Journal of Mathematical Behavior最新文献_第4页

Diagrams as joint epistemic actions: A dialogical account of diagrams in mathematical proofs 作为联合认知行为的图表：数学证明中图表的对话说明

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Journal of Mathematical Behavior Pub Date : 2025-12-01 Epub Date: 2025-06-24 DOI: 10.1016/j.jmathb.2025.101271

Catarina Dutilh Novaes

{"title":"Diagrams as joint epistemic actions: A dialogical account of diagrams in mathematical proofs","authors":"Catarina Dutilh Novaes","doi":"10.1016/j.jmathb.2025.101271","DOIUrl":"10.1016/j.jmathb.2025.101271","url":null,"abstract":"<div><div>The book <em>The Dialogical Roots of Deduction</em> presented a detailed dialogical account of deduction, in particular of mathematical proof. The key idea is that a mathematical proof corresponds to a dialogue between two (fictive) participants, Prover and Skeptic, where Prover attempts to establish that some conclusion follows from certain premises by producing explanatory persuasion in Skeptic. While covering many aspects of mathematical proof, the book did not discuss <em>diagrams</em>, despite their ubiquity in mathematical practice. In this paper, I remedy this important lacuna in the original presentation of the dialogical account. I argue that diagrams play a fundamental epistemic role in eliciting active engagement from Skeptic to understand the argument put forward by Prover. To this end, Prover relies on imperatives to invite Skeptic to construct diagrams. Thus understood, the role of diagrams in mathematical proofs is primarily <em>operative</em> rather than semantic/representational, eliciting ‘hands-on’ engagement. In particular, I argue that diagrams in mathematical proofs are best understood as <em>joint epistemic actions</em>, thus highlighting their role in the production and transmission of (mathematical) knowledge and understanding. I close with some observations on the implications of this account of diagrams for mathematics education.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"80 ","pages":"Article 101271"},"PeriodicalIF":1.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144365763","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

Discursive differences in written feedback of individuals with varied teaching experiences: Towards validating knowledge of content and teaching specific to proof 具有不同教学经验的个人书面反馈的话语差异：对内容和教学具体证明的验证知识

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Journal of Mathematical Behavior Pub Date : 2025-12-01 Epub Date: 2025-06-25 DOI: 10.1016/j.jmathb.2025.101272

Orly Buchbinder , Rebecca Butler , Sharon McCrone

引用次数: 0

Using test cases to refute incorrect existentially quantified propositions: An exploratory study 用测试用例驳斥不正确的存在量化命题：一项探索性研究

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Journal of Mathematical Behavior Pub Date : 2025-12-01 Epub Date: 2025-06-12 DOI: 10.1016/j.jmathb.2025.101268

John Griffith Tupouniua , John Smith

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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 : 2025-12-01 Epub Date: 2025-06-02 DOI: 10.1016/j.jmathb.2025.101260

Gustavo Martínez-Sierra , Kleiver Jesús Villadiego Franco

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Experienced provers’ operative logical principles for evaluating proofs of conditional claims 有经验的证明者评估条件断言证明的操作逻辑原则

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Journal of Mathematical Behavior Pub Date : 2025-12-01 Epub Date: 2025-08-27 DOI: 10.1016/j.jmathb.2025.101282

Steven Ruiz , Mario Gonzalez , Paul Christian Dawkins , Kyeong Hah Roh

引用次数: 0

Upper secondary students’ ways of operationalizing the ‘for all’ statement in examining differentiability of a function using CAS 高中生在用CAS检验函数可微性时对“for all”语句的操作方法

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Journal of Mathematical Behavior Pub Date : 2025-12-01 Epub Date: 2025-07-03 DOI: 10.1016/j.jmathb.2025.101274

Mathilde Kjær Pedersen , Morten Misfeldt , Uffe Thomas Jankvist

{"title":"Upper secondary students’ ways of operationalizing the ‘for all’ statement in examining differentiability of a function using CAS","authors":"Mathilde Kjær Pedersen , Morten Misfeldt , Uffe Thomas Jankvist","doi":"10.1016/j.jmathb.2025.101274","DOIUrl":"10.1016/j.jmathb.2025.101274","url":null,"abstract":"<div><div>Mathematical statements involving logical quantifiers are essential in calculus and for mathematical thinking. At upper secondary level mathematics, students are confronted with the universal quantifier in the definition of differentiability of a function, going from pointwise to global (or piecewise) considerations. Based on empirical cases of students in Danish upper secondary school working with tasks on differentiability, the paper addresses students’ ways of operationalizing the ‘for all’ statement of differentiability when using Computer Algebra Systems (CAS). The analyses of the cases illustrate three different operationalizations, which build on some of the same interpretations of the universal quantifier but turned into actions in different ways. Applying instrumental genesis together with Vergnaud’s notion of scheme, the analyses illustrate how students’ anticipations of dealing with ‘for all’ differ from their operationalizations when transitioning to instrumented techniques. This is important to take into consideration when teaching ‘for all’, designing tasks and selecting if, for what and how CAS should be applied in these settings.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"80 ","pages":"Article 101274"},"PeriodicalIF":1.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144550037","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

Mathematics teaching at girls’ Victoriaschule in Gdańsk from the mid-19th century until World War I 19世纪中期至第一次世界大战期间，Gdańsk维多利亚女子中学的数学教学

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Journal of Mathematical Behavior Pub Date : 2025-09-01 Epub Date: 2025-03-06 DOI: 10.1016/j.jmathb.2025.101243

Karolina Karpińska

{"title":"Mathematics teaching at girls’ Victoriaschule in Gdańsk from the mid-19th century until World War I","authors":"Karolina Karpińska","doi":"10.1016/j.jmathb.2025.101243","DOIUrl":"10.1016/j.jmathb.2025.101243","url":null,"abstract":"<div><div>This paper aims to describe mathematics teaching at the <em>Victoriaschule</em> in Gdańsk during the second half of the 19th century and the early 20th century. Although Gdańsk is currently located in Poland, during the period under consideration it was part of Prussian Poland, which refers to the Polish lands under Prussian rule, and it was formerly known as Danzig. The <em>Victoriaschule</em> was established in 1818 and, three years later, became the first public secondary school for girls in Gdańsk. In the latter half of the 19th century, a teachers’ seminary was also opened there. By the early 20th century, due to the efforts of the then-director, a real gymnasium for girls began operation, allowing students to take matriculation exams and pursue university studies. It became one of the best educational institutions for girls in Prussian Poland. This paper will compare mathematics teaching at the <em>Victoriaschule</em> with that in similar schools for boys and other selected girls’ schools operating at the same time in Prussian Poland, including institutions in Bydgoszcz, Grudziądz, Toruń, Malbork, and Kwidzyn. The analysis will focus on curricula, ministerial orders, school textbooks, and the initiatives of individual school reformers.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"79 ","pages":"Article 101243"},"PeriodicalIF":1.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143562293","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 : 2025-09-01 Epub 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 , 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":"2025-09-01","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

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 : 2025-09-01 Epub Date: 2025-05-19 DOI: 10.1016/j.jmathb.2025.101259

Kristen Vroom, José Saúl Barbosa, Abigail Lippert

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 : 2025-09-01 Epub 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, 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":"2025-09-01","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