Pub Date : 2025-11-04DOI: 10.1016/j.jmathb.2025.101299
Dionne Cross Francis , Pavneet Kaur Bharaj , Kathryn Habib , Anna Hinden , Anna Gustaveson , Ji Hong
{"title":"Corrigendum to “Understanding the role of refutation texts on pre-service teachers’ mathematics-related beliefs” [Journal of Mathematical Behavior 80 (2025), 101278]","authors":"Dionne Cross Francis , Pavneet Kaur Bharaj , Kathryn Habib , Anna Hinden , Anna Gustaveson , Ji Hong","doi":"10.1016/j.jmathb.2025.101299","DOIUrl":"10.1016/j.jmathb.2025.101299","url":null,"abstract":"","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"81 ","pages":"Article 101299"},"PeriodicalIF":1.7,"publicationDate":"2025-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145684568","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-31DOI: 10.1016/j.jmathb.2025.101297
Hortensia Soto, Ashley Armbruster, Emily Varney, Francisco De Jesus Pagan
We explored how undergraduates, enrolled in an introductory linear algebra course, collectively created an assemblage of a shear using 3-D change of basis vectors through intra-actions with their own fabricated material. Our theoretical perspective, inclusive materialism, posits that learning is the invention of a new creation that manifests through imagination in unusual and unexpected ways. It describes mathematics as an assemblage between the body of participants and the body of their materials that give shape to an activity, where affective and aesthetic features contribute to the virtuality of the body of mathematics. Our findings suggest that the class created an assemblage of a shear by (a) introducing or catalyzing the new and (b) showcasing how aesthetics and affect inspire intra-actions. This work contributes to the research at the intersection of linear algebra and embodiment, which can contribute to classroom assessments.
{"title":"The shears know: Creative assemblage with 3-D change of basis vectors","authors":"Hortensia Soto, Ashley Armbruster, Emily Varney, Francisco De Jesus Pagan","doi":"10.1016/j.jmathb.2025.101297","DOIUrl":"10.1016/j.jmathb.2025.101297","url":null,"abstract":"<div><div>We explored how undergraduates, enrolled in an introductory linear algebra course, collectively created an assemblage of a shear using 3-D change of basis vectors through intra-actions with their own fabricated material. Our theoretical perspective, <em>inclusive materialism,</em> posits that learning is the invention of a new creation that manifests through imagination in unusual and unexpected ways. It describes mathematics as an assemblage between the body of participants and the body of their materials that give shape to an activity, where affective and aesthetic features contribute to the virtuality of the body of mathematics. Our findings suggest that the class created an assemblage of a shear by (a) <em>introducing or catalyzing the new</em> and (b) showcasing how aesthetics and affect inspire intra-actions. This work contributes to the research at the intersection of linear algebra and embodiment, which can contribute to classroom assessments.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"81 ","pages":"Article 101297"},"PeriodicalIF":1.7,"publicationDate":"2025-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145416976","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-17DOI: 10.1016/j.jmathb.2025.101295
Konstantinos P. Christou , Eleni Vellidou
This study examines how a function machine learning environment can instantiate a developmental trajectory of understanding variables in first-grade students. The intervention involved exploring input-output relationships and symbolic representations of indeterminate quantities. Data were collected through classroom interactions and interviews at three time points: before, immediately after, and six weeks following the intervention. The analyses revealed multiple developmental pathways. Some students progressed directly from pre-variable reasoning to advanced algebraic applications of variable notation. Others consolidated their understanding at intermediate stages or displayed misconceptions, such as treating letters as labels. Though a few students reverted, most maintained or deepened their new understandings, demonstrating the durability of learning. These results highlight the potential of function machines as instructional tools that facilitate exploration, identify misconceptions, and enable timely guidance. They also show how learning trajectories can inform instructional designs that foster early functional reasoning and challenge deficit views of young learners' algebraic capacities.
{"title":"First graders’ understanding of variables: Learning trajectories in a function machine environment","authors":"Konstantinos P. Christou , Eleni Vellidou","doi":"10.1016/j.jmathb.2025.101295","DOIUrl":"10.1016/j.jmathb.2025.101295","url":null,"abstract":"<div><div>This study examines how a function machine learning environment can instantiate a developmental trajectory of understanding variables in first-grade students. The intervention involved exploring input-output relationships and symbolic representations of indeterminate quantities. Data were collected through classroom interactions and interviews at three time points: before, immediately after, and six weeks following the intervention. The analyses revealed multiple developmental pathways. Some students progressed directly from pre-variable reasoning to advanced algebraic applications of variable notation. Others consolidated their understanding at intermediate stages or displayed misconceptions, such as treating letters as labels. Though a few students reverted, most maintained or deepened their new understandings, demonstrating the durability of learning. These results highlight the potential of function machines as instructional tools that facilitate exploration, identify misconceptions, and enable timely guidance. They also show how learning trajectories can inform instructional designs that foster early functional reasoning and challenge deficit views of young learners' algebraic capacities.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"81 ","pages":"Article 101295"},"PeriodicalIF":1.7,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145324418","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-20DOI: 10.1016/j.jmathb.2025.101284
George Kinnear , Matthew Inglis
The relationship between understanding and aesthetic appraisal in mathematics is an open question, with implications for both the philosophy of mathematics and mathematics education. In this study, we investigated how undergraduate students’ understanding of a mathematical proof relates to their perception of its aesthetic value. Participants were asked to evaluate the proof’s aesthetics and to complete three different assessments of their understanding. The results reveal that self-reported understanding was moderately associated with aesthetic appraisals, while two performance-based measures of understanding showed close-to-zero relationships. These findings challenge the view that aesthetic judgements in mathematics are merely disguised epistemic judgements, and suggest that future research should focus on exploring the non-epistemic factors that shape aesthetic judgements. We conclude by discussing the implications of these results for educational practices that seek to promote aesthetic experiences.
{"title":"Does understanding moderate aesthetic appraisals of proofs?","authors":"George Kinnear , Matthew Inglis","doi":"10.1016/j.jmathb.2025.101284","DOIUrl":"10.1016/j.jmathb.2025.101284","url":null,"abstract":"<div><div>The relationship between understanding and aesthetic appraisal in mathematics is an open question, with implications for both the philosophy of mathematics and mathematics education. In this study, we investigated how undergraduate students’ understanding of a mathematical proof relates to their perception of its aesthetic value. Participants were asked to evaluate the proof’s aesthetics and to complete three different assessments of their understanding. The results reveal that self-reported understanding was moderately associated with aesthetic appraisals, while two performance-based measures of understanding showed close-to-zero relationships. These findings challenge the view that aesthetic judgements in mathematics are merely disguised epistemic judgements, and suggest that future research should focus on exploring the non-epistemic factors that shape aesthetic judgements. We conclude by discussing the implications of these results for educational practices that seek to promote aesthetic experiences.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"81 ","pages":"Article 101284"},"PeriodicalIF":1.7,"publicationDate":"2025-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097144","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-18DOI: 10.1016/j.jmathb.2025.101294
Holly Zolt , Kathleen Melhuish
Quotient groups are a foundational topic within abstract algebra courses, and they provide a context in which rich, powerful, and vivid language can be used to convey an understanding of the mathematics at play. We examined the language mathematicians used to describe their instruction on quotient groups and found that mathematicians draw on several source domains and use various metaphorical expressions when discussing their teaching practices. Of prominence in these findings was the use of a construction source domain which spanned all major aspects of quotient groups. The use of this source domain afforded the use of many metaphorical expressions that are tied to various formal content goals. We detail these findings and discuss how the metaphorical expressions used relate to the formal mathematics content that mathematicians are trying to convey.
{"title":"Laying the groundwork: The grounding metaphors that build quotient groups","authors":"Holly Zolt , Kathleen Melhuish","doi":"10.1016/j.jmathb.2025.101294","DOIUrl":"10.1016/j.jmathb.2025.101294","url":null,"abstract":"<div><div>Quotient groups are a foundational topic within abstract algebra courses, and they provide a context in which rich, powerful, and vivid language can be used to convey an understanding of the mathematics at play. We examined the language mathematicians used to describe their instruction on quotient groups and found that mathematicians draw on several source domains and use various metaphorical expressions when discussing their teaching practices. Of prominence in these findings was the use of a construction source domain which spanned all major aspects of quotient groups. The use of this source domain afforded the use of many metaphorical expressions that are tied to various formal content goals. We detail these findings and discuss how the metaphorical expressions used relate to the formal mathematics content that mathematicians are trying to convey.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"81 ","pages":"Article 101294"},"PeriodicalIF":1.7,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097141","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-13DOI: 10.1016/j.jmathb.2025.101285
John Paul Cook , April Richardson , Zackery Reed , Elise Lockwood , O. Hudson Payne , Cory Wilson
Equivalence transformations – that is, transformations that produce an object that is equivalent to the original – are a unifying conceptual thread in K-16 mathematics. Though researchers have already established that productive reasoning about equivalence transformations hinges on an awareness that the transformed objects are equivalent to the given object, research (a) has not yet explored the various ways in which students might attend to equivalence, and (b) has primarily examined equivalence transformations on only one type of object, leaving open the question of what commonalities might be present in students’ reasoning across transformations of multiple types of objects. In this study, we present our analysis of task-based clinical interviews with university students. This paper’s primary contribution to the literature involves the description and illustration of three common, unified ways in the students productively reasoned about the equivalence of the objects they produced with transformations. Our findings extend the theoretical scope of an existing equivalence framework and suggest that these ways of reasoning can inform efforts to help students overcome the widespread reports of difficulties they experience. We conclude with a discussion of the theoretical implications for research on equivalence transformations across K-16 mathematics.
{"title":"Students’ productive use of equivalence transformations","authors":"John Paul Cook , April Richardson , Zackery Reed , Elise Lockwood , O. Hudson Payne , Cory Wilson","doi":"10.1016/j.jmathb.2025.101285","DOIUrl":"10.1016/j.jmathb.2025.101285","url":null,"abstract":"<div><div>Equivalence transformations – that is, transformations that produce an object that is equivalent to the original – are a unifying conceptual thread in K-16 mathematics. Though researchers have already established that productive reasoning about equivalence transformations hinges on an awareness that the transformed objects are equivalent to the given object, research (a) has not yet explored the various ways in which students might attend to equivalence, and (b) has primarily examined equivalence transformations on only one type of object, leaving open the question of what commonalities might be present in students’ reasoning across transformations of multiple types of objects. In this study, we present our analysis of task-based clinical interviews with university students. This paper’s primary contribution to the literature involves the description and illustration of three common, unified ways in the students productively reasoned about the equivalence of the objects they produced with transformations. Our findings extend the theoretical scope of an existing equivalence framework and suggest that these ways of reasoning can inform efforts to help students overcome the widespread reports of difficulties they experience. We conclude with a discussion of the theoretical implications for research on equivalence transformations across K-16 mathematics.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"81 ","pages":"Article 101285"},"PeriodicalIF":1.7,"publicationDate":"2025-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145050152","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-06DOI: 10.1016/j.jmathb.2025.101283
Erik S. Tillema , Andrew M. Gatza , Weverton Ataide Pinheiro
This paper reports on one study in a series of design research studies that have taken as a guiding design principle that combinatorial and quantitative reasoning can serve as a constructive resource for high school students to establish algebraic structure between a polynomial and its factors. Within this framing, we report on an interview study with eight 10th-12th grade students whose purpose was to investigate their progress towards generalization of the cubic identity . The students worked on this generalization by solving cases of a 3-D combinatorics problem and representing their solutions using 3-D arrays. Findings include the identification of how differences in students’ combinatorial reasoning impacted their reasoning with 3-dimensional arrays and their progress towards a general statement of the cubic identity.
{"title":"Stage 3 high school students’ generalization of a cubic identity","authors":"Erik S. Tillema , Andrew M. Gatza , Weverton Ataide Pinheiro","doi":"10.1016/j.jmathb.2025.101283","DOIUrl":"10.1016/j.jmathb.2025.101283","url":null,"abstract":"<div><div>This paper reports on one study in a series of design research studies that have taken as a guiding design principle that combinatorial and quantitative reasoning can serve as a constructive resource for high school students to establish algebraic structure between a polynomial and its factors. Within this framing, we report on an interview study with eight 10th-12th grade students whose purpose was to investigate their progress towards generalization of the cubic identity <span><math><mrow><msup><mrow><mo>(</mo><mi>x</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mrow><mn>3</mn></mrow></msup><mo>=</mo><mspace></mspace><msup><mrow><mn>1</mn><mo>∙</mo><mo>(</mo><mi>x</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo><mo>+</mo><mn>3</mn><mo>∙</mo><mrow><mfenced><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>∙</mo><mn>1</mn></mrow></mfenced></mrow><mo>+</mo><mn>3</mn><mo>∙</mo><mrow><mfenced><mrow><msup><mrow><mi>x</mi><mo>∙</mo><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfenced></mrow><mo>+</mo><mn>1</mn><mo>∙</mo><mo>(</mo><msup><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></mrow></math></span>. The students worked on this generalization by solving cases of a 3-D combinatorics problem and representing their solutions using 3-D arrays. Findings include the identification of how differences in students’ combinatorial reasoning impacted their reasoning with 3-dimensional arrays and their progress towards a general statement of the cubic identity.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"81 ","pages":"Article 101283"},"PeriodicalIF":1.7,"publicationDate":"2025-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145005201","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-08-27DOI: 10.1016/j.jmathb.2025.101282
Steven Ruiz , Mario Gonzalez , Paul Christian Dawkins , Kyeong Hah Roh
Introduction to proof courses often teach mathematics majors logical principles to support their later interactions with proof. Prior research tells us little about how students draw upon these principles or their justifications in subsequent processes of comprehending proofs. This study investigates what logical principles thirteen experienced undergraduates employ while reading proofs of conditional claims. We also consider whether and how they justify any of those principles. Asking students to read various proofs related to a given conditional statement helped reveal their attention to and reasoning about logical principles. We found that student judgments were almost always logically normative, but their readiness to justify those principles varied more widely. Furthermore, we observe that students interpreted proofs in terms of inferences rather than truth-values showing some disconnect between their operative logic and the ways logic is generally taught in introduction to proof courses.
{"title":"Experienced provers’ operative logical principles for evaluating proofs of conditional claims","authors":"Steven Ruiz , Mario Gonzalez , Paul Christian Dawkins , Kyeong Hah Roh","doi":"10.1016/j.jmathb.2025.101282","DOIUrl":"10.1016/j.jmathb.2025.101282","url":null,"abstract":"<div><div>Introduction to proof courses often teach mathematics majors logical principles to support their later interactions with proof. Prior research tells us little about how students draw upon these principles or their justifications in subsequent processes of comprehending proofs. This study investigates what logical principles thirteen experienced undergraduates employ while reading proofs of conditional claims. We also consider whether and how they justify any of those principles. Asking students to read various proofs related to a given conditional statement helped reveal their attention to and reasoning about logical principles. We found that student judgments were almost always logically normative, but their readiness to justify those principles varied more widely. Furthermore, we observe that students interpreted proofs in terms of inferences rather than truth-values showing some disconnect between their operative logic and the ways logic is generally taught in introduction to proof courses.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"80 ","pages":"Article 101282"},"PeriodicalIF":1.7,"publicationDate":"2025-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144907760","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-08-19DOI: 10.1016/j.jmathb.2025.101281
Jiyeong Yi , Jasmine Sourwine , Shristi Shrestha
This study investigates the shifts in high school mathematics teachers’ instructional practices when working with emergent bilinguals (EBs) after participating in a collaborative situated professional development (CSPD) program alongside researchers. Over the course of one academic year, the teachers engaged in co-planning, co-teaching, and co-reflecting sessions with the research team while integrating research-based strategies to support EBs in learning mathematics. The CSPD also emphasized implementing cognitively demanding and contextually relevant mathematical tasks. The results reveal that the teachers’ instructional practices significantly improved after participation in the CSPD. These improvements include a stronger ability to maintain the cognitive demand of tasks throughout lessons, an increased focus on creating opportunities for students to articulate and explain their mathematical reasoning, and more effective incorporation of meaningful visual aids that enhance comprehension for EBs. These shifts highlight the potential of CSPD to positively impact mathematics instruction for linguistically diverse classrooms.
{"title":"Enhancing mathematical instruction for emergent bilinguals through collaborative situated professional development","authors":"Jiyeong Yi , Jasmine Sourwine , Shristi Shrestha","doi":"10.1016/j.jmathb.2025.101281","DOIUrl":"10.1016/j.jmathb.2025.101281","url":null,"abstract":"<div><div>This study investigates the shifts in high school mathematics teachers’ instructional practices when working with emergent bilinguals (EBs) after participating in a collaborative situated professional development (CSPD) program alongside researchers. Over the course of one academic year, the teachers engaged in co-planning, co-teaching, and co-reflecting sessions with the research team while integrating research-based strategies to support EBs in learning mathematics. The CSPD also emphasized implementing cognitively demanding and contextually relevant mathematical tasks. The results reveal that the teachers’ instructional practices significantly improved after participation in the CSPD. These improvements include a stronger ability to maintain the cognitive demand of tasks throughout lessons, an increased focus on creating opportunities for students to articulate and explain their mathematical reasoning, and more effective incorporation of meaningful visual aids that enhance comprehension for EBs. These shifts highlight the potential of CSPD to positively impact mathematics instruction for linguistically diverse classrooms.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"80 ","pages":"Article 101281"},"PeriodicalIF":1.7,"publicationDate":"2025-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144865843","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-08-16DOI: 10.1016/j.jmathb.2025.101280
Giulia Lisarelli , Bernardo Nannini
This paper introduces discursive tuning as a new commognitive notion for analyzing how students engage with a digital environment and react to unexpected responses they receive from it. Discursive tuning provides a theoretical tool for describing changes in students’ discourse in response to commognitive conflicts arising during their activity with the digital environment. We discuss the notion’s analytical capacity through some episodes from a study in which upper secondary students interact with the dynagraph of the function f(x)= 1/x. Our analysis identifies specific cases of discursive tuning that occur when students attempt to include into their discourse narratives that are consistent with the behavior of the dynagraph or with canonical mathematical discourse. These cases illustrate how discursive tuning provides insight into how students can resolve commognitive conflicts in productive ways.
{"title":"Discursive tuning: The case of digital environments","authors":"Giulia Lisarelli , Bernardo Nannini","doi":"10.1016/j.jmathb.2025.101280","DOIUrl":"10.1016/j.jmathb.2025.101280","url":null,"abstract":"<div><div>This paper introduces discursive tuning as a new commognitive notion for analyzing how students engage with a digital environment and react to unexpected responses they receive from it. Discursive tuning provides a theoretical tool for describing changes in students’ discourse in response to commognitive conflicts arising during their activity with the digital environment. We discuss the notion’s analytical capacity through some episodes from a study in which upper secondary students interact with the dynagraph of the function <em>f(x)</em>= 1<em>/x</em>. Our analysis identifies specific cases of discursive tuning that occur when students attempt to include into their discourse narratives that are consistent with the behavior of the dynagraph or with canonical mathematical discourse. These cases illustrate how discursive tuning provides insight into how students can resolve commognitive conflicts in productive ways.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"80 ","pages":"Article 101280"},"PeriodicalIF":1.7,"publicationDate":"2025-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144852571","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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