{"id":{"repo_id":"texas-state","oai_identifier":"oai:digital.library.txst.edu:10877/22631"},"canonical_url":"https://search.dev.ndltd.org/etd/texas-state/oai:digital.library.txst.edu:10877/22631","repository":{"repo_id":"texas-state","name":"Texas State University","base_url":"https://digital.library.txst.edu/server/oai/request"},"display":{"title":"Undergraduate Developmental Mathematics Students' Fraction Understandings","abstract":"Difficulties with fractions are well-documented for undergraduate developmental mathematics students. Thus, it may not be surprising that fractions act as a gate-keeping topic for college-level mathematics. However, research on the way(s) that undergraduate developmental mathematics students understand fractions is scarce. In my dissertation study, first I synthesize the relevant K–12 fraction literature. Second, I report on findings from initial task-based clinical interviews. I share examples of go-to strategies that were utilized by Vivian and Sofia as they worked through fraction tasks. I share second-order models of the fraction understandings, fraction schemes, and mental operations that Vivian and Sofia demonstrated as they worked through their clinical interview tasks. I include mathematics thinking shared by Vivian and Sofia that is productive toward the measure understanding of fractions. Third, I share the growth in fraction thinking that was demonstrated by Vivian and Sofia as they participated in teaching experiments that were designed to engender growth in the construction of the measure understanding of fractions. Fourth, I share teaching moves and responses to Vivian’s struggles that helped her to struggle productively. Finally, I conclude with a discussion relating how my findings address my research questions and explain how my work relates to existing literature. I close with an explanation of the affordances and limitations of my study and suggest future research.","abstract_html":"Difficulties with fractions are well-documented for undergraduate developmental mathematics students. Thus, it may not be surprising that fractions act as a gate-keeping topic for college-level mathematics. However, research on the way(s) that undergraduate developmental mathematics students understand fractions is scarce. In my dissertation study, first I synthesize the relevant K–12 fraction literature. Second, I report on findings from initial task-based clinical interviews. I share examples of go-to strategies that were utilized by Vivian and Sofia as they worked through fraction tasks. I share second-order models of the fraction understandings, fraction schemes, and mental operations that Vivian and Sofia demonstrated as they worked through their clinical interview tasks. I include mathematics thinking shared by Vivian and Sofia that is productive toward the measure understanding of fractions. Third, I share the growth in fraction thinking that was demonstrated by Vivian and Sofia as they participated in teaching experiments that were designed to engender growth in the construction of the measure understanding of fractions. Fourth, I share teaching moves and responses to Vivian’s struggles that helped her to struggle productively. Finally, I conclude with a discussion relating how my findings address my research questions and explain how my work relates to existing literature. I close with an explanation of the affordances and limitations of my study and suggest future research.","abstract_has_math":false,"creators":["Ford, Lucinda"],"institution":"Texas State University","degree_name":"Doctor of Philosophy","degree_level":"Doctoral","degree_discipline":"Mathematics Education","degree_department":null,"school":null,"contributors":[],"advisors":["Young Lee, Hwa"],"committee_chairs":[],"committee_members":["Dawkins, Paul","Warshauer, Hiroko","Silva, Juanita"],"year":2025,"date_issued":"2025-08","date_published":"2025-08","updated_at":"2026-07-27T21:22:39Z","subjects":["undergraduate developmental mathematics","fractions"],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/10877/22631","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Young Lee, Hwa"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Dawkins, Paul","Warshauer, Hiroko","Silva, Juanita"]},{"key":"dc:creator","label":"Author","values":["Ford, Lucinda"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2025-10-01T14:06:11Z"]},{"key":"dc:date.issued","label":"Date","values":["2025-08"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics Education"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Texas State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["undergraduate developmental mathematics","fractions"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10877/22631"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Difficulties with fractions are well-documented for undergraduate developmental mathematics students. Thus, it may not be surprising that fractions act as a gate-keeping topic for college-level mathematics. However, research on the way(s) that undergraduate developmental mathematics students understand fractions is scarce. In my dissertation study, first I synthesize the relevant K–12 fraction literature. Second, I report on findings from initial task-based clinical interviews. I share examples of go-to strategies that were utilized by Vivian and Sofia as they worked through fraction tasks. I share second-order models of the fraction understandings, fraction schemes, and mental operations that Vivian and Sofia demonstrated as they worked through their clinical interview tasks. I include mathematics thinking shared by Vivian and Sofia that is productive toward the measure understanding of fractions. Third, I share the growth in fraction thinking that was demonstrated by Vivian and Sofia as they participated in teaching experiments that were designed to engender growth in the construction of the measure understanding of fractions. Fourth, I share teaching moves and responses to Vivian’s struggles that helped her to struggle productively. Finally, I conclude with a discussion relating how my findings address my research questions and explain how my work relates to existing literature. I close with an explanation of the affordances and limitations of my study and suggest future research."]},{"key":"dc:format","label":"Dc Format","values":["Text"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["1 file (.pdf)"]},{"key":"dc:title","label":"Title","values":["Undergraduate Developmental Mathematics Students' Fraction Understandings"]}]}],"canonical_facts":{"dc:contributor.advisor":["Young Lee, Hwa"],"dc:contributor.committeemember":["Dawkins, Paul","Warshauer, Hiroko","Silva, Juanita"],"dc:creator":["Ford, Lucinda"],"dc:date.accessioned":["2025-10-01T14:06:11Z"],"dc:date.issued":["2025-08"],"dc:description.abstract":["Difficulties with fractions are well-documented for undergraduate developmental mathematics students. Thus, it may not be surprising that fractions act as a gate-keeping topic for college-level mathematics. However, research on the way(s) that undergraduate developmental mathematics students understand fractions is scarce. In my dissertation study, first I synthesize the relevant K–12 fraction literature. Second, I report on findings from initial task-based clinical interviews. I share examples of go-to strategies that were utilized by Vivian and Sofia as they worked through fraction tasks. I share second-order models of the fraction understandings, fraction schemes, and mental operations that Vivian and Sofia demonstrated as they worked through their clinical interview tasks. I include mathematics thinking shared by Vivian and Sofia that is productive toward the measure understanding of fractions. Third, I share the growth in fraction thinking that was demonstrated by Vivian and Sofia as they participated in teaching experiments that were designed to engender growth in the construction of the measure understanding of fractions. Fourth, I share teaching moves and responses to Vivian’s struggles that helped her to struggle productively. Finally, I conclude with a discussion relating how my findings address my research questions and explain how my work relates to existing literature. I close with an explanation of the affordances and limitations of my study and suggest future research."],"dc:format":["Text"],"dc:format.medium":["1 file (.pdf)"],"dc:identifier.uri":["https://hdl.handle.net/10877/22631"],"dc:language.iso":["en"],"dc:subject":["undergraduate developmental mathematics","fractions"],"dc:title":["Undergraduate Developmental Mathematics Students' Fraction Understandings"],"dc:type":["Dissertation"],"thesis:degree_discipline":["Mathematics Education"],"thesis:degree_level":["Doctoral"],"thesis:degree_name":["Doctor of Philosophy"],"thesis:institution_name":["Texas State University"]},"updated_at":"2026-07-27T21:22:39Z"}