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true; window.loswp.showSignupCaptcha = false window.loswp.willEdgeCache = false; window.loswp.work = {"work":{"id":1023747,"created_at":"2011-10-18T01:01:07.983-07:00","from_world_paper_id":5606142,"updated_at":"2025-02-01T15:32:10.263-08:00","_data":{"publisher":"Wiley Online Library","ai_title_tag":"Eye Movements Reveal Implicit Math Knowledge","grobid_abstract":"To date, a number of studies have demonstrated the existence of mismatches between children's implicit and explicit knowledge at certain points in development that become manifest by their gestures and gaze orientation in different problem solving contexts. Stimulated by this research, we used eye movement measurement to investigate the development of basic knowledge about numerical magnitude in primary school children. Sixty-six children from grades one to three (i.e. 6-9 years) were presented with two parallel versions of a number line estimation task of which one was restricted to behavioural measures, whereas the other included the recording of eye movement data. The results of the eye movement experiment indicate a quantitative increase as well as a qualitative change in children's implicit knowledge about numerical magnitudes in this age group that precedes the overt, that is, behavioural, demonstration of explicit numerical knowledge. The finding that children's eye movements reveal substantially more about the presence of implicit precursors of later explicit knowledge in the numerical domain than classical approaches suggests further exploration of eye movement","publication_date":"2010,1,1","publication_name":"Infant and Child …","grobid_abstract_attachment_id":"51130362"},"document_type":"paper","pre_hit_view_count_baseline":0,"quality":"high","language":"en","title":"What the eyes already 'know': using eye movement measurement to tap into children's implicit numerical magnitude representations","broadcastable":true,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [853670]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "full_page_mobile_sutd_modal"; window.loswp.useOptimizedScribd4genScript = false; window.loginModal = {}; window.loginModal.appleClientId = 'edu.academia.applesignon'; window.userInChina = "false";</script><script defer="" src="https://accounts.google.com/gsi/client"></script><div class="ds-loswp-container"><div class="ds-work-card--grid-container"><div class="ds-work-card--container js-loswp-work-card"><div class="ds-work-card--cover"><div class="ds-work-cover--wrapper"><div class="ds-work-cover--container"><button class="ds-work-cover--clickable js-swp-download-button" data-signup-modal="{"location":"swp-splash-paper-cover","attachmentId":51130362,"attachmentType":"pdf"}"><img alt="First page of “What the eyes already 'know': using eye movement measurement to tap into children's implicit numerical magnitude representations”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/51130362/mini_magick20190126-5844-8i0ooz.png?1548520568" /><img alt="PDF Icon" class="ds-work-cover--file-icon" src="//a.academia-assets.com/images/single_work_splash/adobe_icon.svg" /><div class="ds-work-cover--hover-container"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span><p>Download Free PDF</p></div><div class="ds-work-cover--ribbon-container">Download Free PDF</div><div class="ds-work-cover--ribbon-triangle"></div></button></div></div></div><div class="ds-work-card--work-information"><h1 class="ds-work-card--work-title">What the eyes already 'know': using eye movement measurement to tap into children's implicit numerical magnitude representations</h1><div class="ds-work-card--work-authors ds-work-card--detail"><a class="ds-work-card--author js-wsj-grid-card-author ds2-5-body-md ds2-5-body-link" data-author-id="853670" href="https://fu-berlin.academia.edu/AngelaHeine"><img alt="Profile image of Angela Heine" class="ds-work-card--author-avatar" src="https://0.academia-photos.com/853670/303669/359461/s65_angela.heine.jpg" />Angela Heine</a></div><div class="ds-work-card--detail"><p class="ds-work-card--detail ds2-5-body-sm">2010, Infant and Child …</p><div class="ds-work-card--work-metadata"><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">visibility</span><p class="ds2-5-body-sm" id="work-metadata-view-count">…</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">description</span><p class="ds2-5-body-sm">12 pages</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">link</span><p class="ds2-5-body-sm">1 file</p></div></div><script>(async () => { const workId = 1023747; const worksViewsPath = "/v0/works/views?subdomain_param=api&work_ids%5B%5D=1023747"; const getWorkViews = async (workId) => { const response = await fetch(worksViewsPath); if (!response.ok) { throw new Error('Failed to load work views'); } const data = await response.json(); return data.views[workId]; }; // Get the view count for the work - we send this immediately rather than waiting for // the DOM to load, so it can be available as soon as possible (but without holding up // the backend or other resource requests, because it's a bit expensive and not critical). const viewCount = await getWorkViews(workId); const updateViewCount = (viewCount) => { try { const viewCountNumber = parseInt(viewCount, 10); if (viewCountNumber === 0) { // Remove the whole views element if there are zero views. document.getElementById('work-metadata-view-count')?.parentNode?.remove(); return; } const commaizedViewCount = viewCountNumber.toLocaleString(); const viewCountBody = document.getElementById('work-metadata-view-count'); if (!viewCountBody) { throw new Error('Failed to find work views element'); } viewCountBody.textContent = `${commaizedViewCount} views`; } catch (error) { // Remove the whole views element if there was some issue parsing. document.getElementById('work-metadata-view-count')?.parentNode?.remove(); throw new Error(`Failed to parse view count: ${viewCount}`, error); } }; // If the DOM is still loading, wait for it to be ready before updating the view count. if (document.readyState === "loading") { document.addEventListener('DOMContentLoaded', () => { updateViewCount(viewCount); }); // Otherwise, just update it immediately. } else { updateViewCount(viewCount); } })();</script></div><p class="ds-work-card--work-abstract ds-work-card--detail ds2-5-body-md">To date, a number of studies have demonstrated the existence of mismatches between children's implicit and explicit knowledge at certain points in development that become manifest by their gestures and gaze orientation in different problem solving contexts. Stimulated by this research, we used eye movement measurement to investigate the development of basic knowledge about numerical magnitude in primary school children. Sixty-six children from grades one to three (i.e. 6-9 years) were presented with two parallel versions of a number line estimation task of which one was restricted to behavioural measures, whereas the other included the recording of eye movement data. The results of the eye movement experiment indicate a quantitative increase as well as a qualitative change in children's implicit knowledge about numerical magnitudes in this age group that precedes the overt, that is, behavioural, demonstration of explicit numerical knowledge. The finding that children's eye movements reveal substantially more about the presence of implicit precursors of later explicit knowledge in the numerical domain than classical approaches suggests further exploration of eye movement</p><div class="ds-work-card--button-container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--work-card","attachmentId":51130362,"attachmentType":"pdf","workUrl":"https://www.academia.edu/1023747/What_the_eyes_already_know_using_eye_movement_measurement_to_tap_into_childrens_implicit_numerical_magnitude_representations"}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--work-card","attachmentId":51130362,"attachmentType":"pdf","workUrl":"https://www.academia.edu/1023747/What_the_eyes_already_know_using_eye_movement_measurement_to_tap_into_childrens_implicit_numerical_magnitude_representations"}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div><div class="ds-signup-banner-trigger-container"><div class="ds-signup-banner-trigger ds-signup-banner-trigger-control"></div></div><div class="ds-signup-banner ds-signup-banner-control"><div id="ds-signup-banner-close-button"><button class="ds2-5-button ds2-5-button--secondary ds2-5-button--inverse"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">close</span></button></div><div class="ds-signup-banner-ctas"><img src="//a.academia-assets.com/images/academia-logo-capital-white.svg" /><h4 class="ds2-5-heading-serif-sm">Sign up for access to the world's latest research</h4><button class="ds2-5-button ds2-5-button--inverse ds2-5-button--full-width js-swp-download-button" data-signup-modal="{"location":"signup-banner"}">Sign up for free<span class="material-symbols-outlined" style="font-size: 20px" translate="no">arrow_forward</span></button></div><div class="ds-signup-banner-divider"></div><div class="ds-signup-banner-reasons"><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Get notified about relevant papers</span></div><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Save papers to use in your research</span></div><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Join the discussion with peers</span></div><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Track your impact</span></div></div></div><script>(() => { // Set up signup banner show/hide behavior: // 1. 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Stimulated by this research, we used eye movement measurement to investigate the development of basic knowledge about numerical magnitude in primary school children. Sixty-six children from grades one to three (i.e. 6-9 years) were presented with two parallel versions of a number line estimation task of which one was restricted to behavioural measures, whereas the other included the recording of eye movement data. The results of the eye movement experiment indicate a quantitative increase as well as a qualitative change in children's implicit knowledge about numerical magnitudes in this age group that precedes the overt, that is, behavioural, demonstration of explicit numerical knowledge. The finding that children's eye movements reveal substantially more about the presence of implicit precursors of later explicit knowledge in the numerical domain than classical approaches suggests further exploration of eye movement</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"What the Eyes Already\" Know\": Using Eye Movement Measurement to Tap into Children","attachmentId":50931017,"attachmentType":"pdf","work_url":"https://www.academia.edu/1556200/What_the_Eyes_Already_Know_Using_Eye_Movement_Measurement_to_Tap_into_Children","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/1556200/What_the_Eyes_Already_Know_Using_Eye_Movement_Measurement_to_Tap_into_Children"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="1" data-entity-id="569460" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/569460/A_validation_of_eye_movements_as_a_measure_of_elementary_school_childrens_developing_number_sense">A validation of eye movements as a measure of elementary school children's developing number sense</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="9218" href="https://kuleuven.academia.edu/BertDeSmedt">Bert De Smedt</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Cognitive …, 2008</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"A validation of eye movements as a measure of elementary school children's developing number sense","attachmentId":51354445,"attachmentType":"pdf","work_url":"https://www.academia.edu/569460/A_validation_of_eye_movements_as_a_measure_of_elementary_school_childrens_developing_number_sense","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/569460/A_validation_of_eye_movements_as_a_measure_of_elementary_school_childrens_developing_number_sense"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="2" data-entity-id="569484" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/569484/A_Validation_of_Eye_Movements_as_a_Measure_of_Elementary_School_Children">A Validation of Eye Movements as a Measure of Elementary School Children</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="9218" href="https://kuleuven.academia.edu/BertDeSmedt">Bert De Smedt</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Cognitive …, 2008</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"A Validation of Eye Movements as a Measure of Elementary School Children","attachmentId":51354433,"attachmentType":"pdf","work_url":"https://www.academia.edu/569484/A_Validation_of_Eye_Movements_as_a_Measure_of_Elementary_School_Children","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/569484/A_Validation_of_Eye_Movements_as_a_Measure_of_Elementary_School_Children"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="3" data-entity-id="88110234" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/88110234/How_young_children_view_mathematical_representations_a_study_using_eye_tracking_technology">How young children view mathematical representations: a study using eye-tracking technology</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="977207" href="https://durham.academia.edu/DavidBolden">David Bolden</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Educational Research, 2014</p><p class="ds-related-work--abstract ds2-5-body-sm">Background It has been shown that mathematical representations can aid children's understanding of mathematical concepts (Greeno and Hall 1997) but that children can sometimes have difficulty in interpreting them correctly (Vosniadou 2010). New advances in eye-tracking technology can help in this respect because it allows data to be gathered concerning children's focus of attention and so indicate what aspects of the representations they are focussing on. However, recent eye-tracking technology has not been used to any great degree in investigating the way children view and interpret mathematical representations. Purpose This research explored the use of new advances in eye-tracking technology in investigating how young children view and interpret mathematical representations of multiplication. Sample Nine Year 5 children (four boys, five girls, aged 9-10 years of age) from a local primary (elementary) school in the NorthEast of England were asked to complete the test during school time. The children represented a range of attainment levels across the mathematical domain (three higher, three middle and three lower attaining children) and were selected accordingly by their class teacher. We recognise that this study was only based on a small sample of children, however, this number still allowed us to make meaningful comparisons in particular between the different types of representations presented. Design and methods The study consisted of each child looking at eighteen static slides, one after the other, with each slide presenting a symbolic and a picture representation of multiplication problems. The data that was captured by the eye-tracker and recorded was then analysed quantitatively (e.g. time on each slide, time on each area of interest specified within the software) and qualitatively (video recordings of each child's gaze trajectory during each representation was carried out, thereby allowing a categorisation of the different approaches adopted).</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"How young children view mathematical representations: a study using eye-tracking technology","attachmentId":92150443,"attachmentType":"pdf","work_url":"https://www.academia.edu/88110234/How_young_children_view_mathematical_representations_a_study_using_eye_tracking_technology","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/88110234/How_young_children_view_mathematical_representations_a_study_using_eye_tracking_technology"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="4" data-entity-id="15332523" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/15332523/Development_of_Numerical_Estimation_in_Young_Children">Development of Numerical Estimation in Young Children</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="34447262" href="https://independent.academia.edu/BoothJulie">Julie Booth</a><span>, </span><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="13570" href="https://cmu.academia.edu/RobertSiegler">Robert Siegler</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Child Development, 2004</p><p class="ds-related-work--abstract ds2-5-body-sm">Two experiments examined kindergartners', first graders', and second graders' numerical estimation, the internal representations that gave rise to the estimates, and the general hypothesis that developmental sequences within a domain tend to repeat themselves in new contexts. Development of estimation in this age range on 0-to-100 number lines followed the pattern observed previously with older children on 0-to-1,000 lines. Between kindergarten and second grade (6 and 8 years), patterns of estimates progressed from consistently logarithmic to a mixture of logarithmic and linear to a primarily linear pattern. Individual differences in number-line estimation correlated strongly with math achievement test scores, improved estimation accuracy proved attributable to increased linearity of estimates, and exposure to relevant experience tended to improve estimation accuracy.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Development of Numerical Estimation in Young Children","attachmentId":43327663,"attachmentType":"pdf","work_url":"https://www.academia.edu/15332523/Development_of_Numerical_Estimation_in_Young_Children","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/15332523/Development_of_Numerical_Estimation_in_Young_Children"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="5" data-entity-id="23739743" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/23739743/Numerical_estimation_in_preschoolers">Numerical estimation in preschoolers</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="38015168" href="https://talentgate.academia.edu/DanielaLucangeli">Daniela Lucangeli</a><span>, </span><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="54898533" href="https://independent.academia.edu/ManuelaPiazza1">Manuela Piazza</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Developmental Psychology, 2010</p><p class="ds-related-work--abstract ds2-5-body-sm">Children's sense of numbers before formal education is thought to rely on an approximate number system based on logarithmically compressed analog magnitudes that increases in resolution throughout childhood. School age children performing a numerical estimation task have been shown to increasingly rely on a formally appropriate, linear representation and decrease their use of an intuitive, logarithmic one. We investigated the development of numerical estimation in a younger population (3.5-6.5 y.o.) using 0-to-100 and two novel sets of 1-to-10 and 1-to-20 number lines. Children's estimates shifted from logarithmic to linear in the small number range, whereas they became more accurate but increasingly logarithmic on the larger interval. Estimation accuracy was correlated with knowledge of Arabic numerals and numerical order. These results suggest that the development of numerical estimation is built on a logarithmic coding of numbers -the hallmark of the approximate number system -and is subsequently shaped by the acquisition of cultural practices with numbers.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Numerical estimation in preschoolers","attachmentId":44176607,"attachmentType":"pdf","work_url":"https://www.academia.edu/23739743/Numerical_estimation_in_preschoolers","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/23739743/Numerical_estimation_in_preschoolers"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="6" data-entity-id="14442112" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/14442112/Representational_change_and_strategy_use_in_childrens_number_line_estimation_during_the_first_years_of_primary_school">Representational change and strategy use in children's number line estimation during the first years of primary school</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="33380182" href="https://cambridge.academia.edu/DenesSzucs">Denes Szucs</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Behavioral and Brain Functions, 2012</p><p class="ds-related-work--abstract ds2-5-body-sm">Background: The objective of this study was to scrutinize number line estimation behaviors displayed by children in mathematics classrooms during the first three years of schooling. We extend existing research by not only mapping potential logarithmic-linear shifts but also provide a new perspective by studying in detail the estimation strategies of individual target digits within a number range familiar to children. Methods: Typically developing children (n = 67) from Years 1-3 completed a number-to-position numerical estimation task (0-20 number line). Estimation behaviors were first analyzed via logarithmic and linear regression modeling. Subsequently, using an analysis of variance we compared the estimation accuracy of each digit, thus identifying target digits that were estimated with the assistance of arithmetic strategy.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Representational change and strategy use in children's number line estimation during the first years of primary school","attachmentId":44145014,"attachmentType":"pdf","work_url":"https://www.academia.edu/14442112/Representational_change_and_strategy_use_in_childrens_number_line_estimation_during_the_first_years_of_primary_school","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/14442112/Representational_change_and_strategy_use_in_childrens_number_line_estimation_during_the_first_years_of_primary_school"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="7" data-entity-id="115247863" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/115247863/Numerical_Representation_are_Influenced_by_Spatial_Relation_or_Finger_Counting_An_Eye_Tracking_Study">Numerical Representation are Influenced by Spatial Relation or Finger Counting? An Eye Tracking Study</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="1246144" href="https://uniroma1.academia.edu/FrancescaFederico">Francesca Federico</a></div><p class="ds-related-work--metadata ds2-5-body-xs">International Journal of Psychology & Behavior Analysis, 2017</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Numerical Representation are Influenced by Spatial Relation or Finger Counting? An Eye Tracking Study","attachmentId":111710751,"attachmentType":"pdf","work_url":"https://www.academia.edu/115247863/Numerical_Representation_are_Influenced_by_Spatial_Relation_or_Finger_Counting_An_Eye_Tracking_Study","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/115247863/Numerical_Representation_are_Influenced_by_Spatial_Relation_or_Finger_Counting_An_Eye_Tracking_Study"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="8" data-entity-id="24286986" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/24286986/Objects_Actions_and_Images_A_Perspective_on_Early_Number_Development">Objects, Actions, and Images: A Perspective on Early Number Development</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="4817584" href="https://ucy.academia.edu/DemetraPittaPantazi">Demetra Pitta-Pantazi</a></div><p class="ds-related-work--metadata ds2-5-body-xs">The Journal of Mathematical Behavior, 2000</p><p class="ds-related-work--abstract ds2-5-body-sm">It is the purpose of this paper to present a review of research evidence that indicates the existence of qualitatively different thinking in elementary number development. In doing so the paper summarises empirical evidence obtained over a period of ten years. This evidence first signalled qualitative differences in numerical processing , and was seminal in the development of the notion of procept . More recently it examines the role of imagery in elementary number processing . Its conclusions indicate that in the abstraction of numerical concepts from numerical processes qualitatively different outcomes may arise because children concentrate on different objects or different aspects of the objects which are components of numerical processing.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Objects, Actions, and Images: A Perspective on Early Number Development","attachmentId":44622707,"attachmentType":"pdf","work_url":"https://www.academia.edu/24286986/Objects_Actions_and_Images_A_Perspective_on_Early_Number_Development","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/24286986/Objects_Actions_and_Images_A_Perspective_on_Early_Number_Development"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="9" data-entity-id="126624915" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/126624915/Spontaneous_focusing_on_numerical_order_and_numerical_skills_of_3_to_4_year_old_children">Spontaneous focusing on numerical order and numerical skills of 3- to 4-year-old children</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="174767852" href="https://uab-ro.academia.edu/CristinaNanu">Cristina Nanu</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Educational studies in mathematics, 2024</p><p class="ds-related-work--abstract ds2-5-body-sm">Recent studies have highlighted the importance of ordinality skills in early numerical development. Here, we investigate individual differences in ordering sets of items and suggest that children might also differ in their tendency to spontaneously recognize and use numerical order in everyday situations. This study investigated the individual differences in 3-to 4-year-old children's tendency to spontaneously focus on numerical order (SFONO), and their association with early numerical skills. One hundred fifty children were presented with three SFONO tasks designed as play-like activities, where numerical order was one aspect that could be focused on. In addition, the children were administered tasks addressing spontaneous focusing on numerosity (SFON), numerical ordering, cardinality recognition, and number sequence production. Our results showed that children had substantial individual differences in all measures, including SFONO tendency. Children's SFONO tendency was associated with their early numerical skills. To further investigate the association between SFONO tendency and numerical ordering skills, a hierarchical regression was conducted for a group of children who could successfully order sets from one to three at a minimum and were regarded as likely having the requisite skills to spontaneously focus on numerical order. The findings reveal that SFONO tendency had a unique contribution to children's numerical ordering skills, even after controlling for age, cardinality recognition, and number sequence production. The results suggest that SFONO tendency potentially plays a relevant role in children's numerical development.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Spontaneous focusing on numerical order and numerical skills of 3- to 4-year-old children","attachmentId":120474413,"attachmentType":"pdf","work_url":"https://www.academia.edu/126624915/Spontaneous_focusing_on_numerical_order_and_numerical_skills_of_3_to_4_year_old_children","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/126624915/Spontaneous_focusing_on_numerical_order_and_numerical_skills_of_3_to_4_year_old_children"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div></div></div><div class="ds-sticky-ctas--wrapper js-loswp-sticky-ctas hidden"><div class="ds-sticky-ctas--grid-container"><div class="ds-sticky-ctas--container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--sticky-ctas","attachmentId":51130362,"attachmentType":"pdf","workUrl":null}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--sticky-ctas","attachmentId":51130362,"attachmentType":"pdf","workUrl":null}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div><div class="ds-below-fold--grid-container"><div class="ds-work--container js-loswp-embedded-document"><div class="attachment_preview" data-attachment="Attachment_51130362" style="display: none"><div class="js-scribd-document-container"><div class="scribd--document-loading js-scribd-document-loader" style="display: block;"><img alt="Loading..." src="//a.academia-assets.com/images/loaders/paper-load.gif" /><p>Loading Preview</p></div></div><div style="text-align: center;"><div class="scribd--no-preview-alert js-preview-unavailable"><p>Sorry, preview is currently unavailable. You can download the paper by clicking the button above.</p></div></div></div></div><div class="ds-sidebar--container js-work-sidebar"><div class="ds-related-content--container"><h2 class="ds-related-content--heading">Related papers</h2><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="0" data-entity-id="22581282" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/22581282/Varieties_of_quantity_estimation_in_children">Varieties of quantity estimation in children</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="31659877" href="https://unipd.academia.edu/MarcoZorzi">Marco Zorzi</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Developmental Psychology, 2015</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline 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Pre-School Children’s Spontaneous Focusing on Numerosity and Their Development of Arithmetical Skills at School</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="216082939" href="https://independent.academia.edu/NadinePoltz">Nadine Poltz</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Brain Sciences, 2022</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Does It Count? 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