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$(".js-view-count[data-work-id=21829517]").text(description); $(".js-view-count-work_21829517").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_21829517").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="21829517"><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="41130" href="https://www.academia.edu/Documents/in/Didactics_of_Mathematics">Didactics of Mathematics</a>, <script data-card-contents-for-ri="41130" type="text/json">{"id":41130,"name":"Didactics of Mathematics","url":"https://www.academia.edu/Documents/in/Didactics_of_Mathematics?f_ri=152051","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=152051","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="249208" href="https://www.academia.edu/Documents/in/Qu%C3%A9bec">Québec</a><script data-card-contents-for-ri="249208" type="text/json">{"id":249208,"name":"Québec","url":"https://www.academia.edu/Documents/in/Qu%C3%A9bec?f_ri=152051","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=21829517]'), work: {"id":21829517,"title":"Raisonnement mathématique et formation citoyenne. 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In this article, we aim to analyze the possibilities of using the “Equality Explorer: Basic” resource, available on the Physics Education Technology – PhET Interactive Simulations digital platform, of the University of Colorado Boulder, in light of the skills of the <br />National Common Curricular Base (BNCC) and the Curriculum of Pernambuco, regarding the teaching of equality properties and equivalence principles. The research approach is qualitative and documentary. Data collection was based on general information available at PhET, such as: resource descriptions, instruction manual, activity plans, lesson plans, among others, besides the handling of the “Equality Explorer: Basic,” by which we sought to interpret and develop possible interactive simulations in the light of the skills of the curriculum documents. Among the results, we highlight four skills (from the initial and/or final years of elementary school) that can be developed using the “Equality Explorer: Basic”: (EF03MA11) / (EF03MA11PE); (EF04MA14) / (EF04MA14PE); (EF05MA10) / (EF05MA10PE); and (EF06MA14) / (EF06MA14PE). Therefore, we believe that the resource on screen can encourage the development of students’ algebraic thinking, depending on the modes of its exploration, both in the classroom or in other didactic scenarios.</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/49284960" 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="106cc035e871894add0240204a62b856" rel="nofollow" data-download="{"attachment_id":67669329,"asset_id":49284960,"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/67669329/download_file?st=MTczMzAxOTg4Niw4LjIyMi4yMDguMTQ2&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="138842354" href="https://ufpe.academia.edu/AlmeidaM">Matheus Almeida</a><script data-card-contents-for-user="138842354" type="text/json">{"id":138842354,"first_name":"Matheus","last_name":"Almeida","domain_name":"ufpe","page_name":"AlmeidaM","display_name":"Matheus Almeida","profile_url":"https://ufpe.academia.edu/AlmeidaM?f_ri=152051","photo":"https://0.academia-photos.com/138842354/39108633/80094135/s65_matheus.almeida.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-49284960">+1</span><div class="hidden js-additional-users-49284960"><div><span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a href="https://independent.academia.edu/NunesdeOliveiraM">Maria Eduarda Nunes de Oliveira</a></span></div></div></span><script>(function(){ var popoverSettings = { el: $('.js-work-more-authors-49284960'), placement: 'bottom', hide_delay: 200, html: true, content: function(){ return $('.js-additional-users-49284960').html(); 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container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_49284960 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="49284960"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 49284960; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=49284960]").text(description); $(".js-view-count-work_49284960").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_49284960").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="49284960"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">9</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=152051","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="3611" href="https://www.academia.edu/Documents/in/Digital_Technology">Digital Technology</a>, <script data-card-contents-for-ri="3611" type="text/json">{"id":3611,"name":"Digital Technology","url":"https://www.academia.edu/Documents/in/Digital_Technology?f_ri=152051","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="20411" href="https://www.academia.edu/Documents/in/Algebraic_Thinking">Algebraic Thinking</a>, <script data-card-contents-for-ri="20411" type="text/json">{"id":20411,"name":"Algebraic Thinking","url":"https://www.academia.edu/Documents/in/Algebraic_Thinking?f_ri=152051","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="41130" href="https://www.academia.edu/Documents/in/Didactics_of_Mathematics">Didactics of Mathematics</a><script data-card-contents-for-ri="41130" type="text/json">{"id":41130,"name":"Didactics of Mathematics","url":"https://www.academia.edu/Documents/in/Didactics_of_Mathematics?f_ri=152051","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=49284960]'), work: {"id":49284960,"title":"Explorador Básico de Igualdade da plataforma digital PhET: uma análise acerca das potencialidades didáticas à luz da BNCC e do Currículo de Pernambuco","created_at":"2021-06-18T12:40:44.302-07:00","url":"https://www.academia.edu/49284960/Explorador_B%C3%A1sico_de_Igualdade_da_plataforma_digital_PhET_uma_an%C3%A1lise_acerca_das_potencialidades_did%C3%A1ticas_%C3%A0_luz_da_BNCC_e_do_Curr%C3%ADculo_de_Pernambuco?f_ri=152051","dom_id":"work_49284960","summary":"This excerpt of a research was developed within the Institutional Scientific Initiation Scholarship Program (PIBIC) and the research group Scientific Laboratory for Learning, Research, and Teaching (LACAPE), linked to the Departament of Education of the Federal Rural University of Pernambuco (UFRPE). In this article, we aim to analyze the possibilities of using the “Equality Explorer: Basic” resource, available on the Physics Education Technology – PhET Interactive Simulations digital platform, of the University of Colorado Boulder, in light of the skills of the \nNational Common Curricular Base (BNCC) and the Curriculum of Pernambuco, regarding the teaching of equality properties and equivalence principles. The research approach is qualitative and documentary. Data collection was based on general information available at PhET, such as: resource descriptions, instruction manual, activity plans, lesson plans, among others, besides the handling of the “Equality Explorer: Basic,” by which we sought to interpret and develop possible interactive simulations in the light of the skills of the curriculum documents. Among the results, we highlight four skills (from the initial and/or final years of elementary school) that can be developed using the “Equality Explorer: Basic”: (EF03MA11) / (EF03MA11PE); (EF04MA14) / (EF04MA14PE); (EF05MA10) / (EF05MA10PE); and (EF06MA14) / (EF06MA14PE). Therefore, we believe that the resource on screen can encourage the development of students’ algebraic thinking, depending on the modes of its exploration, both in the classroom or in other didactic scenarios.","downloadable_attachments":[{"id":67669329,"asset_id":49284960,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":138842354,"first_name":"Matheus","last_name":"Almeida","domain_name":"ufpe","page_name":"AlmeidaM","display_name":"Matheus Almeida","profile_url":"https://ufpe.academia.edu/AlmeidaM?f_ri=152051","photo":"https://0.academia-photos.com/138842354/39108633/80094135/s65_matheus.almeida.jpg"},{"id":194517108,"first_name":"Maria Eduarda","last_name":"Nunes de Oliveira","domain_name":"independent","page_name":"NunesdeOliveiraM","display_name":"Maria Eduarda Nunes de Oliveira","profile_url":"https://independent.academia.edu/NunesdeOliveiraM?f_ri=152051","photo":"https://0.academia-photos.com/194517108/57001777/45214787/s65_maria_eduarda.nunes_de_oliveira.jpeg"}],"research_interests":[{"id":2731,"name":"Mathematics Education","url":"https://www.academia.edu/Documents/in/Mathematics_Education?f_ri=152051","nofollow":false},{"id":3611,"name":"Digital Technology","url":"https://www.academia.edu/Documents/in/Digital_Technology?f_ri=152051","nofollow":false},{"id":20411,"name":"Algebraic Thinking","url":"https://www.academia.edu/Documents/in/Algebraic_Thinking?f_ri=152051","nofollow":false},{"id":41130,"name":"Didactics of Mathematics","url":"https://www.academia.edu/Documents/in/Didactics_of_Mathematics?f_ri=152051","nofollow":false},{"id":145280,"name":"Educação Matemática","url":"https://www.academia.edu/Documents/in/Educa%C3%A7%C3%A3o_Matem%C3%A1tica?f_ri=152051"},{"id":152051,"name":"Didactique des mathématiques","url":"https://www.academia.edu/Documents/in/Didactique_des_mathematiques?f_ri=152051"},{"id":472346,"name":"Tecnologias Digitais","url":"https://www.academia.edu/Documents/in/Tecnologias_Digitais?f_ri=152051"},{"id":784705,"name":"Didática da Matemática","url":"https://www.academia.edu/Documents/in/Didatica_da_Matematica?f_ri=152051"},{"id":1601104,"name":"Pensamento Algébrico","url":"https://www.academia.edu/Documents/in/Pensamento_Algebrico?f_ri=152051"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_6135425" data-work_id="6135425" 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/6135425/ERMEL_2006_Apprentissages_g%C3%A9om%C3%A9triques_et_r%C3%A9solution_de_probl%C3%A8mes_au_cycle_3_Hatier">ERMEL (2006), Apprentissages géométriques et résolution de problèmes au cycle 3; Hatier</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/6135425" 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="1c25913cdd0159ad7a6fa7f51b170501" rel="nofollow" data-download="{"attachment_id":36264723,"asset_id":6135425,"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/36264723/download_file?st=MTczMzAxOTg4Niw4LjIyMi4yMDguMTQ2&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="3599567" href="https://univ-reims.academia.edu/FabienEmprin">Fabien Emprin</a><script data-card-contents-for-user="3599567" type="text/json">{"id":3599567,"first_name":"Fabien","last_name":"Emprin","domain_name":"univ-reims","page_name":"FabienEmprin","display_name":"Fabien Emprin","profile_url":"https://univ-reims.academia.edu/FabienEmprin?f_ri=152051","photo":"https://0.academia-photos.com/3599567/3015884/15924458/s65_fabien.emprin.jpg"}</script></span></span></li><li class="js-paper-rank-work_6135425 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="6135425"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 6135425, container: ".js-paper-rank-work_6135425", }); 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(2015). Les Lesson Study : Des situations scolaires aux situations d’apprentissage professionnel pour les enseignants. Revue des HEP et institutions assimilées de Suisse romande et du Tessin(19), 99-105. </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/12009033" 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="b80ee85f4aeb697d89f7984d0d1b25f8" rel="nofollow" data-download="{"attachment_id":37348115,"asset_id":12009033,"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/37348115/download_file?st=MTczMzAxOTg4Niw4LjIyMi4yMDguMTQ2&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=152051","photo":"https://0.academia-photos.com/515022/180027/73742387/s65_clivaz.st_phane.jpg"}</script></span></span></li><li class="js-paper-rank-work_12009033 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="12009033"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 12009033, container: ".js-paper-rank-work_12009033", }); 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","created_at":"2015-04-19T04:00:13.670-07:00","url":"https://www.academia.edu/12009033/Clivaz_S_2015_Les_Lesson_Study_Des_situations_scolaires_aux_situations_d_apprentissage_professionnel_pour_les_enseignants_Revue_des_HEP_et_institutions_assimil%C3%A9es_de_Suisse_romande_et_du_Tessin_19_99_105?f_ri=152051","dom_id":"work_12009033","summary":null,"downloadable_attachments":[{"id":37348115,"asset_id":12009033,"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=152051","photo":"https://0.academia-photos.com/515022/180027/73742387/s65_clivaz.st_phane.jpg"}],"research_interests":[{"id":2731,"name":"Mathematics Education","url":"https://www.academia.edu/Documents/in/Mathematics_Education?f_ri=152051","nofollow":false},{"id":17773,"name":"Teachers' professional development","url":"https://www.academia.edu/Documents/in/Teachers_professional_development-1?f_ri=152051","nofollow":false},{"id":27801,"name":"Mathematics Teacher Education","url":"https://www.academia.edu/Documents/in/Mathematics_Teacher_Education?f_ri=152051","nofollow":false},{"id":41130,"name":"Didactics of Mathematics","url":"https://www.academia.edu/Documents/in/Didactics_of_Mathematics?f_ri=152051","nofollow":false},{"id":152051,"name":"Didactique des mathématiques","url":"https://www.academia.edu/Documents/in/Didactique_des_mathematiques?f_ri=152051"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_68504555" data-work_id="68504555" 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/68504555/Proceedings_of_the_Re_s_sources_2018_International_Conference">Proceedings of the Re(s)sources 2018 International Conference</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 theme of the Re(s)sources 2018 international conference is ‘teachers interacting with resources’ which will be discussed in seven plenary lectures, a plenary panel and four Working Groups. The conference is followed by a young... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_68504555" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">The theme of the Re(s)sources 2018 international conference is ‘teachers interacting with resources’ which will be discussed in seven plenary lectures, a plenary panel and four Working Groups. The conference is followed by a young researcher workshop structured under four sessions. The Re(s)sources 2018 call for contributions concerned participation in the Working Groups, which constitute the essential place for presentation, discussion, and collective work on specific topics related to resources. Each proposal has been peer-reviewed (and subsequently revised), resulting in 70 accepted oral and 7 accepted poster contributions. The present volume, edited by V. Gitirana, T. Miyakawa, M. Rafalska, S. Soury-Lavergne and L. Trouche before the conference, gives access to the presentations of the main moments of Re(s)sources 2018 conference and of the Young Researchers’ Workshop, to the presentations of the lecturers, panelists and WG coordinators, and, essentially, to the whole set of acc...</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/68504555" 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="c23cb57808f739d41a22612151a81395" rel="nofollow" data-download="{"attachment_id":78955411,"asset_id":68504555,"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/78955411/download_file?st=MTczMzAxOTg4Niw4LjIyMi4yMDguMTQ2&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="3126926" href="https://ufpe.academia.edu/VeronicaGitirana">Veronica Gitirana</a><script data-card-contents-for-user="3126926" type="text/json">{"id":3126926,"first_name":"Veronica","last_name":"Gitirana","domain_name":"ufpe","page_name":"VeronicaGitirana","display_name":"Veronica Gitirana","profile_url":"https://ufpe.academia.edu/VeronicaGitirana?f_ri=152051","photo":"https://0.academia-photos.com/3126926/1262460/1575767/s65_veronica.gitirana.jpg"}</script></span></span></li><li class="js-paper-rank-work_68504555 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="68504555"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 68504555, container: ".js-paper-rank-work_68504555", }); 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Trouche before the conference, gives access to the presentations of the main moments of Re(s)sources 2018 conference and of the Young Researchers’ Workshop, to the presentations of the lecturers, panelists and WG coordinators, and, essentially, to the whole set of acc...","downloadable_attachments":[{"id":78955411,"asset_id":68504555,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":3126926,"first_name":"Veronica","last_name":"Gitirana","domain_name":"ufpe","page_name":"VeronicaGitirana","display_name":"Veronica Gitirana","profile_url":"https://ufpe.academia.edu/VeronicaGitirana?f_ri=152051","photo":"https://0.academia-photos.com/3126926/1262460/1575767/s65_veronica.gitirana.jpg"}],"research_interests":[{"id":2731,"name":"Mathematics Education","url":"https://www.academia.edu/Documents/in/Mathematics_Education?f_ri=152051","nofollow":false},{"id":152051,"name":"Didactique des mathématiques","url":"https://www.academia.edu/Documents/in/Didactique_des_mathematiques?f_ri=152051","nofollow":false},{"id":193030,"name":"Teaching resources","url":"https://www.academia.edu/Documents/in/Teaching_resources?f_ri=152051","nofollow":false},{"id":1268087,"name":"Teachers Professional Development","url":"https://www.academia.edu/Documents/in/Teachers_Professional_Development-4?f_ri=152051","nofollow":false},{"id":1852488,"name":"Research on the use of technology in mathematics","url":"https://www.academia.edu/Documents/in/Research_on_the_use_of_technology_in_mathematics?f_ri=152051"},{"id":2201950,"name":"Documentational approach to didactics","url":"https://www.academia.edu/Documents/in/Documentational_approach_to_didactics?f_ri=152051"},{"id":2952591,"name":"Curricular resources","url":"https://www.academia.edu/Documents/in/Curricular_resources?f_ri=152051"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_1361901" data-work_id="1361901" 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/1361901/La_interacci%C3%B3n_con_applets_Java_para_el_aprendizaje_de_las_matem%C3%A1ticas">La interacción con" applets" Java para el aprendizaje de las matemáticas</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/1361901" 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="be950f8c76ea364c4c4c4796592db330" rel="nofollow" data-download="{"attachment_id":37196013,"asset_id":1361901,"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/37196013/download_file?st=MTczMzAxOTg4Niw4LjIyMi4yMDguMTQ2&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="514999" href="https://umontreal.academia.edu/PhilippeRRichard">Philippe R. 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$(".js-view-count[data-work-id=20042882]").text(description); $(".js-view-count-work_20042882").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_20042882").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="20042882"><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="1003" href="https://www.academia.edu/Documents/in/Educational_Technology">Educational Technology</a>, <script data-card-contents-for-ri="1003" type="text/json">{"id":1003,"name":"Educational Technology","url":"https://www.academia.edu/Documents/in/Educational_Technology?f_ri=152051","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=152051","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=152051","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="571797" href="https://www.academia.edu/Documents/in/Introduction_to_Probability">Introduction to Probability</a><script data-card-contents-for-ri="571797" type="text/json">{"id":571797,"name":"Introduction to Probability","url":"https://www.academia.edu/Documents/in/Introduction_to_Probability?f_ri=152051","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=20042882]'), work: {"id":20042882,"title":"Utiliser les mathéma-TIC pour enseigner les probabilités","created_at":"2016-01-05T11:41:49.432-08:00","url":"https://www.academia.edu/20042882/Utiliser_les_mathe_ma_TIC_pour_enseigner_les_probabilite_s?f_ri=152051","dom_id":"work_20042882","summary":null,"downloadable_attachments":[{"id":40973071,"asset_id":20042882,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":6707800,"first_name":"Mathieu","last_name":"Thibault","domain_name":"uqo","page_name":"MathieuThibault","display_name":"Mathieu Thibault","profile_url":"https://uqo.academia.edu/MathieuThibault?f_ri=152051","photo":"https://0.academia-photos.com/6707800/2637112/113551721/s65_mathieu.thibault.jpg"}],"research_interests":[{"id":1003,"name":"Educational Technology","url":"https://www.academia.edu/Documents/in/Educational_Technology?f_ri=152051","nofollow":false},{"id":2731,"name":"Mathematics Education","url":"https://www.academia.edu/Documents/in/Mathematics_Education?f_ri=152051","nofollow":false},{"id":152051,"name":"Didactique des mathématiques","url":"https://www.academia.edu/Documents/in/Didactique_des_mathematiques?f_ri=152051","nofollow":false},{"id":571797,"name":"Introduction to Probability","url":"https://www.academia.edu/Documents/in/Introduction_to_Probability?f_ri=152051","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_9912805" data-work_id="9912805" 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/9912805/Les_vecteurs_dans_lenseignement_secondaire_Aspects_outil_et_objet_dans_les_manuels_%C3%89tude_de_difficult%C3%A9s_d%C3%A9l%C3%A8ves_dans_deux_environnements_papier_and_crayon_et_Cabri_G%C3%A9om%C3%A8tre">Les vecteurs dans l'enseignement secondaire. Aspects outil et objet dans les manuels. Étude de difficultés d'élèves dans deux environnements: papier&crayon et Cabri-Géomètre</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/9912805" 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="ad8d29fcf84f1359ccd23e435528821d" rel="nofollow" data-download="{"attachment_id":36067753,"asset_id":9912805,"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/36067753/download_file?st=MTczMzAxOTg4Niw4LjIyMi4yMDguMTQ2&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="4174713" href="https://cpcs.academia.edu/MarilenaBittar">Marilena Bittar</a><script data-card-contents-for-user="4174713" type="text/json">{"id":4174713,"first_name":"Marilena","last_name":"Bittar","domain_name":"cpcs","page_name":"MarilenaBittar","display_name":"Marilena Bittar","profile_url":"https://cpcs.academia.edu/MarilenaBittar?f_ri=152051","photo":"https://0.academia-photos.com/4174713/1632417/142240695/s65_marilena.bittar.jpeg"}</script></span></span></li><li class="js-paper-rank-work_9912805 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="9912805"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 9912805, container: ".js-paper-rank-work_9912805", }); 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Actes du Colloque du GDM 2013.</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest">Expériences mathématiques uniques et multiples. Actes du Colloque du GDM 2013.</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/16512004" 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="0167a9ee30ec4218fdc133a85e124ab2" rel="nofollow" data-download="{"attachment_id":39027387,"asset_id":16512004,"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/39027387/download_file?st=MTczMzAxOTg4Niw4LjIyMi4yMDguMTQ2&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="35749199" href="https://independent.academia.edu/GDMQu%C3%A9bec">GDM Québec</a><script data-card-contents-for-user="35749199" type="text/json">{"id":35749199,"first_name":"GDM","last_name":"Québec","domain_name":"independent","page_name":"GDMQuébec","display_name":"GDM Québec","profile_url":"https://independent.academia.edu/GDMQu%C3%A9bec?f_ri=152051","photo":"https://0.academia-photos.com/35749199/10351477/11551354/s65_gdm.qu_bec.jpg"}</script></span></span></li><li class="js-paper-rank-work_16512004 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="16512004"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 16512004, container: ".js-paper-rank-work_16512004", }); 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$(".js-view-count[data-work-id=16512004]").text(description); $(".js-view-count-work_16512004").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_16512004").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="16512004"><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="41130" href="https://www.academia.edu/Documents/in/Didactics_of_Mathematics">Didactics of Mathematics</a>, <script data-card-contents-for-ri="41130" type="text/json">{"id":41130,"name":"Didactics of Mathematics","url":"https://www.academia.edu/Documents/in/Didactics_of_Mathematics?f_ri=152051","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=152051","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="249208" href="https://www.academia.edu/Documents/in/Qu%C3%A9bec">Québec</a><script data-card-contents-for-ri="249208" type="text/json">{"id":249208,"name":"Québec","url":"https://www.academia.edu/Documents/in/Qu%C3%A9bec?f_ri=152051","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=16512004]'), work: {"id":16512004,"title":"Expériences mathématiques uniques et multiples. 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Actes du Colloque du GDM 2013.","downloadable_attachments":[{"id":39027387,"asset_id":16512004,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":35749199,"first_name":"GDM","last_name":"Québec","domain_name":"independent","page_name":"GDMQuébec","display_name":"GDM Québec","profile_url":"https://independent.academia.edu/GDMQu%C3%A9bec?f_ri=152051","photo":"https://0.academia-photos.com/35749199/10351477/11551354/s65_gdm.qu_bec.jpg"}],"research_interests":[{"id":41130,"name":"Didactics of Mathematics","url":"https://www.academia.edu/Documents/in/Didactics_of_Mathematics?f_ri=152051","nofollow":false},{"id":152051,"name":"Didactique des mathématiques","url":"https://www.academia.edu/Documents/in/Didactique_des_mathematiques?f_ri=152051","nofollow":false},{"id":249208,"name":"Québec","url":"https://www.academia.edu/Documents/in/Qu%C3%A9bec?f_ri=152051","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_44956339" data-work_id="44956339" 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/44956339/Etude_de_la_transposition_didactique_du_concept_did%C3%A9al_%C3%A9cologie_des_savoirs_et_probl%C3%A9matique_de_lentr%C3%A9e_dans_la_pens%C3%A9e_structuraliste_en_France_et_en_Suisse_romande">Etude de la transposition didactique du concept d'idéal : écologie des savoirs et problématique de l'entrée dans la pensée structuraliste, en France et en Suisse romande</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">Cette thèse s’inscrit dans le champ de la didactique des mathématiques universitaires et a pour but l’étude de la transposition didactique du concept d’idéal. Ce concept mathématiques est enseigné en algèbre abstraite au niveau du... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_44956339" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">Cette thèse s’inscrit dans le champ de la didactique des mathématiques universitaires et a pour but l’étude de la transposition didactique du concept d’idéal. Ce concept mathématiques est enseigné en algèbre abstraite au niveau du Bachelor (la Licence en France). Son enseignement coïncide avec l’entrée dans l’algèbre structuraliste pour les étudiant-es, laquelle s’accompagne d’importantes difficultés dans les apprentissages. Cette étude, menée entre la France et la Suisse romande dans des institutions de niveau Bachelor, a ainsi pour objectif d’étudier l’enseignement de ce concept et, à travers celui-ci, la manière dont l’entrée dans l’algèbre structuraliste est prise en charge par les institutions et leurs professeur-es. Pour ce faire, nous avons d’abord conduit une analyse épistémologique mettant en lumière le rôle de ce concept dans la construction de l’algèbre structuraliste, en lien avec son caractère formalisateur, unificateur, généralisateur et simplificateur. Nous avons ensuite choisi d’entreprendre des études de cas couvrant les différentes institutions que traversent l’étudiant, dans son apprentissage du concept d’idéal. Notre corpus de données est ainsi constitué du matériel pédagogique et des interviews de neuf professeurs : deux enseignants en classes préparatoires aux grandes écoles en France, deux en deuxième année de licence en France, trois en troisième année de licence en France et deux en première et deuxième année de Bachelor en Suisse romande. Pour mener nos analyses, nous nous plaçons dans le cadre de la théorie anthropologique du didactique. L’analyse des interviews permet de caractériser les rapports personnels des enseignants au regard des différents rapports institutionnels auxquels ils sont soumis et des caractéristiques épistémologiques du concept. Ces analyses nous permettent également d’obtenir des descriptions des processus de transposition didactique (externes et internes) ainsi que des contraintes qui pèsent sur ces derniers, classifiées selon les différents niveaux de l’échelle de codétermination didactique. L’effet de ces contraintes sur le développement des organisations mathématiques et didactiques est étudié grâce à des analyses praxéologiques mobilisant la notion de praxéologie structuraliste introduite par Hausberger (2018), conjointement avec d’autres outils (dialectique objets-structures, niveaux structuralistes et transitions de type 1 et 2). Ces dernières mènent à la construction de modèles praxéologiques de référence par enseignant et par institution. Ces modèles nous permettent la comparaison des choix de transposition didactique en lien avec la problématique de l’entrée dans l’algèbre structuraliste, la caractérisation de l’écologie des organisations mathématiques que nous nous efforcerons de mettre en relation avec les contraintes relevées, enfin l’étude des transitions entre les différentes institutions.</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/44956339" 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="4a5fe35cdf33cb998c53b561569a871d" rel="nofollow" data-download="{"attachment_id":65487922,"asset_id":44956339,"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/65487922/download_file?st=MTczMzAxOTg4Niw4LjIyMi4yMDguMTQ2&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="62829684" href="https://hepvs.academia.edu/JulieJovignotCandy">Julie Jovignot</a><script data-card-contents-for-user="62829684" type="text/json">{"id":62829684,"first_name":"Julie","last_name":"Jovignot","domain_name":"hepvs","page_name":"JulieJovignotCandy","display_name":"Julie Jovignot","profile_url":"https://hepvs.academia.edu/JulieJovignotCandy?f_ri=152051","photo":"https://0.academia-photos.com/62829684/16302739/18307376/s65_julie.jovignot-candy.jpg"}</script></span></span></li><li class="js-paper-rank-work_44956339 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="44956339"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 44956339, container: ".js-paper-rank-work_44956339", }); });</script></li><li class="js-percentile-work_44956339 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 = 44956339; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_44956339"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_44956339 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="44956339"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 44956339; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=44956339]").text(description); $(".js-view-count-work_44956339").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_44956339").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="44956339"><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="126811" href="https://www.academia.edu/Documents/in/Epistemologie_des_sciences_humaines_and_sciences_sociales">Epistémologie des sciences humaines & sciences sociales</a>, <script data-card-contents-for-ri="126811" type="text/json">{"id":126811,"name":"Epistémologie des sciences humaines \u0026 sciences sociales","url":"https://www.academia.edu/Documents/in/Epistemologie_des_sciences_humaines_and_sciences_sociales?f_ri=152051","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=152051","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="2948557" href="https://www.academia.edu/Documents/in/theorie_anthropologique_du_didactique">theorie anthropologique du didactique</a><script data-card-contents-for-ri="2948557" type="text/json">{"id":2948557,"name":"theorie anthropologique du didactique","url":"https://www.academia.edu/Documents/in/theorie_anthropologique_du_didactique?f_ri=152051","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=44956339]'), work: {"id":44956339,"title":"Etude de la transposition didactique du concept d'idéal : écologie des savoirs et problématique de l'entrée dans la pensée structuraliste, en France et en Suisse romande","created_at":"2021-01-22T10:41:12.193-08:00","url":"https://www.academia.edu/44956339/Etude_de_la_transposition_didactique_du_concept_did%C3%A9al_%C3%A9cologie_des_savoirs_et_probl%C3%A9matique_de_lentr%C3%A9e_dans_la_pens%C3%A9e_structuraliste_en_France_et_en_Suisse_romande?f_ri=152051","dom_id":"work_44956339","summary":"Cette thèse s’inscrit dans le champ de la didactique des mathématiques universitaires et a pour but l’étude de la transposition didactique du concept d’idéal. Ce concept mathématiques est enseigné en algèbre abstraite au niveau du Bachelor (la Licence en France). Son enseignement coïncide avec l’entrée dans l’algèbre structuraliste pour les étudiant-es, laquelle s’accompagne d’importantes difficultés dans les apprentissages. Cette étude, menée entre la France et la Suisse romande dans des institutions de niveau Bachelor, a ainsi pour objectif d’étudier l’enseignement de ce concept et, à travers celui-ci, la manière dont l’entrée dans l’algèbre structuraliste est prise en charge par les institutions et leurs professeur-es. Pour ce faire, nous avons d’abord conduit une analyse épistémologique mettant en lumière le rôle de ce concept dans la construction de l’algèbre structuraliste, en lien avec son caractère formalisateur, unificateur, généralisateur et simplificateur. Nous avons ensuite choisi d’entreprendre des études de cas couvrant les différentes institutions que traversent l’étudiant, dans son apprentissage du concept d’idéal. Notre corpus de données est ainsi constitué du matériel pédagogique et des interviews de neuf professeurs : deux enseignants en classes préparatoires aux grandes écoles en France, deux en deuxième année de licence en France, trois en troisième année de licence en France et deux en première et deuxième année de Bachelor en Suisse romande. Pour mener nos analyses, nous nous plaçons dans le cadre de la théorie anthropologique du didactique. L’analyse des interviews permet de caractériser les rapports personnels des enseignants au regard des différents rapports institutionnels auxquels ils sont soumis et des caractéristiques épistémologiques du concept. Ces analyses nous permettent également d’obtenir des descriptions des processus de transposition didactique (externes et internes) ainsi que des contraintes qui pèsent sur ces derniers, classifiées selon les différents niveaux de l’échelle de codétermination didactique. L’effet de ces contraintes sur le développement des organisations mathématiques et didactiques est étudié grâce à des analyses praxéologiques mobilisant la notion de praxéologie structuraliste introduite par Hausberger (2018), conjointement avec d’autres outils (dialectique objets-structures, niveaux structuralistes et transitions de type 1 et 2). Ces dernières mènent à la construction de modèles praxéologiques de référence par enseignant et par institution. Ces modèles nous permettent la comparaison des choix de transposition didactique en lien avec la problématique de l’entrée dans l’algèbre structuraliste, la caractérisation de l’écologie des organisations mathématiques que nous nous efforcerons de mettre en relation avec les contraintes relevées, enfin l’étude des transitions entre les différentes institutions.","downloadable_attachments":[{"id":65487922,"asset_id":44956339,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":62829684,"first_name":"Julie","last_name":"Jovignot","domain_name":"hepvs","page_name":"JulieJovignotCandy","display_name":"Julie Jovignot","profile_url":"https://hepvs.academia.edu/JulieJovignotCandy?f_ri=152051","photo":"https://0.academia-photos.com/62829684/16302739/18307376/s65_julie.jovignot-candy.jpg"}],"research_interests":[{"id":126811,"name":"Epistémologie des sciences humaines \u0026 sciences sociales","url":"https://www.academia.edu/Documents/in/Epistemologie_des_sciences_humaines_and_sciences_sociales?f_ri=152051","nofollow":false},{"id":152051,"name":"Didactique des mathématiques","url":"https://www.academia.edu/Documents/in/Didactique_des_mathematiques?f_ri=152051","nofollow":false},{"id":2948557,"name":"theorie anthropologique du didactique","url":"https://www.academia.edu/Documents/in/theorie_anthropologique_du_didactique?f_ri=152051","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_39757689" data-work_id="39757689" 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/39757689/L_analyse_conceptuelle_en_didactique_des_math%C3%A9matiques_sp%C3%A9cificit%C3%A9s_apports_et_perspectives_Actes_du_GDM_2018">L’analyse conceptuelle en didactique des mathématiques; spécificités, apports et perspectives. Actes du GDM 2018.</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest">L’analyse conceptuelle en didactique des mathématiques; spécificités, apports et perspectives. Actes du GDM 2018.</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/39757689" 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="16469f1adde97cd5c4aa6419cc844ed0" rel="nofollow" data-download="{"attachment_id":59939017,"asset_id":39757689,"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/59939017/download_file?st=MTczMzAxOTg4Niw4LjIyMi4yMDguMTQ2&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="35749199" href="https://independent.academia.edu/GDMQu%C3%A9bec">GDM Québec</a><script data-card-contents-for-user="35749199" type="text/json">{"id":35749199,"first_name":"GDM","last_name":"Québec","domain_name":"independent","page_name":"GDMQuébec","display_name":"GDM Québec","profile_url":"https://independent.academia.edu/GDMQu%C3%A9bec?f_ri=152051","photo":"https://0.academia-photos.com/35749199/10351477/11551354/s65_gdm.qu_bec.jpg"}</script></span></span></li><li class="js-paper-rank-work_39757689 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="39757689"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 39757689, container: ".js-paper-rank-work_39757689", }); });</script></li><li class="js-percentile-work_39757689 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 = 39757689; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_39757689"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_39757689 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="39757689"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 39757689; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=39757689]").text(description); $(".js-view-count-work_39757689").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_39757689").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="39757689"><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="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=152051","nofollow":false}</script></span></li><script>(function(){ if (false) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=39757689]'), work: {"id":39757689,"title":"L’analyse conceptuelle en didactique des mathématiques; spécificités, apports et perspectives. Actes du GDM 2018.","created_at":"2019-07-05T11:20:13.618-07:00","url":"https://www.academia.edu/39757689/L_analyse_conceptuelle_en_didactique_des_math%C3%A9matiques_sp%C3%A9cificit%C3%A9s_apports_et_perspectives_Actes_du_GDM_2018?f_ri=152051","dom_id":"work_39757689","summary":"L’analyse conceptuelle en didactique des mathématiques; spécificités, apports et perspectives. Actes du GDM 2018.","downloadable_attachments":[{"id":59939017,"asset_id":39757689,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":35749199,"first_name":"GDM","last_name":"Québec","domain_name":"independent","page_name":"GDMQuébec","display_name":"GDM Québec","profile_url":"https://independent.academia.edu/GDMQu%C3%A9bec?f_ri=152051","photo":"https://0.academia-photos.com/35749199/10351477/11551354/s65_gdm.qu_bec.jpg"}],"research_interests":[{"id":152051,"name":"Didactique des mathématiques","url":"https://www.academia.edu/Documents/in/Didactique_des_mathematiques?f_ri=152051","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_19895776" data-work_id="19895776" 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/19895776/EDUC_387_TEACHING_MATHEMATICS_II_COURSE_NOTES_PART_I_FRACTIONS_OF_QUANTITIES_REVISED_VERSION_">EDUC 387 TEACHING MATHEMATICS II - COURSE NOTES PART I - FRACTIONS OF QUANTITIES (REVISED VERSION)</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 text is intended as a reference for the first part of the course Teaching Mathematics II for prospective elementary school teachers. It focuses on fractions of quantities. The second part focuses on the concepts of rational number,... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_19895776" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">This text is intended as a reference for the first part of the course Teaching Mathematics II for prospective elementary school teachers.  It focuses on fractions of quantities.  The second part focuses on the concepts of rational number, real number, ratio and percent.  It is published separately.<br />Knowledge presented in the text is meant as a foundation for the “Specialized Content Knowledge” (Ball, Thames, & Phelps, 2008) for the teaching of fractions in elementary schools.  It is intended as teachers’ knowledge, not knowledge that could be imparted, as is, to schoolchildren. It is neither the mathematics of school textbooks for children, nor the mathematics of academic textbooks for future mathematicians.  <br /> Our intention is to look at the content to be taught in elementary school about fractions from the point of view of mathematics itself.  We will strive to clarify the meanings of the fundamental concepts (fraction of a quantity, ratio, proportion, etc.) by formulating definitions and using precise language; we will justify techniques and rules of operations on fractions by reasoning; we will analyze the structure of problems about fractions and classify them into types.  In that sense, it is a mathematical knowledge base for making informed decisions in planning lessons, responding to students’ questions and preparing exercises for them.  We will leave aside, for the time being, the issues of the psychology of teaching and learning fractions: how children learn fractions, what difficulties they experience and what teachers can do to help them overcome these difficulties.  These issues will be dealt with in the course Teaching Mathematics III. <br />In Part I of the course notes we focus on fractions as a way to represent the multiplicative relationship between two quantities (lengths, areas, volumes, weights, capacities, market values, etc.).  We view fractions as an answer to the question of how many times one quantity is bigger or smaller than another.  We explicitly define what it means for one quantity to be such and such fraction of another quantity.  In concrete problems we identify and name the quantities that are being compared and the units with which they are measured.  The comparison may require change of unit or conversion from one unit to another.  We become aware of these operations, analyze them and learn how to write them.  In brief, in this course, we make explicit what is often left implicit in teaching fractions to children.  <br />      In Part I of the course notes, we will talk mainly about quantities.  So, for example, instead of talking about abstract numbers, e.g.,  3/4  and  1/8  , and calculating their sum,  3/4+  1/8 = 7/8  , we will be talking about, say, Tom using up  3/4  of a 120-gallon water tank, meaning the quantity of 90 gallons, and Jerry using up  1/8  of the same water tank and asking how much of the tank they used together.  We will be adding quantities, not abstract numbers, expressing this operation in terms of numbers of units (gallons in this case), as<br />3/4  of 120 Gal + 1/8  of 120 Gal =  7/8  of 120 Gal<br />or as 90 Gal + 15 Gal = 105 Gal.  <br />In this text, the concept of fraction of a quantity will be derived from the practices of measurement, particularly the operations of change of unit and unit conversion.  If we want to measure some quantity, the existing units of measurement may not represent it precisely enough, and we have to change those units into some finer ones.  For example, if we measure the length of some tiny piece of metal and find that it measures 1 mm and a little bit and find that 3 such “bits” cover 2 mm, then we will say that 1 bit = 2/3  mm. This is a “conversion equation.”  <br />The approach to fractions through measurement – we call it the Measurement Approach – proposed in this text, is different from the more common Division Approach to fractions through division of numbers, modeled by division of things (e.g., apples or pizzas), or graphical representations of things.  We explain the differences between the Measurement and the Division approaches to fractions in more detail in Chapter I. <br />Chapter II focuses on the practical and theoretical foundations of the Measurement Approach.  It starts by explaining how the notion of a fraction of a quantity could be derived from the historical practices of measurement.  Then the meaning of the phrase “one quantity is such and such fraction of another quantity” is defined in two ways.  One is inspired by barter exchanges where integer multiples of two quantities are equated with each other. The other is based on measuring each of the quantities independently with a common unit and then comparing those measurements multiplicatively.  <br />Because a fraction represents a multiplicative relation between two quantities, the operation of multiplication requires special attention.  When dealing with whole numbers of quantity only, understanding multiplication as repeated addition was enough.  But this meaning cannot be applied to taking, say, three-fifths times some quantity, and we need to redefine the operation of multiplication so that it covers multiplication of both a quantity by a whole number and by a fraction. <br />The definitions introduced in the second chapter constitute the conceptual basis for the subsequent chapters in which a whole arithmetic of fractions of quantities has been developed.  The various operations on fractions of quantities are studied, such as calculating the fraction of a fraction of a quantity; addition of two fractions of a quantity; their subtraction; division of a quantity by a fraction and division of a quantity by a quantity.  The names of these operations include terms known from the arithmetic of whole abstract numbers (e.g., 2 × 3) or whole numbers of quantities (e.g., 2 × 3 kg), such as “addition”, “subtraction”, “multiplication” and “division”, but the meaning of these terms is extended or modified to apply to the domain of fractions of quantities.  <br />The purpose of this elaborate development is to provide future elementary teachers with a coherent theory that fulfills a twofold purpose.  On one hand, it may help them develop a mature understanding of fractions, beyond the understanding they have acquired in school (Ma, 1999).  On the other hand, it may equip them with the practical tools and flexibility to operate in a variety of contexts and within, likely, very different developments of the topic of fractions, which they may encounter in their future practice.  <br />Throughout the text, understanding of fractions of quantities and operations with them is fostered by means of examples, exercises and end-of-chapter “Problem sets.”  Chapters VII (Proportional quantities and proportional reasoning) and VIII (Comparison of fractions of quantities) offer an opportunity to consolidate this understanding in solving somewhat more complex problems.  <br /><br />NOTE: This is a slightly revised and corrected version of the course notes published in 2014 by Concordia University and used as a text in the course EDUC 387 Teaching Mathematics II taught in the Winter 2015 term. An earlier and rather different version of these course notes – using only one definition of fraction of a quantity, and authored by Anna Sierpinska only – has been published in 2013, and used as a text in EDUC 387 Teaching Mathematics II in the Winter of 2014.</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/19895776" 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="00bd0fd197c9cffd9526592fb407bb3e" rel="nofollow" data-download="{"attachment_id":40904800,"asset_id":19895776,"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/40904800/download_file?st=MTczMzAxOTg4Niw4LjIyMi4yMDguMTQ2&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="6824714" href="https://concordia.academia.edu/AnnaSierpinska">Anna Sierpinska</a><script data-card-contents-for-user="6824714" type="text/json">{"id":6824714,"first_name":"Anna","last_name":"Sierpinska","domain_name":"concordia","page_name":"AnnaSierpinska","display_name":"Anna Sierpinska","profile_url":"https://concordia.academia.edu/AnnaSierpinska?f_ri=152051","photo":"https://0.academia-photos.com/6824714/3420311/4022455/s65_anna.sierpinska.jpg"}</script></span></span></li><li class="js-paper-rank-work_19895776 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="19895776"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 19895776, container: ".js-paper-rank-work_19895776", }); 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$(".js-view-count[data-work-id=19895776]").text(description); $(".js-view-count-work_19895776").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_19895776").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="19895776"><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="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=152051","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=152051","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="106182" href="https://www.academia.edu/Documents/in/Pre_Service_Teacher_Education">Pre Service Teacher Education</a>, <script data-card-contents-for-ri="106182" type="text/json">{"id":106182,"name":"Pre Service Teacher Education","url":"https://www.academia.edu/Documents/in/Pre_Service_Teacher_Education?f_ri=152051","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=152051","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=19895776]'), work: {"id":19895776,"title":"EDUC 387 TEACHING MATHEMATICS II - COURSE NOTES PART I - FRACTIONS OF QUANTITIES (REVISED VERSION)","created_at":"2015-12-29T18:21:11.739-08:00","url":"https://www.academia.edu/19895776/EDUC_387_TEACHING_MATHEMATICS_II_COURSE_NOTES_PART_I_FRACTIONS_OF_QUANTITIES_REVISED_VERSION_?f_ri=152051","dom_id":"work_19895776","summary":"This text is intended as a reference for the first part of the course Teaching Mathematics II for prospective elementary school teachers. It focuses on fractions of quantities. The second part focuses on the concepts of rational number, real number, ratio and percent. It is published separately.\nKnowledge presented in the text is meant as a foundation for the “Specialized Content Knowledge” (Ball, Thames, \u0026 Phelps, 2008) for the teaching of fractions in elementary schools. It is intended as teachers’ knowledge, not knowledge that could be imparted, as is, to schoolchildren. It is neither the mathematics of school textbooks for children, nor the mathematics of academic textbooks for future mathematicians. \n\tOur intention is to look at the content to be taught in elementary school about fractions from the point of view of mathematics itself. We will strive to clarify the meanings of the fundamental concepts (fraction of a quantity, ratio, proportion, etc.) by formulating definitions and using precise language; we will justify techniques and rules of operations on fractions by reasoning; we will analyze the structure of problems about fractions and classify them into types. In that sense, it is a mathematical knowledge base for making informed decisions in planning lessons, responding to students’ questions and preparing exercises for them. We will leave aside, for the time being, the issues of the psychology of teaching and learning fractions: how children learn fractions, what difficulties they experience and what teachers can do to help them overcome these difficulties. These issues will be dealt with in the course Teaching Mathematics III. \nIn Part I of the course notes we focus on fractions as a way to represent the multiplicative relationship between two quantities (lengths, areas, volumes, weights, capacities, market values, etc.). We view fractions as an answer to the question of how many times one quantity is bigger or smaller than another. We explicitly define what it means for one quantity to be such and such fraction of another quantity. In concrete problems we identify and name the quantities that are being compared and the units with which they are measured. The comparison may require change of unit or conversion from one unit to another. We become aware of these operations, analyze them and learn how to write them. In brief, in this course, we make explicit what is often left implicit in teaching fractions to children. \n In Part I of the course notes, we will talk mainly about quantities. So, for example, instead of talking about abstract numbers, e.g., 3/4 and 1/8 , and calculating their sum, 3/4+ 1/8 = 7/8 , we will be talking about, say, Tom using up 3/4 of a 120-gallon water tank, meaning the quantity of 90 gallons, and Jerry using up 1/8 of the same water tank and asking how much of the tank they used together. We will be adding quantities, not abstract numbers, expressing this operation in terms of numbers of units (gallons in this case), as\n3/4 of 120 Gal + 1/8 of 120 Gal = 7/8 of 120 Gal\nor as 90 Gal + 15 Gal = 105 Gal. \nIn this text, the concept of fraction of a quantity will be derived from the practices of measurement, particularly the operations of change of unit and unit conversion. If we want to measure some quantity, the existing units of measurement may not represent it precisely enough, and we have to change those units into some finer ones. For example, if we measure the length of some tiny piece of metal and find that it measures 1 mm and a little bit and find that 3 such “bits” cover 2 mm, then we will say that 1 bit = 2/3 mm. This is a “conversion equation.” \nThe approach to fractions through measurement – we call it the Measurement Approach – proposed in this text, is different from the more common Division Approach to fractions through division of numbers, modeled by division of things (e.g., apples or pizzas), or graphical representations of things. We explain the differences between the Measurement and the Division approaches to fractions in more detail in Chapter I. \nChapter II focuses on the practical and theoretical foundations of the Measurement Approach. It starts by explaining how the notion of a fraction of a quantity could be derived from the historical practices of measurement. Then the meaning of the phrase “one quantity is such and such fraction of another quantity” is defined in two ways. One is inspired by barter exchanges where integer multiples of two quantities are equated with each other. The other is based on measuring each of the quantities independently with a common unit and then comparing those measurements multiplicatively. \nBecause a fraction represents a multiplicative relation between two quantities, the operation of multiplication requires special attention. When dealing with whole numbers of quantity only, understanding multiplication as repeated addition was enough. But this meaning cannot be applied to taking, say, three-fifths times some quantity, and we need to redefine the operation of multiplication so that it covers multiplication of both a quantity by a whole number and by a fraction. \nThe definitions introduced in the second chapter constitute the conceptual basis for the subsequent chapters in which a whole arithmetic of fractions of quantities has been developed. The various operations on fractions of quantities are studied, such as calculating the fraction of a fraction of a quantity; addition of two fractions of a quantity; their subtraction; division of a quantity by a fraction and division of a quantity by a quantity. The names of these operations include terms known from the arithmetic of whole abstract numbers (e.g., 2 × 3) or whole numbers of quantities (e.g., 2 × 3 kg), such as “addition”, “subtraction”, “multiplication” and “division”, but the meaning of these terms is extended or modified to apply to the domain of fractions of quantities. \nThe purpose of this elaborate development is to provide future elementary teachers with a coherent theory that fulfills a twofold purpose. On one hand, it may help them develop a mature understanding of fractions, beyond the understanding they have acquired in school (Ma, 1999). On the other hand, it may equip them with the practical tools and flexibility to operate in a variety of contexts and within, likely, very different developments of the topic of fractions, which they may encounter in their future practice. \nThroughout the text, understanding of fractions of quantities and operations with them is fostered by means of examples, exercises and end-of-chapter “Problem sets.” Chapters VII (Proportional quantities and proportional reasoning) and VIII (Comparison of fractions of quantities) offer an opportunity to consolidate this understanding in solving somewhat more complex problems. \n\nNOTE: This is a slightly revised and corrected version of the course notes published in 2014 by Concordia University and used as a text in the course EDUC 387 Teaching Mathematics II taught in the Winter 2015 term. An earlier and rather different version of these course notes – using only one definition of fraction of a quantity, and authored by Anna Sierpinska only – has been published in 2013, and used as a text in EDUC 387 Teaching Mathematics II in the Winter of 2014. \n","downloadable_attachments":[{"id":40904800,"asset_id":19895776,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":6824714,"first_name":"Anna","last_name":"Sierpinska","domain_name":"concordia","page_name":"AnnaSierpinska","display_name":"Anna Sierpinska","profile_url":"https://concordia.academia.edu/AnnaSierpinska?f_ri=152051","photo":"https://0.academia-photos.com/6824714/3420311/4022455/s65_anna.sierpinska.jpg"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics?f_ri=152051","nofollow":false},{"id":2731,"name":"Mathematics Education","url":"https://www.academia.edu/Documents/in/Mathematics_Education?f_ri=152051","nofollow":false},{"id":106182,"name":"Pre Service Teacher Education","url":"https://www.academia.edu/Documents/in/Pre_Service_Teacher_Education?f_ri=152051","nofollow":false},{"id":152051,"name":"Didactique des mathématiques","url":"https://www.academia.edu/Documents/in/Didactique_des_mathematiques?f_ri=152051","nofollow":false},{"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=152051"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_37090993" data-work_id="37090993" 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/37090993/El%C3%A9ments_pour_une_description_des_comp%C3%A9tences_linguistiques_en_langue_de_scolarisation_n%C3%A9cessaires_%C3%A0_l_enseignement_apprentissage_de_l_histoire_dans_le_premier_cycle_de_l_enseignement_secondaire_une_d%C3%A9marche_et_des_points_de_r%C3%A9f%C3%A9rence">Eléments pour une description des compétences linguistiques en langue de scolarisation nécessaires à l’enseignement/apprentissage de l’histoire dans le premier cycle de l’enseignement secondaire : une démarche et des points de référence.</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">2009. Etude pour la Plate-forme de ressources et de références pour l’éducation plurilingue et interculturelle, Conseil de l’Europe. Langues de scolarisation. A servi de cadre à trois analyses concernant les sciences, la littérature et... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_37090993" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">2009. Etude pour la Plate-forme de ressources et de références pour l’éducation plurilingue et interculturelle, Conseil de l’Europe. Langues de scolarisation. A servi de cadre à trois analyses  concernant les sciences, la littérature et les mathématiques **** <a href="https://www.coe.int/fr/web/platform-plurilingual-intercultural-language-education/language-s-in-other-subjects#{"28070427":[]" rel="nofollow">https://www.coe.int/fr/web/platform-plurilingual-intercultural-language-education/language-s-in-other-subjects#{"28070427":[]</a></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/37090993" 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="eded4c9753a4eb6d4390054b36736d8f" rel="nofollow" data-download="{"attachment_id":57042756,"asset_id":37090993,"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/57042756/download_file?st=MTczMzAxOTg4Niw4LjIyMi4yMDguMTQ2&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="76460110" href="https://independent.academia.edu/JeanClaudeBeacco">Jean Claude Beacco</a><script data-card-contents-for-user="76460110" type="text/json">{"id":76460110,"first_name":"Jean Claude","last_name":"Beacco","domain_name":"independent","page_name":"JeanClaudeBeacco","display_name":"Jean Claude Beacco","profile_url":"https://independent.academia.edu/JeanClaudeBeacco?f_ri=152051","photo":"https://0.academia-photos.com/76460110/19035026/160847338/s65_jean_claude.beacco.jpg"}</script></span></span></li><li class="js-paper-rank-work_37090993 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="37090993"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 37090993, container: ".js-paper-rank-work_37090993", }); 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$(".js-view-count[data-work-id=37090993]").text(description); $(".js-view-count-work_37090993").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_37090993").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="37090993"><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="94" href="https://www.academia.edu/Documents/in/Discourse_Analysis">Discourse Analysis</a>, <script data-card-contents-for-ri="94" type="text/json">{"id":94,"name":"Discourse Analysis","url":"https://www.academia.edu/Documents/in/Discourse_Analysis?f_ri=152051","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="8000" href="https://www.academia.edu/Documents/in/French_language">French language</a>, <script data-card-contents-for-ri="8000" type="text/json">{"id":8000,"name":"French language","url":"https://www.academia.edu/Documents/in/French_language?f_ri=152051","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="18841" href="https://www.academia.edu/Documents/in/French_Language_Teaching">French Language Teaching</a>, <script data-card-contents-for-ri="18841" type="text/json">{"id":18841,"name":"French Language Teaching","url":"https://www.academia.edu/Documents/in/French_Language_Teaching?f_ri=152051","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="19296" href="https://www.academia.edu/Documents/in/Francais_Langue_Etrangere">Francais Langue Etrangere</a><script data-card-contents-for-ri="19296" type="text/json">{"id":19296,"name":"Francais Langue Etrangere","url":"https://www.academia.edu/Documents/in/Francais_Langue_Etrangere?f_ri=152051","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=37090993]'), work: {"id":37090993,"title":"Eléments pour une description des compétences linguistiques en langue de scolarisation nécessaires à l’enseignement/apprentissage de l’histoire dans le premier cycle de l’enseignement secondaire : une démarche et des points de référence.","created_at":"2018-07-21T02:35:45.599-07:00","url":"https://www.academia.edu/37090993/El%C3%A9ments_pour_une_description_des_comp%C3%A9tences_linguistiques_en_langue_de_scolarisation_n%C3%A9cessaires_%C3%A0_l_enseignement_apprentissage_de_l_histoire_dans_le_premier_cycle_de_l_enseignement_secondaire_une_d%C3%A9marche_et_des_points_de_r%C3%A9f%C3%A9rence?f_ri=152051","dom_id":"work_37090993","summary":"2009. Etude pour la Plate-forme de ressources et de références pour l’éducation plurilingue et interculturelle, Conseil de l’Europe. Langues de scolarisation. A servi de cadre à trois analyses concernant les sciences, la littérature et les mathématiques **** https://www.coe.int/fr/web/platform-plurilingual-intercultural-language-education/language-s-in-other-subjects#{\"28070427\":[]","downloadable_attachments":[{"id":57042756,"asset_id":37090993,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":76460110,"first_name":"Jean Claude","last_name":"Beacco","domain_name":"independent","page_name":"JeanClaudeBeacco","display_name":"Jean Claude Beacco","profile_url":"https://independent.academia.edu/JeanClaudeBeacco?f_ri=152051","photo":"https://0.academia-photos.com/76460110/19035026/160847338/s65_jean_claude.beacco.jpg"}],"research_interests":[{"id":94,"name":"Discourse Analysis","url":"https://www.academia.edu/Documents/in/Discourse_Analysis?f_ri=152051","nofollow":false},{"id":8000,"name":"French language","url":"https://www.academia.edu/Documents/in/French_language?f_ri=152051","nofollow":false},{"id":18841,"name":"French Language Teaching","url":"https://www.academia.edu/Documents/in/French_Language_Teaching?f_ri=152051","nofollow":false},{"id":19296,"name":"Francais Langue Etrangere","url":"https://www.academia.edu/Documents/in/Francais_Langue_Etrangere?f_ri=152051","nofollow":false},{"id":66444,"name":"Didactique des langues","url":"https://www.academia.edu/Documents/in/Didactique_des_langues?f_ri=152051"},{"id":89843,"name":"Scientific Discourse","url":"https://www.academia.edu/Documents/in/Scientific_Discourse?f_ri=152051"},{"id":152051,"name":"Didactique des mathématiques","url":"https://www.academia.edu/Documents/in/Didactique_des_mathematiques?f_ri=152051"},{"id":166148,"name":"Didactique du français langue étrangère","url":"https://www.academia.edu/Documents/in/Didactique_du_francais_langue_etrangere?f_ri=152051"},{"id":196166,"name":"Didactique des sciences","url":"https://www.academia.edu/Documents/in/Didactique_des_sciences?f_ri=152051"},{"id":417468,"name":"Didactique De L'Histoire","url":"https://www.academia.edu/Documents/in/Didactique_De_LHistoire?f_ri=152051"},{"id":2896021,"name":"Langue de scolarisation","url":"https://www.academia.edu/Documents/in/Langue_de_scolarisation?f_ri=152051"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_41791419" data-work_id="41791419" 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/41791419/De_l_approche_instrumentale_%C3%A0_l_approche_documentaire_du_didactique_une_histoire_d_appropriations_crois%C3%A9es_et_d_hybridations_th%C3%A9oriques">De l’approche instrumentale à l’approche documentaire du didactique : une histoire d’appropriations croisées et d’hybridations théoriques</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">On proposera, dans cette intervention, une réflexion sur les sources et la dynamique d’une approche conceptuelle qui veut saisir le travail des enseignants à partir des outils qu’ils s’approprient, de l’œuvre qu’ils constituent et des... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_41791419" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">On proposera, dans cette intervention, une réflexion sur les sources et la dynamique d’une approche conceptuelle qui veut saisir le travail des enseignants à partir des outils qu’ils s’approprient, de l’œuvre qu’ils constituent et des collectifs qu’ils (ou qui les) rassemblent. Cette réflexion se fera en cinq temps, à partir de considérations sur : l’approche instrumentale ; l’approche documentaire du didactique ; la diversité nécessaire des points de vue ; la diversité des évolutions conceptuelles ; et enfin la notion d’accomplissement.<br />L’approche instrumentale est partie d’une réflexion générale sur la façon dont l’environnement conditionne l’action humaine (Trouche, 2000), mais elle s’est vraiment développée en s’intéressant à des artefacts particuliers (les calculatrices, et les logiciels de calcul formel), et en se nourrissant d’interactions avec d’autres approches théoriques, aux niveaux national et international (Guin & Trouche 2002 ; Guin, Ruthven & Trouche, 2005). On questionnera les fondements politico-épistémologiques de ces développements (Monaghan, Trouche, & Borwein 2017).<br />C’est fondamentalement un entrelacement d’évolutions technologiques (l’émergence d’Internet) et conceptuelles (une appréhension holistique du travail du professeur ; et une compréhension plus profonde de la notion d’instrumentalisation) qui a conduit à l’extension de l’approche instrumentale à l’approche documentaire, aux niveaux national et international (Gueudet & Trouche, 2008 ; Gueudet, Pepin & Trouche, 2012), les deux niveaux étant d’emblée inter reliés. On questionnera ici les relations entre hybridation de communautés scientifiques et hybridations théoriques.<br />Du fait de la complexité de l’étude de l’interaction des professeurs avec les ressources de leur enseignement, on mettra en évidence l’intérêt de la diversité des croisements : des approches théoriques (Trouche et al. 2019) ; des disciplines d’enseignement (Messaoui, 2019) ; et des points de vue linguistico-culturels (Wang et al., 2019).<br />A partir d’un focus sur la notion d’orchestration instrumentale (Drijvers, Grauwin, & Trouche, soumis), on montrera que les évolutions théoriques ne peuvent se résumer à de grandes tendances : ces tendances sont la résultante de multiples évolutions, qui ont toutes leur logique propre.<br />Le passage à la position de retraité est l’occasion de (se) poser la question de l’accomplissement, ou de la cohérence d’un travail scientifique. Même si, bien sûr, on peut rendre compte de lignes de cohérence, on soulignera quelques éléments d’intranquillité (Said, 2012) qui peuvent éclairer ce qui a été fait, et ce qui n’a pas été fait.</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/41791419" 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="80308fad1c477b0ddcc6a57cfd263b7a" rel="nofollow" data-download="{"attachment_id":61943026,"asset_id":41791419,"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/61943026/download_file?st=MTczMzAxOTg4Niw4LjIyMi4yMDguMTQ2&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="486697" href="https://ens-lyon.academia.edu/LucTrouche">Luc Trouche</a><script data-card-contents-for-user="486697" type="text/json">{"id":486697,"first_name":"Luc","last_name":"Trouche","domain_name":"ens-lyon","page_name":"LucTrouche","display_name":"Luc Trouche","profile_url":"https://ens-lyon.academia.edu/LucTrouche?f_ri=152051","photo":"https://0.academia-photos.com/486697/165503/17898170/s65_luc.trouche.png"}</script></span></span></li><li class="js-paper-rank-work_41791419 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="41791419"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 41791419, container: ".js-paper-rank-work_41791419", }); });</script></li><li class="js-percentile-work_41791419 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 = 41791419; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_41791419"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_41791419 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="41791419"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 41791419; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=41791419]").text(description); $(".js-view-count-work_41791419").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_41791419").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="41791419"><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="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=152051","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="1179966" href="https://www.academia.edu/Documents/in/Approche_Instrumentale">Approche Instrumentale</a>, <script data-card-contents-for-ri="1179966" type="text/json">{"id":1179966,"name":"Approche Instrumentale","url":"https://www.academia.edu/Documents/in/Approche_Instrumentale?f_ri=152051","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="2553199" href="https://www.academia.edu/Documents/in/approche_documentaire_du_didactique">approche documentaire du didactique</a><script data-card-contents-for-ri="2553199" type="text/json">{"id":2553199,"name":"approche documentaire du didactique","url":"https://www.academia.edu/Documents/in/approche_documentaire_du_didactique?f_ri=152051","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=41791419]'), work: {"id":41791419,"title":"De l’approche instrumentale à l’approche documentaire du didactique : une histoire d’appropriations croisées et d’hybridations théoriques","created_at":"2020-01-30T09:55:58.546-08:00","url":"https://www.academia.edu/41791419/De_l_approche_instrumentale_%C3%A0_l_approche_documentaire_du_didactique_une_histoire_d_appropriations_crois%C3%A9es_et_d_hybridations_th%C3%A9oriques?f_ri=152051","dom_id":"work_41791419","summary":"On proposera, dans cette intervention, une réflexion sur les sources et la dynamique d’une approche conceptuelle qui veut saisir le travail des enseignants à partir des outils qu’ils s’approprient, de l’œuvre qu’ils constituent et des collectifs qu’ils (ou qui les) rassemblent. Cette réflexion se fera en cinq temps, à partir de considérations sur : l’approche instrumentale ; l’approche documentaire du didactique ; la diversité nécessaire des points de vue ; la diversité des évolutions conceptuelles ; et enfin la notion d’accomplissement.\nL’approche instrumentale est partie d’une réflexion générale sur la façon dont l’environnement conditionne l’action humaine (Trouche, 2000), mais elle s’est vraiment développée en s’intéressant à des artefacts particuliers (les calculatrices, et les logiciels de calcul formel), et en se nourrissant d’interactions avec d’autres approches théoriques, aux niveaux national et international (Guin \u0026 Trouche 2002 ; Guin, Ruthven \u0026 Trouche, 2005). On questionnera les fondements politico-épistémologiques de ces développements (Monaghan, Trouche, \u0026 Borwein 2017).\nC’est fondamentalement un entrelacement d’évolutions technologiques (l’émergence d’Internet) et conceptuelles (une appréhension holistique du travail du professeur ; et une compréhension plus profonde de la notion d’instrumentalisation) qui a conduit à l’extension de l’approche instrumentale à l’approche documentaire, aux niveaux national et international (Gueudet \u0026 Trouche, 2008 ; Gueudet, Pepin \u0026 Trouche, 2012), les deux niveaux étant d’emblée inter reliés. On questionnera ici les relations entre hybridation de communautés scientifiques et hybridations théoriques.\nDu fait de la complexité de l’étude de l’interaction des professeurs avec les ressources de leur enseignement, on mettra en évidence l’intérêt de la diversité des croisements : des approches théoriques (Trouche et al. 2019) ; des disciplines d’enseignement (Messaoui, 2019) ; et des points de vue linguistico-culturels (Wang et al., 2019).\nA partir d’un focus sur la notion d’orchestration instrumentale (Drijvers, Grauwin, \u0026 Trouche, soumis), on montrera que les évolutions théoriques ne peuvent se résumer à de grandes tendances : ces tendances sont la résultante de multiples évolutions, qui ont toutes leur logique propre.\nLe passage à la position de retraité est l’occasion de (se) poser la question de l’accomplissement, ou de la cohérence d’un travail scientifique. Même si, bien sûr, on peut rendre compte de lignes de cohérence, on soulignera quelques éléments d’intranquillité (Said, 2012) qui peuvent éclairer ce qui a été fait, et ce qui n’a pas été fait.\n","downloadable_attachments":[{"id":61943026,"asset_id":41791419,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":486697,"first_name":"Luc","last_name":"Trouche","domain_name":"ens-lyon","page_name":"LucTrouche","display_name":"Luc Trouche","profile_url":"https://ens-lyon.academia.edu/LucTrouche?f_ri=152051","photo":"https://0.academia-photos.com/486697/165503/17898170/s65_luc.trouche.png"}],"research_interests":[{"id":152051,"name":"Didactique des mathématiques","url":"https://www.academia.edu/Documents/in/Didactique_des_mathematiques?f_ri=152051","nofollow":false},{"id":1179966,"name":"Approche Instrumentale","url":"https://www.academia.edu/Documents/in/Approche_Instrumentale?f_ri=152051","nofollow":false},{"id":2553199,"name":"approche documentaire du didactique","url":"https://www.academia.edu/Documents/in/approche_documentaire_du_didactique?f_ri=152051","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_41493875" data-work_id="41493875" 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/41493875/Variations_autour_dun_probl%C3%A8me_de_g%C3%A9om%C3%A9trie">Variations autour d'un problème de géométrie</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">Nous reprenons dans ce papier un problème de géométrie proposé en 1990 comme exercice d'une épreuve des olympiades de mathématiques organisée au Maroc pour des élèves du secon-daire (niveau seconde). Aucun élève n'a réussi à le résoudre.... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_41493875" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">Nous reprenons dans ce papier un problème de géométrie proposé en 1990 comme exercice d'une épreuve des olympiades de mathématiques organisée au Maroc pour des élèves du secon-daire (niveau seconde). Aucun élève n'a réussi à le résoudre. Pire encore, plusieurs enseignants ont éprouvé des difficultés en cherchant à le résoudre. Nous proposons dans ce papier plusieurs mé-thodes de solution, allant du niveau collège (troisième) jusqu'au niveau lycée (seconde et première scientifique). Quand j'avais proposé le problème il y a une trentaine d'années, j'étais loin de soupçonner dans le temps que celui-ci est potentiellement très riche. Ainsi, il peut être proposé comme activité aux élèves du lycée pour introduire les notions de fonctions homographiques, de limite et d'asymptote. Nous terminons ces variations autour de ce problème en proposant comme exercice un pro-blème analogue permettant d'introduire, , auprès des élèves de seconde, les notions de fonction quadratique, d'extrémums (maximum et minimum), de parité, etc. Abstract We resume in this paper a problem of geometry proposed in 1990 like an exercice of a test of mathematical olympiads organized in Morocco for pupils of high school (second level). No student was able to solve it. Worse still, many teachers have found difficulties in trying to solve it. We propose in this paper several methods of solutions, ranging from college level (third class) to hight school level (second class and scientific first). When I proposed the problem about thirty years ago, I was far from suspecting that's this one is potentially rich. Thus, after solving it, it can be proposed as an activity to hight school students (second class) to introduce homographic functions, the notions of limit and asymptote. We end these variations around this problem by proposing as an exercise a similar problem allowing to introduce the notions of quadratic functions, parity and extremums, to the students of the second class.</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/41493875" 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="6127823b7098e61887d22b96a7508460" rel="nofollow" data-download="{"attachment_id":61664856,"asset_id":41493875,"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/61664856/download_file?st=MTczMzAxOTg4Niw4LjIyMi4yMDguMTQ2&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="11786533" href="https://sorbonne-fr.academia.edu/TAMIMIAbdelkader">TAMIMI Abdelkader</a><script data-card-contents-for-user="11786533" type="text/json">{"id":11786533,"first_name":"TAMIMI","last_name":"Abdelkader","domain_name":"sorbonne-fr","page_name":"TAMIMIAbdelkader","display_name":"TAMIMI Abdelkader","profile_url":"https://sorbonne-fr.academia.edu/TAMIMIAbdelkader?f_ri=152051","photo":"https://0.academia-photos.com/11786533/3400155/71233585/s65_tamimi.abdelkader.jpg"}</script></span></span></li><li class="js-paper-rank-work_41493875 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="41493875"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 41493875, container: ".js-paper-rank-work_41493875", }); });</script></li><li class="js-percentile-work_41493875 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 = 41493875; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_41493875"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_41493875 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="41493875"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 41493875; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=41493875]").text(description); $(".js-view-count-work_41493875").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_41493875").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="41493875"><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="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=152051","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=152051","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="715592" href="https://www.academia.edu/Documents/in/Enseignement">Enseignement</a><script data-card-contents-for-ri="715592" type="text/json">{"id":715592,"name":"Enseignement","url":"https://www.academia.edu/Documents/in/Enseignement?f_ri=152051","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=41493875]'), work: {"id":41493875,"title":"Variations autour d'un problème de géométrie","created_at":"2020-01-02T15:43:53.664-08:00","url":"https://www.academia.edu/41493875/Variations_autour_dun_probl%C3%A8me_de_g%C3%A9om%C3%A9trie?f_ri=152051","dom_id":"work_41493875","summary":"Nous reprenons dans ce papier un problème de géométrie proposé en 1990 comme exercice d'une épreuve des olympiades de mathématiques organisée au Maroc pour des élèves du secon-daire (niveau seconde). Aucun élève n'a réussi à le résoudre. Pire encore, plusieurs enseignants ont éprouvé des difficultés en cherchant à le résoudre. Nous proposons dans ce papier plusieurs mé-thodes de solution, allant du niveau collège (troisième) jusqu'au niveau lycée (seconde et première scientifique). Quand j'avais proposé le problème il y a une trentaine d'années, j'étais loin de soupçonner dans le temps que celui-ci est potentiellement très riche. Ainsi, il peut être proposé comme activité aux élèves du lycée pour introduire les notions de fonctions homographiques, de limite et d'asymptote. Nous terminons ces variations autour de ce problème en proposant comme exercice un pro-blème analogue permettant d'introduire, , auprès des élèves de seconde, les notions de fonction quadratique, d'extrémums (maximum et minimum), de parité, etc. Abstract We resume in this paper a problem of geometry proposed in 1990 like an exercice of a test of mathematical olympiads organized in Morocco for pupils of high school (second level). No student was able to solve it. Worse still, many teachers have found difficulties in trying to solve it. We propose in this paper several methods of solutions, ranging from college level (third class) to hight school level (second class and scientific first). When I proposed the problem about thirty years ago, I was far from suspecting that's this one is potentially rich. Thus, after solving it, it can be proposed as an activity to hight school students (second class) to introduce homographic functions, the notions of limit and asymptote. We end these variations around this problem by proposing as an exercise a similar problem allowing to introduce the notions of quadratic functions, parity and extremums, to the students of the second class.","downloadable_attachments":[{"id":61664856,"asset_id":41493875,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":11786533,"first_name":"TAMIMI","last_name":"Abdelkader","domain_name":"sorbonne-fr","page_name":"TAMIMIAbdelkader","display_name":"TAMIMI Abdelkader","profile_url":"https://sorbonne-fr.academia.edu/TAMIMIAbdelkader?f_ri=152051","photo":"https://0.academia-photos.com/11786533/3400155/71233585/s65_tamimi.abdelkader.jpg"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics?f_ri=152051","nofollow":false},{"id":152051,"name":"Didactique des mathématiques","url":"https://www.academia.edu/Documents/in/Didactique_des_mathematiques?f_ri=152051","nofollow":false},{"id":715592,"name":"Enseignement","url":"https://www.academia.edu/Documents/in/Enseignement?f_ri=152051","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_50137431" data-work_id="50137431" 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/50137431/La_trigonom%C3%A9trie_dans_le_discours_scolaire_analyse_%C3%A9nonciative_et_conceptuelle">La trigonométrie dans le discours scolaire, analyse énonciative et conceptuelle</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">Dans ce travail, l’objet d’apprentissage "Cercle trigonométrique" est identifié comme obstacle didactique producteur de vacuités dans le discours scolaire à propos de la trigonométrie. Le cadre de la géométrie analytique y est sollicité... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_50137431" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">Dans ce travail, l’objet d’apprentissage "Cercle trigonométrique" est identifié comme obstacle didactique producteur de vacuités dans le discours scolaire à propos de la trigonométrie. Le cadre de la géométrie analytique y est sollicité pour le franchissement de cet obstacle et pour le remplissement de ces vacuités. Portés par ce franchissement et par ce remplissement, les linéaments de l’Algèbre et de l’Analyse y sont retracés à l’adresse des élèves de la fin de la scolarité obligatoire.</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/50137431" 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="538297b7d87e24daa0aa176d8947c572" rel="nofollow" data-download="{"attachment_id":68235842,"asset_id":50137431,"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/68235842/download_file?st=MTczMzAxOTg4Niw4LjIyMi4yMDguMTQ2&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="12036843" href="https://independent.academia.edu/mohamedbahra">mohamed bahra</a><script data-card-contents-for-user="12036843" type="text/json">{"id":12036843,"first_name":"mohamed","last_name":"bahra","domain_name":"independent","page_name":"mohamedbahra","display_name":"mohamed bahra","profile_url":"https://independent.academia.edu/mohamedbahra?f_ri=152051","photo":"https://0.academia-photos.com/12036843/3485109/4094597/s65_mohamed.bahra.png"}</script></span></span></li><li class="js-paper-rank-work_50137431 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="50137431"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 50137431, container: ".js-paper-rank-work_50137431", }); });</script></li><li class="js-percentile-work_50137431 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 = 50137431; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_50137431"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_50137431 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="50137431"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 50137431; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=50137431]").text(description); $(".js-view-count-work_50137431").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_50137431").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="50137431"><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="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=152051","nofollow":false}</script></span></li><script>(function(){ if (false) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=50137431]'), work: {"id":50137431,"title":"La trigonométrie dans le discours scolaire, analyse énonciative et conceptuelle","created_at":"2021-07-21T12:32:58.830-07:00","url":"https://www.academia.edu/50137431/La_trigonom%C3%A9trie_dans_le_discours_scolaire_analyse_%C3%A9nonciative_et_conceptuelle?f_ri=152051","dom_id":"work_50137431","summary":"Dans ce travail, l’objet d’apprentissage \"Cercle trigonométrique\" est identifié comme obstacle didactique producteur de vacuités dans le discours scolaire à propos de la trigonométrie. Le cadre de la géométrie analytique y est sollicité pour le franchissement de cet obstacle et pour le remplissement de ces vacuités. Portés par ce franchissement et par ce remplissement, les linéaments de l’Algèbre et de l’Analyse y sont retracés à l’adresse des élèves de la fin de la scolarité obligatoire.","downloadable_attachments":[{"id":68235842,"asset_id":50137431,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":12036843,"first_name":"mohamed","last_name":"bahra","domain_name":"independent","page_name":"mohamedbahra","display_name":"mohamed bahra","profile_url":"https://independent.academia.edu/mohamedbahra?f_ri=152051","photo":"https://0.academia-photos.com/12036843/3485109/4094597/s65_mohamed.bahra.png"}],"research_interests":[{"id":152051,"name":"Didactique des mathématiques","url":"https://www.academia.edu/Documents/in/Didactique_des_mathematiques?f_ri=152051","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_21828883" data-work_id="21828883" 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/21828883/L_enseignement_des_math%C3%A9matiques_dans_un_contexte_interdisciplinaire_Actes_du_Colloque_du_GDM_2008">L’enseignement des mathématiques dans un contexte interdisciplinaire. Actes du Colloque du GDM 2008.</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/21828883" 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="554d68401e080e054c1e895c1e65664e" rel="nofollow" data-download="{"attachment_id":42579549,"asset_id":21828883,"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/42579549/download_file?st=MTczMzAxOTg4Niw4LjIyMi4yMDguMTQ2&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="35749199" href="https://independent.academia.edu/GDMQu%C3%A9bec">GDM Québec</a><script data-card-contents-for-user="35749199" type="text/json">{"id":35749199,"first_name":"GDM","last_name":"Québec","domain_name":"independent","page_name":"GDMQuébec","display_name":"GDM Québec","profile_url":"https://independent.academia.edu/GDMQu%C3%A9bec?f_ri=152051","photo":"https://0.academia-photos.com/35749199/10351477/11551354/s65_gdm.qu_bec.jpg"}</script></span></span></li><li class="js-paper-rank-work_21828883 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="21828883"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 21828883, container: ".js-paper-rank-work_21828883", }); 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$(".js-view-count[data-work-id=21828883]").text(description); $(".js-view-count-work_21828883").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_21828883").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="21828883"><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="41130" href="https://www.academia.edu/Documents/in/Didactics_of_Mathematics">Didactics of Mathematics</a>, <script data-card-contents-for-ri="41130" type="text/json">{"id":41130,"name":"Didactics of Mathematics","url":"https://www.academia.edu/Documents/in/Didactics_of_Mathematics?f_ri=152051","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=152051","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="249208" href="https://www.academia.edu/Documents/in/Qu%C3%A9bec">Québec</a><script data-card-contents-for-ri="249208" type="text/json">{"id":249208,"name":"Québec","url":"https://www.academia.edu/Documents/in/Qu%C3%A9bec?f_ri=152051","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=21828883]'), work: {"id":21828883,"title":"L’enseignement des mathématiques dans un contexte interdisciplinaire. 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L’étude de ce thème questionne les rapports entre... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_12119400" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">Le texte est le résultat d'une réflexion collective autour du thème « L'expérimentation dans nos recherches en didactique des mathématiques : méthodologie et position du chercheur ». L’étude de ce thème questionne les rapports entre chercheurs et acteurs sur le terrain expérimental (élèves, enseignants, groupe d’enseignants). Le chercheur fait explicitement ou implicitement des choix sur sa place dans le dispositif expérimental, les modalités d’interactions ou d’intervention avec les personnes, ou même les modes de recueil de données. Qu’est ce qui oriente ces choix, et sont-ils toujours pertinents ? <br />Les premières réflexions ramènent à l’idée que la problématique, la méthodologie, le terrain expérimental et la position du chercheur sont liés. Nous présenterons dans cette communication les questions issues de ce séminaire permettant de croiser les regards autour des différents dispositifs de recherche mis en oeuvre par des jeunes chercheurs dans le domaine. <br /> <br />Référence du texte : <br />Daina A., Mathé A., Pelay N., & Sabra H. (2011), L'expérimentation dans nos recherches en didactique des mathématiques : méthodologie et position du chercheur. Réflexion autour du thème du IVème séminaire des jeunes chercheurs de l’ARDM. In Abboud-Blanchard M. & Flükiger A. (Eds.), Actes du séminaire national de didactique des mathématiques, pp. 57-76., IREM Paris 7.</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/12119400" 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="34522d62018d36f68520a545281d10dc" rel="nofollow" data-download="{"attachment_id":37431216,"asset_id":12119400,"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/37431216/download_file?st=MTczMzAxOTg4Niw4LjIyMi4yMDguMTQ2&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="503353" href="https://univ-reims.academia.edu/HusseinSabra">Hussein Sabra</a><script data-card-contents-for-user="503353" type="text/json">{"id":503353,"first_name":"Hussein","last_name":"Sabra","domain_name":"univ-reims","page_name":"HusseinSabra","display_name":"Hussein Sabra","profile_url":"https://univ-reims.academia.edu/HusseinSabra?f_ri=152051","photo":"https://0.academia-photos.com/503353/180513/210454/s65_hussein.sabra.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-12119400">+1</span><div class="hidden js-additional-users-12119400"><div><span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a href="https://univ-paris7.academia.edu/NicolasPelay">Nicolas Pelay</a></span></div></div></span><script>(function(){ var popoverSettings = { el: $('.js-work-more-authors-12119400'), placement: 'bottom', hide_delay: 200, html: true, content: function(){ return $('.js-additional-users-12119400').html(); 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L’étude de ce thème questionne les rapports entre chercheurs et acteurs sur le terrain expérimental (élèves, enseignants, groupe d’enseignants). Le chercheur fait explicitement ou implicitement des choix sur sa place dans le dispositif expérimental, les modalités d’interactions ou d’intervention avec les personnes, ou même les modes de recueil de données. Qu’est ce qui oriente ces choix, et sont-ils toujours pertinents ?\r\nLes premières réflexions ramènent à l’idée que la problématique, la méthodologie, le terrain expérimental et la position du chercheur sont liés. Nous présenterons dans cette communication les questions issues de ce séminaire permettant de croiser les regards autour des différents dispositifs de recherche mis en oeuvre par des jeunes chercheurs dans le domaine. \r\n\r\nRéférence du texte : \r\nDaina A., Mathé A., Pelay N., \u0026 Sabra H. (2011), L'expérimentation dans nos recherches en didactique des mathématiques : méthodologie et position du chercheur. Réflexion autour du thème du IVème séminaire des jeunes chercheurs de l’ARDM. In Abboud-Blanchard M. \u0026 Flükiger A. 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class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/32160685" 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="69f35e75789514daffd37c27680b66c0" rel="nofollow" data-download="{"attachment_id":52398483,"asset_id":32160685,"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/52398483/download_file?st=MTczMzAxOTg4Niw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" 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Actes du Colloque du GDM 2012.</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest">La recherche sur la résolution de problèmes en mathématiques: au-delà d'une compétence, au-delà des constats. 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Actes du Colloque du GDM 2014.</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest">Croisements variés de concepts, d'approches et de théories : les enjeux de la création en recherche en didactique des mathématiques. Actes du Colloque du GDM 2014.</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/16510903" 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="8ef5a6c7d29d3ebb09860658e26b4a39" rel="nofollow" data-download="{"attachment_id":39026857,"asset_id":16510903,"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/39026857/download_file?st=MTczMzAxOTg4Nyw4LjIyMi4yMDguMTQ2&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="35749199" href="https://independent.academia.edu/GDMQu%C3%A9bec">GDM Québec</a><script data-card-contents-for-user="35749199" type="text/json">{"id":35749199,"first_name":"GDM","last_name":"Québec","domain_name":"independent","page_name":"GDMQuébec","display_name":"GDM Québec","profile_url":"https://independent.academia.edu/GDMQu%C3%A9bec?f_ri=152051","photo":"https://0.academia-photos.com/35749199/10351477/11551354/s65_gdm.qu_bec.jpg"}</script></span></span></li><li class="js-paper-rank-work_16510903 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="16510903"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 16510903, container: ".js-paper-rank-work_16510903", }); 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Losego (éd.), 2014. Actes du colloque « Sociologie et didactiques : vers une transgression des frontières », 13 et 14 septembre 2012, Lausanne : Haute Ecole Pédagogique de Vaud. http://www.hepl.ch/sociodidac/actes/</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">Les sociologues et les didacticiens ont un terrain de rencontre, celui de la construction et de la transmission des savoirs scolaires. Ainsi, de nombreux concepts didactiques ont une dimension sociale, à commencer par celui de «... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_9212236" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">Les sociologues et les didacticiens ont un terrain de rencontre, celui de la <br />construction et de la transmission des savoirs scolaires. Ainsi, de nombreux <br />concepts didactiques ont une dimension sociale, à commencer par celui <br />de « transposition didactique ». Cependant, sur la longue période, les <br />deux communautés se sont largement ignorées, en vertu d’une division <br />du travail intellectuel. Placées au coeur de la transmission des savoirs, <br />les didactiques se sont essentiellement préoccupées des dimensions <br />cognitives et ont pu tendre parfois à une certaine normativité. En revanche, <br />la sociologie a longtemps traité l’école comme une sorte de boîte noire. <br />Elle a négligé les processus d’apprentissage ce qui explique en grande <br />partie son relativisme. Mais depuis le début des années 2000, la sociologie <br />de l’éducation réinvestit fortement l’étude des savoirs scolaires : sa <br />participation plus grande à la formation des enseignants l’a physiquement <br />rapprochée des contenus d’enseignement. Les autorités politiques ont <br />été conduites, par la « culture de l’évaluation » et notamment par les <br />grandes évaluations internationales (PISA, TIMMS, etc.), à réformer les <br />plans d’études et à ériger ainsi la question des contenus d’enseignement <br />en débat de société. Par ailleurs, les didactiques intègrent de plus en <br />plus le social dans leurs différents modèles. Elles étudient des contextes <br />d’acquisition des savoirs plus variés, qu’ils soient formels ou informels. <br />Il est donc possible aujourd’hui de dépasser les frontières disciplinaires <br />pour construire de nouveaux concepts et les faire migrer d’un champ <br />de recherche à l’autre. Ces migrations ouvrent de nouveaux territoires <br />communs à la sociologie et aux didactiques que le colloque a pu explorer.</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/9212236" 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="1f5036e7f222fafab7ebb4f06c0ce7b2" rel="nofollow" data-download="{"attachment_id":51538683,"asset_id":9212236,"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/51538683/download_file?st=MTczMzAxOTg4Nyw4LjIyMi4yMDguMTQ2&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="59613970" href="https://independent.academia.edu/PatrickTrabal">Patrick Trabal</a><script data-card-contents-for-user="59613970" type="text/json">{"id":59613970,"first_name":"Patrick","last_name":"Trabal","domain_name":"independent","page_name":"PatrickTrabal","display_name":"Patrick Trabal","profile_url":"https://independent.academia.edu/PatrickTrabal?f_ri=152051","photo":"/images/s65_no_pic.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-9212236">+11</span><div class="hidden js-additional-users-9212236"><div><span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a href="https://independent.academia.edu/PhLo">Ph Lo</a></span></div><div><span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a href="https://hepl.academia.edu/stephaneclivaz">Clivaz Stéphane</a></span></div><div><span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a href="https://unige.academia.edu/LauraWeiss">Laura Weiss</a></span></div><div><span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a href="https://independent.academia.edu/VincentVal%C3%A9rie">Valérie Vincent</a></span></div><div><span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a href="https://independent.academia.edu/Fran%C3%A7oisBaluteau">François Baluteau</a></span></div><div><span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a href="https://independent.academia.edu/AnneMonnier1">Anne Monnier</a></span></div><div><span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a href="https://univ-antilles.academia.edu/MariePaulePoggi">Marie-Paule Poggi</a></span></div><div><span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a href="https://65.academia.edu/juliennetter">julien netter</a></span></div><div><span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a href="https://independent.academia.edu/VeroniqueLeclercq">Véronique Leclercq</a></span></div><div><span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a href="https://univ-nantes.academia.edu/GRodriguezmunoz">G. Rodriguez-munoz</a></span></div><div><span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a href="https://independent.academia.edu/ElisabehChatel">Elisabeh Chatel</a></span></div></div></span><script>(function(){ var popoverSettings = { el: $('.js-work-more-authors-9212236'), placement: 'bottom', hide_delay: 200, html: true, content: function(){ return $('.js-additional-users-9212236').html(); } } new HoverPopover(popoverSettings); })();</script></li><li class="js-paper-rank-work_9212236 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="9212236"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 9212236, container: ".js-paper-rank-work_9212236", }); });</script></li><li class="js-percentile-work_9212236 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 = 9212236; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_9212236"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_9212236 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="9212236"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 9212236; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=9212236]").text(description); $(".js-view-count-work_9212236").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_9212236").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="9212236"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">10</a>  </div><span class="InlineList-item-text u-textTruncate u-pl10x"><a class="InlineList-item-text" data-has-card-for-ri="974" href="https://www.academia.edu/Documents/in/Sociology_of_Education">Sociology of Education</a>, <script data-card-contents-for-ri="974" type="text/json">{"id":974,"name":"Sociology of Education","url":"https://www.academia.edu/Documents/in/Sociology_of_Education?f_ri=152051","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="2993" href="https://www.academia.edu/Documents/in/Sociology_of_Knowledge">Sociology of Knowledge</a>, <script data-card-contents-for-ri="2993" type="text/json">{"id":2993,"name":"Sociology of Knowledge","url":"https://www.academia.edu/Documents/in/Sociology_of_Knowledge?f_ri=152051","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="50361" href="https://www.academia.edu/Documents/in/Sociologie">Sociologie</a>, <script data-card-contents-for-ri="50361" type="text/json">{"id":50361,"name":"Sociologie","url":"https://www.academia.edu/Documents/in/Sociologie?f_ri=152051","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="50471" href="https://www.academia.edu/Documents/in/Didactique_Du_Francais">Didactique Du Français</a><script data-card-contents-for-ri="50471" type="text/json">{"id":50471,"name":"Didactique Du Français","url":"https://www.academia.edu/Documents/in/Didactique_Du_Francais?f_ri=152051","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=9212236]'), work: {"id":9212236,"title":"Ph. Losego (éd.), 2014. Actes du colloque « Sociologie et didactiques : vers une transgression des frontières », 13 et 14 septembre 2012, Lausanne : Haute Ecole Pédagogique de Vaud. http://www.hepl.ch/sociodidac/actes/","created_at":"2014-11-09T17:22:11.162-08:00","url":"https://www.academia.edu/9212236/Ph_Losego_%C3%A9d_2014_Actes_du_colloque_Sociologie_et_didactiques_vers_une_transgression_des_fronti%C3%A8res_13_et_14_septembre_2012_Lausanne_Haute_Ecole_P%C3%A9dagogique_de_Vaud_http_www_hepl_ch_sociodidac_actes_?f_ri=152051","dom_id":"work_9212236","summary":"Les sociologues et les didacticiens ont un terrain de rencontre, celui de la\r\nconstruction et de la transmission des savoirs scolaires. Ainsi, de nombreux\r\nconcepts didactiques ont une dimension sociale, à commencer par celui\r\nde « transposition didactique ». Cependant, sur la longue période, les\r\ndeux communautés se sont largement ignorées, en vertu d’une division\r\ndu travail intellectuel. Placées au coeur de la transmission des savoirs,\r\nles didactiques se sont essentiellement préoccupées des dimensions\r\ncognitives et ont pu tendre parfois à une certaine normativité. En revanche,\r\nla sociologie a longtemps traité l’école comme une sorte de boîte noire.\r\nElle a négligé les processus d’apprentissage ce qui explique en grande\r\npartie son relativisme. Mais depuis le début des années 2000, la sociologie\r\nde l’éducation réinvestit fortement l’étude des savoirs scolaires : sa\r\nparticipation plus grande à la formation des enseignants l’a physiquement\r\nrapprochée des contenus d’enseignement. Les autorités politiques ont\r\nété conduites, par la « culture de l’évaluation » et notamment par les\r\ngrandes évaluations internationales (PISA, TIMMS, etc.), à réformer les\r\nplans d’études et à ériger ainsi la question des contenus d’enseignement\r\nen débat de société. Par ailleurs, les didactiques intègrent de plus en\r\nplus le social dans leurs différents modèles. 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Actes du Colloque de GDM 2016.</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest">La diversité des mathématiques : dimensions sociopolitiques, culturelles et historiques de la discipline en classe. 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Actes du Colloque du GDM 1999.</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/21830144" 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="9746dd9b7c95b79fee181f5ec6001d02" rel="nofollow" data-download="{"attachment_id":42580388,"asset_id":21830144,"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/42580388/download_file?st=MTczMzAxOTg4Nyw4LjIyMi4yMDguMTQ2&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="35749199" href="https://independent.academia.edu/GDMQu%C3%A9bec">GDM Québec</a><script data-card-contents-for-user="35749199" type="text/json">{"id":35749199,"first_name":"GDM","last_name":"Québec","domain_name":"independent","page_name":"GDMQuébec","display_name":"GDM Québec","profile_url":"https://independent.academia.edu/GDMQu%C3%A9bec?f_ri=152051","photo":"https://0.academia-photos.com/35749199/10351477/11551354/s65_gdm.qu_bec.jpg"}</script></span></span></li><li class="js-paper-rank-work_21830144 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="21830144"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 21830144, container: ".js-paper-rank-work_21830144", }); 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Après quelques préliminaires, nous expliciterons ce que signifie observation de classe et prise d'informations sur le système-classe. Puis nous montrerons comment la modélisation rendue nécessaire par la multiplicité des variables et la complexité de leurs modes d'action dépend du cadre théorique dans lequel se place le chercheur et donc des outils qu'il met en oeuvre pour ses analyses ainsi que des dispositifs d'observation dont il dispose. L'observation de classe ne s'effectue pas dans un contexte isolé, elle s'inclut dans une problématique de recherche. Nous détaillerons ensuite les moments clefs de l'observation ainsi que les précautions qui doivent les accompagner. Nous illustrerons nos propos par la présentation de deux études de cas. MOTS CLES : didactique des mathématiques, problématique de recherche, observation de classe, modélisation, enseignant. PRELIMINAIRES L'année 2016 est une année importante pour l'avancée de la recherche en Didactique Des Mathématiques (DDM) au Brésil puisque nous sommes réunis au premier symposium LADIMA de recherche en DDM qui vient couronner, après des années où étaient seulement reconnues ici les sciences de l'éducation et en leur sein, l'éducation mathématique, la création officielle par la Société Brésilienne d'Education Mathématique du Groupe de Travail de DDM. Cette année est aussi une année importante pour la CFEM sur le plan international. C'est en effet en juillet 2016 que s'est déroulé à Hambourg, le treizième congrès ICME, le plus grand événement international concernant l'enseignement des mathématiques, au cours duquel a eu lieu la présentation et comparaison de quatre grandes traditions didactiques d'Europe continentale, celles de l'Allemagne, de la France, de l'Italie et des Pays-Bas. Pour ce qui est de la tradition française, un groupe s'est constitué au sein de la CFEM et a réalisé une publication consacrée aux collaborations avec les pays du Sud, Afrique, Amérique latine, Asie. Dix équipes travaillant dans ces pays (dont T. M. Mendonça Campos & J. Trgalová pour le Brésil) ont réalisé un document qui reflète cette tradition dans la diversité de ses facettes, montre où elle puise ses sources et ce qui l'a façonnée et comment la</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/42853773" 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="5541cffcb59e5a9fbc234133b7bec5a0" rel="nofollow" data-download="{"attachment_id":63090994,"asset_id":42853773,"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/63090994/download_file?st=MTczMzAxOTg4Nyw4LjIyMi4yMDguMTQ2&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="157177184" href="https://independent.academia.edu/ClaudeComiti">Claude Comiti</a><script data-card-contents-for-user="157177184" type="text/json">{"id":157177184,"first_name":"Claude","last_name":"Comiti","domain_name":"independent","page_name":"ClaudeComiti","display_name":"Claude Comiti","profile_url":"https://independent.academia.edu/ClaudeComiti?f_ri=152051","photo":"/images/s65_no_pic.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-42853773">+1</span><div class="hidden js-additional-users-42853773"><div><span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a href="https://independent.academia.edu/LSANTOSFARIAS">Luiz Marcio SANTOS FARIAS</a></span></div></div></span><script>(function(){ var popoverSettings = { el: $('.js-work-more-authors-42853773'), placement: 'bottom', hide_delay: 200, html: true, content: function(){ return $('.js-additional-users-42853773').html(); 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container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_42853773 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="42853773"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 42853773; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=42853773]").text(description); $(".js-view-count-work_42853773").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_42853773").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="42853773"><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="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=152051","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="200348" href="https://www.academia.edu/Documents/in/Mod%C3%A9lisation">Modélisation</a>, <script data-card-contents-for-ri="200348" type="text/json">{"id":200348,"name":"Modélisation","url":"https://www.academia.edu/Documents/in/Mod%C3%A9lisation?f_ri=152051","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="3633738" href="https://www.academia.edu/Documents/in/enseignant">enseignant</a><script data-card-contents-for-ri="3633738" type="text/json">{"id":3633738,"name":"enseignant","url":"https://www.academia.edu/Documents/in/enseignant?f_ri=152051","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=42853773]'), work: {"id":42853773,"title":"IMPORTANCE ET MÉTHODOLOGIE DE L'OBSERVATION DE CLASSE POUR LES RECHERCHES EN DIDACTIQUE ET RÔLE DE LA PROBLÉMATIQUE DE RECHERCHE POUR LA MODÉLISATION NÉCESSAIRE LORS DE L'ANALYSE DES OBSERVATIONS","created_at":"2020-04-25T15:24:31.077-07:00","url":"https://www.academia.edu/42853773/IMPORTANCE_ET_M%C3%89THODOLOGIE_DE_LOBSERVATION_DE_CLASSE_POUR_LES_RECHERCHES_EN_DIDACTIQUE_ET_R%C3%94LE_DE_LA_PROBL%C3%89MATIQUE_DE_RECHERCHE_POUR_LA_MOD%C3%89LISATION_N%C3%89CESSAIRE_LORS_DE_LANALYSE_DES_OBSERVATIONS?f_ri=152051","dom_id":"work_42853773","summary":"RESUME On ne peut se contenter, pour certaines problématiques de recherche, d'interviews d'enseignants ou de travaux ou questionnaires d'élèves ou encore d'observations cliniques : par exemple, si l'on s'intéresse aux interactions, à propos d'un savoir, entre les acteurs du système enseigné, à un moment donné, et en particulier à la modélisation du rôle de l'enseignant. Après quelques préliminaires, nous expliciterons ce que signifie observation de classe et prise d'informations sur le système-classe. Puis nous montrerons comment la modélisation rendue nécessaire par la multiplicité des variables et la complexité de leurs modes d'action dépend du cadre théorique dans lequel se place le chercheur et donc des outils qu'il met en oeuvre pour ses analyses ainsi que des dispositifs d'observation dont il dispose. L'observation de classe ne s'effectue pas dans un contexte isolé, elle s'inclut dans une problématique de recherche. Nous détaillerons ensuite les moments clefs de l'observation ainsi que les précautions qui doivent les accompagner. Nous illustrerons nos propos par la présentation de deux études de cas. MOTS CLES : didactique des mathématiques, problématique de recherche, observation de classe, modélisation, enseignant. PRELIMINAIRES L'année 2016 est une année importante pour l'avancée de la recherche en Didactique Des Mathématiques (DDM) au Brésil puisque nous sommes réunis au premier symposium LADIMA de recherche en DDM qui vient couronner, après des années où étaient seulement reconnues ici les sciences de l'éducation et en leur sein, l'éducation mathématique, la création officielle par la Société Brésilienne d'Education Mathématique du Groupe de Travail de DDM. Cette année est aussi une année importante pour la CFEM sur le plan international. C'est en effet en juillet 2016 que s'est déroulé à Hambourg, le treizième congrès ICME, le plus grand événement international concernant l'enseignement des mathématiques, au cours duquel a eu lieu la présentation et comparaison de quatre grandes traditions didactiques d'Europe continentale, celles de l'Allemagne, de la France, de l'Italie et des Pays-Bas. Pour ce qui est de la tradition française, un groupe s'est constitué au sein de la CFEM et a réalisé une publication consacrée aux collaborations avec les pays du Sud, Afrique, Amérique latine, Asie. Dix équipes travaillant dans ces pays (dont T. M. Mendonça Campos \u0026 J. Trgalová pour le Brésil) ont réalisé un document qui reflète cette tradition dans la diversité de ses facettes, montre où elle puise ses sources et ce qui l'a façonnée et comment la","downloadable_attachments":[{"id":63090994,"asset_id":42853773,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":157177184,"first_name":"Claude","last_name":"Comiti","domain_name":"independent","page_name":"ClaudeComiti","display_name":"Claude Comiti","profile_url":"https://independent.academia.edu/ClaudeComiti?f_ri=152051","photo":"/images/s65_no_pic.png"},{"id":65911262,"first_name":"Luiz Marcio","last_name":"SANTOS FARIAS","domain_name":"independent","page_name":"LSANTOSFARIAS","display_name":"Luiz Marcio SANTOS FARIAS","profile_url":"https://independent.academia.edu/LSANTOSFARIAS?f_ri=152051","photo":"https://0.academia-photos.com/65911262/25620571/24325591/s65_luiz_marcio.santos_farias.jpg"}],"research_interests":[{"id":152051,"name":"Didactique des mathématiques","url":"https://www.academia.edu/Documents/in/Didactique_des_mathematiques?f_ri=152051","nofollow":false},{"id":200348,"name":"Modélisation","url":"https://www.academia.edu/Documents/in/Mod%C3%A9lisation?f_ri=152051","nofollow":false},{"id":3633738,"name":"enseignant","url":"https://www.academia.edu/Documents/in/enseignant?f_ri=152051","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_38106544" data-work_id="38106544" 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/38106544/Interactions_et_films_de_classe_pour_r%C3%A9fl%C3%A9chir_la_formation_%C3%A0_l_enseignement_des_Math%C3%A9matiques_en_Fran%C3%A7ais_langue_seconde_D%C3%A9crire_pour_mieux_former_">Interactions et films de classe pour réfléchir la formation à l’enseignement des Mathématiques en Français langue seconde. Décrire pour mieux former ?</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">Le mouvement de professionnalisation du corps enseignant engagé ces dernières décennies conduit à s’intéresser aux agir professoraux pour cerner « non seulement la multidimensionnalité de la pratique enseignante mais aussi la dialectique... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_38106544" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">Le mouvement de professionnalisation du corps enseignant engagé ces dernières décennies conduit à s’intéresser aux agir professoraux pour cerner « non seulement la multidimensionnalité de la pratique enseignante mais aussi la dialectique à l’œuvre entre les processus d’enseignement-apprentissage en situation et l’expérience du professionnel » (Vinatier & Altet, 2008: 10). Dans une perspective de formation (initiale et continue) à l’enseignement, l’un des enjeux est de décrire du mieux possible l’ensemble des modalités et enjeux de la relation enseignement-apprentissage (Numa-Bocage, 2007) pour mettre en exergue les « manières de faire et procédés pour faire » (Vinatier & Altet, 2008 : 10). Dans un contexte d’éducation bilingue, comme dans les programmes d’immersion au Canada, il s’agit également d’étudier les modalités d’intégration des contenus linguistiques et disciplinaires pour dégager les implications que ces dernières peuvent engendrer pour la formation 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/38106544" 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="f4f71b26a18b69add4aa12cf5607c2da" rel="nofollow" data-download="{"attachment_id":58135381,"asset_id":38106544,"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/58135381/download_file?st=MTczMzAxOTg4Nyw4LjIyMi4yMDguMTQ2&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="9366706" href="https://sfu.academia.edu/Dani%C3%A8leMOORE">Danièle MOORE</a><script data-card-contents-for-user="9366706" type="text/json">{"id":9366706,"first_name":"Danièle","last_name":"MOORE","domain_name":"sfu","page_name":"DanièleMOORE","display_name":"Danièle MOORE","profile_url":"https://sfu.academia.edu/Dani%C3%A8leMOORE?f_ri=152051","photo":"https://0.academia-photos.com/9366706/3037035/7889852/s65_dani_le.moore.png"}</script></span></span></li><li class="js-paper-rank-work_38106544 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="38106544"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 38106544, container: ".js-paper-rank-work_38106544", }); });</script></li><li class="js-percentile-work_38106544 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 = 38106544; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_38106544"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_38106544 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="38106544"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 38106544; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=38106544]").text(description); $(".js-view-count-work_38106544").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_38106544").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="38106544"><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="11492" href="https://www.academia.edu/Documents/in/Ethnography_Research_Methodology_">Ethnography (Research Methodology)</a>, <script data-card-contents-for-ri="11492" type="text/json">{"id":11492,"name":"Ethnography (Research Methodology)","url":"https://www.academia.edu/Documents/in/Ethnography_Research_Methodology_?f_ri=152051","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="66444" href="https://www.academia.edu/Documents/in/Didactique_des_langues">Didactique des langues</a>, <script data-card-contents-for-ri="66444" type="text/json">{"id":66444,"name":"Didactique des langues","url":"https://www.academia.edu/Documents/in/Didactique_des_langues?f_ri=152051","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=152051","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="157576" href="https://www.academia.edu/Documents/in/Formation_initiale_des_enseignants">Formation initiale des enseignants</a><script data-card-contents-for-ri="157576" type="text/json">{"id":157576,"name":"Formation initiale des enseignants","url":"https://www.academia.edu/Documents/in/Formation_initiale_des_enseignants?f_ri=152051","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=38106544]'), work: {"id":38106544,"title":"Interactions et films de classe pour réfléchir la formation à l’enseignement des Mathématiques en Français langue seconde. Décrire pour mieux former ?","created_at":"2019-01-07T16:36:57.250-08:00","url":"https://www.academia.edu/38106544/Interactions_et_films_de_classe_pour_r%C3%A9fl%C3%A9chir_la_formation_%C3%A0_l_enseignement_des_Math%C3%A9matiques_en_Fran%C3%A7ais_langue_seconde_D%C3%A9crire_pour_mieux_former_?f_ri=152051","dom_id":"work_38106544","summary":"Le mouvement de professionnalisation du corps enseignant engagé ces dernières décennies conduit à s’intéresser aux agir professoraux pour cerner « non seulement la multidimensionnalité de la pratique enseignante mais aussi la dialectique à l’œuvre entre les processus d’enseignement-apprentissage en situation et l’expérience du professionnel » (Vinatier \u0026 Altet, 2008: 10). Dans une perspective de formation (initiale et continue) à l’enseignement, l’un des enjeux est de décrire du mieux possible l’ensemble des modalités et enjeux de la relation enseignement-apprentissage (Numa-Bocage, 2007) pour mettre en exergue les « manières de faire et procédés pour faire » (Vinatier \u0026 Altet, 2008 : 10). Dans un contexte d’éducation bilingue, comme dans les programmes d’immersion au Canada, il s’agit également d’étudier les modalités d’intégration des contenus linguistiques et disciplinaires pour dégager les implications que ces dernières peuvent engendrer pour la formation des enseignants.","downloadable_attachments":[{"id":58135381,"asset_id":38106544,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":9366706,"first_name":"Danièle","last_name":"MOORE","domain_name":"sfu","page_name":"DanièleMOORE","display_name":"Danièle MOORE","profile_url":"https://sfu.academia.edu/Dani%C3%A8leMOORE?f_ri=152051","photo":"https://0.academia-photos.com/9366706/3037035/7889852/s65_dani_le.moore.png"}],"research_interests":[{"id":11492,"name":"Ethnography (Research Methodology)","url":"https://www.academia.edu/Documents/in/Ethnography_Research_Methodology_?f_ri=152051","nofollow":false},{"id":66444,"name":"Didactique des langues","url":"https://www.academia.edu/Documents/in/Didactique_des_langues?f_ri=152051","nofollow":false},{"id":152051,"name":"Didactique des mathématiques","url":"https://www.academia.edu/Documents/in/Didactique_des_mathematiques?f_ri=152051","nofollow":false},{"id":157576,"name":"Formation initiale des enseignants","url":"https://www.academia.edu/Documents/in/Formation_initiale_des_enseignants?f_ri=152051","nofollow":false},{"id":166148,"name":"Didactique du français langue étrangère","url":"https://www.academia.edu/Documents/in/Didactique_du_francais_langue_etrangere?f_ri=152051"},{"id":625192,"name":"Formation Continue Des Enseignants","url":"https://www.academia.edu/Documents/in/Formation_Continue_Des_Enseignants?f_ri=152051"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_33843737" data-work_id="33843737" 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/33843737/Comprendre_le_travail_des_professeurs_avec_les_ressources_de_leur_enseignement_un_questionnement_didactique_et_informatique">Comprendre le travail des professeurs avec les ressources de leur enseignement, un questionnement didactique et informatique</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 conférence est le résultat d'un travail conjoint entre Franck Bellemain et Luc Trouche, qui prend sa source dans une collaboration ancienne, mobilisant les équipes Edumatec au Brésil et EducTice en France. Un temps fort a été l'Ecole... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_33843737" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">La conférence est le résultat d'un travail conjoint entre Franck Bellemain et Luc Trouche, qui prend sa source dans une collaboration ancienne, mobilisant les équipes Edumatec au Brésil et EducTice en France. Un temps fort a été l'Ecole des hautes études de la CAPES qui s'est tenue en février et mars 2015 à Recife (Trouche 2015). Cette école a depuis donné matière à de nouvelles ressources (Assis & Lucena, 2015 ; Lucena & Assis, 2015 ; Baltar, 2016). La première partie de la conférence (sections 1, 2 et 3) a été présentée par Luc Trouche et Katiane Rocha ; la deuxième partie de la conférence, en l'absence de Franck Bellemain, empêché, a été coordonnée par Verônica Gitirana, et a fait intervenir Cibelle Assis, Ricardo Tibúrcio, Rogério Ignácio et Rosilângela Lucena. Nous tenons à remercier vivement les personnes qui ont contribué à la traduction, à l'oral et à l'écrit, du français au portugais, Cibelle Assis, Paula Baltar, Paulo Faria et Rosilângela Lucena.</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/33843737" 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="4d158f5d5e18a5004489efcf8e864d80" rel="nofollow" data-download="{"attachment_id":53825244,"asset_id":33843737,"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/53825244/download_file?st=MTczMzAxOTg4Nyw4LjIyMi4yMDguMTQ2&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="486697" href="https://ens-lyon.academia.edu/LucTrouche">Luc Trouche</a><script data-card-contents-for-user="486697" type="text/json">{"id":486697,"first_name":"Luc","last_name":"Trouche","domain_name":"ens-lyon","page_name":"LucTrouche","display_name":"Luc Trouche","profile_url":"https://ens-lyon.academia.edu/LucTrouche?f_ri=152051","photo":"https://0.academia-photos.com/486697/165503/17898170/s65_luc.trouche.png"}</script></span></span></li><li class="js-paper-rank-work_33843737 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="33843737"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 33843737, container: ".js-paper-rank-work_33843737", }); });</script></li><li class="js-percentile-work_33843737 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 = 33843737; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_33843737"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_33843737 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="33843737"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 33843737; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=33843737]").text(description); $(".js-view-count-work_33843737").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_33843737").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="33843737"><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="16957" href="https://www.academia.edu/Documents/in/EIAH">EIAH</a>, <script data-card-contents-for-ri="16957" type="text/json">{"id":16957,"name":"EIAH","url":"https://www.academia.edu/Documents/in/EIAH?f_ri=152051","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=152051","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="625192" href="https://www.academia.edu/Documents/in/Formation_Continue_Des_Enseignants">Formation Continue Des Enseignants</a>, <script data-card-contents-for-ri="625192" type="text/json">{"id":625192,"name":"Formation Continue Des Enseignants","url":"https://www.academia.edu/Documents/in/Formation_Continue_Des_Enseignants?f_ri=152051","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="2553199" href="https://www.academia.edu/Documents/in/approche_documentaire_du_didactique">approche documentaire du didactique</a><script data-card-contents-for-ri="2553199" type="text/json">{"id":2553199,"name":"approche documentaire du didactique","url":"https://www.academia.edu/Documents/in/approche_documentaire_du_didactique?f_ri=152051","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=33843737]'), work: {"id":33843737,"title":"Comprendre le travail des professeurs avec les ressources de leur enseignement, un questionnement didactique et informatique","created_at":"2017-07-11T02:46:52.398-07:00","url":"https://www.academia.edu/33843737/Comprendre_le_travail_des_professeurs_avec_les_ressources_de_leur_enseignement_un_questionnement_didactique_et_informatique?f_ri=152051","dom_id":"work_33843737","summary":"La conférence est le résultat d'un travail conjoint entre Franck Bellemain et Luc Trouche, qui prend sa source dans une collaboration ancienne, mobilisant les équipes Edumatec au Brésil et EducTice en France. Un temps fort a été l'Ecole des hautes études de la CAPES qui s'est tenue en février et mars 2015 à Recife (Trouche 2015). Cette école a depuis donné matière à de nouvelles ressources (Assis \u0026 Lucena, 2015 ; Lucena \u0026 Assis, 2015 ; Baltar, 2016). La première partie de la conférence (sections 1, 2 et 3) a été présentée par Luc Trouche et Katiane Rocha ; la deuxième partie de la conférence, en l'absence de Franck Bellemain, empêché, a été coordonnée par Verônica Gitirana, et a fait intervenir Cibelle Assis, Ricardo Tibúrcio, Rogério Ignácio et Rosilângela Lucena. Nous tenons à remercier vivement les personnes qui ont contribué à la traduction, à l'oral et à l'écrit, du français au portugais, Cibelle Assis, Paula Baltar, Paulo Faria et Rosilângela Lucena.","downloadable_attachments":[{"id":53825244,"asset_id":33843737,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":486697,"first_name":"Luc","last_name":"Trouche","domain_name":"ens-lyon","page_name":"LucTrouche","display_name":"Luc Trouche","profile_url":"https://ens-lyon.academia.edu/LucTrouche?f_ri=152051","photo":"https://0.academia-photos.com/486697/165503/17898170/s65_luc.trouche.png"}],"research_interests":[{"id":16957,"name":"EIAH","url":"https://www.academia.edu/Documents/in/EIAH?f_ri=152051","nofollow":false},{"id":152051,"name":"Didactique des mathématiques","url":"https://www.academia.edu/Documents/in/Didactique_des_mathematiques?f_ri=152051","nofollow":false},{"id":625192,"name":"Formation Continue Des Enseignants","url":"https://www.academia.edu/Documents/in/Formation_Continue_Des_Enseignants?f_ri=152051","nofollow":false},{"id":2553199,"name":"approche documentaire du didactique","url":"https://www.academia.edu/Documents/in/approche_documentaire_du_didactique?f_ri=152051","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_9841408" data-work_id="9841408" 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/9841408/Les_erreurs_langagi%C3%A8res_en_math%C3%A9matiques">Les erreurs langagières en mathématiques</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">Dans cet article, nous faisons ressortir l'importance de maîtriser les langages symbolique, graphique et naturel pour réussir en mathématiques. Nous montrons, entre autres, que des erreurs de syntaxe en langage naturel (en l'occurrence,... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_9841408" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">Dans cet article, nous faisons ressortir l'importance de maîtriser les langages symbolique, graphique et naturel pour réussir en mathématiques. Nous montrons, entre autres, que des erreurs de syntaxe en langage naturel (en l'occurrence, en français) entraînent fréquemment des erreurs en mathématiques. Autrement dit, la syntaxe n'a pas sa place que dans les cours de français. <br /> <br />Pour un développement de cette approche didactique, on peut consulter : Intervenir sur les langages en mathématiques et en sciences, Montréal, Modulo, 2003 (Prix spécial du ministre de l'Éducation du Québec 2003-2004). <br /> <br />De plus, c'est à la lumière de cette approche didactique qu'a été rédigé le manuel "Calcul différentiel", Modulo, 2010.</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/9841408" 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="ae08b2f342e2590a4740dff15365930e" rel="nofollow" data-download="{"attachment_id":36007126,"asset_id":9841408,"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/36007126/download_file?st=MTczMzAxOTg4Nyw4LjIyMi4yMDguMTQ2&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="2552276" href="https://umontreal.academia.edu/MarcoB%C3%A9langer">Marco Bélanger</a><script data-card-contents-for-user="2552276" type="text/json">{"id":2552276,"first_name":"Marco","last_name":"Bélanger","domain_name":"umontreal","page_name":"MarcoBélanger","display_name":"Marco Bélanger","profile_url":"https://umontreal.academia.edu/MarcoB%C3%A9langer?f_ri=152051","photo":"https://0.academia-photos.com/2552276/6436821/7280652/s65_marco.b_langer.jpg"}</script></span></span></li><li class="js-paper-rank-work_9841408 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="9841408"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 9841408, container: ".js-paper-rank-work_9841408", }); 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$(".js-view-count[data-work-id=9841408]").text(description); $(".js-view-count-work_9841408").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_9841408").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="9841408"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">9</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><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=152051","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=152051","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="120084" href="https://www.academia.edu/Documents/in/Sciences_de_l%C3%A9ducation">Sciences de l'éducation</a>, <script data-card-contents-for-ri="120084" type="text/json">{"id":120084,"name":"Sciences de l'éducation","url":"https://www.academia.edu/Documents/in/Sciences_de_l%C3%A9ducation?f_ri=152051","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=152051","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=9841408]'), work: {"id":9841408,"title":"Les erreurs langagières en mathématiques","created_at":"2014-12-19T10:46:46.978-08:00","url":"https://www.academia.edu/9841408/Les_erreurs_langagi%C3%A8res_en_math%C3%A9matiques?f_ri=152051","dom_id":"work_9841408","summary":"Dans cet article, nous faisons ressortir l'importance de maîtriser les langages symbolique, graphique et naturel pour réussir en mathématiques. Nous montrons, entre autres, que des erreurs de syntaxe en langage naturel (en l'occurrence, en français) entraînent fréquemment des erreurs en mathématiques. Autrement dit, la syntaxe n'a pas sa place que dans les cours de français. \r\n\r\nPour un développement de cette approche didactique, on peut consulter : Intervenir sur les langages en mathématiques et en sciences, Montréal, Modulo, 2003 (Prix spécial du ministre de l'Éducation du Québec 2003-2004).\r\n\r\nDe plus, c'est à la lumière de cette approche didactique qu'a été rédigé le manuel \"Calcul différentiel\", Modulo, 2010.","downloadable_attachments":[{"id":36007126,"asset_id":9841408,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":2552276,"first_name":"Marco","last_name":"Bélanger","domain_name":"umontreal","page_name":"MarcoBélanger","display_name":"Marco Bélanger","profile_url":"https://umontreal.academia.edu/MarcoB%C3%A9langer?f_ri=152051","photo":"https://0.academia-photos.com/2552276/6436821/7280652/s65_marco.b_langer.jpg"}],"research_interests":[{"id":922,"name":"Education","url":"https://www.academia.edu/Documents/in/Education?f_ri=152051","nofollow":false},{"id":2731,"name":"Mathematics Education","url":"https://www.academia.edu/Documents/in/Mathematics_Education?f_ri=152051","nofollow":false},{"id":120084,"name":"Sciences de l'éducation","url":"https://www.academia.edu/Documents/in/Sciences_de_l%C3%A9ducation?f_ri=152051","nofollow":false},{"id":152051,"name":"Didactique des mathématiques","url":"https://www.academia.edu/Documents/in/Didactique_des_mathematiques?f_ri=152051","nofollow":false},{"id":211072,"name":"Pedagogie","url":"https://www.academia.edu/Documents/in/Pedagogie?f_ri=152051"},{"id":402510,"name":"Didactique des mathématiques, Mathematical Knowledge for Teaching, Mathematics Teacher Education","url":"https://www.academia.edu/Documents/in/Didactique_des_mathematiques_Mathematical_Knowledge_for_Teaching_Mathematics_Teacher_Education?f_ri=152051"},{"id":1172776,"name":"Enseignement Des Mathématiques","url":"https://www.academia.edu/Documents/in/Enseignement_Des_Mathematiques?f_ri=152051"},{"id":1488920,"name":"Introduction à la didactique des sciences et des mathématiques","url":"https://www.academia.edu/Documents/in/Introduction_a_la_didactique_des_sciences_et_des_mathematiques?f_ri=152051"},{"id":1727220,"name":"Difficultés d’apprentissage","url":"https://www.academia.edu/Documents/in/Difficult%C3%A9s_d_apprentissage?f_ri=152051"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_32368669" data-work_id="32368669" 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/32368669/Une_%C3%A9tude_de_la_transposition_didactique_du_concept_did%C3%A9al">Une étude de la transposition didactique du concept d'idéal</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">Les difficultés des étudiants en algèbre et surtout en algèbre structuraliste sont bien connues des enseignants. Nous nous sommes intéressée dans notre mémoire au concept d’idéal qui est central en algèbre structuraliste et qui est... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_32368669" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">Les difficultés des étudiants en algèbre et surtout en algèbre structuraliste sont bien connues<br />des enseignants. Nous nous sommes intéressée dans notre mémoire au concept d’idéal qui est<br />central en algèbre structuraliste et qui est enseigné dès la licence. Nous avons conduit une étude<br />épistémologique mettant en lumière le fait que ce concept est le fruit d’une longue évolution<br />qui n’apparaît sous sa forme actuelle qu’au XXème siècle. Cette étude nous a permis également<br />de confirmer le caractère formalisateur, unificateur et généralisateur de ce concept, ce qui induit<br />des contraintes sur les situations que l’on peut mettre en oeuvre pour son apprentissage, et plus<br />généralement sur le processus de transposition didactique. La deuxième partie de notre mémoire<br />est consacrée à l’étude de la transposition didactique du concept d’idéal telle qu’elle se dégage<br />de l’étude écologique de plusieurs manuels. Nous étudions en particulier les choix, qu’ils soient<br />écologiques, en rapport au contenu méta ou à la dialectique outil-objet, faits par les auteurs selon<br />les institutions de destination (Classes préparatoires aux grandes écoles, Licence, Master).</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/32368669" 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="5d42d70079dda83328b42f6c0348308a" rel="nofollow" data-download="{"attachment_id":52573120,"asset_id":32368669,"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/52573120/download_file?st=MTczMzAxOTg4Nyw4LjIyMi4yMDguMTQ2&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="62829684" href="https://hepvs.academia.edu/JulieJovignotCandy">Julie Jovignot</a><script data-card-contents-for-user="62829684" type="text/json">{"id":62829684,"first_name":"Julie","last_name":"Jovignot","domain_name":"hepvs","page_name":"JulieJovignotCandy","display_name":"Julie Jovignot","profile_url":"https://hepvs.academia.edu/JulieJovignotCandy?f_ri=152051","photo":"https://0.academia-photos.com/62829684/16302739/18307376/s65_julie.jovignot-candy.jpg"}</script></span></span></li><li class="js-paper-rank-work_32368669 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="32368669"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 32368669, container: ".js-paper-rank-work_32368669", }); 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$(".js-view-count[data-work-id=32368669]").text(description); $(".js-view-count-work_32368669").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_32368669").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="32368669"><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="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=152051","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="41130" href="https://www.academia.edu/Documents/in/Didactics_of_Mathematics">Didactics of Mathematics</a>, <script data-card-contents-for-ri="41130" type="text/json">{"id":41130,"name":"Didactics of Mathematics","url":"https://www.academia.edu/Documents/in/Didactics_of_Mathematics?f_ri=152051","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=152051","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="265943" href="https://www.academia.edu/Documents/in/Philosophie_Epistemologie_et_Histoire_Des_Sciences">Philosophie, Epistémologie et Histoire Des Sciences</a><script data-card-contents-for-ri="265943" type="text/json">{"id":265943,"name":"Philosophie, Epistémologie et Histoire Des Sciences","url":"https://www.academia.edu/Documents/in/Philosophie_Epistemologie_et_Histoire_Des_Sciences?f_ri=152051","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=32368669]'), work: {"id":32368669,"title":"Une étude de la transposition didactique du concept d'idéal","created_at":"2017-04-10T13:04:12.537-07:00","url":"https://www.academia.edu/32368669/Une_%C3%A9tude_de_la_transposition_didactique_du_concept_did%C3%A9al?f_ri=152051","dom_id":"work_32368669","summary":"Les difficultés des étudiants en algèbre et surtout en algèbre structuraliste sont bien connues\ndes enseignants. Nous nous sommes intéressée dans notre mémoire au concept d’idéal qui est\ncentral en algèbre structuraliste et qui est enseigné dès la licence. Nous avons conduit une étude\népistémologique mettant en lumière le fait que ce concept est le fruit d’une longue évolution\nqui n’apparaît sous sa forme actuelle qu’au XXème siècle. Cette étude nous a permis également\nde confirmer le caractère formalisateur, unificateur et généralisateur de ce concept, ce qui induit\ndes contraintes sur les situations que l’on peut mettre en oeuvre pour son apprentissage, et plus\ngénéralement sur le processus de transposition didactique. La deuxième partie de notre mémoire\nest consacrée à l’étude de la transposition didactique du concept d’idéal telle qu’elle se dégage\nde l’étude écologique de plusieurs manuels. Nous étudions en particulier les choix, qu’ils soient\nécologiques, en rapport au contenu méta ou à la dialectique outil-objet, faits par les auteurs selon\nles institutions de destination (Classes préparatoires aux grandes écoles, Licence, Master).","downloadable_attachments":[{"id":52573120,"asset_id":32368669,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":62829684,"first_name":"Julie","last_name":"Jovignot","domain_name":"hepvs","page_name":"JulieJovignotCandy","display_name":"Julie Jovignot","profile_url":"https://hepvs.academia.edu/JulieJovignotCandy?f_ri=152051","photo":"https://0.academia-photos.com/62829684/16302739/18307376/s65_julie.jovignot-candy.jpg"}],"research_interests":[{"id":815,"name":"Epistemology","url":"https://www.academia.edu/Documents/in/Epistemology?f_ri=152051","nofollow":false},{"id":41130,"name":"Didactics of Mathematics","url":"https://www.academia.edu/Documents/in/Didactics_of_Mathematics?f_ri=152051","nofollow":false},{"id":152051,"name":"Didactique des mathématiques","url":"https://www.academia.edu/Documents/in/Didactique_des_mathematiques?f_ri=152051","nofollow":false},{"id":265943,"name":"Philosophie, Epistémologie et Histoire Des Sciences","url":"https://www.academia.edu/Documents/in/Philosophie_Epistemologie_et_Histoire_Des_Sciences?f_ri=152051","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_11371593" data-work_id="11371593" 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/11371593/Inscription_du_r%C3%A9cit_dans_le_milieu_en_r%C3%A9solution_de_probl%C3%A8mes_de_math%C3%A9matiques_%C3%89tudes_des_contraintes_didactiques_des_apports_et_des_limites_dans_la_construction_de_raisonnement">Inscription du récit dans le milieu en résolution de problèmes de mathématiques : Études des contraintes didactiques, des apports et des limites dans la construction de raisonnement</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">Dans le cadre de notre thèse en didactique des mathématiques, nous explorons la pertinence du récit en tant que mode de pensée et support potentiel à la construction de raisonnement. Nous soutenons l’hypothèse que lors d’une activité de... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_11371593" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">Dans le cadre de notre thèse en didactique des mathématiques, nous explorons la pertinence du récit en tant que mode de pensée et support potentiel à la construction de raisonnement. Nous soutenons l’hypothèse que lors d’une activité de résolution de problèmes de mathématiques, la construction d’un récit visant à répondre à une situation problématique peut être un élément déclencheur, producteur et structurant du raisonnement. En nous appuyant sur différents travaux qui ont souligné les fonctions heuristiques et structurantes du récit, nous avons caractérisé au plan théorique et mis à l’épreuve expérimentalement un milieu didactique permettant d’envisager une co-construction entre récit et raisonnement. <br />La situation de résolution de problèmes que nous proposons, construite autour d’un jeu, amène les élèves à produire des récits descriptifs (basés sur des parties effectivement réalisées) et des récits d’anticipation (basés sur des parties imaginaires). Nos résultats mettent en évidence que le récit enrichit le milieu didactique au sens proposé par Hersant (2010), en particulier au travers de l’acte de construction par les élèves. Celui-ci soutient l’établissement du raisonnement et sa justification mathématique. C’est en produisant différents types de récits que les élèves, tout en prenant en charge les contraintes mathématiques de la situation, s’affranchissent du monde sensible et s’engagent dans une véritable activité de preuve mathématique (production d’exemples, de contre-exemples, de conjectures, d’argumentations, etc.).</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/11371593" 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="fc0ae0a359ef7f65f1f69c39b49bcd13" rel="nofollow" data-download="{"attachment_id":36938554,"asset_id":11371593,"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/36938554/download_file?st=MTczMzAxOTg4Nyw4LjIyMi4yMDguMTQ2&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="27576821" href="https://univ-artois.academia.edu/MarianneMoulin">Marianne Moulin</a><script data-card-contents-for-user="27576821" type="text/json">{"id":27576821,"first_name":"Marianne","last_name":"Moulin","domain_name":"univ-artois","page_name":"MarianneMoulin","display_name":"Marianne Moulin","profile_url":"https://univ-artois.academia.edu/MarianneMoulin?f_ri=152051","photo":"https://0.academia-photos.com/27576821/8348326/28832733/s65_marianne.moulin.jpg"}</script></span></span></li><li class="js-paper-rank-work_11371593 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="11371593"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 11371593, container: ".js-paper-rank-work_11371593", }); 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$(".js-view-count[data-work-id=11371593]").text(description); $(".js-view-count-work_11371593").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_11371593").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="11371593"><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="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=152051","nofollow":false}</script></span></li><script>(function(){ if (false) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=11371593]'), work: {"id":11371593,"title":"Inscription du récit dans le milieu en résolution de problèmes de mathématiques : Études des contraintes didactiques, des apports et des limites dans la construction de raisonnement","created_at":"2015-03-11T06:54:11.569-07:00","url":"https://www.academia.edu/11371593/Inscription_du_r%C3%A9cit_dans_le_milieu_en_r%C3%A9solution_de_probl%C3%A8mes_de_math%C3%A9matiques_%C3%89tudes_des_contraintes_didactiques_des_apports_et_des_limites_dans_la_construction_de_raisonnement?f_ri=152051","dom_id":"work_11371593","summary":"Dans le cadre de notre thèse en didactique des mathématiques, nous explorons la pertinence du récit en tant que mode de pensée et support potentiel à la construction de raisonnement. Nous soutenons l’hypothèse que lors d’une activité de résolution de problèmes de mathématiques, la construction d’un récit visant à répondre à une situation problématique peut être un élément déclencheur, producteur et structurant du raisonnement. En nous appuyant sur différents travaux qui ont souligné les fonctions heuristiques et structurantes du récit, nous avons caractérisé au plan théorique et mis à l’épreuve expérimentalement un milieu didactique permettant d’envisager une co-construction entre récit et raisonnement.\r\nLa situation de résolution de problèmes que nous proposons, construite autour d’un jeu, amène les élèves à produire des récits descriptifs (basés sur des parties effectivement réalisées) et des récits d’anticipation (basés sur des parties imaginaires). Nos résultats mettent en évidence que le récit enrichit le milieu didactique au sens proposé par Hersant (2010), en particulier au travers de l’acte de construction par les élèves. Celui-ci soutient l’établissement du raisonnement et sa justification mathématique. C’est en produisant différents types de récits que les élèves, tout en prenant en charge les contraintes mathématiques de la situation, s’affranchissent du monde sensible et s’engagent dans une véritable activité de preuve mathématique (production d’exemples, de contre-exemples, de conjectures, d’argumentations, etc.).","downloadable_attachments":[{"id":36938554,"asset_id":11371593,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":27576821,"first_name":"Marianne","last_name":"Moulin","domain_name":"univ-artois","page_name":"MarianneMoulin","display_name":"Marianne Moulin","profile_url":"https://univ-artois.academia.edu/MarianneMoulin?f_ri=152051","photo":"https://0.academia-photos.com/27576821/8348326/28832733/s65_marianne.moulin.jpg"}],"research_interests":[{"id":152051,"name":"Didactique des mathématiques","url":"https://www.academia.edu/Documents/in/Didactique_des_mathematiques?f_ri=152051","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_5037912" data-work_id="5037912" 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/5037912/Apprentissage_des_probabilite_s_chez_des_e_le_ves_du_secondaire_dans_une_se_quence_denseignement_base_e_sur_la_simulation_de_jeux_de_hasard_et_dargent_e_mergence_de_conceptions">Apprentissage des probabilités chez des élèves du secondaire dans une séquence d'enseignement basée sur la simulation de jeux de hasard et d'argent : émergence de conceptions</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/5037912" 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="cef3fec5d96041435aef05eb16ef9b5a" rel="nofollow" data-download="{"attachment_id":32267333,"asset_id":5037912,"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/32267333/download_file?st=MTczMzAxOTg4Nyw4LjIyMi4yMDguMTQ2&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="6707800" href="https://uqo.academia.edu/MathieuThibault">Mathieu Thibault</a><script data-card-contents-for-user="6707800" type="text/json">{"id":6707800,"first_name":"Mathieu","last_name":"Thibault","domain_name":"uqo","page_name":"MathieuThibault","display_name":"Mathieu Thibault","profile_url":"https://uqo.academia.edu/MathieuThibault?f_ri=152051","photo":"https://0.academia-photos.com/6707800/2637112/113551721/s65_mathieu.thibault.jpg"}</script></span></span></li><li class="js-paper-rank-work_5037912 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="5037912"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 5037912, container: ".js-paper-rank-work_5037912", }); 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L’apprentissage du 3D à l’école, des situations d’apprentissage a la formation des enseignants, Repère n° 76, Topic éditions</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/6135332" 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="4c3c714c316aeab70a567e421654727b" rel="nofollow" data-download="{"attachment_id":33192258,"asset_id":6135332,"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/33192258/download_file?st=MTczMzAxOTg4Nyw4LjIyMi4yMDguMTQ2&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="3599567" href="https://univ-reims.academia.edu/FabienEmprin">Fabien Emprin</a><script data-card-contents-for-user="3599567" type="text/json">{"id":3599567,"first_name":"Fabien","last_name":"Emprin","domain_name":"univ-reims","page_name":"FabienEmprin","display_name":"Fabien Emprin","profile_url":"https://univ-reims.academia.edu/FabienEmprin?f_ri=152051","photo":"https://0.academia-photos.com/3599567/3015884/15924458/s65_fabien.emprin.jpg"}</script></span></span></li><li class="js-paper-rank-work_6135332 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="6135332"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 6135332, container: ".js-paper-rank-work_6135332", }); });</script></li><li class="js-percentile-work_6135332 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 6135332; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_6135332"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_6135332 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="6135332"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 6135332; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=6135332]").text(description); $(".js-view-count-work_6135332").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_6135332").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="6135332"><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="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=152051","nofollow":false}</script></span></li><script>(function(){ if (false) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=6135332]'), work: {"id":6135332,"title":"Douaire, J. 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Education","url":"https://www.academia.edu/Documents/in/Mathematics_Education?f_ri=152051","nofollow":false},{"id":152051,"name":"Didactique des mathématiques","url":"https://www.academia.edu/Documents/in/Didactique_des_mathematiques?f_ri=152051","nofollow":false},{"id":424159,"name":"Didactic of Mathematics","url":"https://www.academia.edu/Documents/in/Didactic_of_Mathematics?f_ri=152051","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_25053104 coauthored" data-work_id="25053104" 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/25053104/LA_SOUFFRANCE_%C3%80_L%C3%89COLE_LE_CAS_DES_MATH%C3%89MATIQUES_SOUFFRANCE_OU_PLAISIR_ET_LIBERT%C3%89">LA SOUFFRANCE À L'ÉCOLE. LE CAS DES MATHÉMATIQUES : SOUFFRANCE OU PLAISIR ET LIBERTÉ</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">Nous voulons montrer la possibilité de créer des conditions d'apprentissage tenant la souffrance à distance et rendant positive la tonalité des vécus mathématiques. Par choix épistémologique, nous considérons les mathématiques et leur... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_25053104" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">Nous voulons montrer la possibilité de créer des conditions d'apprentissage tenant la souffrance à distance et rendant positive la tonalité des vécus mathématiques. Par choix épistémologique, nous considérons les mathématiques et leur apprentissage tels qu'ils apparaissent au sujet et par là la singularité du sujet apprenant. Les techniques de l'explicitation permettent de mettre en acte ces choix et notre modèle de la conscience fonde la validité scientifique de l'entretien d'explicitation. Du côté des mathématiques, nous reconnaissons la nécessité d'une rupture épistémologique entre pensée du sens commun et pensée scientifique. Pour certains chercheurs, la souffrance résulte de ce que l'école fait entrer de force les élèves dans le mode de pensée scientifique. Cette rupture et le pouvoir de violence symbolique des mathématiques doivent-ils nécessairement engendrer de la souffrance ? Nos recherches nous amènent à tenir une position divergente : la souffrance des élèves est la conséquence du fait qu'ils n'entrent pas dans le monde mathématique. Nous examinerons comment nous pouvons répondre à nos buts : mieux enseigner les mathématiques au plus grand nombre en proposant aux élèves un chemin pour faire l'expérience des mathématiques et y éprouver plaisir et liberté.</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/25053104" 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="7ebce04bacfbef9b0cb1d744f6211f7a" rel="nofollow" data-download="{"attachment_id":45375389,"asset_id":25053104,"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/45375389/download_file?st=MTczMzAxOTg4Nyw4LjIyMi4yMDguMTQ2&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="48275901" href="https://independent.academia.edu/MaurelMaryse">Maryse Maurel</a><script data-card-contents-for-user="48275901" type="text/json">{"id":48275901,"first_name":"Maryse","last_name":"Maurel","domain_name":"independent","page_name":"MaurelMaryse","display_name":"Maryse Maurel","profile_url":"https://independent.academia.edu/MaurelMaryse?f_ri=152051","photo":"https://0.academia-photos.com/48275901/12708869/14135743/s65_maryse.maurel.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-25053104">+1</span><div class="hidden js-additional-users-25053104"><div><span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a href="https://independent.academia.edu/CatherineSackur">Catherine Sackur</a></span></div></div></span><script>(function(){ var popoverSettings = { el: $('.js-work-more-authors-25053104'), placement: 'bottom', hide_delay: 200, html: true, content: function(){ return $('.js-additional-users-25053104').html(); 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Pour certains chercheurs, la souffrance résulte de ce que l'école fait entrer de force les élèves dans le mode de pensée scientifique. Cette rupture et le pouvoir de violence symbolique des mathématiques doivent-ils nécessairement engendrer de la souffrance ? Nos recherches nous amènent à tenir une position divergente : la souffrance des élèves est la conséquence du fait qu'ils n'entrent pas dans le monde mathématique. Nous examinerons comment nous pouvons répondre à nos buts : mieux enseigner les mathématiques au plus grand nombre en proposant aux élèves un chemin pour faire l'expérience des mathématiques et y éprouver plaisir et liberté.","downloadable_attachments":[{"id":45375389,"asset_id":25053104,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":48275901,"first_name":"Maryse","last_name":"Maurel","domain_name":"independent","page_name":"MaurelMaryse","display_name":"Maryse Maurel","profile_url":"https://independent.academia.edu/MaurelMaryse?f_ri=152051","photo":"https://0.academia-photos.com/48275901/12708869/14135743/s65_maryse.maurel.jpg"},{"id":48495923,"first_name":"Catherine","last_name":"Sackur","domain_name":"independent","page_name":"CatherineSackur","display_name":"Catherine Sackur","profile_url":"https://independent.academia.edu/CatherineSackur?f_ri=152051","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":152051,"name":"Didactique des mathématiques","url":"https://www.academia.edu/Documents/in/Didactique_des_mathematiques?f_ri=152051","nofollow":false},{"id":1405002,"name":"Entretien D'explicitation","url":"https://www.academia.edu/Documents/in/Entretien_Dexplicitation?f_ri=152051","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_43104790" data-work_id="43104790" 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/43104790/Th%C3%A8se_de_doctorat_Jocelyne_Samir_ISSA">Thèse de doctorat-Jocelyne Samir ISSA</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">Dans la présente recherche, nous nous intéressons au processus d’enseignement/apprentissage de la notion de conique au Liban en termes de conceptions et de difficultés. En premier lieu, l’analyse épistémologique met en relief la richesse... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_43104790" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">Dans la présente recherche, nous nous intéressons au processus d’enseignement/apprentissage de la notion de conique au Liban en termes de conceptions et de difficultés. En premier lieu, l’analyse épistémologique met en relief la richesse de cet objet tant en définitions qu’en représentations sémiotiques. En deuxième lieu, nous dressons un état des lieux de l’enseignement de la notion de conique au Liban: nous analysons la progression de l’enseignement de cette notion suite à la réforme mise en place en 2000 puis analysons l’exploitation « officielle » de la notion de conique à travers l’analyse des problèmes proposés au sujet des coniques au baccalauréat libanais. En troisième lieu, nous menons une analyse détaillée des deux manuels les plus utilisés dans le contexte libanais. Cette analyse est faite selon trois axes complémentaires: une analyse anthropologique selon la théorie anthropologique de Chevallard, une analyse conceptuelle selon la théorie des champs conceptuels de Vergnaud et une analyse des représentations selon la théorie des registres sémiotiques de Duval. Ces analyses permettent de déterminer deux conceptions de cet objet qui en émergent : une conception d’« habillage algébrique » et une autre d'« habillage géométrique ». En quatrième lieu, nous sondons l’avis des enseignants sur la façon selon laquelle ils conçoivent l’enseignement des coniques ainsi que sur les difficultés rencontrées par les élèves dans l’apprentissage des coniques. En cinquième lieu, l’analyse d’un test proposé à un échantillon d’élèves de SG montre la différence entre la réussite des tâches mobilisant ces conceptions ainsi que l’importance de la conversion pour la résolution de problème ; un des objectifs fondamentaux de l’apprentissage des mathématiques. Finalement, une séquence d’apprentissage des coniques visant mettre en relief les définitions géométriques des coniques est proposée</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/43104790" 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="40e0659185406c9f802984faf5ccb27d" rel="nofollow" data-download="{"attachment_id":63358768,"asset_id":43104790,"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/63358768/download_file?st=MTczMzAxOTg4Nyw4LjIyMi4yMDguMTQ2&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="158493261" href="https://independent.academia.edu/JocelyneIssa">Jocelyne Issa</a><script data-card-contents-for-user="158493261" type="text/json">{"id":158493261,"first_name":"Jocelyne","last_name":"Issa","domain_name":"independent","page_name":"JocelyneIssa","display_name":"Jocelyne Issa","profile_url":"https://independent.academia.edu/JocelyneIssa?f_ri=152051","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_43104790 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="43104790"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 43104790, container: ".js-paper-rank-work_43104790", }); 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En premier lieu, l’analyse épistémologique met en relief la richesse de cet objet tant en définitions qu’en représentations sémiotiques. En deuxième lieu, nous dressons un état des lieux de l’enseignement de la notion de conique au Liban: nous analysons la progression de l’enseignement de cette notion suite à la réforme mise en place en 2000 puis analysons l’exploitation « officielle » de la notion de conique à travers l’analyse des problèmes proposés au sujet des coniques au baccalauréat libanais. En troisième lieu, nous menons une analyse détaillée des deux manuels les plus utilisés dans le contexte libanais. Cette analyse est faite selon trois axes complémentaires: une analyse anthropologique selon la théorie anthropologique de Chevallard, une analyse conceptuelle selon la théorie des champs conceptuels de Vergnaud et une analyse des représentations selon la théorie des registres sémiotiques de Duval. Ces analyses permettent de déterminer deux conceptions de cet objet qui en émergent : une conception d’« habillage algébrique » et une autre d'« habillage géométrique ». En quatrième lieu, nous sondons l’avis des enseignants sur la façon selon laquelle ils conçoivent l’enseignement des coniques ainsi que sur les difficultés rencontrées par les élèves dans l’apprentissage des coniques. En cinquième lieu, l’analyse d’un test proposé à un échantillon d’élèves de SG montre la différence entre la réussite des tâches mobilisant ces conceptions ainsi que l’importance de la conversion pour la résolution de problème ; un des objectifs fondamentaux de l’apprentissage des mathématiques. Finalement, une séquence d’apprentissage des coniques visant mettre en relief les définitions géométriques des coniques est proposée\n","downloadable_attachments":[{"id":63358768,"asset_id":43104790,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":158493261,"first_name":"Jocelyne","last_name":"Issa","domain_name":"independent","page_name":"JocelyneIssa","display_name":"Jocelyne Issa","profile_url":"https://independent.academia.edu/JocelyneIssa?f_ri=152051","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":57518,"name":"Conception","url":"https://www.academia.edu/Documents/in/Conception?f_ri=152051","nofollow":false},{"id":152051,"name":"Didactique des mathématiques","url":"https://www.academia.edu/Documents/in/Didactique_des_mathematiques?f_ri=152051","nofollow":false},{"id":3659874,"name":"Conique","url":"https://www.academia.edu/Documents/in/Conique?f_ri=152051","nofollow":false},{"id":3660014,"name":"Difficulté","url":"https://www.academia.edu/Documents/in/Difficult%C3%A9?f_ri=152051","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_36567682" data-work_id="36567682" 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/36567682/Apports_dune_analyse_prax%C3%A9ologique_le_cas_de_l%C3%A9tude_de_la_transposition_didactique_du_concept_did%C3%A9al">Apports d'une analyse praxéologique : le cas de l'étude de la transposition didactique du concept d'idéal</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">Dans cette communication faite au Week-end Jeunes Chercheurs 2017 de l'ARDM à la Grande-Motte, nous montrerons que la Théorie Anthropologique du Didactique (Chevallard, 1998) complétée par la notion de praxéologie structuraliste... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_36567682" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">Dans cette communication faite au Week-end Jeunes Chercheurs 2017 de l'ARDM à la Grande-Motte, nous montrerons que la Théorie Anthropologique du Didactique (Chevallard, 1998) complétée par la notion de praxéologie structuraliste (Hausberger, 2016) est un outil pour l'analyse didactique de la transposition didactique du concept d'idéal. Nous illustrerons ce propos grâce à l'analyse d'une série d'exercices d'un manuel d'algèbre de licence (Escofier, 2011).</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/36567682" 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="25585bc96ec196c6cdcc5cec5a6a09b2" rel="nofollow" data-download="{"attachment_id":56493653,"asset_id":36567682,"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/56493653/download_file?st=MTczMzAxOTg4Nyw4LjIyMi4yMDguMTQ2&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="62829684" href="https://hepvs.academia.edu/JulieJovignotCandy">Julie Jovignot</a><script data-card-contents-for-user="62829684" type="text/json">{"id":62829684,"first_name":"Julie","last_name":"Jovignot","domain_name":"hepvs","page_name":"JulieJovignotCandy","display_name":"Julie Jovignot","profile_url":"https://hepvs.academia.edu/JulieJovignotCandy?f_ri=152051","photo":"https://0.academia-photos.com/62829684/16302739/18307376/s65_julie.jovignot-candy.jpg"}</script></span></span></li><li class="js-paper-rank-work_36567682 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="36567682"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 36567682, container: ".js-paper-rank-work_36567682", }); 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