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Journal of Mathematical Behavior最新文献

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Philosophy of mathematical practice and mathematics education: Cross-fertilization, dialogue and prospects
IF 1
Journal of Mathematical Behavior Pub Date : 2024-12-09 DOI: 10.1016/j.jmathb.2024.101208
Yacin Hamami
{"title":"Philosophy of mathematical practice and mathematics education: Cross-fertilization, dialogue and prospects","authors":"Yacin Hamami","doi":"10.1016/j.jmathb.2024.101208","DOIUrl":"10.1016/j.jmathb.2024.101208","url":null,"abstract":"<div><div>Mathematics education and the philosophy of mathematical practice are two fields of research whose domains of investigation overlap in a striking way. And yet, interactions between the two fields have been very limited so far, research being mostly conducted in parallel, sometimes on the very same issues. As a consequence, the potential for interaction and cross-fertilization between the two fields remains largely under-explored and under-exploited. The aim of this article is to encourage these interactions by indicating a number of concrete research opportunities where existing contributions in one field may lead to original developments in the other.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"78 ","pages":"Article 101208"},"PeriodicalIF":1.0,"publicationDate":"2024-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143132652","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
Advances in research on mathematical problem posing: Focus on task variables 数学问题的研究进展：关注任务变量
IF 1
Journal of Mathematical Behavior Pub Date : 2024-12-01 DOI: 10.1016/j.jmathb.2024.101186
Jinfa Cai , Boris Koichu , Benjamin Rott , Chunlian Jiang
{"title":"Advances in research on mathematical problem posing: Focus on task variables","authors":"Jinfa Cai ,&nbsp;Boris Koichu ,&nbsp;Benjamin Rott ,&nbsp;Chunlian Jiang","doi":"10.1016/j.jmathb.2024.101186","DOIUrl":"10.1016/j.jmathb.2024.101186","url":null,"abstract":"<div><div>In this paper, we aim to present an overarching picture of Mathematical Problem Posing (MPP) with a focus on the impact of task variables on MPP products and processes. Admittedly, there are many different settings with which to approach research related to task variables and their associated products and processes in MPP among mathematics students and teachers. In this paper, we approached related research in three kinds of settings: (1) the individual setting, (2) the group setting, and (3) the classroom setting. We then provide some theoretical considerations and literature review in examining task variables in MPP based on four questions: (1) What variables are considered in research on MPP? (2) What methods do researchers use to examine variables in MPP? (3) What do we learn from research on variables about MPP? (4) What might be future directions of research on MPP involving variables?</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"76 ","pages":"Article 101186"},"PeriodicalIF":1.0,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142748221","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
Overcoming impasses in proving processes: Novice provers’ productive actions when encountering stuck points 克服证明过程中的僵局：新手证明者在遇到瓶颈时的富有成效的行动
IF 1
Journal of Mathematical Behavior Pub Date : 2024-11-28 DOI: 10.1016/j.jmathb.2024.101211
Yaomingxin Lu
{"title":"Overcoming impasses in proving processes: Novice provers’ productive actions when encountering stuck points","authors":"Yaomingxin Lu","doi":"10.1016/j.jmathb.2024.101211","DOIUrl":"10.1016/j.jmathb.2024.101211","url":null,"abstract":"<div><div>Research has shown that many undergraduate students struggle to learn to prove, including those who major in mathematics (Moore, 1994; Selden, 2012). While studies have explored how expert mathematicians construct proofs to inform teaching practices, expert strategies might not be equally beneficial to novice provers with limited abilities in proving. Novice provers often face difficulties and impasses when engaged in problem-solving or proving tasks. Looking through the lenses of impasses, this study provides a more fine-grained account by characterizing novice provers’ navigating actions when they encounter impasses to better support them in their proving processes. This research draws on task-based interviews conducted with undergraduates enrolled in a transition-to-proof course. A framework was developed to identify productive actions students took when navigating stuck points in the proving process. The result of this study shows that productive actions around stuck points can develop important proof skills in students, even if the student did not ultimately complete the proof successfully. Therefore, instructors are encouraged to recognize and support these productive actions, prioritizing them over mere proof completion when guiding students in their proving processes.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"77 ","pages":"Article 101211"},"PeriodicalIF":1.0,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142748741","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
Decentering to support responsive teaching for middle school students 去中心化支持中学生响应式教学
IF 1
Journal of Mathematical Behavior Pub Date : 2024-11-28 DOI: 10.1016/j.jmathb.2024.101205
Amy J. Hackenberg , Fetiye Aydeniz Temizer , Rebecca S. Borowski
{"title":"Decentering to support responsive teaching for middle school students","authors":"Amy J. Hackenberg ,&nbsp;Fetiye Aydeniz Temizer ,&nbsp;Rebecca S. Borowski","doi":"10.1016/j.jmathb.2024.101205","DOIUrl":"10.1016/j.jmathb.2024.101205","url":null,"abstract":"<div><div>A classroom study was conducted to understand how to engage in responsive teaching with 18 seventh grade students at three stages of units coordination during a unit on proportional reasoning co-taught by the first author and classroom teacher. In the unit, students worked on making two cars travel the same speed. Students at all three stages of units coordination learned to do so, as reported elsewhere (Hackenberg et al., 2023). This paper focuses on the practice of inquiring responsively in small groups. We found that teacher-researcher decentering was a mechanism underlying this practice. Decentering involves adopting the perspective of another person by setting one’s own perspective to the side and using the other’s perspective as a basis for interaction. We found that two patterns of decentering actions and a type of question, leveraging questions, supported students across stages of units coordination to sustain challenges and learn.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"77 ","pages":"Article 101205"},"PeriodicalIF":1.0,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142748740","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
Whole number and fraction reorganization of knowledge: A case of Dalton and Angela, two third grade children with intensive supports in mathematics 整数和分数知识的重组：道尔顿和安吉拉--两名三年级数学强化辅导儿童的案例
IF 1
Journal of Mathematical Behavior Pub Date : 2024-11-25 DOI: 10.1016/j.jmathb.2024.101212
Beth L. MacDonald , Allison M. Kroesch , Neet Priya Bajwa , Jeffrey Barrett , Jessica H. Hunt , Jennifer Tobias
{"title":"Whole number and fraction reorganization of knowledge: A case of Dalton and Angela, two third grade children with intensive supports in mathematics","authors":"Beth L. MacDonald ,&nbsp;Allison M. Kroesch ,&nbsp;Neet Priya Bajwa ,&nbsp;Jeffrey Barrett ,&nbsp;Jessica H. Hunt ,&nbsp;Jennifer Tobias","doi":"10.1016/j.jmathb.2024.101212","DOIUrl":"10.1016/j.jmathb.2024.101212","url":null,"abstract":"<div><div>We examined how whole number knowledge and fraction knowledge may interact, conducting task-based interviews with two third-grade children with ISM.<span><span><sup>2</sup></span></span> Results indicate that these two children with ISM developed fraction knowledge through meaningful activity involving their whole number schemes and their rudimentary fraction knowledge; the participants leveraged their number sequences, use of doubles, partitioning operations, and iterating operations to construct fraction task solutions. Questions remain regarding how children with ISM may use and develop nuanced forms of iteration and partitioning for both their whole number and fraction learning over longer spans of time and how these forms of development may suggest varying forms of participatory and anticipatory stages of reasoning.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"77 ","pages":"Article 101212"},"PeriodicalIF":1.0,"publicationDate":"2024-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142705550","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
Teachers’ engagement with language practices through a geometry lesson study 教师通过几何课研究参与语言实践
IF 1
Journal of Mathematical Behavior Pub Date : 2024-11-21 DOI: 10.1016/j.jmathb.2024.101207
Lisnet Mwadzaangati , Jill Adler
{"title":"Teachers’ engagement with language practices through a geometry lesson study","authors":"Lisnet Mwadzaangati ,&nbsp;Jill Adler","doi":"10.1016/j.jmathb.2024.101207","DOIUrl":"10.1016/j.jmathb.2024.101207","url":null,"abstract":"<div><div>Our study focuses on teachers’ engagement with language practices through their participation in an adapted lesson study (LS) focusing on introduction to the concept of similarity and the meaning of ‘similar’ in a lesson on similar triangles. We use data from textbook analysis, lesson planning, lessons and lesson reflection sessions to explore teachers’ engagement with language practices and how these evolved over a LS cycle. Working with the notion of dilemmas in teaching as ‘sources of praxis’ (Adler, 1998), we identified inter-connected teaching dilemmas, engagement with which led to a wider use of language registers and representations in the second lesson and with these, opening opportunities for elaborating the meaning of similar triangles. We describe the dilemmas that emerged and their related language practices, evidence teachers’ engagement with these in their talk and their teaching, and argue that LS can create conditions for teachers’ learning about language practices in teaching.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"76 ","pages":"Article 101207"},"PeriodicalIF":1.0,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142704873","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
Complementary dimensions of the Theory of Didactic Situations in Mathematics and the Theory of Social Interactionism: Synthesizing the Topaze effect and the funnel pattern 数学教学情境理论和社会互动理论的互补维度：综合托帕兹效应和漏斗模式
IF 1
Journal of Mathematical Behavior Pub Date : 2024-11-21 DOI: 10.1016/j.jmathb.2024.101194
Heidi Strømskag
{"title":"Complementary dimensions of the Theory of Didactic Situations in Mathematics and the Theory of Social Interactionism: Synthesizing the Topaze effect and the funnel pattern","authors":"Heidi Strømskag","doi":"10.1016/j.jmathb.2024.101194","DOIUrl":"10.1016/j.jmathb.2024.101194","url":null,"abstract":"<div><div>This study examines the theory of didactic situations in mathematics (TDS) and the theory of social interactionism (TSI), employing strategies from the networking of theories schema to uncover potential complementarities between them. These theories provide different a priori perspectives on mathematics classroom interaction: TDS focuses on the functioning of mathematical knowledge in adidactic situations, while TSI centers on the emergence of mathematical meanings through the interactive accomplishment of intersubjectivity. The study gives rise to a hypothesis concerning complementary dimensions of the theoretical frameworks, particularly regarding social interaction and related classroom regulations. This hypothesis is empirically substantiated through theoretical triangulation of a dataset from a mathematics classroom. The TDS analysis, considering the mathematical knowledge in question, identifies a Topaze effect within the dataset, whereas the TSI analysis construes the empirical facts as exhibiting a funnel pattern of interaction. It is argued that the interpretations mutually enhance each other’s explanatory power.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"76 ","pages":"Article 101194"},"PeriodicalIF":1.0,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142704872","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
A lens for exploring which dimensions contribute to a justification’s proofiness 探索哪些因素有助于证明理由的可证明性的视角
IF 1
Journal of Mathematical Behavior Pub Date : 2024-11-20 DOI: 10.1016/j.jmathb.2024.101204
Dov Zazkis , Andre Rouhani
{"title":"A lens for exploring which dimensions contribute to a justification’s proofiness","authors":"Dov Zazkis ,&nbsp;Andre Rouhani","doi":"10.1016/j.jmathb.2024.101204","DOIUrl":"10.1016/j.jmathb.2024.101204","url":null,"abstract":"<div><div>This study extends the investigation of students’ conceptions of what makes a written justification a proof by introducing a novel theoretical lens—the proofiness lens. Under a proofiness lens a justification is conceptualized as occurring in a multi-dimensional space with each dimension influencing the extent to which that justification is considered a proof. In this work, we target a single potential dimension, the proof-to-procedure continuum, although, other dimensions emerged from students’ work. Our data allows us to explore how sensitive students are to the proof-to-procedure dimension of proofiness. Additionally, all students in our study were attentive to writing style as an emergent dimension. We demonstrate that the proofiness lens and its associated methodology shed light on which dimensions of proofs students attend to and why.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"76 ","pages":"Article 101204"},"PeriodicalIF":1.0,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142704874","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
Mature intuition and mathematical understanding 成熟的直觉和数学理解力
IF 1
Journal of Mathematical Behavior Pub Date : 2024-11-18 DOI: 10.1016/j.jmathb.2024.101203
William D'Alessandro , Irma Stevens
{"title":"Mature intuition and mathematical understanding","authors":"William D'Alessandro ,&nbsp;Irma Stevens","doi":"10.1016/j.jmathb.2024.101203","DOIUrl":"10.1016/j.jmathb.2024.101203","url":null,"abstract":"<div><div>Mathematicians often describe the importance of well-developed intuition to productive research and successful learning. But neither education researchers nor philosophers interested in epistemic dimensions of mathematical practice have yet given the topic the sustained attention it deserves. The trouble is partly that intuition in the relevant sense lacks a usefully clear characterization, so we begin by offering one: mature intuition, we say, is the capacity for fast, fluent, reliable and insightful inference with respect to some subject matter. We illustrate the role of mature intuition in mathematical practice with an assortment of examples, including data from a sequence of clinical interviews in which a student improves upon initially misleading covariational intuitions. Finally, we show how the study of intuition can yield insights for philosophers and education theorists. First, it contributes to a longstanding debate in epistemology by undermining <em>epistemicism</em>, the view that an agent’s degree of objectual understanding is determined exclusively by their knowledge, beliefs and credences. We argue on the contrary that intuition can contribute directly and independently to understanding. Second, we identify potential pedagogical avenues towards the development of mature intuition, highlighting strategies including <em>adding imagery</em>, <em>developing associations</em>, <em>establishing confidence</em> and <em>generalizing concepts</em>.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"76 ","pages":"Article 101203"},"PeriodicalIF":1.0,"publicationDate":"2024-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142704875","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
Gender-related differences and social entanglements in mathematics education during 19th century: The subject of geometry 19 世纪数学教育中与性别有关的差异和社会纠葛：几何学科
IF 1
Journal of Mathematical Behavior Pub Date : 2024-11-17 DOI: 10.1016/j.jmathb.2024.101209
Polly Thanailaki
{"title":"Gender-related differences and social entanglements in mathematics education during 19th century: The subject of geometry","authors":"Polly Thanailaki","doi":"10.1016/j.jmathb.2024.101209","DOIUrl":"10.1016/j.jmathb.2024.101209","url":null,"abstract":"<div><div>This paper examines mathematics teaching and learning, specifically of Geometry, in Greek girls’ schools in the 19th century. It explores how educational laws and school practice defined its teaching. Research has proved that female students received only the basics in Geometry, substantially less than what was offered to male students in all-boys’ schools. Also, the Geometry textbooks designed for girls are discussed. The problems considered in the article are at the intersection of economic, political and ideological issues. The study draws on a wide range of primary sources such as school archives and records as well as government gazettes. In particular, the school archives of the <em>Philekpedeutiki Etaireia</em> provide this research with a rich source of information regarding female schooling in 19th century.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"76 ","pages":"Article 101209"},"PeriodicalIF":1.0,"publicationDate":"2024-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142652722","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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