Journal of Mathematical Behavior最新文献_第5页

Combinatorial and quantitative reasoning: Stage 3 high school students’ reason about combinatorics problems and their representation as 3-D arrays 组合和定量推理：第三阶段高中生对组合问题的推理及其三维数组表示法

IF 1.7

Journal of Mathematical Behavior Pub Date : 2024-02-02 DOI: 10.1016/j.jmathb.2024.101125

Erik S. Tillema , Andrew M. Gatza , Weverton Ataide Pinheiro

{"title":"Combinatorial and quantitative reasoning: Stage 3 high school students’ reason about combinatorics problems and their representation as 3-D arrays","authors":"Erik S. Tillema , Andrew M. Gatza , Weverton Ataide Pinheiro","doi":"10.1016/j.jmathb.2024.101125","DOIUrl":"https://doi.org/10.1016/j.jmathb.2024.101125","url":null,"abstract":"<div><p>Researchers have identified three stages of units coordination that influence a range of domains of student reasoning. The primary foci of this research have been students’ reasoning in discrete, non-combinatorial whole number contexts, and with fractions, ratios, proportions, and rates represented using length quantities. This study extends this prior work by examining connections between eight high school students’ combinatorial reasoning and their representation of this reasoning using 3-D arrays. All students in the study were at stage 3 of units coordination. Findings include differentiation between two student groups: one group had interiorized three-levels-of-units, but had not interiorized four-levels-of-units; and the other group had interiorized four-levels-of-units. This differentiation was coordinated with differences in how they reasoned to produce 3-D arrays. The findings from the study indicate how combinatorics problems can support quantitative reasoning, where combinatorial and quantitative reasoning are framed as a foundation for algebraic reasoning.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139674665","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}

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“Guess what they would make you do on this one”: The discourse of a high-stakes exam in an AP Calculus classroom "猜猜他们会让你做什么？AP 微积分课堂上的高风险考试话语

IF 1.7

Journal of Mathematical Behavior Pub Date : 2024-02-02 DOI: 10.1016/j.jmathb.2024.101127

Sunghwan Byun , Beth Herbel-Eisenmann

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Teaching mathematics through problem posing: Elements of the task 通过提出问题进行数学教学：任务要素

IF 1.7

Journal of Mathematical Behavior Pub Date : 2024-02-02 DOI: 10.1016/j.jmathb.2024.101133

Janaína Poffo Possamai , Norma Suely Gomes Allevato

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Attending to task variables when engaging in group problem posing for elementary level mathematics 在小学数学小组讨论中关注任务变量

IF 1.7

Journal of Mathematical Behavior Pub Date : 2024-02-01 DOI: 10.1016/j.jmathb.2024.101128

Aisling Leavy, Mairéad Hourigan

{"title":"Attending to task variables when engaging in group problem posing for elementary level mathematics","authors":"Aisling Leavy, Mairéad Hourigan","doi":"10.1016/j.jmathb.2024.101128","DOIUrl":"https://doi.org/10.1016/j.jmathb.2024.101128","url":null,"abstract":"<div><p>In light of the growing interest in research examining problem posing, this study explores an under-researched aspect – group problem posing. It examines the role of problem situations and prompts, introduced within a problem posing intervention, on the nature of the problems posed by groups of pre-service elementary teachers for children in two 4th grade classes. The impact of the group on the problem posing process was also explored. The findings reveal improvements in the quality of the problems posed due to a number of factors including the use of textbook problems as initial problem situations that supported problem reformulation, the constructive role of prompts to focus attention on desirable problem features and the valuable role of feedback in determining problem aptness. A challenge when problem posing was difficulty coordinating attention to multiple problem features, however, this was mediated by the affordance of working in groups which served to share the responsibility for, and enhance, problem quality alongside the use of the F-PosE problem posing framework which focused attention on desirable problem features.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0732312324000051/pdfft?md5=a4174bfa6bca3d3e97a11095ab27e051&pid=1-s2.0-S0732312324000051-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139675127","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

Problem-posing tasks and their influence on pre-service teachers’ creative problem-posing performance and self-efficacy 提出问题的任务及其对职前教师提出创造性问题的表现和自我效能感的影响

IF 1.7

Journal of Mathematical Behavior Pub Date : 2024-01-30 DOI: 10.1016/j.jmathb.2024.101130

Lukas Baumanns , Benjamin Rott

{"title":"Problem-posing tasks and their influence on pre-service teachers’ creative problem-posing performance and self-efficacy","authors":"Lukas Baumanns , Benjamin Rott","doi":"10.1016/j.jmathb.2024.101130","DOIUrl":"10.1016/j.jmathb.2024.101130","url":null,"abstract":"<div><p>In problem-posing research, the influence of task variables on problem-posing outcomes is a relatively new endeavor. To systematically vary task variables, we designed eight problem-posing tasks by crossing two problem-posing situations (unstructured vs. structured) with two problem-posing prompts (open vs. closed) and two mathematical contexts (patterns vs. geometry). Using this design, we investigated the influence of these task variables on (1) creative problem-posing performance, (2) problem-posing self-efficacy, and (3) the relationship between self-efficacy and creative problem-posing performance in 187 pre-service teachers. The analyses show that (1) the influence of the situation and prompt is small and topic-specific, (2) that self-efficacy is significantly lower in unstructured situations with an open prompt than in the other tasks, and (3) that creative problem-posing performance and self-efficacy are correlated negatively. The findings imply a need for more detailed investigations regarding the influence on creative problem-posing performance and for which subjects it is relevant.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0732312324000075/pdfft?md5=970e182433cd5746789885155aca8ba3&pid=1-s2.0-S0732312324000075-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139648695","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

Variables in planning and carrying out a problem-posing task in early childhood education 幼儿教育中计划和执行提出问题任务的变量

IF 1.7

Journal of Mathematical Behavior Pub Date : 2024-01-25 DOI: 10.1016/j.jmathb.2024.101131

Enrique Carmona-Medeiro , Juan Pedro Martín-Díaz , Nuria Climent

引用次数: 0

Mathematics teachers’ specialized knowledge mobilized through problem transformation 通过问题转化调动数学教师的专业知识

IF 1.7

Journal of Mathematical Behavior Pub Date : 2024-01-25 DOI: 10.1016/j.jmathb.2024.101132

M. Montes , J. Chico , J.P. Martín-Díaz , E. Badillo

{"title":"Mathematics teachers’ specialized knowledge mobilized through problem transformation","authors":"M. Montes , J. Chico , J.P. Martín-Díaz , E. Badillo","doi":"10.1016/j.jmathb.2024.101132","DOIUrl":"10.1016/j.jmathb.2024.101132","url":null,"abstract":"<div><p>In this study we address two issues related to problem-posing tasks in teacher education: (i) the characterization of the specialized knowledge mobilized by prospective teachers when carrying out these tasks and (ii) the identification of the prospective teachers’ pedagogical intentions in making adaptations to textbook problems. We asked prospective teachers to outline their suggestions for transforming a multiplicative problem so as to “promote the understanding” of their potential pupils. We then carried out a content analysis of their responses using the Mathematics Teachers’ Specialized Knowledge model of teachers’ specialized knowledge and identified their pedagogical intentions by means of the constant comparison method. The results show that prospective primary teachers mobilized both mathematical and pedagogical content knowledge in their responses to the problem reformulation task. Further, four distinct pedagogical intentions emerged that drew on different interpretations of the task prompt, and this influenced the type of transformation the prospective primary teachers suggested and the knowledge they mobilized in their answers.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0732312324000099/pdfft?md5=68e09bf54f7b4e8af9310aee63c7220c&pid=1-s2.0-S0732312324000099-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139579777","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

Do task variables of self-generated problems influence interest? Authenticity, openness, complexity, and students’ interest in solving self-generated modelling problems 自创问题的任务变量会影响兴趣吗？真实性、开放性、复杂性与学生解决自创建模问题的兴趣

IF 1.7

Journal of Mathematical Behavior Pub Date : 2024-01-23 DOI: 10.1016/j.jmathb.2024.101129

Janina Krawitz , Luisa Hartmann , Stanislaw Schukajlow

{"title":"Do task variables of self-generated problems influence interest? Authenticity, openness, complexity, and students’ interest in solving self-generated modelling problems","authors":"Janina Krawitz , Luisa Hartmann , Stanislaw Schukajlow","doi":"10.1016/j.jmathb.2024.101129","DOIUrl":"https://doi.org/10.1016/j.jmathb.2024.101129","url":null,"abstract":"<div><p>Problem posing—generating one’s own problems—is considered a powerful teaching approach for fostering students’ motivation such as their interest. However, research investigating the effects of task variables of self-generated problems on students’ interest is largely missing. In this contribution, we present a study with 105 ninth- and tenth-graders to address the question of whether the task variables modelling potential, assessed by openness and authenticity, or complexity of self-generated problems have an impact on students’ interest in solving them. Further, we investigated whether the effect of task variables of self-generated problems on students’ interest differed among students with different levels of mathematical competence. High modelling potential had a positive effect on interest in solving the problem for students with low mathematical competence, whereas it had a negative effect for those with high mathematical competence. However, complexity of self-generated problems did not affect students’ interest in solving problems.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0732312324000063/pdfft?md5=251ea0e01b6ed0b8168180abcd5f5419&pid=1-s2.0-S0732312324000063-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139549399","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

Conceptualizing reasoning practices in the context of sociomathematical issues 在社会数学问题背景下的推理实践概念化

IF 1.7

Journal of Mathematical Behavior Pub Date : 2024-01-23 DOI: 10.1016/j.jmathb.2024.101124

Sean Chorney , Kyle R. Evans , Megan Staples

引用次数: 0

Primary students’ relational thinking and computation strategies with concrete-to-symbolic representations of subtraction as difference 小学生用具体符号表示减法差的关系思维和计算策略

IF 1.7

Journal of Mathematical Behavior Pub Date : 2024-01-12 DOI: 10.1016/j.jmathb.2023.101121

Karina J. Wilkie , Sarah Hopkins

{"title":"Primary students’ relational thinking and computation strategies with concrete-to-symbolic representations of subtraction as difference","authors":"Karina J. Wilkie , Sarah Hopkins","doi":"10.1016/j.jmathb.2023.101121","DOIUrl":"https://doi.org/10.1016/j.jmathb.2023.101121","url":null,"abstract":"<div><p>Children are highly inclined to attend to the properties of numbers, operations and equality when given helpful tools for doing so. Our aim was to investigate early algebraic thinking with the compensation property of equality for subtraction. We provided 22 (9–11-year-old) students with physical blocks for building vertical towers and conducted individual interviews with them as they completed a sequence of 15 tasks involving subtraction as difference using concrete, numeric, and symbolic representations. Relational thinking was evidenced across a range of subtraction calculation skill levels. Those students who could use both indirect addition and take-away strategies flexibly, depending on the size of the numbers involved, were more likely to evidence attention to generality with symbolic equations. The shift to symbolic equations elicited some students’ productive attempts to connect subtraction as difference and subtraction as take way but seemed to hinder others by provoking a return to take away calculations rather than relational thinking strategies.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0732312323000913/pdfft?md5=f4d71bb9fd084eb6787d2856b753c492&pid=1-s2.0-S0732312323000913-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139433545","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