Mathematical Thinking and Learning最新文献_第7页

Construction of the cardinality principle through counting: critique and conjecture 通过计数构建基数原则:批判与猜想

IF 1.6 4区教育学

Mathematical Thinking and Learning Pub Date : 2021-12-02 DOI: 10.1080/10986065.2021.2012737

Martin A. Simon, Daniela Della Volpe, Arundhati Velamur

引用次数: 2

Embodied learning at a distance: from sensory-motor experience to constructing and understanding a sine graph 体现远程学习：从感觉运动体验到构建和理解正弦图

IF 1.6 4区教育学

Mathematical Thinking and Learning Pub Date : 2021-11-16 DOI: 10.1080/10986065.2021.1983691

A. Shvarts, Gitte van Helden

{"title":"Embodied learning at a distance: from sensory-motor experience to constructing and understanding a sine graph","authors":"A. Shvarts, Gitte van Helden","doi":"10.1080/10986065.2021.1983691","DOIUrl":"https://doi.org/10.1080/10986065.2021.1983691","url":null,"abstract":"ABSTRACT Educational technologies develop quickly. Which functions of face-to-face education can be substituted by technology for distance learning? One of the risks of online education is the lack of embodied interactions. We investigate what embodied interactive technologies might offer for teaching trigonometry when learning at a distance. In a multiple case study, we analyze the potential of embodied action-based design for fostering conceptual understanding of a sine graph. It appears that independent learning with tablet-based activities leads to acquiring new sensory-motor coordinations. Some students include these new embodied experiences into mathematical discourse and trigonometry problem solving themselves, while others still need some support from a teacher. However, distantly acquired embodied experiences can be easily recalled in a few days after learning and serve well as a substrate for further conceptualization and problem-solving. The results speak for a clear contribution that embodied design might provide for grounding conceptual understanding in distance learning. However, we expect embodied design to be particularly helpful in a blended learning format.","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":"25 1","pages":"409 - 437"},"PeriodicalIF":1.6,"publicationDate":"2021-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43236675","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

Learning mathematics as occasioned by disturbance 学习数学是由干扰引起的

IF 1.6 4区教育学

Mathematical Thinking and Learning Pub Date : 2021-10-24 DOI: 10.1080/10986065.2021.1993034

J. Mason

引用次数: 0

Learning through explaining and engaging with others’ mathematical ideas 通过解释和参与他人的数学思想来学习

IF 1.6 4区教育学

Mathematical Thinking and Learning Pub Date : 2021-10-17 DOI: 10.1080/10986065.2021.1990744

N. Webb, M. Franke, N. Johnson, Marsha Ing, Joy Zimmerman

{"title":"Learning through explaining and engaging with others’ mathematical ideas","authors":"N. Webb, M. Franke, N. Johnson, Marsha Ing, Joy Zimmerman","doi":"10.1080/10986065.2021.1990744","DOIUrl":"https://doi.org/10.1080/10986065.2021.1990744","url":null,"abstract":"ABSTRACT Educators, researchers, and policy makers recognize that student participation in classroom mathematics conversations, especially explaining one’s own thinking and engaging with others’ ideas, can promote students’ mathematics learning. However, precisely how participating in these ways supports learning has not often been examined in detail. Using in-depth analyses of videotaped whole-class discussions, small-group collaborative work, and private partner conversations in two third-grade mathematics classrooms on six occasions over a five- month period, we show advances that students made in their mathematical thinking or mathematical work in the context of explaining their thinking and/or engaging with others’ ideas. The detailed analyses focus on students who had previously scored low on standardized tests of mathematics proficiency. The results show how students not considered to have extensive mathematics knowledge can forge new connections between mathematical ideas and representations, and extend their problem-solving strategies in ways that are directly related to their participation.","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":"25 1","pages":"438 - 464"},"PeriodicalIF":1.6,"publicationDate":"2021-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47065433","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 7

Radford’s theory of objectification: a cultural-historical theory of learning, knowing, and becoming 拉德福德的物化理论：一种关于学习、认识和成为的文化历史理论

IF 1.6 4区教育学

Mathematical Thinking and Learning Pub Date : 2021-09-29 DOI: 10.1080/10986065.2021.1984070

Michael N. Fried

引用次数: 0

Kindergarten students’ mathematics knowledge at work: the mathematics for programming robot toys 幼儿园学生在工作中的数学知识:编程机器人玩具的数学

IF 1.6 4区教育学

Mathematical Thinking and Learning Pub Date : 2021-09-29 DOI: 10.1080/10986065.2021.1982666

Jessica F. Shumway, Lise E. Welch, Joseph S. Kozlowski, Jody Clarke-Midura, Victor R. Lee

{"title":"Kindergarten students’ mathematics knowledge at work: the mathematics for programming robot toys","authors":"Jessica F. Shumway, Lise E. Welch, Joseph S. Kozlowski, Jody Clarke-Midura, Victor R. Lee","doi":"10.1080/10986065.2021.1982666","DOIUrl":"https://doi.org/10.1080/10986065.2021.1982666","url":null,"abstract":"ABSRACT The purpose of this study was to explore how kindergarten students (aged 5–6 years) engaged with mathematics as they learned programming with robot coding toys. We video-recorded 16 teaching sessions of kindergarten students’ (N = 36) mathematical and programming activities. Students worked in small groups (4–5 students) with robot coding toys on the floor in their classrooms, solving tasks that involved programming these toys to move to various locations on a grid. Drawing on a semiotic mediation perspective, we analyzed video data to identify the mathematics concepts and skills students demonstrated and the overlapping mathematics-programming knowledge exhibited by the students during these programming tasks. We found that kindergarten children used spatial, measurement, and number knowledge, and the design of the tasks, affordances of the robots, and types of programming knowledge influenced how the students engaged with mathematics. The paper concludes with a discussion about the intersections of mathematics and programming knowledge in early childhood, and how programming robot toys elicited opportunities for students to engage with mathematics in dynamic and interconnected ways, thus creating an entry point to reassert mathematics beyond the traditional school content and curriculum.","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":"25 1","pages":"380 - 408"},"PeriodicalIF":1.6,"publicationDate":"2021-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46148624","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 17

Professional noticing coherence: exploring relationships between component processes 专业注意一致性：探索组件过程之间的关系

IF 1.6 4区教育学

Mathematical Thinking and Learning Pub Date : 2021-09-22 DOI: 10.1080/10986065.2021.1977086

Jonathan Thomas, David M. Dueber, Molly H. Fisher, C. Jong, E. Schack

引用次数: 4

Between expert and student perspectives: on the intersection of affect and heuristic-didactic discourse in the undergraduate classroom 在专家和学生的观点之间:关于本科课堂中情感和启发式教学话语的交集

IF 1.6 4区教育学

Mathematical Thinking and Learning Pub Date : 2021-08-25 DOI: 10.1080/10986065.2021.1940432

Ofer Marmur, B. Koichu

{"title":"Between expert and student perspectives: on the intersection of affect and heuristic-didactic discourse in the undergraduate classroom","authors":"Ofer Marmur, B. Koichu","doi":"10.1080/10986065.2021.1940432","DOIUrl":"https://doi.org/10.1080/10986065.2021.1940432","url":null,"abstract":"ABSTRACT This paper explores student emotion and learning experiences fostered by lecturing-style instruction in Real-Analysis problem-centered lessons. We focus on two lessons that were taught by two reputable instructors and involved challenging, mathematically-related problems the students did not understand. Nonetheless, one lesson evoked negative emotional reactions, while the other positive emotional reactions – a phenomenon we aimed at explaining. The main data comprise the filmed lessons and subsequent stimulated-recall interviews with nine students. The analysis draws on conceptual tools from three perspectives: mathematical discourse, variation theory, and a recently developed construct of key memorable events (KMEs) that offers an affective-cognitive lens for investigating the interrelation between teaching and learning. The findings indicate that the positively-perceived lesson contained instances of what we call heuristic-didactic discourse: a meta-level discourse that presents heuristics monitored from an expert’s perspective, yet derived from a student’s perspective. Implications for research and practice are drawn.","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":"25 1","pages":"115 - 144"},"PeriodicalIF":1.6,"publicationDate":"2021-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46965499","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

Connecting mathematical modeling and social justice through problem posing 通过问题提出将数学建模与社会正义联系起来

IF 1.6 4区教育学

Mathematical Thinking and Learning Pub Date : 2021-08-14 DOI: 10.1080/10986065.2021.1966713

Hyunyi Jung, Marta T. Magiera

{"title":"Connecting mathematical modeling and social justice through problem posing","authors":"Hyunyi Jung, Marta T. Magiera","doi":"10.1080/10986065.2021.1966713","DOIUrl":"https://doi.org/10.1080/10986065.2021.1966713","url":null,"abstract":"ABSTRACT This paper contributes to accumulating the knowledge base about prospective elementary school teachers’ (PTs’) understanding of socio-critical modeling by exploring how PTs make connections to features of mathematical modeling and social justice while posing mathematical problems and reflecting on their problem-posing. We present a conceptual framework for posing problems that connect social justice issues with the features of mathematical modeling. Drawing on the analysis of 36 individual modeling problems generated by the PTs and 36 written reflections PTs completed throughout their problem-posing activity, we illustrate various ways in which PTs connect the multi-faceted features of mathematical modeling (i.e., realistic context, model development, and shareable process) and social justice (i.e., micro – and macro – level). The PT-posed problems were categorized as (a) modeling problems presenting micro – and macro-level social justice issues (27%), (b) modeling problems presenting micro-level social justice issues (22%), (c) contextualized mathematical problems presenting micro – and macro-level social justice issues (25%), and (d) contextualized mathematical problems presenting micro-level social justice issues (17%). Our work describing the complexity of posing social justice-oriented mathematical modeling (SJMM) problems and articulating decisions PTs make while posing SJMM problems set directions for future efforts and research in teacher preparation.","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":"25 1","pages":"232 - 251"},"PeriodicalIF":1.6,"publicationDate":"2021-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44117548","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 5

Undergraduate students’ interpretations of expressions from calculus statements within the graphical register 本科生对图形寄存器中微积分语句表达的解释

IF 1.6 4区教育学

Mathematical Thinking and Learning Pub Date : 2021-07-26 DOI: 10.1080/10986065.2021.1943608

E. Parr

{"title":"Undergraduate students’ interpretations of expressions from calculus statements within the graphical register","authors":"E. Parr","doi":"10.1080/10986065.2021.1943608","DOIUrl":"https://doi.org/10.1080/10986065.2021.1943608","url":null,"abstract":"ABSTRACT The purpose of this study is to investigate how students interpret expressions from calculus statements in the graphical register. To this end, I conducted 150-minute clinical interviews with 13 undergraduate mathematics students who had completed at least one calculus course. In the interviews, students evaluated six calculus statements for various real-valued functions depicted in graphs in the Cartesian plane. From my analysis of these interviews, I found four distinct interpretations of expressions in the graphical register that students used in this study while evaluating the statements using the graphs. I describe the characteristics of these four interpretations, which I refer to as (1) nominal, (2) ordinal, (3) cardinal, and (4) magnitude. For some students, the use of these interpretations supported their graphical reasoning and correct evaluations of the statements. For other students, the use of some interpretations rather than others presented obstacles to their graphical understanding of the expressions in the statement. For instance, seven of the students never used a magnitude interpretation (interpreting an expression as a distance in the graph), even when working with difference expressions. I discuss implications of these findings for teaching with graphs across levels and directions for future research.","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":"25 1","pages":"177 - 207"},"PeriodicalIF":1.6,"publicationDate":"2021-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/10986065.2021.1943608","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42985735","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0