Pub Date : 2025-06-12DOI: 10.1016/j.jmathb.2025.101268
John Griffith Tupouniua , John Smith
Towards the goal of extending the applicability of test cases to the context of existentially quantified propositions, the present study explores how test cases might support learners with refuting their incorrect existentially quantified propositions. We present and analyze data from two separate instances in which two in-service primary school teachers initially made incorrect existentially quantified propositions and then were asked to find a valid example of their respective propositions (i.e., an element of the subject that satisfies the predicate). The participants were given, and sometimes generated their own, test cases which led to an iterative process of ruling out potential examples and classes of potential examples. Our analysis of this iterative process as it emerged within our specific research setting, comprising among aspects, particular researcher-participant interactions, sheds light on how these test cases afford and support the development and refinement of the learners’ respective existentially quantified propositions.
{"title":"Using test cases to refute incorrect existentially quantified propositions: An exploratory study","authors":"John Griffith Tupouniua , John Smith","doi":"10.1016/j.jmathb.2025.101268","DOIUrl":"10.1016/j.jmathb.2025.101268","url":null,"abstract":"<div><div>Towards the goal of extending the applicability of test cases to the context of existentially quantified propositions, the present study explores how test cases might support learners with refuting their incorrect existentially quantified propositions. We present and analyze data from two separate instances in which two in-service primary school teachers initially made incorrect existentially quantified propositions and then were asked to find a valid example of their respective propositions (i.e., an element of the subject that satisfies the predicate). The participants were given, and sometimes generated their own, test cases which led to an iterative process of ruling out potential examples and classes of potential examples. Our analysis of this iterative process as it emerged within our specific research setting, comprising among aspects, particular researcher-participant interactions, sheds light on how these test cases afford and support the development and refinement of the learners’ respective existentially quantified propositions.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"80 ","pages":"Article 101268"},"PeriodicalIF":1.0,"publicationDate":"2025-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144263431","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 : 2025-06-11DOI: 10.1016/j.jmathb.2025.101269
Anthony Tucci , Paul Christian Dawkins , Kyeong Hah Roh
This paper presents five categories of undergraduate student justifications regarding the question of whether a converse proof proves a conditional statement. Two categories of justification supported students’ judgments that converse proofs cannot so prove, which is the normative interpretation. These normative judgments depended upon students spontaneously seeking uniform rules of proving across various conditional statements or assigning a direction to the statements and proof. The other three categories of justification supported students to affirm that converse proofs prove. Students offering these justifications do so because they do not perceive any distinction in meaning between a statement and its converse when both are true. The rationality of these nonnormative justifications suggests the need for further work to understand how we can help students understand the normative rules of logic.
{"title":"Student justifications regarding converse independence","authors":"Anthony Tucci , Paul Christian Dawkins , Kyeong Hah Roh","doi":"10.1016/j.jmathb.2025.101269","DOIUrl":"10.1016/j.jmathb.2025.101269","url":null,"abstract":"<div><div>This paper presents five categories of undergraduate student justifications regarding the question of whether a converse proof proves a conditional statement. Two categories of justification supported students’ judgments that converse proofs cannot so prove, which is the normative interpretation. These normative judgments depended upon students spontaneously seeking uniform rules of proving across various conditional statements or assigning a direction to the statements and proof. The other three categories of justification supported students to affirm that converse proofs prove. Students offering these justifications do so because they do not perceive any distinction in meaning between a statement and its converse when both are true. The rationality of these nonnormative justifications suggests the need for further work to understand how we can help students understand the normative rules of logic.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"80 ","pages":"Article 101269"},"PeriodicalIF":1.0,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144263306","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 : 2025-06-02DOI: 10.1016/j.jmathb.2025.101267
Miriam Sanders , Michelle Kwok , Micayla Gooden
Being able to solve word problems requires understanding and skills to address the complex interaction between distinct yet interrelated mathematical, linguistic, and contextual features. As word problems increase in complexity by requiring multiple steps in the solution process, students are faced with additional challenges. Effective integration of problem posing into mathematics curricula and instruction requires providing teachers and preservice teachers with comprehensive problem posing instruction. To this end, the authors have employed a variety of problem posing tasks and strategies to support pre-service teachers. The authors analyze 56 samples of problems posed by preservice teachers enrolled in a problem solving course. The findings illuminate the mathematical and linguistic features of two-step word problems to understand what makes for clear, solvable word problems. Implications include resources to inform curricular development, assessment, as well as future research directions in the complexities of two-step word problems.
{"title":"What makes a math word problem solvable and clear? An analysis of pre-service teachers' two-step problem posing","authors":"Miriam Sanders , Michelle Kwok , Micayla Gooden","doi":"10.1016/j.jmathb.2025.101267","DOIUrl":"10.1016/j.jmathb.2025.101267","url":null,"abstract":"<div><div>Being able to solve word problems requires understanding and skills to address the complex interaction between distinct yet interrelated mathematical, linguistic, and contextual features. As word problems increase in complexity by requiring multiple steps in the solution process, students are faced with additional challenges. Effective integration of problem posing into mathematics curricula and instruction requires providing teachers and preservice teachers with comprehensive problem posing instruction. To this end, the authors have employed a variety of problem posing tasks and strategies to support pre-service teachers. The authors analyze 56 samples of problems posed by preservice teachers enrolled in a problem solving course. The findings illuminate the mathematical and linguistic features of two-step word problems to understand what makes for clear, solvable word problems. Implications include resources to inform curricular development, assessment, as well as future research directions in the complexities of two-step word problems.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"80 ","pages":"Article 101267"},"PeriodicalIF":1.0,"publicationDate":"2025-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144194683","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}
This study investigates how high school students develop covariational reasoning in the context of trigonometric functions by integrating dynamic GeoGebra applets within a design-based research framework. Guided by a Hypothetical Learning Trajectory (HLT), the research compares the expected progression of reasoning—from coordination of values to smooth continuous covariation—with the actual reasoning manifested by students during iterative instructional cycles. Qualitative analyses of students’ task artifacts and verbal explanations reveal distinct learning trajectories among participants, highlighting the importance of task sequencing, explicit scaffolding, and dynamic visualization for fostering continuous reasoning. The findings inform instructional design by identifying key areas for differentiated support and further refinement of digital interventions in mathematics education.
{"title":"Exploring students’ covariational reasoning in sine and cosine functions: A comparison of expected and manifested learning trajectories with dynamic tasks","authors":"Gustavo Martínez-Sierra , Kleiver Jesús Villadiego Franco","doi":"10.1016/j.jmathb.2025.101260","DOIUrl":"10.1016/j.jmathb.2025.101260","url":null,"abstract":"<div><div>This study investigates how high school students develop covariational reasoning in the context of trigonometric functions by integrating dynamic GeoGebra applets within a design-based research framework. Guided by a Hypothetical Learning Trajectory (HLT), the research compares the expected progression of reasoning—from coordination of values to smooth continuous covariation—with the actual reasoning manifested by students during iterative instructional cycles. Qualitative analyses of students’ task artifacts and verbal explanations reveal distinct learning trajectories among participants, highlighting the importance of task sequencing, explicit scaffolding, and dynamic visualization for fostering continuous reasoning. The findings inform instructional design by identifying key areas for differentiated support and further refinement of digital interventions in mathematics education.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"80 ","pages":"Article 101260"},"PeriodicalIF":1.0,"publicationDate":"2025-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144194682","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 : 2025-05-19DOI: 10.1016/j.jmathb.2025.101259
Kristen Vroom, José Saúl Barbosa, Abigail Lippert
Traditional approaches to undergraduate classrooms tend to present mathematical theorems and proofs as finished products, hiding the mathematical activity that went into their development. In this study, we crafted opportunities for two undergraduate students in a teaching experiment setting to engage in the activity of making and proving their own conjectures. We investigated how these students (with the guidance of a teacher-researcher) used an Euler diagram and examples to support their conjecturing and proving activity. The students’ evolving Euler diagram served as an organizer for their examples, allowing them to capture particular instances of the concepts and structural relationships between the concepts. By identifying different ways that the students leveraged this evolving Euler diagram with their examples, we provide insight about beneficial tools for students to engage in such mathematical activity.
{"title":"How two undergraduates used examples and an Euler diagram for making and proving conjectures","authors":"Kristen Vroom, José Saúl Barbosa, Abigail Lippert","doi":"10.1016/j.jmathb.2025.101259","DOIUrl":"10.1016/j.jmathb.2025.101259","url":null,"abstract":"<div><div>Traditional approaches to undergraduate classrooms tend to present mathematical theorems and proofs as finished products, hiding the mathematical activity that went into their development. In this study, we crafted opportunities for two undergraduate students in a teaching experiment setting to engage in the activity of making and proving their own conjectures. We investigated how these students (with the guidance of a teacher-researcher) used an Euler diagram and examples to support their conjecturing and proving activity. The students’ evolving Euler diagram served as an organizer for their examples, allowing them to capture particular instances of the concepts and structural relationships between the concepts. By identifying different ways that the students leveraged this evolving Euler diagram with their examples, we provide insight about beneficial tools for students to engage in such mathematical activity.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"79 ","pages":"Article 101259"},"PeriodicalIF":1.0,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144089855","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 : 2025-04-30DOI: 10.1016/j.jmathb.2025.101258
Mirko Maracci , Gabriella Pocalana , Greta Carlino
This article is focused on the potential of spreadsheets to foster the transition from arithmetic to algebra in students who have not yet been exposed to formal algebra instruction. We study the potential of the pseudo-random number generator functionality of spreadsheets with the theory of semiotic mediation. Results are reported from a teaching sequence in which 6th-grade students (aged 11–12) are given tasks in spreadsheets incorporating this functionality. We analyze the artefact signs produced by a pair of students while solving the tasks, in terms of the processes pointed out by Radford as distinguishing features of algebraic thinking: addressing indeterminacy, denoting indeterminate numbers and operating on indeterminate numbers. In light of this analysis, we discuss the actual unfolding of the hypothesized semiotic potential of the pseudo-random number generator functionality, together with difficulties and cautions emerged, as well as possible refinements in the design of future iterations of the intervention.
{"title":"The semiotic potential of pseudo-random numbers for the idea of indeterminacy in algebra","authors":"Mirko Maracci , Gabriella Pocalana , Greta Carlino","doi":"10.1016/j.jmathb.2025.101258","DOIUrl":"10.1016/j.jmathb.2025.101258","url":null,"abstract":"<div><div>This article is focused on the potential of spreadsheets to foster the transition from arithmetic to algebra in students who have not yet been exposed to formal algebra instruction. We study the potential of the pseudo-random number generator functionality of spreadsheets with the theory of semiotic mediation. Results are reported from a teaching sequence in which 6th-grade students (aged 11–12) are given tasks in spreadsheets incorporating this functionality. We analyze the artefact signs produced by a pair of students while solving the tasks, in terms of the processes pointed out by Radford as distinguishing features of algebraic thinking: addressing indeterminacy, denoting indeterminate numbers and operating on indeterminate numbers. In light of this analysis, we discuss the actual unfolding of the hypothesized semiotic potential of the pseudo-random number generator functionality, together with difficulties and cautions emerged, as well as possible refinements in the design of future iterations of the intervention.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"79 ","pages":"Article 101258"},"PeriodicalIF":1.0,"publicationDate":"2025-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143886237","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 : 2025-04-21DOI: 10.1016/j.jmathb.2025.101256
Emma C. Gargroetzi , Lynne M. Zummo , Alexandra R. Aguilar , Emma P. Bene
Amid global turmoil, the mathematical demands of civic life and the civic demands of mathematics education are greater than ever. International goals of mathematics education include preparation for civic life. Curricula focused on receptive analytic activities, however, positions youth as underdeveloped civic actors needing preparation for responsible future participation rather than treating them as civic actors today. To better understand how youth use mathematics in their civic participation today, we conceptualize quantitative civic literacies as the practices of reinscribing quantitative information into civic participation. We investigate quantitative civic literacies in youth digital civic media about racial justice, the COVID-19 pandemic, and the climate crisis, drawing data from a US-based, public radio-hosted, digital media platform called Let’s Talk about Election 2020. Findings identified six quantitative civic literacies engaged by youth; youth used quantitative forms including counts and locations, relationship and change, and uncertainty in making civic arguments to (1) communicate the magnitude of an issue, (2) situate an issue in space or time, (3) reason about causation or propose a theory of change, (4) provide specificity through narrative detail, (5) make claims about identity, and (6) reveal injustice. Beyond providing logical argumentation and legitimacy, numbers were used by youth to activate empathy and mobilize ethical calls in attempts to move others to action. With these insights, we provide inroads for a mathematics education for civic life that builds on a more expansive understanding of the rhetorical potential of numbers and of youth as civic actors to nurture youth quantitative civic literacies.
在全球动荡中，公民生活对数学的需求和公民对数学教育的需求比以往任何时候都要大。数学教育的国际目标包括为公民生活做准备。然而，课程侧重于接受性分析活动，将青年定位为欠发达的公民行为体，需要为负责任的未来参与做准备，而不是将他们视为今天的公民行为体。为了更好地理解今天的年轻人如何在公民参与中使用数学，我们将定量公民素养定义为将定量信息重新写入公民参与的实践。我们调查了青年数字公民媒体中关于种族正义、COVID-19大流行和气候危机的定量公民素养，并从美国公共广播主持的数字媒体平台“Let 's Talk about Election 2020”中获取数据。调查结果确定了青年参与的六种定量公民素养；青年在进行公民辩论时使用数量形式，包括数量和位置，关系和变化，以及不确定性，以(1)传达问题的严重性，(2)将问题置于空间或时间中，(3)推理因果关系或提出变化理论，(4)通过叙事细节提供特殊性，(5)对身份提出要求，(6)揭示不公正。除了提供合乎逻辑的论证和合法性之外，年轻人还用数字来激发同理心，动员道德呼吁，试图推动他人采取行动。有了这些见解，我们为公民生活的数学教育提供了进展，这种教育建立在对数字和青年作为公民行动者的修辞潜力的更广泛理解的基础上，以培养青年的定量公民素养。
{"title":"Quantitative civic literacies: “Let’s talk about election 2020” and youth use of numbers in digital civic media","authors":"Emma C. Gargroetzi , Lynne M. Zummo , Alexandra R. Aguilar , Emma P. Bene","doi":"10.1016/j.jmathb.2025.101256","DOIUrl":"10.1016/j.jmathb.2025.101256","url":null,"abstract":"<div><div>Amid global turmoil, the mathematical demands of civic life and the civic demands of mathematics education are greater than ever. International goals of mathematics education include preparation for civic life. Curricula focused on receptive analytic activities, however, positions youth as underdeveloped civic actors needing preparation for responsible future participation rather than treating them as civic actors today. To better understand how youth use mathematics in their civic participation today, we conceptualize <em>quantitative civic literacies</em> as the practices of reinscribing quantitative information into civic participation. We investigate quantitative civic literacies in youth digital civic media about racial justice, the COVID-19 pandemic, and the climate crisis, drawing data from a US-based, public radio-hosted, digital media platform called <em>Let’s Talk about Election 2020</em>. Findings identified six quantitative civic literacies engaged by youth; youth used quantitative forms including counts and locations, relationship and change, and uncertainty in making civic arguments to (1) communicate the magnitude of an issue, (2) situate an issue in space or time, (3) reason about causation or propose a theory of change, (4) provide specificity through narrative detail, (5) make claims about identity, and (6) reveal injustice. Beyond providing logical argumentation and legitimacy, numbers were used by youth to activate empathy and mobilize ethical calls in attempts to move others to action. With these insights, we provide inroads for a mathematics education for civic life that builds on a more expansive understanding of the rhetorical potential of numbers and of youth as civic actors to nurture youth quantitative civic literacies.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"79 ","pages":"Article 101256"},"PeriodicalIF":1.0,"publicationDate":"2025-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143851851","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 : 2025-04-11DOI: 10.1016/j.jmathb.2025.101257
Hong Chen, Leigh Disney, Liang Li
Measurement is an essential and valuable mathematics concept closely linked to everyday life and is often one of the first few mathematics concepts children learn in educational contexts. Currently, limited research exists that investigates how implementing imaginary play could create conditions in supporting children’s learning of informal length measurement as they transition to school. To support children’s learning of informal length measurement, this study adapted Li and Disney’s (2021) Conceptual PlayWorld [CPW] in mathematics to conduct an educational experiment investigating how the implementation of CPW creates the conditions to support children’s learning during the transition to school. We argue that in the CPW, the use of imagination and the teacher’s dramatisation of the mathematics conceptual problems allowed opportunities for children to demonstrate and explore informal length measurement using their everyday understanding of concepts. In turn, it supports the teacher in embedding mathematical learning opportunities in the imaginary play context. CPW can be considered an alternative pedagogical approach that incorporates mathematical exploration through imaginary play, creates opportunities to support children to engage with and understand measurement concepts.
{"title":"Children’s mathematics concept learning of informal length measurement: Conceptual PlayWorld as an innovative approach in the beginning of primary school period","authors":"Hong Chen, Leigh Disney, Liang Li","doi":"10.1016/j.jmathb.2025.101257","DOIUrl":"10.1016/j.jmathb.2025.101257","url":null,"abstract":"<div><div>Measurement is an essential and valuable mathematics concept closely linked to everyday life and is often one of the first few mathematics concepts children learn in educational contexts. Currently, limited research exists that investigates how implementing imaginary play could create conditions in supporting children’s learning of informal length measurement as they transition to school. To support children’s learning of informal length measurement, this study adapted Li and Disney’s (2021) Conceptual PlayWorld [CPW] in mathematics to conduct an educational experiment investigating how <em>the implementation of CPW</em> creates the conditions to support children’s learning during the transition to school. We argue that in the CPW, the use of imagination and the teacher’s dramatisation of the mathematics conceptual problems allowed opportunities for children to demonstrate and explore informal length measurement using their everyday understanding of concepts. In turn, it supports the teacher in embedding mathematical learning opportunities in the imaginary play context. CPW can be considered an alternative pedagogical approach that incorporates mathematical exploration through imaginary play, creates opportunities to support children to engage with and understand measurement concepts.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"79 ","pages":"Article 101257"},"PeriodicalIF":1.0,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143816773","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 : 2025-03-29DOI: 10.1016/j.jmathb.2025.101254
Fresan R. Magnate
This study investigated the mathematical model for squid traps (Bubo) as one fishing gear in Gigantes Island, Western Visayas, Philippines. Field notes, video recordings, interviews, and participant observations were conducted from constructing the squid trap (Bubo) to its application. A mutual interrogation approach was utilized as approach to ethnomodeling to present cultural practices of the “manugbubo” and the parallel and beyond of these practices in academic mathematics. The model of a squid trap (Bubo) displays symmetry, congruence, similarity, angles, transversal, triangles, and parallelograms. The angles formed within a squid trap can aid in understanding concepts such as sine, cosine, and tangent, as well as their applications in solving problems related to right triangles. Using this squid trap model in teaching mathematics will encourage teachers and learners to value the richness of mathematical knowledge and appreciate academic mathematics, knowing its presence in their daily activities in their community.
{"title":"An ethnomodel of squid trap “Bubo” in Gigantes Island, Western Visayas, Philippines","authors":"Fresan R. Magnate","doi":"10.1016/j.jmathb.2025.101254","DOIUrl":"10.1016/j.jmathb.2025.101254","url":null,"abstract":"<div><div>This study investigated the mathematical model for squid traps (Bubo) as one fishing gear in Gigantes Island, Western Visayas, Philippines. Field notes, video recordings, interviews, and participant observations were conducted from constructing the squid trap (Bubo) to its application. A mutual interrogation approach was utilized as approach to ethnomodeling to present cultural practices of the “manugbubo” and the parallel and beyond of these practices in academic mathematics. The model of a squid trap (Bubo) displays symmetry, congruence, similarity, angles, transversal, triangles, and parallelograms. The angles formed within a squid trap can aid in understanding concepts such as sine, cosine, and tangent, as well as their applications in solving problems related to right triangles. Using this squid trap model in teaching mathematics will encourage teachers and learners to value the richness of mathematical knowledge and appreciate academic mathematics, knowing its presence in their daily activities in their community.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"79 ","pages":"Article 101254"},"PeriodicalIF":1.0,"publicationDate":"2025-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143726146","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 : 2025-03-26DOI: 10.1016/j.jmathb.2025.101255
Elijah Chudnoff , Silvia De Toffoli
Recent works in the philosophy of mathematical practice and mathematical education have challenged orthodox views of mathematical explanation by developing Understanding-first accounts according to which mathematical explanation should be cashed out in terms of understanding. In this article, we explore two arguments that might have motivated this move, (i) the context-sensitivity argument and (ii) the inadequacy of knowing why argument. We show that although these arguments are derived from compelling observations, they ultimately rest on a misunderstanding of what Explanation-first accounts are committed to and an underestimation of the resources available to them. By clarifying the terms at play in the debate and distinguishing different objects of evaluation, we show that the insightful observations about practice and education made by challengers to the orthodoxy are in fact best accounted for within the traditional Explanation-first framework.
{"title":"What mathematical explanation need not be","authors":"Elijah Chudnoff , Silvia De Toffoli","doi":"10.1016/j.jmathb.2025.101255","DOIUrl":"10.1016/j.jmathb.2025.101255","url":null,"abstract":"<div><div>Recent works in the philosophy of mathematical practice and mathematical education have challenged orthodox views of mathematical explanation by developing Understanding-first accounts according to which mathematical explanation should be cashed out in terms of understanding. In this article, we explore two arguments that might have motivated this move, (i) <em>the context-sensitivity argument</em> and (ii) <em>the inadequacy of knowing why argument</em>. We show that although these arguments are derived from compelling observations, they ultimately rest on a misunderstanding of what Explanation-first accounts are committed to and an underestimation of the resources available to them. By clarifying the terms at play in the debate and distinguishing different objects of evaluation, we show that the insightful observations about practice and education made by challengers to the orthodoxy are in fact best accounted for within the traditional Explanation-first framework.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"79 ","pages":"Article 101255"},"PeriodicalIF":1.0,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143706218","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}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号