Journal of Mathematical Behavior最新文献_第5页

Snapshots of sameness: Characterizations of mathematical sameness across student groups 同一性的剪影：不同学生群体的数学同一性特征

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Journal of Mathematical Behavior Pub Date : 2024-10-03 DOI: 10.1016/j.jmathb.2024.101193

Rachel Rupnow , Rosaura Uscanga , Anna Marie Bergman , Cassandra Mohr

{"title":"Snapshots of sameness: Characterizations of mathematical sameness across student groups","authors":"Rachel Rupnow , Rosaura Uscanga , Anna Marie Bergman , Cassandra Mohr","doi":"10.1016/j.jmathb.2024.101193","DOIUrl":"10.1016/j.jmathb.2024.101193","url":null,"abstract":"<div><div>Sameness is foundational to mathematics but has only recently become an area of focus in mathematics education research. In this paper, we describe characterizations of sameness generated by four student groups: discrete mathematics students, linear algebra students, abstract algebra students, and graduate students. Based on qualitative analysis of open response surveys, we compare these groups’ characterizations of sameness; note the subcomponents discussed and variation within each dimension; and highlight experiences influential to students’ perceptions of sameness. Findings include interpretability of sameness as a big idea, nascent development of thematic connections across courses, emphases on current course material rather than connections to prior courses for students solicited from a particular course, greater reflectiveness from the graduate student group, and abstract algebra as an impactful course. Implications include a need for thoughtful examinations of how “big ideas” develop among students and what experiences might support such development.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"76 ","pages":"Article 101193"},"PeriodicalIF":1.0,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142428275","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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What are explanatory proofs in mathematics and how can they contribute to teaching and learning? 什么是数学解释性证明，它们如何促进教学？

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Journal of Mathematical Behavior Pub Date : 2024-09-26 DOI: 10.1016/j.jmathb.2024.101191

Marc Lange

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Encouraging students to explain their ideas when learning mathematics: A psychological perspective 鼓励学生在学习数学时解释自己的想法：心理学视角

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Journal of Mathematical Behavior Pub Date : 2024-09-24 DOI: 10.1016/j.jmathb.2024.101192

Bethany Rittle-Johnson

{"title":"Encouraging students to explain their ideas when learning mathematics: A psychological perspective","authors":"Bethany Rittle-Johnson","doi":"10.1016/j.jmathb.2024.101192","DOIUrl":"10.1016/j.jmathb.2024.101192","url":null,"abstract":"<div><div>Children’s <em>self-explanations</em> are answers to voiced why and how questions that attempt to make sense of new information for oneself. They often are not sophisticated or generalizable. Despite this, prompting children to generate explanations often improves their learning. After providing examples of children’s explanations, this article summarizes empirical evidence for the learning benefits of prompting people to generate explanations when learning mathematics. There is strong evidence that prompting learners to explain leads to greater conceptual knowledge, procedural knowledge and procedural transfer when knowledge is assessed immediately after the learning session; there is limited evidence for greater procedural transfer after a delay. Scaffolding high-quality explanations via training or structured responses, designing prompts to carefully balance attention to important content, prompting learners to explain correct information, and prompting learners to explain why incorrect information is incorrect when appropriate, increases the benefits of prompts to generate explanations.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"76 ","pages":"Article 101192"},"PeriodicalIF":1.0,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0732312324000695/pdfft?md5=da899ecf252efeddeeea91ce27ec15c7&pid=1-s2.0-S0732312324000695-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142314687","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

Lecturers' use of questions in undergraduate mathematics lectures 讲师在本科数学授课中使用问题的情况

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Journal of Mathematical Behavior Pub Date : 2024-09-18 DOI: 10.1016/j.jmathb.2024.101190

George Kinnear , Gemma Hood , Eloise Lardet , Colette Sheard , Colin Foster

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Creating and sharing linear algebra metaphors as an assessment for engaging students beyond the cognitive domain 创建和分享线性代数隐喻，将其作为吸引学生参与认知领域以外活动的一种评估方法

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Journal of Mathematical Behavior Pub Date : 2024-09-11 DOI: 10.1016/j.jmathb.2024.101189

Hortensia Soto , Jessi Lajos , Vladislav Kokushkin

{"title":"Creating and sharing linear algebra metaphors as an assessment for engaging students beyond the cognitive domain","authors":"Hortensia Soto , Jessi Lajos , Vladislav Kokushkin","doi":"10.1016/j.jmathb.2024.101189","DOIUrl":"10.1016/j.jmathb.2024.101189","url":null,"abstract":"<div><p>In this research, we investigated how a summative assessment of creating and sharing metaphors for linear algebra concepts supported undergraduate students’ affective, behavioral, and cognitive engagement. All seven research participants were enrolled in an introductory linear algebra course designed to develop students’ geometric understanding of linear algebra concepts in <em>R</em><sup><em>2</em></sup> and <em>R</em><sup><em>3</em></sup>. Using embodied cognition and an engagement framework, we analyzed students’ written responses and video-taped their focus group discussion. Our findings suggest that this summative assessment (a) privileged mathematical aesthetics and the affective domain of learning, (b) engaged students in binding formal aspects of linear algebra concepts with metaphors that they enacted via embodiment, and (c) was an opportunity to demonstrate learning and higher-order cognition. Thus, illustrating that assessments can focus on aesthetic and affective domains of mathematics while simultaneously integrating serious mathematical cognition. We conclude by offering adaptations of this assessment for other mathematics courses.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"76 ","pages":"Article 101189"},"PeriodicalIF":1.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142167340","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

Secondary teachers’ guided reinvention of the definitions of reducible and irreducible elements 中学教师在指导下重塑可还原和不可还原元素的定义

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Journal of Mathematical Behavior Pub Date : 2024-09-11 DOI: 10.1016/j.jmathb.2024.101188

Kaitlyn Stephens Serbin , Younggon Bae , Sthefanía Espinosa

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Engagement with student written work as an instantiation of and proxy for how college calculus instructors engage with student thinking 参与学生的书面作业，作为大学微积分教师如何参与学生思维的实例和代表

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Journal of Mathematical Behavior Pub Date : 2024-09-05 DOI: 10.1016/j.jmathb.2024.101187

Jessica Gehrtz , Jess Ellis Hagman , Victoria Barron

{"title":"Engagement with student written work as an instantiation of and proxy for how college calculus instructors engage with student thinking","authors":"Jessica Gehrtz , Jess Ellis Hagman , Victoria Barron","doi":"10.1016/j.jmathb.2024.101187","DOIUrl":"10.1016/j.jmathb.2024.101187","url":null,"abstract":"<div><p>Teachers who use student thinking to make instructional decisions tend to create more positive learning experiences for students and support conceptual understanding. Looking at student work is one way college instructors learn about student thinking. We interviewed eight calculus instructors to investigate what they noticed when examining student work. Reflexive thematic analysis allowed us to classify instructors by the stance they adopted when looking at student work. Instructors who adopted an evaluative stance responded by providing examples or explaining how to solve the problem, often taking on the intellectual work of solving the problem. Instructors who adopted an interpretive stance responded by providing examples or asking guiding questions informed by the student’s thinking. We then extended our analyses to illustrate two instructional archetypes (Interpreter and Evaluator), to highlight how the stance taken when examining student work can serve as a proxy for how instructors engage with student thinking more broadly.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"76 ","pages":"Article 101187"},"PeriodicalIF":1.0,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0732312324000646/pdfft?md5=79808339f06402b0a6a1c331e5c9fa74&pid=1-s2.0-S0732312324000646-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142147683","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

Developing (Pedagogical) content knowledge of constant rate of change: The case of Samantha 发展有关恒定变化率的（教学）内容知识：萨曼莎的案例

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Journal of Mathematical Behavior Pub Date : 2024-08-31 DOI: 10.1016/j.jmathb.2024.101179

Michael A. Tallman , John Weaver , Taylor Johnson

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Use of mathematical problems rooted in primary historical sources to reveal preservice teachers’ mathematical content knowledge 利用源于原始史料的数学问题揭示职前教师的数学内容知识

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Journal of Mathematical Behavior Pub Date : 2024-08-24 DOI: 10.1016/j.jmathb.2024.101177

Ioannis Papadopoulos

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Does use of a hypothetical learning progression promote learning of the cardinal-count concept and give-n performance? 使用假定的学习进度是否能促进对心算概念的学习并提高学习成绩？

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Journal of Mathematical Behavior Pub Date : 2024-08-23 DOI: 10.1016/j.jmathb.2024.101178

Arthur J. Baroody , Douglas H. Clements , Julie Sarama

{"title":"Does use of a hypothetical learning progression promote learning of the cardinal-count concept and give-n performance?","authors":"Arthur J. Baroody , Douglas H. Clements , Julie Sarama","doi":"10.1016/j.jmathb.2024.101178","DOIUrl":"10.1016/j.jmathb.2024.101178","url":null,"abstract":"<div><p>The general aim of the research was to conduct a rare test of the efficacy of hypothetical learning progressions (HLPs) and a basic assumption of basing instruction on HLPs, namely teaching each successive level is more efficacious than skipping lower levels and teaching the target level directly. The specific aim was evaluating whether counting-based cardinality concepts unfold in a stepwise manner. The research involved a pretest—delayed-posttest design with random assignment of 14 preschoolers to two conditions. The experimental intervention was based on an HLP for cardinality development (first promoting levels that presumably support and are necessary for the target level and then the target knowledge). The active-control treatment entailed a Teach-to-Target approach (first promoting irrelevant cardinality knowledge about recognizing written numbers and then directly teaching the same target-level goals with the same explicit instruction and similar games). A mix of quantitative and qualitative analyses indicated HLP participants performed significantly and substantially better than Teach-to-Target participants on target-level concept and skill measures. Moreover, the former tended to make sensible errors, whereas the latter generally responded cluelessly.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"76 ","pages":"Article 101178"},"PeriodicalIF":1.0,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142058329","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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