Journal of Mathematical Behavior最新文献_第10页

Enhancing language-responsive meaning-making processes as an epistemic catalyst for developing multiplicative reasoning in young children 增强语言反应意义生成过程作为幼儿发展乘法推理的认知催化剂

IF 1.7

Journal of Mathematical Behavior Pub Date : 2023-06-01 DOI: 10.1016/j.jmathb.2023.101034

Daniela Götze , Annica Baiker

引用次数: 0

Is it a function? Generalizing from single- to multivariable settings 这是一个函数吗？从单变量到多变量设置的泛化

IF 1.7

Journal of Mathematical Behavior Pub Date : 2023-06-01 DOI: 10.1016/j.jmathb.2023.101036

Allison Dorko

引用次数: 0

Learning about multiplication by comparing algorithms: “One times one, but actually they are ten times ten” 通过比较算法学习乘法：“一乘一，但实际上是十乘十”

IF 1.7

Journal of Mathematical Behavior Pub Date : 2023-06-01 DOI: 10.1016/j.jmathb.2022.101024

Anna Ethelwyn Baccaglini-Frank , Silvia Funghi , Mirko Maracci , Alessandro Ramploud

{"title":"Learning about multiplication by comparing algorithms: “One times one, but actually they are ten times ten”","authors":"Anna Ethelwyn Baccaglini-Frank , Silvia Funghi , Mirko Maracci , Alessandro Ramploud","doi":"10.1016/j.jmathb.2022.101024","DOIUrl":"https://doi.org/10.1016/j.jmathb.2022.101024","url":null,"abstract":"<div><p>Multiplication algorithms in primary school are still frequently introduced with little attention to meaning. We present a case study focusing on a third grade class that engaged in comparing two algorithms and discussing “why they both work”. The objectives of the didactical intervention were to foster students' development of mathematical meanings concerning multiplication algorithms, and their development of an attitude to judge and compare the value and efficiency of different algorithms. Underlying hypotheses were that it is possible to promote the simultaneous unfolding of the semiotic potential of two algorithms, considered as cultural artifacts, with respect to the objectives of the didactical intervention, and to establish a fruitful synergy between the two algorithms. As results, this study sheds light onto the new theoretical construct of “bridging sign”, illuminating students’ meaning-making processes involving more than one artifact; and it provides important insight into the actual unfolding of the hypothesized potential of the algorithms.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50176931","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 do open-ended problems promote indirect argumentation? Conceptual replications in a Japanese secondary school 开放式问题如何促进间接论证？日本中学的概念复制

IF 1.7

Journal of Mathematical Behavior Pub Date : 2023-06-01 DOI: 10.1016/j.jmathb.2022.101026

Ryoto Hakamata , Yusuke Uegatani , Toru Hayata

引用次数: 0

Investigating two teachers’ development of combinatorial meaning for algebraic structure 考察两位教师对代数结构组合意义的发展

IF 1.7

Journal of Mathematical Behavior Pub Date : 2023-06-01 DOI: 10.1016/j.jmathb.2023.101039

Lori J. Burch

{"title":"Investigating two teachers’ development of combinatorial meaning for algebraic structure","authors":"Lori J. Burch","doi":"10.1016/j.jmathb.2023.101039","DOIUrl":"https://doi.org/10.1016/j.jmathb.2023.101039","url":null,"abstract":"<div><p>This paper reports on the results of a four-day teaching experiment that supported two algebra teachers to develop a <em>combinatorial meaning</em> for algebraic structure. The purpose of the teaching episodes was to support the teachers (a) to establish a <em>combinatorial understanding</em> for algebraic structure (Tillema & Burch, 2022) by generalizing the cubic identity, <span><math><mrow><msup><mrow><mfenced><mrow><mi>a</mi><mo>+</mo><mi>b</mi></mrow></mfenced></mrow><mrow><mn>3</mn></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>+</mo><mn>3</mn><msup><mrow><mi>a</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>b</mi><mo>+</mo><mn>3</mn><mi>a</mi><msup><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>b</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></math></span>, as a symbolization of quantitative and combinatorial relationships out of a contextualized problem (Tillema & Gatza, 2016) and (b) to develop a <em>combinatorial meaning</em> as a mobilization of their understanding through a series of algebraic tasks (cf. Thompson et al., 2014). The findings from this study contribute to research literature on teachers’ mathematical meanings within secondary algebra by investigating how teachers’ combinatorial meanings developed and how differences in their combinatorial meanings impacted their algebraic reasoning. The findings demonstrate a combinatorial pathway for supporting the development of expanding and factoring as reversible polynomial operations (cf. Sangwin & Jones, 2017).</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50177018","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

Understanding authority in small-group co-constructions of mathematical proof 理解数学证明的小组共建中的权威性

IF 1.7

Journal of Mathematical Behavior Pub Date : 2023-06-01 DOI: 10.1016/j.jmathb.2022.101015

Sarah K. Bleiler-Baxter , Jordan E. Kirby , Samuel D. Reed

{"title":"Understanding authority in small-group co-constructions of mathematical proof","authors":"Sarah K. Bleiler-Baxter , Jordan E. Kirby , Samuel D. Reed","doi":"10.1016/j.jmathb.2022.101015","DOIUrl":"https://doi.org/10.1016/j.jmathb.2022.101015","url":null,"abstract":"<div><p>Authority becomes <em>shared</em> in mathematics classrooms when perceived sources of valid mathematical knowledge extend beyond the teacher/textbook and allow both students and disciplinary modes of reasoning to hold authority. The goal of this research is to better understand classroom situations that are intended to facilitate shared authority over proof, namely small-group episodes where students are <em>granted</em> authority (Gerson & Bateman, 2010) to co-construct mathematical proofs. We sought to better understand the content of undergraduate students’ attention during group proving and the sources of legitimacy for students. Using Stylianides’ (2007) definition of proof as an analytical frame, we found that student discourse focused primarily upon the mode of argumentation, followed by the mode of argument representation, and then the set of accepted statements. We identified four themes with respect to the sources of authority students relied upon in their group proving: (1) the course rubric, (2) peers’ confidence, (3) form and symbols, and (4) logical structure. Implications for research and practice are presented.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50176930","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

Measuring interaction quality in mathematics instruction: How differences in operationalizations matter methodologically 衡量数学教学中的互动质量：操作上的差异如何在方法上产生影响

IF 1.7

Journal of Mathematical Behavior Pub Date : 2023-06-01 DOI: 10.1016/j.jmathb.2023.101054

Kim Quabeck , Kirstin Erath , Susanne Prediger

{"title":"Measuring interaction quality in mathematics instruction: How differences in operationalizations matter methodologically","authors":"Kim Quabeck , Kirstin Erath , Susanne Prediger","doi":"10.1016/j.jmathb.2023.101054","DOIUrl":"https://doi.org/10.1016/j.jmathb.2023.101054","url":null,"abstract":"<div><p>Quality of interaction can enhance or constrain students’ mathematical learning opportunities. However, quantitative video studies have measured the quality of interaction with very heterogeneous conceptualizations and operationalizations. This project sought to disentangle typical methodological choices to assess interaction quality in six quality dimensions, each of them in task-based, move-based, and practice-based operationalizations. The empirical part of the study compared different conceptualizations with their corresponding operationalizations and used them to code video data from middle school students (n = 210) organized into 49 small groups who worked on the same curriculum materials. The analysis revealed that different conceptualizations and operationalizations led to substantially different findings, so their distinction turned out to be of high methodological relevance. These results highlight the importance of making methodological choices explicit and call for a stronger academic discourse on how to conceptualize and operationalize interaction quality in video studies.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50177013","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: 1

Does collaborative and experiential work influence the solution of real-context estimation problems? A study with prospective teachers 合作和经验工作是否会影响真实上下文估计问题的解决？对未来教师的研究

IF 1.7

Journal of Mathematical Behavior Pub Date : 2023-06-01 DOI: 10.1016/j.jmathb.2023.101040

C. Segura , I. Ferrando , L. Albarracín

引用次数: 1

Teaching routines and student-centered mathematics instruction: The essential role of conferring to understand student thinking and reasoning 教学常规与以学生为中心的数学教学：讨论对理解学生思维和推理的重要作用

IF 1.7

Journal of Mathematical Behavior Pub Date : 2023-06-01 DOI: 10.1016/j.jmathb.2023.101032

Eva Thanheiser , Kathleen Melhuish

引用次数: 3

Proof construction and in-process validation – Validation activities of undergraduates in constructing mathematical proofs 证明构建和过程验证——本科生构建数学证明的验证活动

IF 1.7

Journal of Mathematical Behavior Pub Date : 2023-06-01 DOI: 10.1016/j.jmathb.2023.101064

Katharina Kirsten , Gilbert Greefrath

{"title":"Proof construction and in-process validation – Validation activities of undergraduates in constructing mathematical proofs","authors":"Katharina Kirsten , Gilbert Greefrath","doi":"10.1016/j.jmathb.2023.101064","DOIUrl":"https://doi.org/10.1016/j.jmathb.2023.101064","url":null,"abstract":"<div><p>Proof construction and proof validation are two situations of high importance in mathematical teaching and research. While both situations have usually been studied separately, the current study focuses on possible intersections. Based on research on acceptance criteria and validation strategies, 11 undergraduates’ proof construction processes are investigated in terms of the effective and non-effective validation activities that occur. By conducting a qualitative content analysis with subsequent type construction, we identified six different validation activities, namely <em>reviewing</em>, <em>rating</em>, <em>correcting errors</em>, <em>reassuring</em>, <em>expressing doubts</em>, and <em>improving</em>. Although some of these activities tend to be associated with successful or unsuccessful proving processes, their effectiveness depends primarily on their specific implementation. For example, reviewing is effective when accompanied by a knowledge-generating approach and based on structure- or meaning-oriented criteria to provide deeper understanding. Thus, the results suggest that difficulties in proof construction could be partly attributed to inadequate validation strategies or their poor implementation.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50177016","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