{"id":{"repo_id":"cambridge","oai_identifier":"oai:www.repository.cam.ac.uk:1810/379845"},"canonical_url":"https://search.dev.ndltd.org/etd/cambridge/oai:www.repository.cam.ac.uk:1810/379845","repository":{"repo_id":"cambridge","name":"Cambridge University","base_url":"https://api.repository.cam.ac.uk/server/oai/request"},"display":{"title":"Lakatos-style proving activity in primary school: A mixed-methods study to explore and support teachers’ mathematical knowledge and views","abstract":"Proof has long been central to mathematics and is increasingly recognised as an important element in school mathematics. This PhD research focuses on the development and refinement of conjectures based on the examination of supportive examples and counterexamples, which is a core aspect of Lakatos’ (1976) philosophical account of the role of proof in mathematics. While prior research indicates the feasibility and benefits of students’ engagement with Lakatos-style proving activity, little is known about teachers’ readiness and willingness to incorporate it into their teaching, especially at the primary school level. Addressing this research gap, this mixed-methods study explores two research questions: [RQ1] What are the characteristics of primary school teachers’ mathematical knowledge and views related to Lakatos-style activity? [RQ2] What can be the affordances of primary school teachers’ interaction as a group with an environment featuring comic-style classroom episodes about Lakatos-style activity? Guided by theoretical frameworks on teachers’ mathematical knowledge (regarding content, students, and teaching practices) and views (regarding perceived value, cost, and expectancy) relevant to Lakatos-style activity, developed for the purposes of this study, I designed and implemented a two-stage study involving both quantitative and qualitative methods of data collection and analysis. To address RQ1, a vignette-based survey was conducted with 331 participants, comprising both pre- and in-service primary teachers. I designed 16 comic-style episodes representing a wide range of classroom situations, teaching approaches, conjecture modification techniques, and student understandings relevant to Lakatos-style activity. Survey participants engaged with these episodes and responded to 66 Likert-scale items. The findings indicate that teachers generally hold moderate knowledge levels, with some variation across different knowledge components. Participants generally expressed high perceived value, manageable perceived cost, and cautiously optimistic expectations about incorporating Lakatos-style activity into their teaching. Six teacher profiles emerged, each representing a unique combination of knowledge and view characteristics, underscoring the importance of considering teacher backgrounds when designing teacher preparation programmes. Furthermore, intriguing correlations among, and predictors for, teachers’ knowledge, views and profile membership were also identified and discussed. To address RQ2, a vignette-based focus groups study was conducted with two pre-service and two in-service teacher groups, comprising a total of 22 participants. The results of the previous stage’s profile analysis guided the formation of groups, in which each member represented a different teacher profile. This ensured heterogeneity and group standardisation, enabling comparability within and across groups. Participants engaged in alternating rounds of individual and group work on comic-style classroom episodes and Likert-scale items, different from, yet equivalent to those used in the survey. The findings suggest that discourse-based collaborative environments featuring comic-style classroom episodes can create a productive space for preparing teachers to teach Lakatos-style activity. This environment not only helped uncover varying teacher perspectives, but also enabled shifts in teachers’ knowledge and views. The important roles played by teacher profiles, pre- or in-service teacher status, and group size and composition were explored, revealing their potential influence on group dynamics, interactions, and outcomes. Participants noted numerous advantages in both the preparation environment they engaged with and Lakatos-style activity itself, expressing willingness to incorporate it into their classrooms, if adequately supported. Lakatos-style proving activity can create opportunities for the classroom to work on meaningful and authentic mathematical tasks. This research contributes to the literature by illuminating the previously uncharted territory of teacher knowledge and views relevant to this type of activity, and by showcasing the potential of using discourse-based collaborative environments with comic-style classroom episodes to support their development. Therefore, this research takes a step forward in promoting the role of Lakatos-style activity in the primary school classroom and beyond.","abstract_html":"Proof has long been central to mathematics and is increasingly recognised as an important element in school mathematics. This PhD research focuses on the development and refinement of conjectures based on the examination of supportive examples and counterexamples, which is a core aspect of Lakatos’ (1976) philosophical account of the role of proof in mathematics. While prior research indicates the feasibility and benefits of students’ engagement with Lakatos-style proving activity, little is known about teachers’ readiness and willingness to incorporate it into their teaching, especially at the primary school level. Addressing this research gap, this mixed-methods study explores two research questions: [RQ1] What are the characteristics of primary school teachers’ mathematical knowledge and views related to Lakatos-style activity? [RQ2] What can be the affordances of primary school teachers’ interaction as a group with an environment featuring comic-style classroom episodes about Lakatos-style activity? Guided by theoretical frameworks on teachers’ mathematical knowledge (regarding content, students, and teaching practices) and views (regarding perceived value, cost, and expectancy) relevant to Lakatos-style activity, developed for the purposes of this study, I designed and implemented a two-stage study involving both quantitative and qualitative methods of data collection and analysis. To address RQ1, a vignette-based survey was conducted with 331 participants, comprising both pre- and in-service primary teachers. I designed 16 comic-style episodes representing a wide range of classroom situations, teaching approaches, conjecture modification techniques, and student understandings relevant to Lakatos-style activity. Survey participants engaged with these episodes and responded to 66 Likert-scale items. The findings indicate that teachers generally hold moderate knowledge levels, with some variation across different knowledge components. Participants generally expressed high perceived value, manageable perceived cost, and cautiously optimistic expectations about incorporating Lakatos-style activity into their teaching. Six teacher profiles emerged, each representing a unique combination of knowledge and view characteristics, underscoring the importance of considering teacher backgrounds when designing teacher preparation programmes. Furthermore, intriguing correlations among, and predictors for, teachers’ knowledge, views and profile membership were also identified and discussed. To address RQ2, a vignette-based focus groups study was conducted with two pre-service and two in-service teacher groups, comprising a total of 22 participants. The results of the previous stage’s profile analysis guided the formation of groups, in which each member represented a different teacher profile. This ensured heterogeneity and group standardisation, enabling comparability within and across groups. Participants engaged in alternating rounds of individual and group work on comic-style classroom episodes and Likert-scale items, different from, yet equivalent to those used in the survey. The findings suggest that discourse-based collaborative environments featuring comic-style classroom episodes can create a productive space for preparing teachers to teach Lakatos-style activity. This environment not only helped uncover varying teacher perspectives, but also enabled shifts in teachers’ knowledge and views. The important roles played by teacher profiles, pre- or in-service teacher status, and group size and composition were explored, revealing their potential influence on group dynamics, interactions, and outcomes. Participants noted numerous advantages in both the preparation environment they engaged with and Lakatos-style activity itself, expressing willingness to incorporate it into their classrooms, if adequately supported. Lakatos-style proving activity can create opportunities for the classroom to work on meaningful and authentic mathematical tasks. This research contributes to the literature by illuminating the previously uncharted territory of teacher knowledge and views relevant to this type of activity, and by showcasing the potential of using discourse-based collaborative environments with comic-style classroom episodes to support their development. Therefore, this research takes a step forward in promoting the role of Lakatos-style activity in the primary school classroom and beyond.","abstract_has_math":false,"creators":["Deslis, Dimitrios"],"institution":"University of Cambridge","degree_name":"Doctor of Philosophy (PhD)","degree_level":"Doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Stylianides, Andreas","Jamnik, mateja"],"committee_chairs":[],"committee_members":[],"year":2024,"date_issued":"2024-09-30","date_published":"2024-09-30","updated_at":"2026-07-24T01:33:00Z","subjects":["Argumentation and proof","Comic-style vignettes","Conjecture refinement","Focus groups","Lakatos-style proving activity","Mathematics education","Mixed methods","Primary school","Proof and proving","Supportive examples and counterexamples","Survey","Teacher education","Teachers’ mathematical knowledge","Teachers’ views"],"languages":["eng"],"rights":[],"rights_urls":["https://www.repository.cam.ac.uk/bitstreams/f3b5f71c-2227-4089-90ce-c2e0ff82a3fd/download","http://purl.org/NET/rdflicense/allrightsreserved"],"identifier_entries":[]},"links":{"outbound_url":"https://doi.org/10.17863/CAM.115816","outbound_label":"DOI","outbound_source":"dc:identifier.doi"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Stylianides, Andreas","Jamnik, mateja"]},{"key":"dc:creator","label":"Author","values":["Deslis, Dimitrios"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2024-09-30"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Cambridge"]},{"key":"dc:relation.isreferencedby.uri","label":"Dc Relation Isreferencedby URI","values":["https://www.repository.cam.ac.uk/handle/1810/379845"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Argumentation and proof","Comic-style vignettes","Conjecture refinement","Focus groups","Lakatos-style proving activity","Mathematics education","Mixed methods","Primary school","Proof and proving","Supportive examples and counterexamples","Survey","Teacher education","Teachers’ mathematical knowledge","Teachers’ views"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["https://www.repository.cam.ac.uk/bitstreams/f3b5f71c-2227-4089-90ce-c2e0ff82a3fd/download","http://purl.org/NET/rdflicense/allrightsreserved"]},{"key":"dc:rights.embargotype","label":"Dc Rights Embargotype","values":["controlled.access"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.17863/CAM.115816"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://www.repository.cam.ac.uk/bitstreams/05770904-77c6-4a96-844b-dc7642824acd/download"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Proof has long been central to mathematics and is increasingly recognised as an important element in school mathematics. This PhD research focuses on the development and refinement of conjectures based on the examination of supportive examples and counterexamples, which is a core aspect of Lakatos’ (1976) philosophical account of the role of proof in mathematics. While prior research indicates the feasibility and benefits of students’ engagement with Lakatos-style proving activity, little is known about teachers’ readiness and willingness to incorporate it into their teaching, especially at the primary school level. Addressing this research gap, this mixed-methods study explores two research questions: [RQ1] What are the characteristics of primary school teachers’ mathematical knowledge and views related to Lakatos-style activity? [RQ2] What can be the affordances of primary school teachers’ interaction as a group with an environment featuring comic-style classroom episodes about Lakatos-style activity? Guided by theoretical frameworks on teachers’ mathematical knowledge (regarding content, students, and teaching practices) and views (regarding perceived value, cost, and expectancy) relevant to Lakatos-style activity, developed for the purposes of this study, I designed and implemented a two-stage study involving both quantitative and qualitative methods of data collection and analysis. To address RQ1, a vignette-based survey was conducted with 331 participants, comprising both pre- and in-service primary teachers. I designed 16 comic-style episodes representing a wide range of classroom situations, teaching approaches, conjecture modification techniques, and student understandings relevant to Lakatos-style activity. Survey participants engaged with these episodes and responded to 66 Likert-scale items. The findings indicate that teachers generally hold moderate knowledge levels, with some variation across different knowledge components. Participants generally expressed high perceived value, manageable perceived cost, and cautiously optimistic expectations about incorporating Lakatos-style activity into their teaching. Six teacher profiles emerged, each representing a unique combination of knowledge and view characteristics, underscoring the importance of considering teacher backgrounds when designing teacher preparation programmes. Furthermore, intriguing correlations among, and predictors for, teachers’ knowledge, views and profile membership were also identified and discussed. To address RQ2, a vignette-based focus groups study was conducted with two pre-service and two in-service teacher groups, comprising a total of 22 participants. The results of the previous stage’s profile analysis guided the formation of groups, in which each member represented a different teacher profile. This ensured heterogeneity and group standardisation, enabling comparability within and across groups. Participants engaged in alternating rounds of individual and group work on comic-style classroom episodes and Likert-scale items, different from, yet equivalent to those used in the survey. The findings suggest that discourse-based collaborative environments featuring comic-style classroom episodes can create a productive space for preparing teachers to teach Lakatos-style activity. This environment not only helped uncover varying teacher perspectives, but also enabled shifts in teachers’ knowledge and views. The important roles played by teacher profiles, pre- or in-service teacher status, and group size and composition were explored, revealing their potential influence on group dynamics, interactions, and outcomes. Participants noted numerous advantages in both the preparation environment they engaged with and Lakatos-style activity itself, expressing willingness to incorporate it into their classrooms, if adequately supported. Lakatos-style proving activity can create opportunities for the classroom to work on meaningful and authentic mathematical tasks. This research contributes to the literature by illuminating the previously uncharted territory of teacher knowledge and views relevant to this type of activity, and by showcasing the potential of using discourse-based collaborative environments with comic-style classroom episodes to support their development. 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This PhD research focuses on the development and refinement of conjectures based on the examination of supportive examples and counterexamples, which is a core aspect of Lakatos’ (1976) philosophical account of the role of proof in mathematics. While prior research indicates the feasibility and benefits of students’ engagement with Lakatos-style proving activity, little is known about teachers’ readiness and willingness to incorporate it into their teaching, especially at the primary school level. Addressing this research gap, this mixed-methods study explores two research questions: [RQ1] What are the characteristics of primary school teachers’ mathematical knowledge and views related to Lakatos-style activity? [RQ2] What can be the affordances of primary school teachers’ interaction as a group with an environment featuring comic-style classroom episodes about Lakatos-style activity? Guided by theoretical frameworks on teachers’ mathematical knowledge (regarding content, students, and teaching practices) and views (regarding perceived value, cost, and expectancy) relevant to Lakatos-style activity, developed for the purposes of this study, I designed and implemented a two-stage study involving both quantitative and qualitative methods of data collection and analysis. To address RQ1, a vignette-based survey was conducted with 331 participants, comprising both pre- and in-service primary teachers. I designed 16 comic-style episodes representing a wide range of classroom situations, teaching approaches, conjecture modification techniques, and student understandings relevant to Lakatos-style activity. Survey participants engaged with these episodes and responded to 66 Likert-scale items. The findings indicate that teachers generally hold moderate knowledge levels, with some variation across different knowledge components. Participants generally expressed high perceived value, manageable perceived cost, and cautiously optimistic expectations about incorporating Lakatos-style activity into their teaching. Six teacher profiles emerged, each representing a unique combination of knowledge and view characteristics, underscoring the importance of considering teacher backgrounds when designing teacher preparation programmes. Furthermore, intriguing correlations among, and predictors for, teachers’ knowledge, views and profile membership were also identified and discussed. To address RQ2, a vignette-based focus groups study was conducted with two pre-service and two in-service teacher groups, comprising a total of 22 participants. The results of the previous stage’s profile analysis guided the formation of groups, in which each member represented a different teacher profile. This ensured heterogeneity and group standardisation, enabling comparability within and across groups. Participants engaged in alternating rounds of individual and group work on comic-style classroom episodes and Likert-scale items, different from, yet equivalent to those used in the survey. The findings suggest that discourse-based collaborative environments featuring comic-style classroom episodes can create a productive space for preparing teachers to teach Lakatos-style activity. This environment not only helped uncover varying teacher perspectives, but also enabled shifts in teachers’ knowledge and views. The important roles played by teacher profiles, pre- or in-service teacher status, and group size and composition were explored, revealing their potential influence on group dynamics, interactions, and outcomes. Participants noted numerous advantages in both the preparation environment they engaged with and Lakatos-style activity itself, expressing willingness to incorporate it into their classrooms, if adequately supported. Lakatos-style proving activity can create opportunities for the classroom to work on meaningful and authentic mathematical tasks. This research contributes to the literature by illuminating the previously uncharted territory of teacher knowledge and views relevant to this type of activity, and by showcasing the potential of using discourse-based collaborative environments with comic-style classroom episodes to support their development. Therefore, this research takes a step forward in promoting the role of Lakatos-style activity in the primary school classroom and beyond."],"dc:format.checksum.md5":["ff87a8f4ca9470f9d5e423c101426930","87eda9de84448d1f82354d60eee3eb5f"],"dc:identifier.doi":["https://doi.org/10.17863/CAM.115816"],"dc:identifier.uri":["https://www.repository.cam.ac.uk/bitstreams/05770904-77c6-4a96-844b-dc7642824acd/download"],"dc:language":["eng"],"dc:publisher.institution":["University of Cambridge"],"dc:relation.isreferencedby.uri":["https://www.repository.cam.ac.uk/handle/1810/379845"],"dc:rights":["https://www.repository.cam.ac.uk/bitstreams/f3b5f71c-2227-4089-90ce-c2e0ff82a3fd/download","http://purl.org/NET/rdflicense/allrightsreserved"],"dc:rights.embargotype":["controlled.access"],"dc:subject":["Argumentation and proof","Comic-style vignettes","Conjecture refinement","Focus groups","Lakatos-style proving activity","Mathematics education","Mixed methods","Primary school","Proof and proving","Supportive examples and counterexamples","Survey","Teacher education","Teachers’ mathematical knowledge","Teachers’ views"],"dc:title":["Lakatos-style proving activity in primary school: A mixed-methods study to explore and support teachers’ mathematical knowledge and views"],"dc:type":["Thesis"],"dc:type.qualificationlevel":["Doctoral"],"dc:type.qualificationname":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T01:33:00Z"}