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Teaching practice aimed at promoting student engagement with metarules of defining 旨在促进学生参与定义元规则的教学实践
IF 1
Journal of Mathematical Behavior Pub Date : 2024-12-01 Epub Date: 2024-10-22 DOI: 10.1016/j.jmathb.2024.101197
Jungeun Park , Jason Martin , Michael Oehrtman , Douglas Rizzolo
{"title":"Teaching practice aimed at promoting student engagement with metarules of defining","authors":"Jungeun Park ,&nbsp;Jason Martin ,&nbsp;Michael Oehrtman ,&nbsp;Douglas Rizzolo","doi":"10.1016/j.jmathb.2024.101197","DOIUrl":"10.1016/j.jmathb.2024.101197","url":null,"abstract":"<div><div>By viewing students’ learning to define as learning about meta-discursive rules about defining and how to engage with them in their activity of defining, we investigated teaching practices that aim to promote such learning by analyzing a teaching experiment in which Calculus II students reinvented a formal definition of a limit. The teaching practices we identified addressed how students view defining tasks by providing a method to check whether their narratives satisfied the metarules that they aimed to follow and also provided guidance about how to revise their definitions to satisfy those metarules. Our results provide an example for the teaching practice that promotes student learning about and engagement with new meta-discursive rules that existing literature called for in general, especially in their reinvention of a formal definition of a mathematical object.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"76 ","pages":"Article 101197"},"PeriodicalIF":1.0,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142531531","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
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？
IF 1
Journal of Mathematical Behavior Pub Date : 2024-12-01 Epub Date: 2024-09-26 DOI: 10.1016/j.jmathb.2024.101191
Marc Lange
{"title":"What are explanatory proofs in mathematics and how can they contribute to teaching and learning?","authors":"Marc Lange","doi":"10.1016/j.jmathb.2024.101191","DOIUrl":"10.1016/j.jmathb.2024.101191","url":null,"abstract":"<div><div>This paper will examine several simple examples (drawn from the mathematics literature) where there are multiple proofs of the same theorem, but only some of these proofs are widely regarded by mathematicians as explanatory. These examples will motivate an account of explanatory proofs in mathematics. Along the way, the paper will discuss why <em>deus ex machina</em> proofs are not explanatory, what a mathematical coincidence is, and how a theorem's proper setting reflects the naturalness of various mathematical kinds. The paper will also investigate how context influences which features of a theorem are salient and consequently which proofs are explanatory. The paper will discuss several ways in which explanatory proofs can contribute to teaching and learning, including how shifts in context (and hence in a proof’s explanatory power) can be exploited in a classroom setting, leading students to dig more deeply into why some theorem holds. More generally, the paper will examine how “Why?” questions operate in mathematical thinking, teaching, and learning.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"76 ","pages":"Article 101191"},"PeriodicalIF":1.0,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142324193","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
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 : 2024-12-01 Epub 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":"2024-12-01","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
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
IF 1
Journal of Mathematical Behavior Pub Date : 2024-12-01 Epub Date: 2024-09-18 DOI: 10.1016/j.jmathb.2024.101190
George Kinnear , Gemma Hood , Eloise Lardet , Colette Sheard , Colin Foster
{"title":"Lecturers' use of questions in undergraduate mathematics lectures","authors":"George Kinnear ,&nbsp;Gemma Hood ,&nbsp;Eloise Lardet ,&nbsp;Colette Sheard ,&nbsp;Colin Foster","doi":"10.1016/j.jmathb.2024.101190","DOIUrl":"10.1016/j.jmathb.2024.101190","url":null,"abstract":"<div><p>Mathematics lecturers frequently ask questions in their lectures, and these questions presumably play an important role in students’ thinking about and learning of the lecture content. We replicated and developed a coding scheme used in previous research in the US to categorise lecturers’ questions in a sample of 136 lectures given by 24 lecturers at a research-intensive UK university. We found that the coding scheme could be applied reliably, and that factual questions were predominant (as in previous research). We explore differences in the lecturers’ use of questions – both between our UK sample and the previous US work, and between individual lecturers in our sample. We note the presence of strings of related successive questions from the lecturer, which we term ‘question chains’. We explore the nature of these, examine their prevalence, and seek to account for them in terms of the lecturers’ possible intentions.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"76 ","pages":"Article 101190"},"PeriodicalIF":1.0,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0732312324000671/pdfft?md5=eed3542583cd33645c2f09865c9e4dd8&pid=1-s2.0-S0732312324000671-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142238787","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
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 : 2024-12-01 Epub 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":"2024-12-01","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
Mathematical understanding – Common themes in philosophy and mathematics education 数学理解 - 哲学与数学教育的共同主题
IF 1
Journal of Mathematical Behavior Pub Date : 2024-12-01 Epub Date: 2024-11-07 DOI: 10.1016/j.jmathb.2024.101202
Jessica Carter
{"title":"Mathematical understanding – Common themes in philosophy and mathematics education","authors":"Jessica Carter","doi":"10.1016/j.jmathb.2024.101202","DOIUrl":"10.1016/j.jmathb.2024.101202","url":null,"abstract":"<div><div>We present different characterizations of mathematical understanding given by mathematicians, philosophers of mathematics, and mathematics educators. One purpose is to illustrate the diversity of these characterizations. Although the descriptions of understanding may seem incompatible, the paper ends by pointing to some shared themes. They include an emphasis on qualities such as relations and unification. Additionally, we note that re-presentation, including visual representations, is thought to play a role in understanding.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"76 ","pages":"Article 101202"},"PeriodicalIF":1.0,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142652723","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
Different types of talk in mixed-attainment problem-solving groups: Contributions to individual students’ combinatorial thinking 混合成绩解题小组中的不同谈话类型：对学生个人组合思维的贡献
IF 1
Journal of Mathematical Behavior Pub Date : 2024-12-01 Epub Date: 2024-11-16 DOI: 10.1016/j.jmathb.2024.101206
Maria Larsson , Hanna Fredriksdotter , Nina Klang
{"title":"Different types of talk in mixed-attainment problem-solving groups: Contributions to individual students’ combinatorial thinking","authors":"Maria Larsson ,&nbsp;Hanna Fredriksdotter ,&nbsp;Nina Klang","doi":"10.1016/j.jmathb.2024.101206","DOIUrl":"10.1016/j.jmathb.2024.101206","url":null,"abstract":"<div><div>This study contributes to previous research on collaborative approaches to instruction in mathematics. The study focuses on the relationships between the type of talk in groups and individual students’ combinatorial thinking. Four case studies of mixed-attainment groups of middle-school students working with mathematical problem solving in combinatorics were conducted. Video-recordings of dyad and group work, as well as interviews with four students (one per group), were analyzed. The results reveal how affordances and constraints in different types of talk (exploratory, cumulative, disputational talk) in mixed-attainment groups can contribute to individual students’ combinatorial thinking. The results highlight the interconnectedness of collective and individual reasoning in combinatorics, emphasizing the role of quality of group talk.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"76 ","pages":"Article 101206"},"PeriodicalIF":1.0,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142652724","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
Abstract algebra students’ conceptual metaphors for isomorphism and homomorphism 抽象代数学生对同构和同态的概念隐喻
IF 1
Journal of Mathematical Behavior Pub Date : 2024-09-01 Epub Date: 2024-06-20 DOI: 10.1016/j.jmathb.2024.101173
Rachel Rupnow , Brooke Randazzo
{"title":"Abstract algebra students’ conceptual metaphors for isomorphism and homomorphism","authors":"Rachel Rupnow ,&nbsp;Brooke Randazzo","doi":"10.1016/j.jmathb.2024.101173","DOIUrl":"https://doi.org/10.1016/j.jmathb.2024.101173","url":null,"abstract":"<div><p>Group isomorphism and homomorphism are core concepts in abstract algebra, and student understanding of isomorphism has received extensive attention in line with the centrality of this topic. However, limited work has directly examined student conceptions of homomorphism or what metaphors students use to express their thought processes while problem solving. Based on interviews with four students, we contrast two students who used predominantly formal definition and mapping-centered metaphors for homomorphism with two who additionally used sameness-centered metaphors and note that the usage or non-usage of sameness-centered metaphors was not indicative of successful problem solving. Implications include the alignment between students’ metaphors and those used in instruction, indicating the importance of attending to metaphors when teaching, and the importance of discussing what is intended by some sameness-based metaphors, such as operation-preservation.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"75 ","pages":"Article 101173"},"PeriodicalIF":1.0,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141434861","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
New kinds of embodied interactions that arise in augmented reality dynamic geometry software 增强现实动态几何软件中出现的新型体现式互动
IF 1
Journal of Mathematical Behavior Pub Date : 2024-09-01 Epub Date: 2024-06-25 DOI: 10.1016/j.jmathb.2024.101175
Candace Walkington , Mitchell J. Nathan , Jonathan Hunnicutt , Julianna Washington , Monique Zhou
{"title":"New kinds of embodied interactions that arise in augmented reality dynamic geometry software","authors":"Candace Walkington ,&nbsp;Mitchell J. Nathan ,&nbsp;Jonathan Hunnicutt ,&nbsp;Julianna Washington ,&nbsp;Monique Zhou","doi":"10.1016/j.jmathb.2024.101175","DOIUrl":"https://doi.org/10.1016/j.jmathb.2024.101175","url":null,"abstract":"<div><p>Dynamic geometry software (DGS) has long been studied in mathematics education as a way for students to explore and interact with geometric objects and figures. Recent advances in Augmented Reality (AR) technologies that allow dynamic three-dimensional mathematical objects to appear in students’ environment as holograms have changed the nature of what is possible for a DGS, particularly with respect to embodiment. New forms of embodied interactions may arise in AR-based DGS, as students gesture and move their bodies through their environment, taking different perspectives to interact with these immersive shapes projected in three dimensions. In the present study, we examine videos of 28 high school students interacting with an AR-based version of the DGS GeoGebra, while wearing the Microsoft HoloLens 2 headsets. We document the novel kinds of embodied interactions that the AR environment affords, relating to (1) perspective and orientation, (2) scale, (3) three dimensions. Based on our analysis, we give important directions for future research on DGS and implications for the design of the next generation of holographic DGS.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"75 ","pages":"Article 101175"},"PeriodicalIF":1.0,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S073231232400052X/pdfft?md5=52834f5c84f9c81469fd3a2de5c68290&pid=1-s2.0-S073231232400052X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141479172","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
Disrupting racial storylines about black girls in mathematics through teaching content and building relationships 通过教学内容和建立关系，打破数学领域关于黑人女孩的种族故事情节
IF 1.7
Journal of Mathematical Behavior Pub Date : 2024-09-01 Epub Date: 2024-06-15 DOI: 10.1016/j.jmathb.2024.101167
Charles E. Wilkes II , Dan Battey
{"title":"Disrupting racial storylines about black girls in mathematics through teaching content and building relationships","authors":"Charles E. Wilkes II ,&nbsp;Dan Battey","doi":"10.1016/j.jmathb.2024.101167","DOIUrl":"https://doi.org/10.1016/j.jmathb.2024.101167","url":null,"abstract":"<div><p>This study is a qualitative case study that focuses on the instructional practice of a white woman teacher with three Black girls. We draw upon literature that describes racial storylines for Black girls to focus on how a white Woman teacher navigates racial storylines to enact instructional practices that are humanzing for Black girls. Specifically, we show how interactions the teacher has with three Black girls disrupt racial storylines about invisibility/hypervisibility, behavior, and ability. Implications of this work pushes back against the idea that Black girls are monolithic and illustrate practices in mathematics that support the success of Black girls.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"75 ","pages":"Article 101167"},"PeriodicalIF":1.7,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0732312324000440/pdfft?md5=606d16a90b2c4b9e79e6a03a705b3db1&pid=1-s2.0-S0732312324000440-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141328316","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
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