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Journal of Mathematical Behavior最新文献

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Math-LIGHT problem posing by three experts with different fields of expertise: Why? What? and How? 由三位不同专业领域的专家提出数学问题：为什么？是什么？
IF 1.7
Journal of Mathematical Behavior Pub Date : 2024-06-07 DOI: 10.1016/j.jmathb.2024.101158
Roza Leikin, Regina Ovodenko
{"title":"Math-LIGHT problem posing by three experts with different fields of expertise: Why? What? and How?","authors":"Roza Leikin,&nbsp;Regina Ovodenko","doi":"10.1016/j.jmathb.2024.101158","DOIUrl":"https://doi.org/10.1016/j.jmathb.2024.101158","url":null,"abstract":"<div><p>The Math-LIGHT program is directed at promoting literacy-rich mathematical instruction in middle school. A team of designers with different types of expertise pose Math-Light problems. We perform comparative analysis of problem-posing activities by experts with different types of expertise. We demonstrate that Activity Theory (Leontiev, 1978) is a powerful theoretical framework for the analysis of the structure of problem posing activity. Framed by activity theory we ask “Why?” questions to understand the main goals of posing problems; “What?” questions are directed at the characteristics of the PP process and PP products; and “How?” questions are aimed at identifying the tools used by the designers to fit the conditions in which the problems are implemented. We find that the three designers’ problem-posing activities are complimentary and suggest that the cooperative problem posing process is essential for posing problems that integrate different perspectives and thus allow more goals to be attained.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"75 ","pages":"Article 101158"},"PeriodicalIF":1.7,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141290633","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
How do people compare visualizations of fraction magnitudes? Evidence from adults’ and children’s eye movements with continuous and discretized tape diagrams 人们如何比较分数大小的可视化？连续和离散磁带图中成人和儿童眼球运动的证据
IF 1.7
Journal of Mathematical Behavior Pub Date : 2024-05-27 DOI: 10.1016/j.jmathb.2024.101160
Sabrina Schwarzmeier , Andreas Obersteiner , Martha Wagner Alibali , Vijay Marupudi
{"title":"How do people compare visualizations of fraction magnitudes? Evidence from adults’ and children’s eye movements with continuous and discretized tape diagrams","authors":"Sabrina Schwarzmeier ,&nbsp;Andreas Obersteiner ,&nbsp;Martha Wagner Alibali ,&nbsp;Vijay Marupudi","doi":"10.1016/j.jmathb.2024.101160","DOIUrl":"https://doi.org/10.1016/j.jmathb.2024.101160","url":null,"abstract":"<div><p>Adults and children are able to compare visually represented fractions. Past studies show that people are more efficient with continuous visualizations than with discretized ones, but the specific reasons are unclear. Presumably, continuous visualizations highlight magnitudes more directly, while discretized ones encourage less efficient strategies such as counting. In two experiments, adults and children compared the magnitudes of continuous and discretized tape diagrams of fractions. In both experiments, participants answered more accurately, faster, and with fewer eye saccades when the visualizations were continuous rather than discretized. Sequences of saccades indicated that participants used counting strategies less often with continuous than discretized diagrams. The results suggest that adults and children are more efficient with continuous than discretized visualizations because they use more efficient, magnitude-based strategies with continuous visualizations. The findings indicate that integrating continuous visualizations in classroom teaching more frequently could be beneficial for supporting students in developing fraction magnitude concepts.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"75 ","pages":"Article 101160"},"PeriodicalIF":1.7,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0732312324000373/pdfft?md5=27411acdb4e78b0d4a65db5fbe56e7a3&pid=1-s2.0-S0732312324000373-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141239606","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
Students’ reception of two alternative arrangements of mathematical symbols and words: Differences in focus and text navigation 学生对两种数学符号和文字排列方式的接受情况：重点和文本导航的差异
IF 1.7
Journal of Mathematical Behavior Pub Date : 2024-05-24 DOI: 10.1016/j.jmathb.2024.101159
Ulrika Wikström Hultdin, Mathias Norqvist
{"title":"Students’ reception of two alternative arrangements of mathematical symbols and words: Differences in focus and text navigation","authors":"Ulrika Wikström Hultdin,&nbsp;Mathias Norqvist","doi":"10.1016/j.jmathb.2024.101159","DOIUrl":"https://doi.org/10.1016/j.jmathb.2024.101159","url":null,"abstract":"<div><p>To engage with specialized subject content, students must develop adequate reading skills. In mathematics, this includes to integrate information from different semiotic resources. This study elucidates how differences in the structural connections between mathematical symbols and written language in mathematics texts can affect the reading process. With the help of eye-tracking techniques, we investigated differences in focus and navigation when 15-year-olds read task texts in two distinct designs: a traditional design with written language presented in lines and all connections based on semantics; and a design including a graphic emphasizing links between symbols and explanations. While the graphic design was found to facilitate fast interpretation of the symbol–language connections, the traditional design seemed to encourage global reading, involving more text parts. When designing texts for mathematics learning, structural connections may be chosen to adapt texts to various student groups and purposes.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"75 ","pages":"Article 101159"},"PeriodicalIF":1.7,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0732312324000361/pdfft?md5=0fd27d08805618e0b9565b6f2dc819f4&pid=1-s2.0-S0732312324000361-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141095608","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
Multi-variable narratives in qualitative research on mathematical problem posing 数学问题提出定性研究中的多变量叙事
IF 1.7
Journal of Mathematical Behavior Pub Date : 2024-05-06 DOI: 10.1016/j.jmathb.2024.101157
Boris Koichu, Jason Cooper
{"title":"Multi-variable narratives in qualitative research on mathematical problem posing","authors":"Boris Koichu,&nbsp;Jason Cooper","doi":"10.1016/j.jmathb.2024.101157","DOIUrl":"https://doi.org/10.1016/j.jmathb.2024.101157","url":null,"abstract":"<div><p>We substantiate the following claim: multi-variable narrative in qualitative research on problem posing bears promise for a better understanding of causality relationships between ways in which problem-posing activities are organized on the one hand, and characteristics of processes, products, and effects of problem posing on the other hand. Our notion of multi-variable narrative is first introduced by means of a hypothetical scenario. We then discuss relationships between different types of variables while adapting the terminology developed in mediation analysis literature to problem-posing situations and suggest heuristics for choosing problem-posing variables in research that aspires to inform practice. This is followed by an illustration in the context of a problem-posing activity by mathematics teachers. The illustration shows how features of the posed problems can be related to the problem-posing task organization, and how these relations may be mediated or moderated by particular features of the problem-posers, and by choices they make.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"74 ","pages":"Article 101157"},"PeriodicalIF":1.7,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140843063","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
Exploring and promoting a student's covariational reasoning and developing graphing meanings 探索和促进学生的协变推理并发展图形意义
IF 1.7
Journal of Mathematical Behavior Pub Date : 2024-05-04 DOI: 10.1016/j.jmathb.2024.101156
Teo Paoletti , Irma E. Stevens , Srujana Acharya , Claudine Margolis , Allison Olshefke-Clark , Allison L Gantt
{"title":"Exploring and promoting a student's covariational reasoning and developing graphing meanings","authors":"Teo Paoletti ,&nbsp;Irma E. Stevens ,&nbsp;Srujana Acharya ,&nbsp;Claudine Margolis ,&nbsp;Allison Olshefke-Clark ,&nbsp;Allison L Gantt","doi":"10.1016/j.jmathb.2024.101156","DOIUrl":"https://doi.org/10.1016/j.jmathb.2024.101156","url":null,"abstract":"<div><p>Despite the importance of graphical reasoning, graph construction and interpretation has been shown to be nontrivial. Paoletti et al. (2023) presented a framework that allows for a fine-grained analysis of students’ graphical reasoning as they conceive of graphs as representing two covarying quantities. In this paper, we show how the framework can be used to not only characterize a student’s graphing meanings and reasoning, but also to diagnose complexities in a student's development of such reasoning, <em>and</em> to design tasks that provide opportunities to resolve such complexities. We draw on data from a teaching experiment with a sixth-grade student in the U.S. to highlight how the framework allowed us to identify indications and contraindications of the student’s engaging in reasoning compatible with the framework. Further, we describe how this analysis supported us in designing a task that was aligned with the framework and proved productive in supporting the student's learning. We conclude with a discussion of our findings and their implications for task design and future research.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"74 ","pages":"Article 101156"},"PeriodicalIF":1.7,"publicationDate":"2024-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140825975","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 expertise of novices: A framework for prospective teacher’s noticing of children’s mathematical thinking 新手的专业知识：未来教师注意儿童数学思维的框架
IF 1.7
Journal of Mathematical Behavior Pub Date : 2024-04-30 DOI: 10.1016/j.jmathb.2024.101151
John Bragelman , Julie M. Amador , Alison Castro Superfine
{"title":"The expertise of novices: A framework for prospective teacher’s noticing of children’s mathematical thinking","authors":"John Bragelman ,&nbsp;Julie M. Amador ,&nbsp;Alison Castro Superfine","doi":"10.1016/j.jmathb.2024.101151","DOIUrl":"https://doi.org/10.1016/j.jmathb.2024.101151","url":null,"abstract":"<div><p>The purpose of this study was to articulate nuances within the process of learning to notice and to provide a framework for characterizing the capabilities of noticing in prospective mathematics teachers. We collected and analyzed data on teacher noticing based on classroom videos from prospective teachers in a mathematics content course. We analyzed data in accordance with existing research-based frameworks on noticing and in consideration with literature on expertise. We provide the Framework for the Expertise of Noticing, which describes noticing expertise along five dimensions: Evidence-based Noticing; Concrete vs. Abstract Characteristics in Noticing; Individual vs. Pattern Focus in Noticing; Task vs. Contextualized Perspective in Noticing; and Cognitive vs. Metacognitive Characteristics in Noticing. The framework is a tool for mathematics education researchers and teacher educators who study and support the development of noticing in prospective teachers.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"74 ","pages":"Article 101151"},"PeriodicalIF":1.7,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140816727","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
Using abstraction to analyze instructional tasks and their implementation 使用抽象方法分析教学任务及其实施情况
IF 1.7
Journal of Mathematical Behavior Pub Date : 2024-04-18 DOI: 10.1016/j.jmathb.2024.101153
Kevin C. Moore , Erin Wood , Shaffiq Welji , Mike Hamilton , Anne Waswa , Amy B. Ellis , Halil I. Tasova
{"title":"Using abstraction to analyze instructional tasks and their implementation","authors":"Kevin C. Moore ,&nbsp;Erin Wood ,&nbsp;Shaffiq Welji ,&nbsp;Mike Hamilton ,&nbsp;Anne Waswa ,&nbsp;Amy B. Ellis ,&nbsp;Halil I. Tasova","doi":"10.1016/j.jmathb.2024.101153","DOIUrl":"https://doi.org/10.1016/j.jmathb.2024.101153","url":null,"abstract":"<div><p>Over the past few decades, Piaget’s forms of abstraction have proved productive for developing explanatory models of student and teacher knowledge, yet the broader applicability of his abstraction forms to mathematics education remains an open question. In this paper, we adopt the Piagetian forms of abstraction to accomplish two interrelated goals. Firstly, we analyze instructional tasks to develop hypothetical accounts of the abstractions that might occur during students’ engagement with them. Secondly, we draw on middle- and secondary-grades classroom data to discuss the abstractions that occurred during the implementation of those instructional tasks. Because this paper represents an initial attempt at extending the applicability of Piagetian forms of abstraction, we close with potential implications of such use and possible avenues for future research. Most notably, we highlight the complexities involved in supporting abstraction through curriculum and instruction.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"74 ","pages":"Article 101153"},"PeriodicalIF":1.7,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140605127","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
Teacher emotions and in-the-moment decision making in the secondary mathematics classroom 中学数学课堂上教师的情绪与即时决策
IF 1.7
Journal of Mathematical Behavior Pub Date : 2024-04-17 DOI: 10.1016/j.jmathb.2024.101152
Styliani Kyriaki Kourti, Despina Potari
{"title":"Teacher emotions and in-the-moment decision making in the secondary mathematics classroom","authors":"Styliani Kyriaki Kourti,&nbsp;Despina Potari","doi":"10.1016/j.jmathb.2024.101152","DOIUrl":"https://doi.org/10.1016/j.jmathb.2024.101152","url":null,"abstract":"<div><p>Our study focuses on the interplay of two secondary school mathematics teachers’ emotions and decision-making in pivotal teaching moments. We highlight the interaction between teacher emotions and in-the-moment decision-making, and resources that coordinate this interplay, suggesting a theoretical and methodological way of addressing it. Our analyzed data comes from three teachers’ lessons and four semi-structured interviews. When analyzing pivotal moments where the teacher handles students’ errors, it appeared that teacher emotions and resources are interrelated elements of the decision-making. Findings show that: (1) teachers’ emotions, while handling students’ errors, are mostly negative, but differ in their kind and source; (2) the formation of teacher emotions and actions often seems to draw on the same resources (social-spatial, anticipatory-temporal, moral-ideological dimensions, and teacher’s responsibility about mathematics; (3)teachers’ actions, while handling students’ errors, differ in relation to the resources and the emotions that coordinate their formation.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"74 ","pages":"Article 101152"},"PeriodicalIF":1.7,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140558520","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 student development of use of grouping and mathematical properties 将学生使用分组和数学性质的发展联系起来
IF 1.7
Journal of Mathematical Behavior Pub Date : 2024-04-16 DOI: 10.1016/j.jmathb.2024.101154
Brandon G. McMillan
{"title":"Connecting student development of use of grouping and mathematical properties","authors":"Brandon G. McMillan","doi":"10.1016/j.jmathb.2024.101154","DOIUrl":"https://doi.org/10.1016/j.jmathb.2024.101154","url":null,"abstract":"<div><p>Understanding algebraic properties is a key component of building mathematical thinking across grades K-8, yet less is known about the development of students' use of mathematical properties within their strategies. This article presents results from four conversations with 24 5th-grade students over a school year, that focus on examining the development of students grouping within strategies for multiplication and division problems. Findings add to previous research on student strategies within multiplication and division by detailing some of the nuances in students' use of grouping. Additionally, a focus on student strategies reveals students' progression in more explicit use of grouping underlies the development of more planful use of the distributive and associative properties of multiplication.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"74 ","pages":"Article 101154"},"PeriodicalIF":1.7,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140554604","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
Scaffolds for seeing, using, and articulating logical structures in proofs: Design research study with high school students 在证明中观察、使用和阐述逻辑结构的支架：以高中生为对象的设计研究
IF 1.7
Journal of Mathematical Behavior Pub Date : 2024-04-15 DOI: 10.1016/j.jmathb.2023.101123
Kerstin Hein , Susanne Prediger
{"title":"Scaffolds for seeing, using, and articulating logical structures in proofs: Design research study with high school students","authors":"Kerstin Hein ,&nbsp;Susanne Prediger","doi":"10.1016/j.jmathb.2023.101123","DOIUrl":"https://doi.org/10.1016/j.jmathb.2023.101123","url":null,"abstract":"<div><p>Logical structures count as critical learning content for learning to prove. They are often not sufficiently explicated, and students struggle to use and articulate them in their proofs. In this design research study, we adopt a scaffolding approach to engage high school students in using and articulating logical structures. The qualitative analysis of the design experiments reveals the potentials and limitations of graphical scaffolds, showing how graphical scaffolds must and can be complemented by linguistic scaffolds to enable students to select and combine arguments in a deductive chain and write a proof text. Implications for language-responsive proof teaching and learning are discussed.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"74 ","pages":"Article 101123"},"PeriodicalIF":1.7,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0732312323000937/pdfft?md5=b7cd20507f16adaabe76d44b76ab2547&pid=1-s2.0-S0732312323000937-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140552704","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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