{"id":{"repo_id":"toronto-retro","oai_identifier":"oai:utoronto.scholaris.ca:1807/33971"},"canonical_url":"https://search.dev.ndltd.org/etd/toronto-retro/oai:utoronto.scholaris.ca:1807/33971","repository":{"repo_id":"toronto-retro","name":"University of Toronto","base_url":"https://utoronto.scholaris.ca/server/oai/request"},"display":{"title":"Student Learning Heterogeneity in School Mathematics","abstract":"The phrase \"opportunities to learn\" (OTL) is most commonly interpreted in institutional, or inter-individual, terms but it can also be viewed as a cognitive, or intra-individual, phenomenon. How student learning heterogeneity (LH) - learning differences manifested when children's understanding is later assessed - is understood varies by OTL interpretation. In this study, I argue that the cognitive underpinning of learning disability, learning difficulty, typical achievement, and gifted achievement in mathematics is not well understood in part because of the ambiguity of LH assumptions in previous studies. Data from 104,315 Ontario students who had responded to provincially-mandated mathematics tests in grades 3, 6, and 9 dataset were analyzed using latent trait analysis (LTM) and latent class analysis (LCA). The tests were constructed to distinguish four achievement levels per grade and, either five curriculum strands (grades 3 and 6), three strands (grade 9 applied) or four strands (grade 9 academic). Best-fitting LTM models reflected 3- or 4-factors (grade 9 applied and grades 3, 6, 9 academic, respectively). Best-fitting LCA solutions reflected 4- or 5-classes (grade 3, 6 and grade 9 applied, academic, respectively). There were differences in relative proportions of students who were distributed across levels and classes. Moreover, grade 9 models were more complex than the reported four achievement levels. To explore intrinsic modeled results further, latent factors were plotted against latent classes. Implications of institutional versus cognitive interpretations are discussed.","abstract_html":"The phrase "opportunities to learn" (OTL) is most commonly interpreted in institutional, or inter-individual, terms but it can also be viewed as a cognitive, or intra-individual, phenomenon. How student learning heterogeneity (LH) - learning differences manifested when children's understanding is later assessed - is understood varies by OTL interpretation. In this study, I argue that the cognitive underpinning of learning disability, learning difficulty, typical achievement, and gifted achievement in mathematics is not well understood in part because of the ambiguity of LH assumptions in previous studies. Data from 104,315 Ontario students who had responded to provincially-mandated mathematics tests in grades 3, 6, and 9 dataset were analyzed using latent trait analysis (LTM) and latent class analysis (LCA). The tests were constructed to distinguish four achievement levels per grade and, either five curriculum strands (grades 3 and 6), three strands (grade 9 applied) or four strands (grade 9 academic). Best-fitting LTM models reflected 3- or 4-factors (grade 9 applied and grades 3, 6, 9 academic, respectively). Best-fitting LCA solutions reflected 4- or 5-classes (grade 3, 6 and grade 9 applied, academic, respectively). There were differences in relative proportions of students who were distributed across levels and classes. Moreover, grade 9 models were more complex than the reported four achievement levels. To explore intrinsic modeled results further, latent factors were plotted against latent classes. Implications of institutional versus cognitive interpretations are discussed.","abstract_has_math":false,"creators":["Cunningham, Malcolm"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Human Development and Applied Psychology","school":null,"contributors":[],"advisors":["Childs, Ruth A."],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-12-11","date_published":"2012-12-11","updated_at":"2026-07-27T21:28:13Z","subjects":["latent variable analysis","mathematics","large-scale assesment","learning heterogeneity"],"languages":["en_ca"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/1807/33971","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Childs, Ruth A."]},{"key":"dc:contributor.department","label":"Department","values":["Human Development and Applied Psychology"]},{"key":"dc:creator","label":"Author","values":["Cunningham, Malcolm"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2012-11"]},{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2012-12-11T15:46:23Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["NO_RESTRICTION","2012-12-11T15:46:23Z"]},{"key":"dc:date.issued","label":"Date","values":["2012-12-11"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["latent variable analysis","mathematics","large-scale assesment","learning heterogeneity"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en_ca"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/1807/33971"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The phrase \"opportunities to learn\" (OTL) is most commonly interpreted in institutional, or inter-individual, terms but it can also be viewed as a cognitive, or intra-individual, phenomenon. How student learning heterogeneity (LH) - learning differences manifested when children's understanding is later assessed - is understood varies by OTL interpretation. In this study, I argue that the cognitive underpinning of learning disability, learning difficulty, typical achievement, and gifted achievement in mathematics is not well understood in part because of the ambiguity of LH assumptions in previous studies. Data from 104,315 Ontario students who had responded to provincially-mandated mathematics tests in grades 3, 6, and 9 dataset were analyzed using latent trait analysis (LTM) and latent class analysis (LCA). The tests were constructed to distinguish four achievement levels per grade and, either five curriculum strands (grades 3 and 6), three strands (grade 9 applied) or four strands (grade 9 academic). Best-fitting LTM models reflected 3- or 4-factors (grade 9 applied and grades 3, 6, 9 academic, respectively). Best-fitting LCA solutions reflected 4- or 5-classes (grade 3, 6 and grade 9 applied, academic, respectively). There were differences in relative proportions of students who were distributed across levels and classes. Moreover, grade 9 models were more complex than the reported four achievement levels. To explore intrinsic modeled results further, latent factors were plotted against latent classes. Implications of institutional versus cognitive interpretations are discussed."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["PhD"]},{"key":"dc:title","label":"Title","values":["Student Learning Heterogeneity in School Mathematics"]}]}],"canonical_facts":{"dc:contributor.advisor":["Childs, Ruth A."],"dc:contributor.department":["Human Development and Applied Psychology"],"dc:creator":["Cunningham, Malcolm"],"dc:date":["2012-11"],"dc:date.accessioned":["2012-12-11T15:46:23Z"],"dc:date.available":["NO_RESTRICTION","2012-12-11T15:46:23Z"],"dc:date.issued":["2012-12-11"],"dc:description.abstract":["The phrase \"opportunities to learn\" (OTL) is most commonly interpreted in institutional, or inter-individual, terms but it can also be viewed as a cognitive, or intra-individual, phenomenon. How student learning heterogeneity (LH) - learning differences manifested when children's understanding is later assessed - is understood varies by OTL interpretation. In this study, I argue that the cognitive underpinning of learning disability, learning difficulty, typical achievement, and gifted achievement in mathematics is not well understood in part because of the ambiguity of LH assumptions in previous studies. Data from 104,315 Ontario students who had responded to provincially-mandated mathematics tests in grades 3, 6, and 9 dataset were analyzed using latent trait analysis (LTM) and latent class analysis (LCA). The tests were constructed to distinguish four achievement levels per grade and, either five curriculum strands (grades 3 and 6), three strands (grade 9 applied) or four strands (grade 9 academic). Best-fitting LTM models reflected 3- or 4-factors (grade 9 applied and grades 3, 6, 9 academic, respectively). Best-fitting LCA solutions reflected 4- or 5-classes (grade 3, 6 and grade 9 applied, academic, respectively). There were differences in relative proportions of students who were distributed across levels and classes. Moreover, grade 9 models were more complex than the reported four achievement levels. To explore intrinsic modeled results further, latent factors were plotted against latent classes. Implications of institutional versus cognitive interpretations are discussed."],"dc:description.degree":["PhD"],"dc:identifier.uri":["http://hdl.handle.net/1807/33971"],"dc:language.iso":["en_ca"],"dc:subject":["latent variable analysis","mathematics","large-scale assesment","learning heterogeneity"],"dc:title":["Student Learning Heterogeneity in School Mathematics"],"dc:type":["Thesis"]},"updated_at":"2026-07-27T21:28:13Z"}