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What makes a math word problem solvable and clear? An analysis of pre-service teachers' two-step problem posing 是什么让数学题易于解决且清晰明了？职前教师两步问题提出分析
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Journal of Mathematical Behavior Pub Date : 2025-06-02 DOI: 10.1016/j.jmathb.2025.101267
Miriam Sanders , Michelle Kwok , Micayla Gooden
{"title":"What makes a math word problem solvable and clear? An analysis of pre-service teachers' two-step problem posing","authors":"Miriam Sanders ,&nbsp;Michelle Kwok ,&nbsp;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}
引用次数: 0
Exploring students’ covariational reasoning in sine and cosine functions: A comparison of expected and manifested learning trajectories with dynamic tasks 探索学生在正弦和余弦函数中的协变推理：动态任务中预期和实际学习轨迹的比较
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Journal of Mathematical Behavior Pub Date : 2025-06-02 DOI: 10.1016/j.jmathb.2025.101260
Gustavo Martínez-Sierra , Kleiver Jesús Villadiego Franco
{"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 ,&nbsp;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}
引用次数: 0
How two undergraduates used examples and an Euler diagram for making and proving conjectures 两个大学生是如何用例子和欧拉图来做出和证明猜想的
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Journal of Mathematical Behavior Pub Date : 2025-05-19 DOI: 10.1016/j.jmathb.2025.101259
Kristen Vroom, José Saúl Barbosa, Abigail Lippert
{"title":"How two undergraduates used examples and an Euler diagram for making and proving conjectures","authors":"Kristen Vroom,&nbsp;José Saúl Barbosa,&nbsp;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}
引用次数: 0
The semiotic potential of pseudo-random numbers for the idea of indeterminacy in algebra 伪随机数在代数不确定性思想中的符号学潜力
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Journal of Mathematical Behavior Pub Date : 2025-04-30 DOI: 10.1016/j.jmathb.2025.101258
Mirko Maracci , Gabriella Pocalana , Greta Carlino
{"title":"The semiotic potential of pseudo-random numbers for the idea of indeterminacy in algebra","authors":"Mirko Maracci ,&nbsp;Gabriella Pocalana ,&nbsp;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}
引用次数: 0
Quantitative civic literacies: “Let’s talk about election 2020” and youth use of numbers in digital civic media 定量公民素养：数字公民媒体中的 "让我们来谈谈 2020 年大选 "和青少年对数字的使用
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Journal of Mathematical Behavior Pub Date : 2025-04-21 DOI: 10.1016/j.jmathb.2025.101256
Emma C. Gargroetzi , Lynne M. Zummo , Alexandra R. Aguilar , Emma P. Bene
{"title":"Quantitative civic literacies: “Let’s talk about election 2020” and youth use of numbers in digital civic media","authors":"Emma C. Gargroetzi ,&nbsp;Lynne M. Zummo ,&nbsp;Alexandra R. Aguilar ,&nbsp;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}
引用次数: 0
Children’s mathematics concept learning of informal length measurement: Conceptual PlayWorld as an innovative approach in the beginning of primary school period 儿童非正式长度测量的数学概念学习：小学初期概念游戏世界作为一种创新方法
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Journal of Mathematical Behavior Pub Date : 2025-04-11 DOI: 10.1016/j.jmathb.2025.101257
Hong Chen, Leigh Disney, Liang Li
{"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,&nbsp;Leigh Disney,&nbsp;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}
引用次数: 0
An ethnomodel of squid trap “Bubo” in Gigantes Island, Western Visayas, Philippines 菲律宾西维萨亚斯岛的巨型岛鱿鱼陷阱“Bubo”的民族模型
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Journal of Mathematical Behavior Pub Date : 2025-03-29 DOI: 10.1016/j.jmathb.2025.101254
Fresan R. Magnate
{"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}
引用次数: 0
What mathematical explanation need not be 用不着什么数学解释
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Journal of Mathematical Behavior Pub Date : 2025-03-26 DOI: 10.1016/j.jmathb.2025.101255
Elijah Chudnoff , Silvia De Toffoli
{"title":"What mathematical explanation need not be","authors":"Elijah Chudnoff ,&nbsp;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}
引用次数: 0
Notations for neurodiverse learners 神经多样性学习者的符号
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Journal of Mathematical Behavior Pub Date : 2025-03-25 DOI: 10.1016/j.jmathb.2025.101240
Sophie Marchand , Dirk Schlimm
{"title":"Notations for neurodiverse learners","authors":"Sophie Marchand ,&nbsp;Dirk Schlimm","doi":"10.1016/j.jmathb.2025.101240","DOIUrl":"10.1016/j.jmathb.2025.101240","url":null,"abstract":"<div><div>Notations are essential for mathematics, mathematical logic, and many other disciplines. In order for them to be used, they have to be learned and understood, which is relative to the perceptual and cognitive resources of their users. However, most reflections about the design of notations have not taken into consideration the diversity of possible users. In recent years, various groups of people have been identified who exhibit specific strengths and challenges with regard to the reading and processing of written information. This gives us the opportunity to reflect on how particular choices in the design of mathematical and logical notations can hinder and support the ease of reading and understanding for neurodiverse groups of students.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"79 ","pages":"Article 101240"},"PeriodicalIF":1.0,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143696996","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Logical implications as mathematical objects: Characterizing epistemological obstacles experienced in introductory proofs courses 作为数学对象的逻辑蕴涵：描述在入门证明课程中经历的认识论障碍
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Journal of Mathematical Behavior Pub Date : 2025-03-21 DOI: 10.1016/j.jmathb.2025.101253
Anderson Norton , Joseph Antonides , Rachel Arnold , Vladislav Kokushkin
{"title":"Logical implications as mathematical objects: Characterizing epistemological obstacles experienced in introductory proofs courses","authors":"Anderson Norton ,&nbsp;Joseph Antonides ,&nbsp;Rachel Arnold ,&nbsp;Vladislav Kokushkin","doi":"10.1016/j.jmathb.2025.101253","DOIUrl":"10.1016/j.jmathb.2025.101253","url":null,"abstract":"<div><div>Understanding the cognitive challenges students experience in proofs-based mathematics courses is a necessary precursor for supporting them in meeting those challenges. We report on results from a pair of clinical interviews with each of seven STEM majors enrolled in an introductory proofs course. We investigate the epistemological obstacles they experienced in interaction with the interviewer and how those experiences might relate to their treatment of logical implications as actions, objects, or pseudo-objects. We share profiles for each of the seven students, characterizing their treatment of logical implications and their experiences of related epistemological obstacles. These profiles indicate marked differences between epistemological obstacles experienced during interactions with students who treat logical implications as objects, versus actions or pseudo-objects. Results suggest that proof-based mathematics courses should focus centrally on supporting students’ constructions of logical implications as mathematical objects.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"79 ","pages":"Article 101253"},"PeriodicalIF":1.0,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143680519","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}
引用次数: 0
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