发布求助
文献互助 智能选刊 最新文献

Journal of Mathematical Behavior最新文献

筛选
英文 中文
The impact of advanced mathematics in teaching school mathematics through secondary teachers’ reflections on students’ reasoning 从中学教师对学生推理能力的反思看高等数学对学校数学教学的影响
IF 1
Journal of Mathematical Behavior Pub Date : 2025-07-17 DOI: 10.1016/j.jmathb.2025.101277
Theodossios Zachariades , Charalampos Sakonidis , Sotirios Zoitsakos
{"title":"The impact of advanced mathematics in teaching school mathematics through secondary teachers’ reflections on students’ reasoning","authors":"Theodossios Zachariades ,&nbsp;Charalampos Sakonidis ,&nbsp;Sotirios Zoitsakos","doi":"10.1016/j.jmathb.2025.101277","DOIUrl":"10.1016/j.jmathb.2025.101277","url":null,"abstract":"<div><div>In this paper, we examine the impact of advanced mathematics on secondary school mathematics teaching through teachers' reflections on students' reasoning. Our study explored this impact by examining how 100 in-service secondary mathematics teachers reflected on four students’ answers provided in a hypothetical teaching scenario related to numbers with double decimal representation. The notions of nonlocal and local neighborhoods of mathematics knowledge were employed to analyze the data. The results suggest that the impact of advanced mathematics on teaching identified in teachers’ reflections is related to the interplay between local and nonlocal neighborhoods of the mathematical knowledge being taught. This interplay is productive when it is epistemologically sound and is often influenced by contextual and temporal characteristics of the teaching context (e.g., the tasks provided and the associations encouraged in the moment during teaching).</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"80 ","pages":"Article 101277"},"PeriodicalIF":1.0,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144657077","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
Networking theories of quantitative reasoning and mathematical reasoning to explore students’ understanding of functions 网络理论的定量推理和数学推理探索学生对函数的理解
IF 1
Journal of Mathematical Behavior Pub Date : 2025-07-11 DOI: 10.1016/j.jmathb.2025.101276
Nigar Altindis
{"title":"Networking theories of quantitative reasoning and mathematical reasoning to explore students’ understanding of functions","authors":"Nigar Altindis","doi":"10.1016/j.jmathb.2025.101276","DOIUrl":"10.1016/j.jmathb.2025.101276","url":null,"abstract":"<div><div>This study examines the reasoning processes of secondary school students while they solve tasks that model functional relationships. It networks theories of quantitative reasoning (QR) and mathematical reasoning (MR) by comparing and contrasting while also coordinating and combining covariational reasoning (CR) with MR to investigate students’ understanding of functions within a quantitatively rich problem-solving process. The analysis draws on data from a small-scale teaching experiment involving eight participants. Students operating at Mental Actions 1–2 primarily relied on memorized strategies and surface-level properties, leading to rigid, procedural responses. In particular, students often invoked graphical forms and symbolic conventions—such as the visual shape of a graph or algebraic templates—as fixed cues for function type. This use of shape thinking and conventions reinforced imitative reasoning, as students applied familiar patterns without analyzing underlying quantitative relationships. Conversely, students demonstrating Mental Actions 3–5 exhibited creative reasoning, engaging deeply with covarying relationships to construct well-supported mathematical arguments. This study underscores the bidirectional relationship between CR and imitative reasoning, suggesting that reliance on procedural strategies both arises from and perpetuates limited conceptual understanding.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"80 ","pages":"Article 101276"},"PeriodicalIF":1.0,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144605697","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
“I want them to see their magic!”: Two teachers working within structural constraints to help cultivate their Black girl students’ positive mathematics identities “我要让他们看到自己的魔法！”：两位教师在结构约束下帮助培养黑人女学生的积极数学身份
IF 1
Journal of Mathematical Behavior Pub Date : 2025-07-03 DOI: 10.1016/j.jmathb.2025.101273
Brittany L. Marshall , Dan Battey
{"title":"“I want them to see their magic!”: Two teachers working within structural constraints to help cultivate their Black girl students’ positive mathematics identities","authors":"Brittany L. Marshall ,&nbsp;Dan Battey","doi":"10.1016/j.jmathb.2025.101273","DOIUrl":"10.1016/j.jmathb.2025.101273","url":null,"abstract":"<div><div>Traditional mathematics logics produce inequities that result in the perpetuation of the myths of racialized and gendered hierarchies of mathematical ability (Hottinger, 2016; Martin, 2007). There are few examples of classroom spaces that provide positive mathematics experiences for Black girls, while trying to resist traditional logics. This study looks at two successful teachers, bolstered by the nominations of their administrator and students, who navigate common structural constraints yet build strong positive mathematics identities in their middle-school Black girls. The findings show how these teachers embody aspects of BlackFMP to create safe spaces for Black girls even as they navigated school structures and mindsets that uphold traditional mathematics logics.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"80 ","pages":"Article 101273"},"PeriodicalIF":1.0,"publicationDate":"2025-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144534637","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
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
IF 1
Journal of Mathematical Behavior Pub 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 ,&nbsp;Morten Misfeldt ,&nbsp;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":"2025-07-03","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
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
IF 1
Journal of Mathematical Behavior Pub Date : 2025-06-25 DOI: 10.1016/j.jmathb.2025.101272
Orly Buchbinder , Rebecca Butler , Sharon McCrone
{"title":"Discursive differences in written feedback of individuals with varied teaching experiences: Towards validating knowledge of content and teaching specific to proof","authors":"Orly Buchbinder ,&nbsp;Rebecca Butler ,&nbsp;Sharon McCrone","doi":"10.1016/j.jmathb.2025.101272","DOIUrl":"10.1016/j.jmathb.2025.101272","url":null,"abstract":"<div><div>Fostering student engagement with mathematical reasoning and proving requires a special kind of teacher knowledge – Mathematical Knowledge for Teaching Proof (MKT-P). One important component of MKT-P is Knowledge of Content and Teaching specific to Proof (KCT-P), which is knowledge of pedagogical practices for supporting student learning of proof. Providing effective feedback on students' mathematical arguments is one of the key aspects of KCT-P. This study examined the qualitative differences in written feedback of secondary teachers, undergraduate mathematics and computer science majors, and pre-service teachers participating in a capstone course focused on mathematical reasoning and proving. The discursive distinctions in the groups’ feedback, along with changes in the feedback of prospective teachers, provide empirical support for the construct of KCT-P as knowledge unique to teachers, which develops with experience.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"80 ","pages":"Article 101272"},"PeriodicalIF":1.0,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144470653","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
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
IF 1
Journal of Mathematical Behavior Pub 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":"2025-06-24","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
Issues in teaching mathematics due to switching to English as a medium of instruction within primary schools of Rwanda 卢旺达小学改用英语作为教学媒介导致的数学教学问题
IF 1
Journal of Mathematical Behavior Pub Date : 2025-06-19 DOI: 10.1016/j.jmathb.2025.101270
Fidele Ukobizaba , Jean Francois Maniraho , Alphonse Uworwabayeho
{"title":"Issues in teaching mathematics due to switching to English as a medium of instruction within primary schools of Rwanda","authors":"Fidele Ukobizaba ,&nbsp;Jean Francois Maniraho ,&nbsp;Alphonse Uworwabayeho","doi":"10.1016/j.jmathb.2025.101270","DOIUrl":"10.1016/j.jmathb.2025.101270","url":null,"abstract":"<div><div>This study employed a qualitative research design to investigate issues in teaching and learning mathematics resulting from the switch to English as the medium of instruction (MoI) in primary schools in Rwanda. The study involved 18 upper primary mathematics teachers selected conveniently within Nyamagabe District, Rwanda. Thus, a semi-structured interview was used to collect qualitative data. Data were analyzed thematically. The study's results showed that teachers appreciated the policy of shifting to English as the Medium of Instruction and had a positive perspective on the use of English during instruction. However, teachers struggle to deliver the content in English. They sometimes teach using a combination of English and other languages, including Kinyarwanda. Teachers use textbooks written in the Anglophone or Francophone system to prepare richer content. Thus, challenges such as using mathematical symbols interchangeably were reported. Misusing mathematical symbols may affect students' conceptual understanding.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"80 ","pages":"Article 101270"},"PeriodicalIF":1.0,"publicationDate":"2025-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144314328","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
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
IF 1
Journal of Mathematical Behavior Pub Date : 2025-06-12 DOI: 10.1016/j.jmathb.2025.101268
John Griffith Tupouniua , John Smith
{"title":"Using test cases to refute incorrect existentially quantified propositions: An exploratory study","authors":"John Griffith Tupouniua ,&nbsp;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}
引用次数: 0
Student justifications regarding converse independence 学生对反向独立的论证
IF 1
Journal of Mathematical Behavior Pub Date : 2025-06-11 DOI: 10.1016/j.jmathb.2025.101269
Anthony Tucci , Paul Christian Dawkins , Kyeong Hah Roh
{"title":"Student justifications regarding converse independence","authors":"Anthony Tucci ,&nbsp;Paul Christian Dawkins ,&nbsp;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}
引用次数: 0
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
IF 1
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
下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：604180095
Book学术官方微信