"Ayfer","last_name":"Eker","domain_name":"independent","page_name":"AyferEker","display_name":"Ayfer Eker","profile_url":"https://independent.academia.edu/AyferEker?f_ri=66102","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":221,"name":"Psychology","url":"https://www.academia.edu/Documents/in/Psychology?f_ri=66102","nofollow":false},{"id":18866,"name":"Beliefs","url":"https://www.academia.edu/Documents/in/Beliefs?f_ri=66102","nofollow":false},{"id":27801,"name":"Mathematics Teacher Education","url":"https://www.academia.edu/Documents/in/Mathematics_Teacher_Education?f_ri=66102","nofollow":false},{"id":42162,"name":"Emotions","url":"https://www.academia.edu/Documents/in/Emotions?f_ri=66102","nofollow":false},{"id":42968,"name":"Coaching","url":"https://www.academia.edu/Documents/in/Coaching?f_ri=66102"},{"id":50025,"name":"Teacher Identity","url":"https://www.academia.edu/Documents/in/Teacher_Identity?f_ri=66102"},{"id":50581,"name":"Self Efficacy","url":"https://www.academia.edu/Documents/in/Self_Efficacy?f_ri=66102"},{"id":55490,"name":"Mathematical Thinking","url":"https://www.academia.edu/Documents/in/Mathematical_Thinking?f_ri=66102"},{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102"},{"id":240653,"name":"Teachers Beliefs","url":"https://www.academia.edu/Documents/in/Teachers_Beliefs?f_ri=66102"},{"id":508371,"name":"Curriculum and Pedagogy","url":"https://www.academia.edu/Documents/in/Curriculum_and_Pedagogy?f_ri=66102"},{"id":1266753,"name":"Teachers Motivation and Emotions for Professional Development","url":"https://www.academia.edu/Documents/in/Teachers_Motivation_and_Emotions_for_Professional_Development-1?f_ri=66102"},{"id":1268087,"name":"Teachers Professional Development","url":"https://www.academia.edu/Documents/in/Teachers_Professional_Development-4?f_ri=66102"},{"id":1286528,"name":"Professional Noticing","url":"https://www.academia.edu/Documents/in/Professional_Noticing?f_ri=66102"},{"id":4037789,"name":"mathematical quality of instruction","url":"https://www.academia.edu/Documents/in/mathematical_quality_of_instruction?f_ri=66102"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_67010881" data-work_id="67010881" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/67010881/_Mis_alignment_between_noticing_and_instructional_quality_The_role_of_psychological_and_cognitive_constructs">(Mis) alignment between noticing and instructional quality: The role of psychological and cognitive constructs</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">In this study, we investigated the relationship between teachers’ post-instruction noticing (PIN) and the quality of their mathematics instruction. We analyzed the conversations of elementary teachers around five coached lessons and... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_67010881" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">In this study, we investigated the relationship between teachers’ post-instruction noticing (PIN) and the quality of their mathematics instruction. We analyzed the conversations of elementary teachers around five coached lessons and scored their level of post-instruction noticing and the mathematical quality of the instruction of the lesson. We compared teachers’ PIN levels with their instructional quality, using scores from the Mathematical Quality of Instruction (MQI) rubric, for each coached lesson. There was both alignment and discrepancies between the level of PIN and MQI scores. Explorations of the cognitive and psychological constructs that seemed to influence teacher’s noticing showed that mathematical knowledge for teaching (MKT), efficacy, beliefs, emotions, and identity was influential on teachers’ PIN although they seemed to influence teachers differently. In some cases, the constructs appeared to support attentiveness to students’ thinking and in other cases they did no...</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/67010881" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="210381477" href="https://independent.academia.edu/EkerAyfer">Ayfer Eker</a><script data-card-contents-for-user="210381477" type="text/json">{"id":210381477,"first_name":"Ayfer","last_name":"Eker","domain_name":"independent","page_name":"EkerAyfer","display_name":"Ayfer Eker","profile_url":"https://independent.academia.edu/EkerAyfer?f_ri=66102","photo":"https://0.academia-photos.com/210381477/70000459/58409720/s65_ayfer.eker.png"}</script></span></span></li><li class="js-paper-rank-work_67010881 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="67010881"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 67010881, container: ".js-paper-rank-work_67010881", }); });</script></li><li class="js-percentile-work_67010881 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 67010881; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_67010881"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_67010881 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="67010881"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 67010881; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=67010881]").text(description); $(".js-view-count-work_67010881").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_67010881").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="67010881"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">15</a>  </div><span class="InlineList-item-text u-textTruncate u-pl10x"><a class="InlineList-item-text" data-has-card-for-ri="221" href="https://www.academia.edu/Documents/in/Psychology">Psychology</a>, <script data-card-contents-for-ri="221" type="text/json">{"id":221,"name":"Psychology","url":"https://www.academia.edu/Documents/in/Psychology?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="18866" href="https://www.academia.edu/Documents/in/Beliefs">Beliefs</a>, <script data-card-contents-for-ri="18866" type="text/json">{"id":18866,"name":"Beliefs","url":"https://www.academia.edu/Documents/in/Beliefs?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="27801" href="https://www.academia.edu/Documents/in/Mathematics_Teacher_Education">Mathematics Teacher Education</a>, <script data-card-contents-for-ri="27801" type="text/json">{"id":27801,"name":"Mathematics Teacher Education","url":"https://www.academia.edu/Documents/in/Mathematics_Teacher_Education?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="42162" href="https://www.academia.edu/Documents/in/Emotions">Emotions</a><script data-card-contents-for-ri="42162" type="text/json">{"id":42162,"name":"Emotions","url":"https://www.academia.edu/Documents/in/Emotions?f_ri=66102","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=67010881]'), work: {"id":67010881,"title":"(Mis) alignment between noticing and instructional quality: The role of psychological and cognitive constructs","created_at":"2022-01-03T22:45:18.607-08:00","url":"https://www.academia.edu/67010881/_Mis_alignment_between_noticing_and_instructional_quality_The_role_of_psychological_and_cognitive_constructs?f_ri=66102","dom_id":"work_67010881","summary":"In this study, we investigated the relationship between teachers’ post-instruction noticing (PIN) and the quality of their mathematics instruction. We analyzed the conversations of elementary teachers around five coached lessons and scored their level of post-instruction noticing and the mathematical quality of the instruction of the lesson. We compared teachers’ PIN levels with their instructional quality, using scores from the Mathematical Quality of Instruction (MQI) rubric, for each coached lesson. There was both alignment and discrepancies between the level of PIN and MQI scores. Explorations of the cognitive and psychological constructs that seemed to influence teacher’s noticing showed that mathematical knowledge for teaching (MKT), efficacy, beliefs, emotions, and identity was influential on teachers’ PIN although they seemed to influence teachers differently. In some cases, the constructs appeared to support attentiveness to students’ thinking and in other cases they did no...","downloadable_attachments":[],"ordered_authors":[{"id":210381477,"first_name":"Ayfer","last_name":"Eker","domain_name":"independent","page_name":"EkerAyfer","display_name":"Ayfer Eker","profile_url":"https://independent.academia.edu/EkerAyfer?f_ri=66102","photo":"https://0.academia-photos.com/210381477/70000459/58409720/s65_ayfer.eker.png"}],"research_interests":[{"id":221,"name":"Psychology","url":"https://www.academia.edu/Documents/in/Psychology?f_ri=66102","nofollow":false},{"id":18866,"name":"Beliefs","url":"https://www.academia.edu/Documents/in/Beliefs?f_ri=66102","nofollow":false},{"id":27801,"name":"Mathematics Teacher Education","url":"https://www.academia.edu/Documents/in/Mathematics_Teacher_Education?f_ri=66102","nofollow":false},{"id":42162,"name":"Emotions","url":"https://www.academia.edu/Documents/in/Emotions?f_ri=66102","nofollow":false},{"id":42968,"name":"Coaching","url":"https://www.academia.edu/Documents/in/Coaching?f_ri=66102"},{"id":50025,"name":"Teacher Identity","url":"https://www.academia.edu/Documents/in/Teacher_Identity?f_ri=66102"},{"id":50581,"name":"Self Efficacy","url":"https://www.academia.edu/Documents/in/Self_Efficacy?f_ri=66102"},{"id":55490,"name":"Mathematical Thinking","url":"https://www.academia.edu/Documents/in/Mathematical_Thinking?f_ri=66102"},{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102"},{"id":240653,"name":"Teachers Beliefs","url":"https://www.academia.edu/Documents/in/Teachers_Beliefs?f_ri=66102"},{"id":508371,"name":"Curriculum and Pedagogy","url":"https://www.academia.edu/Documents/in/Curriculum_and_Pedagogy?f_ri=66102"},{"id":1266753,"name":"Teachers Motivation and Emotions for Professional Development","url":"https://www.academia.edu/Documents/in/Teachers_Motivation_and_Emotions_for_Professional_Development-1?f_ri=66102"},{"id":1268087,"name":"Teachers Professional Development","url":"https://www.academia.edu/Documents/in/Teachers_Professional_Development-4?f_ri=66102"},{"id":1286528,"name":"Professional Noticing","url":"https://www.academia.edu/Documents/in/Professional_Noticing?f_ri=66102"},{"id":4037789,"name":"mathematical quality of instruction","url":"https://www.academia.edu/Documents/in/mathematical_quality_of_instruction?f_ri=66102"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_44399690" data-work_id="44399690" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/44399690/Predictive_Validity_of_Entry_Level_Mathematical_on_Mathematical_Knowledge_of_Pre_service_Teachers_for_Teaching_Basic_School_mathematics_in_Ghana">Predictive Validity of Entry Level Mathematical on Mathematical Knowledge of Pre-service Teachers for Teaching Basic School mathematics in Ghana</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">Introduction: Knowledge about teaching mathematics remains a contentious issue in the preparation of pre-service teachers in Ghana. This study explored relationships among entry-level mathematical knowledge (ELMK), mathematics content... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_44399690" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">Introduction: Knowledge about teaching mathematics remains a contentious issue in the preparation of pre-service teachers in Ghana. This study explored relationships among entry-level mathematical knowledge (ELMK), mathematics content knowledge (MCK) and mathematics pedagogical content knowledge (MPCK) scores of pre-service teachers in colleges of education (CoEs) in Ghana. Methods: The cross-sectional survey design was adopted for this study. A total of 998 pre-service teachers from ten (10) public colleges of education were sampled via multi-stage sampling technique. Structured questionnaire and unstructured observation schedule were used for the survey. College mathematics test results were used as secondary data. The data were analysed using descriptive statistics (frequency count, percentage) and inferential statistics (Pearson's correlation, paired-samples t-test and regression analysis) with the aid of Statistical Package for Social Sciences software version 22. Results: The majority of pre-service teachers in Ghanaian colleges of education had average but relatively weak grades in ELMCK. ELMCK did not significantly predict pre-service teachers' MCK statistically (p ≥ 0.05) although a statistically significant positive correlation existed between the variables. Although a negative correlation existed between ELMCK and PMCK, ELMCK significantly predicted pre-service teachers' PMCK statistically (p ≤ 0.05) but the effect size was statistically negligible. Conclusions: This study concluded that, CoEs in Ghana admit pre-service teachers with average but weak grades in ELMK. Therefore, Ghanaian CoEs should structure and introduce PMCK alongside MCK for pre-service teachers. Mathematics tutors in CoEs should organize remedial lessons for pre-service teachers to scale-up their MCK and PMCK that adequately equip them with MKT.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/44399690" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="88a2e09fecc34729c866aec7fe1ba956" rel="nofollow" data-download="{"attachment_id":64807691,"asset_id":44399690,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/64807691/download_file?st=MTczMzAyOTA0OCw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="37769006" href="https://texilaconnect.academia.edu/TexilaInternationalJournal">Texila International Journal</a><script data-card-contents-for-user="37769006" type="text/json">{"id":37769006,"first_name":"Texila International","last_name":"Journal","domain_name":"texilaconnect","page_name":"TexilaInternationalJournal","display_name":"Texila International Journal","profile_url":"https://texilaconnect.academia.edu/TexilaInternationalJournal?f_ri=66102","photo":"https://0.academia-photos.com/37769006/15581072/16233473/s65_texila_international.journal.png"}</script></span></span></li><li class="js-paper-rank-work_44399690 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="44399690"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 44399690, container: ".js-paper-rank-work_44399690", }); 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$(".js-view-count[data-work-id=44399690]").text(description); $(".js-view-count-work_44399690").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_44399690").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="44399690"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">3</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="66102" href="https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching">Mathematical Knowledge for Teaching</a>, <script data-card-contents-for-ri="66102" type="text/json">{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="82717" href="https://www.academia.edu/Documents/in/Pre-service_teachers">Pre-service teachers</a>, <script data-card-contents-for-ri="82717" type="text/json">{"id":82717,"name":"Pre-service teachers","url":"https://www.academia.edu/Documents/in/Pre-service_teachers?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="90962" href="https://www.academia.edu/Documents/in/Academic_research">Academic research</a><script data-card-contents-for-ri="90962" type="text/json">{"id":90962,"name":"Academic research","url":"https://www.academia.edu/Documents/in/Academic_research?f_ri=66102","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=44399690]'), work: {"id":44399690,"title":"Predictive Validity of Entry Level Mathematical on Mathematical Knowledge of Pre-service Teachers for Teaching Basic School mathematics in Ghana","created_at":"2020-10-30T04:10:37.682-07:00","url":"https://www.academia.edu/44399690/Predictive_Validity_of_Entry_Level_Mathematical_on_Mathematical_Knowledge_of_Pre_service_Teachers_for_Teaching_Basic_School_mathematics_in_Ghana?f_ri=66102","dom_id":"work_44399690","summary":"Introduction: Knowledge about teaching mathematics remains a contentious issue in the preparation of pre-service teachers in Ghana. This study explored relationships among entry-level mathematical knowledge (ELMK), mathematics content knowledge (MCK) and mathematics pedagogical content knowledge (MPCK) scores of pre-service teachers in colleges of education (CoEs) in Ghana. Methods: The cross-sectional survey design was adopted for this study. A total of 998 pre-service teachers from ten (10) public colleges of education were sampled via multi-stage sampling technique. Structured questionnaire and unstructured observation schedule were used for the survey. College mathematics test results were used as secondary data. The data were analysed using descriptive statistics (frequency count, percentage) and inferential statistics (Pearson's correlation, paired-samples t-test and regression analysis) with the aid of Statistical Package for Social Sciences software version 22. Results: The majority of pre-service teachers in Ghanaian colleges of education had average but relatively weak grades in ELMCK. ELMCK did not significantly predict pre-service teachers' MCK statistically (p ≥ 0.05) although a statistically significant positive correlation existed between the variables. Although a negative correlation existed between ELMCK and PMCK, ELMCK significantly predicted pre-service teachers' PMCK statistically (p ≤ 0.05) but the effect size was statistically negligible. Conclusions: This study concluded that, CoEs in Ghana admit pre-service teachers with average but weak grades in ELMK. Therefore, Ghanaian CoEs should structure and introduce PMCK alongside MCK for pre-service teachers. Mathematics tutors in CoEs should organize remedial lessons for pre-service teachers to scale-up their MCK and PMCK that adequately equip them with MKT.","downloadable_attachments":[{"id":64807691,"asset_id":44399690,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":37769006,"first_name":"Texila International","last_name":"Journal","domain_name":"texilaconnect","page_name":"TexilaInternationalJournal","display_name":"Texila International Journal","profile_url":"https://texilaconnect.academia.edu/TexilaInternationalJournal?f_ri=66102","photo":"https://0.academia-photos.com/37769006/15581072/16233473/s65_texila_international.journal.png"}],"research_interests":[{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102","nofollow":false},{"id":82717,"name":"Pre-service teachers","url":"https://www.academia.edu/Documents/in/Pre-service_teachers?f_ri=66102","nofollow":false},{"id":90962,"name":"Academic research","url":"https://www.academia.edu/Documents/in/Academic_research?f_ri=66102","nofollow":false}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_5820308 coauthored" data-work_id="5820308" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/5820308/La_ejemplificaci%C3%B3n_del_concepto_de_funci%C3%B3n_diferencias_entre_profesores_noveles_y_profesores_expertos">La ejemplificación del concepto de función: diferencias entre profesores noveles y profesores expertos</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item 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data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="8549619" href="https://uhu.academia.edu/LuisCarlosContrerasGonz%C3%A1lez">Luis Carlos Contreras-González</a><script data-card-contents-for-user="8549619" type="text/json">{"id":8549619,"first_name":"Luis Carlos","last_name":"Contreras-González","domain_name":"uhu","page_name":"LuisCarlosContrerasGonzález","display_name":"Luis Carlos Contreras-González","profile_url":"https://uhu.academia.edu/LuisCarlosContrerasGonz%C3%A1lez?f_ri=66102","photo":"https://0.academia-photos.com/8549619/2864436/3345461/s65_luis_carlos.contreras.jpg"}</script></span></span><span class="u-displayInlineBlock InlineList-item-text"> and <span class="u-textDecorationUnderline u-clickable InlineList-item-text js-work-more-authors-5820308">+1</span><div class="hidden js-additional-users-5820308"><div><span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a href="https://independent.academia.edu/CarlosFigueiredo18">Carlos Figueiredo</a></span></div></div></span><script>(function(){ var popoverSettings = { el: $('.js-work-more-authors-5820308'), placement: 'bottom', hide_delay: 200, html: true, content: function(){ return $('.js-additional-users-5820308').html(); } } new HoverPopover(popoverSettings); })();</script></li><li class="js-paper-rank-work_5820308 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="5820308"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 5820308, container: ".js-paper-rank-work_5820308", }); 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function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=5820308]").text(description); $(".js-view-count-work_5820308").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_5820308").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="5820308"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">2</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="66102" href="https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching">Mathematical Knowledge for Teaching</a>, <script data-card-contents-for-ri="66102" type="text/json">{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="475627" href="https://www.academia.edu/Documents/in/Exemplification">Exemplification</a><script data-card-contents-for-ri="475627" type="text/json">{"id":475627,"name":"Exemplification","url":"https://www.academia.edu/Documents/in/Exemplification?f_ri=66102","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=5820308]'), work: {"id":5820308,"title":"La ejemplificación del concepto de función: diferencias entre profesores noveles y profesores expertos","created_at":"2014-01-23T19:24:20.481-08:00","url":"https://www.academia.edu/5820308/La_ejemplificaci%C3%B3n_del_concepto_de_funci%C3%B3n_diferencias_entre_profesores_noveles_y_profesores_expertos?f_ri=66102","dom_id":"work_5820308","summary":null,"downloadable_attachments":[{"id":32830226,"asset_id":5820308,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":8549619,"first_name":"Luis Carlos","last_name":"Contreras-González","domain_name":"uhu","page_name":"LuisCarlosContrerasGonzález","display_name":"Luis Carlos Contreras-González","profile_url":"https://uhu.academia.edu/LuisCarlosContrerasGonz%C3%A1lez?f_ri=66102","photo":"https://0.academia-photos.com/8549619/2864436/3345461/s65_luis_carlos.contreras.jpg"},{"id":38281109,"first_name":"Carlos","last_name":"Figueiredo","domain_name":"independent","page_name":"CarlosFigueiredo18","display_name":"Carlos Figueiredo","profile_url":"https://independent.academia.edu/CarlosFigueiredo18?f_ri=66102","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":66102,"name":"Mathematical Knowledge for Teaching","url":"https://www.academia.edu/Documents/in/Mathematical_Knowledge_for_Teaching?f_ri=66102","nofollow":false},{"id":475627,"name":"Exemplification","url":"https://www.academia.edu/Documents/in/Exemplification?f_ri=66102","nofollow":false}]}, }) } })();</script></ul></li></ul></div></div></div><div class="u-taCenter Pagination"><ul class="pagination"></ul></div></div><div class="hidden-xs hidden-sm"><div class="u-pl6x"><div style="width: 300px;"><div class="panel panel-flat u-mt7x"><div class="panel-heading u-p5x"><div class="u-tcGrayDark u-taCenter u-fw700 u-textUppercase">Related Topics</div></div><ul class="list-group"><li class="list-group-item media_v2 u-mt0x u-p3x"><div class="media-body"><div class="u-tcGrayDarker u-fw700"><a class="u-tcGrayDarker" 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