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Journal of Mathematical Behavior最新文献

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An exploratory mixed methods study about teacher candidates’ descriptions of children’s confusion, productive struggle, and mistakes in an elementary mathematics methods course 小学数学方法课程中教师候选人对儿童的困惑、有成效的挣扎和错误的描述的混合方法探索性研究
IF 1.7
Journal of Mathematical Behavior Pub Date : 2023-12-12 DOI: 10.1016/j.jmathb.2023.101103
Crystal Kalinec-Craig , Anthony Rios
{"title":"An exploratory mixed methods study about teacher candidates’ descriptions of children’s confusion, productive struggle, and mistakes in an elementary mathematics methods course","authors":"Crystal Kalinec-Craig ,&nbsp;Anthony Rios","doi":"10.1016/j.jmathb.2023.101103","DOIUrl":"https://doi.org/10.1016/j.jmathb.2023.101103","url":null,"abstract":"<div><p><span>Recognizing and describing children's mathematical thinking in humanizing ways, especially when students engage in confusion, productive struggle, and mistakes, is a complex and challenging process. This paper describes an exploratory, mixed-methods study about how elementary teacher candidates (TCs) describe children's thinking as a right to exercise and to value their humanity when learning mathematics. The study analyzed transcripts from 64 TCs' </span>summative assessments, which consisted of mock parent-teacher conferences (MPTC). Findings suggest that TCs described children's confusion, productive struggle, and mistakes (RotL 1 and 2) as: a teacher's observation, an opportunity for students to correct or clarify their thinking, an opportunity for teachers to adjust instruction or provide support, and as a normal part of the learning process. More importantly, some TCs reassured children that learners have fundamental rights when learning mathematics, especially when feeling confused and claiming a mistake. Implications for research and teacher education are discussed. Keywords: Elementary, teacher education, mathematics, mixed methods, rehumanizing, Torres’ rights of the learner</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"73 ","pages":"Article 101103"},"PeriodicalIF":1.7,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138577535","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
The role of topology in the construction of students’ optimization schema for two-variable functions 拓扑在学生二元函数优化图式构建中的作用
IF 1.7
Journal of Mathematical Behavior Pub Date : 2023-11-30 DOI: 10.1016/j.jmathb.2023.101106
Rafael Martínez-Planell , Maria Trigueros , Vahid Borji
{"title":"The role of topology in the construction of students’ optimization schema for two-variable functions","authors":"Rafael Martínez-Planell ,&nbsp;Maria Trigueros ,&nbsp;Vahid Borji","doi":"10.1016/j.jmathb.2023.101106","DOIUrl":"https://doi.org/10.1016/j.jmathb.2023.101106","url":null,"abstract":"<div><p>This study uses Action-Process-Object-Schema theory (APOS) to examine students’ understanding of two-variable function optimization<span>. A genetic decomposition (GD) based on the notion of Schema is proposed. This is a conjecture of mental structures and relations that students may construct to understand the optimization of these functions. The GD was tested with semi-structured interviews with eleven students who had just finished an introductory multivariable calculus course. Results show that giving explicit attention during instruction to the topological structure of the domain of the function to be optimized and the use of GD-based activities was effective in promoting students’ understanding of two-variable function optimization. On the theoretical side, the study contributes to a better understanding of the APOS notions of Schema, Schema-triad, and types of relations between Schema components that have not been used extensively in the literature and that proved to be a powerful tool to model students’ learning.</span></p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"73 ","pages":"Article 101106"},"PeriodicalIF":1.7,"publicationDate":"2023-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138471812","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
Connecting operation-choice problems by the variation principle: Sixth graders’ operational or deeper relational pathways 用变异原理连接操作选择问题:六年级学生的操作或更深的关系路径
IF 1.7
Journal of Mathematical Behavior Pub Date : 2023-11-28 DOI: 10.1016/j.jmathb.2023.101104
Cristina Zorrilla , Anna-Katharina Roos , Ceneida Fernández , Salvador Llinares , Susanne Prediger
{"title":"Connecting operation-choice problems by the variation principle: Sixth graders’ operational or deeper relational pathways","authors":"Cristina Zorrilla ,&nbsp;Anna-Katharina Roos ,&nbsp;Ceneida Fernández ,&nbsp;Salvador Llinares ,&nbsp;Susanne Prediger","doi":"10.1016/j.jmathb.2023.101104","DOIUrl":"https://doi.org/10.1016/j.jmathb.2023.101104","url":null,"abstract":"<div><p>Many empirical studies documented students’ challenges with operation-choice problems, in particular for multiplication and division with rational numbers. The design principle of problem variation was suggested to overcome these challenges by engaging students in making connections between inverse operation-choice problems of multiplication and division, and between problems with natural numbers and fractions/decimals, but so far, this approach was hardly investigated empirically. In this study, we investigate 17 sixth graders’ modelling pathways through sets of operation-choice problems that are systematically designed according to the variation principle. In the qualitative analysis, we identify five pathways by which students solve the problems and sometimes connect them. While one pathway uses deep relational connections, others only draw superficial and operational connections and others stay with informal strategies without connecting them to formal operations.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"73 ","pages":"Article 101104"},"PeriodicalIF":1.7,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0732312323000743/pdfft?md5=8c124bd03ba8ef2782606b5062156520&pid=1-s2.0-S0732312323000743-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138448700","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
Reasoning productively across algebraic contexts: Students develop coordinated notions of inverse 在代数背景下有效地推理:学生发展反的协调概念
IF 1.7
Journal of Mathematical Behavior Pub Date : 2023-10-19 DOI: 10.1016/j.jmathb.2023.101099
John Paul Cook , Kathleen Melhuish , Rosaura Uscanga
{"title":"Reasoning productively across algebraic contexts: Students develop coordinated notions of inverse","authors":"John Paul Cook ,&nbsp;Kathleen Melhuish ,&nbsp;Rosaura Uscanga","doi":"10.1016/j.jmathb.2023.101099","DOIUrl":"https://doi.org/10.1016/j.jmathb.2023.101099","url":null,"abstract":"<div><p>The concept of inverse is threaded throughout K-16 mathematics. Scholars frequently advocate for students to understand the underlying structure: combining an element and its inverse through the binary operations yields the relevant identity element. This ‘coordinated’ way of reasoning is challenging for students to employ; however, little is known about how students might reason en route to developing it. In this study, we analyze a teaching experiment with two beginning abstract algebra students through the lens of three ways of reasoning about inverse: inverse as an undoing, inverse as a manipulated element, and inverse as a coordination of the binary operation, identity, and set. In particular, we examine the implications of these ways of reasoning as students work to develop inverse as a coordination. We identify pedagogical tools and facets of instructional design that appeared to support students’ development of inverse as a coordination. We further suggest that all three ways of reasoning can support productive activity with inverses.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"72 ","pages":"Article 101099"},"PeriodicalIF":1.7,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49875826","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
Examining the concept of inverse: Theory-building via a standalone literature review 检视逆的概念:透过独立文献回顾建立理论
IF 1.7
Journal of Mathematical Behavior Pub Date : 2023-10-14 DOI: 10.1016/j.jmathb.2023.101100
John Paul Cook , April Richardson , Steve Strand , Zackery Reed , Kathleen Melhuish
{"title":"Examining the concept of inverse: Theory-building via a standalone literature review","authors":"John Paul Cook ,&nbsp;April Richardson ,&nbsp;Steve Strand ,&nbsp;Zackery Reed ,&nbsp;Kathleen Melhuish","doi":"10.1016/j.jmathb.2023.101100","DOIUrl":"https://doi.org/10.1016/j.jmathb.2023.101100","url":null,"abstract":"<div><p>Inverse is a critical topic throughout the K–16 mathematics curriculum where students encounter the notion of mathematical inverse across many contexts. The literature base on inverses is substantial, yet context-specific and compartmentalized. That is, extant research examines students’ reasoning with inverses within specific algebraic contexts. It is currently unclear what might be involved in productively reasoning with inverses across algebraic contexts, and whether the specific ways of reasoning from the literature can be abstracted to more general ways of reasoning about inverse. To address this issue, we conducted a standalone literature review to explicate and exemplify three cross-context ways of reasoning that, we hypothesize, can support students’ productive engagement with inverses in a variety of algebraic contexts: <em>inverse as an undoing</em>, <em>inverse as a manipulated element</em>, and <em>inverse as a coordination of the binary operation, identity, and set</em>. Findings also include explicating affordances and constraints for each of these ways of reasoning. Finally, we reflect on when and how standalone literature reviews can serve the purpose of unifying fragmented and obscured insights about key mathematical ideas.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"72 ","pages":"Article 101100"},"PeriodicalIF":1.7,"publicationDate":"2023-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49875825","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
Learners building conceptual understandings of mathematics: Conditions for promoting growth in understanding – A global perspective from ICME-14 学习者建立对数学的概念性理解:促进理解增长的条件-来自ICME-14的全球视角
IF 1.7
Journal of Mathematical Behavior Pub Date : 2023-10-04 DOI: 10.1016/j.jmathb.2023.101101
Jenni Ingram, Stéphane Clivaz, Carolyn A. Maher, Louise Wilkinson
{"title":"Learners building conceptual understandings of mathematics: Conditions for promoting growth in understanding – A global perspective from ICME-14","authors":"Jenni Ingram,&nbsp;Stéphane Clivaz,&nbsp;Carolyn A. Maher,&nbsp;Louise Wilkinson","doi":"10.1016/j.jmathb.2023.101101","DOIUrl":"https://doi.org/10.1016/j.jmathb.2023.101101","url":null,"abstract":"","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"72 ","pages":"Article 101101"},"PeriodicalIF":1.7,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49875824","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
Noticing of argumentation: A comparison between pre-service and in-service secondary-school mathematics teachers 论述注意:职前与在职中学数学教师之比较
IF 1.7
Journal of Mathematical Behavior Pub Date : 2023-09-22 DOI: 10.1016/j.jmathb.2023.101098
Samaher Nama , Maysa Hayeen-Halloun , Michal Ayalon
{"title":"Noticing of argumentation: A comparison between pre-service and in-service secondary-school mathematics teachers","authors":"Samaher Nama ,&nbsp;Maysa Hayeen-Halloun ,&nbsp;Michal Ayalon","doi":"10.1016/j.jmathb.2023.101098","DOIUrl":"https://doi.org/10.1016/j.jmathb.2023.101098","url":null,"abstract":"<div><p>This study compares pre-service mathematics teachers’ (PSMTs) and in-service mathematics teachers’ (ISMTs) noticing of argumentation at the secondary-school level. Thirty-five PSMTs and 32 ISMTs engaged in analyzing argumentation classroom situations (ACSs) using an ACS-report format emphasizing two sub-skills of noticing: attending and interpretation. Analysis of the participants’ ACS reports revealed differences between the two research groups. The ISMTs paid a high level of attention to all four aspects: ‘co-constructing of arguments’, ‘critiquing arguments’, ‘mutual respect’, and ‘working toward consensus-building’, whereas the PSMTs paid a high level of attention to ‘mutual respect’ and ‘co-constructing of arguments’ aspects only. In terms of interpretation, the ISMTs outperformed the PSMTs in interpreting the argumentation through the lenses of ‘task characteristics’, ‘teaching strategies’, and ‘student cognitive characteristics’. The findings are interpreted in light of both theory and practice.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"72 ","pages":"Article 101098"},"PeriodicalIF":1.7,"publicationDate":"2023-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49875830","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
Applying a new framework of connections between mathematical symbols and natural language 应用数学符号与自然语言之间联系的新框架
IF 1.7
Journal of Mathematical Behavior Pub Date : 2023-09-12 DOI: 10.1016/j.jmathb.2023.101097
Ulrika Wikström Hultdin, Ewa Bergqvist, Tomas Bergqvist, Lotta Vingsle, Magnus Österholm
{"title":"Applying a new framework of connections between mathematical symbols and natural language","authors":"Ulrika Wikström Hultdin,&nbsp;Ewa Bergqvist,&nbsp;Tomas Bergqvist,&nbsp;Lotta Vingsle,&nbsp;Magnus Österholm","doi":"10.1016/j.jmathb.2023.101097","DOIUrl":"https://doi.org/10.1016/j.jmathb.2023.101097","url":null,"abstract":"<div><p>A reader of mathematical text must often switch between reading mathematical symbols and reading words. In this study, five different categories of structural connections between symbols and language, which invite such switches, are presented in a framework. The framework was applied in a study of Swedish mathematics textbooks, where 180 randomly selected pages from different educational stages were analyzed. The results showed a significant change in communication patterns as students progress through school. From a predomination of connections based on proximity found in year two, there is a gradual change to a predomination of symbols interwoven in sentences in year eight. Furthermore, more qualitative investigations of the different connections complemented the quantification, both through further explanations of the quantitative results, and through more examples of differences in communication patterns. The implications for readers of mathematics texts are discussed.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"72 ","pages":"Article 101097"},"PeriodicalIF":1.7,"publicationDate":"2023-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49875829","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
Impact of prompts on students’ mathematical problem posing 提示对学生提出数学问题的影响
IF 1.7
Journal of Mathematical Behavior Pub Date : 2023-09-08 DOI: 10.1016/j.jmathb.2023.101087
Jinfa Cai, Hua Ran, Stephen Hwang, Yue Ma, Jaepil Han, Faith Muirhead
{"title":"Impact of prompts on students’ mathematical problem posing","authors":"Jinfa Cai,&nbsp;Hua Ran,&nbsp;Stephen Hwang,&nbsp;Yue Ma,&nbsp;Jaepil Han,&nbsp;Faith Muirhead","doi":"10.1016/j.jmathb.2023.101087","DOIUrl":"https://doi.org/10.1016/j.jmathb.2023.101087","url":null,"abstract":"<div><p>This study used three pairs of problem-posing tasks to examine the impact of different prompts on students’ problem posing. Two kinds of prompts were involved. The first asked students to pose 2–3 different mathematical problems without specifying other requirements for the problems, whereas the second kind of prompt did specify additional requirements. A total of 2124 students’ responses were analyzed to examine the impact of the prompts along multiple dimensions. In response to problem-posing prompts with more specific requirements, students tended to engage in more in-depth mathematical thinking and posed much more linguistically and semantically complex problems with more relationships or steps required to solve them. The findings from this study not only contribute to our understanding of problem-posing processes but also have direct implications for teaching mathematics through problem posing.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"72 ","pages":"Article 101087"},"PeriodicalIF":1.7,"publicationDate":"2023-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49875831","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
Geometry, groceries, and gardens: Learning mathematics and social justice through a nested, equity-directed instructional approach 几何、食品杂货和花园：通过嵌套的、以公平为导向的教学方法学习数学和社会正义
IF 1.7
Journal of Mathematical Behavior Pub Date : 2023-09-01 DOI: 10.1016/j.jmathb.2023.101069
Frances K. Harper , Queshonda J. Kudaisi
{"title":"Geometry, groceries, and gardens: Learning mathematics and social justice through a nested, equity-directed instructional approach","authors":"Frances K. Harper ,&nbsp;Queshonda J. Kudaisi","doi":"10.1016/j.jmathb.2023.101069","DOIUrl":"https://doi.org/10.1016/j.jmathb.2023.101069","url":null,"abstract":"<div><p>We addressed the call for explorations of how BIPOC students’ “experiences in secondary mathematics classrooms might advance transformative, equity-focused, pedagogical models” (Joseph et al., 2019, p. 149) by exploring how a nested, equity-directed approach created different kinds of opportunities for students to take up, shift, or resist what it means to teach, learn, and do mathematics. Specifically, we looked at efforts to engage equity-directed dominant and critical approaches through a series of three mathematics projects aimed at investigating food insecurity as a social (in)justice issue using geometry. Our analysis focused on a subset of data generated during three projects from different times of the year. Findings revealed that the teacher more readily enacted critical equity-directed practices than dominant ones; that students more readily embraced those critical practices; and that students expected their use of mathematics and exploration of social issues to align with authentic, real-world situations.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"71 ","pages":"Article 101069"},"PeriodicalIF":1.7,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50182173","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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