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Journal of Mathematical Behavior最新文献

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Whole number and fraction reorganization of knowledge: A case of Dalton and Angela, two third grade children with intensive supports in mathematics 整数和分数知识的重组：道尔顿和安吉拉--两名三年级数学强化辅导儿童的案例
IF 1
Journal of Mathematical Behavior Pub Date : 2025-03-01 Epub Date: 2024-11-25 DOI: 10.1016/j.jmathb.2024.101212
Beth L. MacDonald , Allison M. Kroesch , Neet Priya Bajwa , Jeffrey Barrett , Jessica H. Hunt , Jennifer Tobias
{"title":"Whole number and fraction reorganization of knowledge: A case of Dalton and Angela, two third grade children with intensive supports in mathematics","authors":"Beth L. MacDonald ,&nbsp;Allison M. Kroesch ,&nbsp;Neet Priya Bajwa ,&nbsp;Jeffrey Barrett ,&nbsp;Jessica H. Hunt ,&nbsp;Jennifer Tobias","doi":"10.1016/j.jmathb.2024.101212","DOIUrl":"10.1016/j.jmathb.2024.101212","url":null,"abstract":"<div><div>We examined how whole number knowledge and fraction knowledge may interact, conducting task-based interviews with two third-grade children with ISM.<span><span><sup>2</sup></span></span> Results indicate that these two children with ISM developed fraction knowledge through meaningful activity involving their whole number schemes and their rudimentary fraction knowledge; the participants leveraged their number sequences, use of doubles, partitioning operations, and iterating operations to construct fraction task solutions. Questions remain regarding how children with ISM may use and develop nuanced forms of iteration and partitioning for both their whole number and fraction learning over longer spans of time and how these forms of development may suggest varying forms of participatory and anticipatory stages of reasoning.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"77 ","pages":"Article 101212"},"PeriodicalIF":1.0,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142705550","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
Decentering to support responsive teaching for middle school students 去中心化支持中学生响应式教学
IF 1
Journal of Mathematical Behavior Pub Date : 2025-03-01 Epub Date: 2024-11-28 DOI: 10.1016/j.jmathb.2024.101205
Amy J. Hackenberg , Fetiye Aydeniz Temizer , Rebecca S. Borowski
{"title":"Decentering to support responsive teaching for middle school students","authors":"Amy J. Hackenberg ,&nbsp;Fetiye Aydeniz Temizer ,&nbsp;Rebecca S. Borowski","doi":"10.1016/j.jmathb.2024.101205","DOIUrl":"10.1016/j.jmathb.2024.101205","url":null,"abstract":"<div><div>A classroom study was conducted to understand how to engage in responsive teaching with 18 seventh grade students at three stages of units coordination during a unit on proportional reasoning co-taught by the first author and classroom teacher. In the unit, students worked on making two cars travel the same speed. Students at all three stages of units coordination learned to do so, as reported elsewhere (Hackenberg et al., 2023). This paper focuses on the practice of inquiring responsively in small groups. We found that teacher-researcher decentering was a mechanism underlying this practice. Decentering involves adopting the perspective of another person by setting one’s own perspective to the side and using the other’s perspective as a basis for interaction. We found that two patterns of decentering actions and a type of question, leveraging questions, supported students across stages of units coordination to sustain challenges and learn.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"77 ","pages":"Article 101205"},"PeriodicalIF":1.0,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142748740","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
Mathematizing the world: A routine to advance mathematizing in the elementary classroom 世界数学化：在小学课堂上推进数学化的常规方法
IF 1
Journal of Mathematical Behavior Pub Date : 2024-12-01 Epub Date: 2024-10-22 DOI: 10.1016/j.jmathb.2024.101196
Julia M. Aguirre , Erin E. Turner , Elzena McVicar , Amy Roth McDuffie , Mary Q. Foote , Erin Carll
{"title":"Mathematizing the world: A routine to advance mathematizing in the elementary classroom","authors":"Julia M. Aguirre ,&nbsp;Erin E. Turner ,&nbsp;Elzena McVicar ,&nbsp;Amy Roth McDuffie ,&nbsp;Mary Q. Foote ,&nbsp;Erin Carll","doi":"10.1016/j.jmathb.2024.101196","DOIUrl":"10.1016/j.jmathb.2024.101196","url":null,"abstract":"<div><div>The Mathematizing-the-World routine (MWR) is an efficient culturally responsive instructional routine for mathematizing that explicitly supports problem posing using an image or object. Given the under-representation of problem-posing studies in elementary school settings, our qualitative study analyzed student responses from 56 MWR enactments in grade 3–5 classrooms in two regions of the United States. Our findings include detailed examples of the MWR in action, including how three open-ended prompts engaged younger students in mathematizing and posing problems related to authentic, real-world situations. We summarize findings across the 56 MWR classroom enactments focusing on the understandings about the context and the mathematical ideas evidenced in student responses. Our findings demonstrate the potential of the MWR as a catalyst for eliciting and communicating diverse student ideas while engaged in the problem-posing process. We discuss research and practice implications for this routine to support mathematizing, and specifically problem posing in the elementary classroom.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"76 ","pages":"Article 101196"},"PeriodicalIF":1.0,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142531530","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
On mathematics education for women in Russia prior to 1917 关于 1917 年之前俄罗斯妇女的数学教育
IF 1
Journal of Mathematical Behavior Pub Date : 2024-12-01 Epub Date: 2024-11-05 DOI: 10.1016/j.jmathb.2024.101201
Alexander Karp
{"title":"On mathematics education for women in Russia prior to 1917","authors":"Alexander Karp","doi":"10.1016/j.jmathb.2024.101201","DOIUrl":"10.1016/j.jmathb.2024.101201","url":null,"abstract":"<div><div>This paper attempts to describe women’s mathematics education in certain types of educational institutions in Russia before 1917. The history of women’s education (inclusive of the humanities) begins effectively in the eighteenth century. This education was inevitably limited, since the role assigned to women did not imply any special study of mathematics – mathematics was needed primarily for maintaining the household. To be sure, to this was also added the problem of intellectual development, which sometimes led to girls being taught geometry, and even algebra, although this did not happen often. At the same time, women’s mathematical talents could be valued quite highly. Gradually, the situation changed, and already in the twentieth century the opinion that women’s mathematics education should not differ from men’s was very widely expressed. This paper analyzes various views expressed in surviving documents, as well as textbooks written for girls, and memoirs that make it possible to imagine to a certain degree how exactly the teaching of mathematics at women’s educational institutions was implemented and perceived.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"76 ","pages":"Article 101201"},"PeriodicalIF":1.0,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587201","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
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
IF 1
Journal of Mathematical Behavior Pub Date : 2024-12-01 Epub Date: 2024-08-24 DOI: 10.1016/j.jmathb.2024.101177
Ioannis Papadopoulos
{"title":"Use of mathematical problems rooted in primary historical sources to reveal preservice teachers’ mathematical content knowledge","authors":"Ioannis Papadopoulos","doi":"10.1016/j.jmathb.2024.101177","DOIUrl":"10.1016/j.jmathb.2024.101177","url":null,"abstract":"<div><p>In this paper, the use of mathematical problems rooted in primary historical sources as a diagnostic tool for identifying learners’ understanding about area and volume is examined. The study follows preservice teachers in the context of a compulsory course in mathematics education while dealing with such problems embedding errors and challenging mistaken beliefs about the area of quadrilaterals and the volume of the cube. Although the initial aim was to involve the participants in inquiry-based activities, in the end, the history of mathematics served as a means to reveal the complete or partial understanding of the concepts making evident at the same time the participants’ misconceptions such as the overgeneralization of the rule ‘length times breadth’ and the confusion between area and perimeter concerning the area of the quadrilaterals task, and the illusion of linearity and the confusion between volume and surface area concerning the volume of the cube task.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"76 ","pages":"Article 101177"},"PeriodicalIF":1.0,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142058328","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
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
IF 1
Journal of Mathematical Behavior Pub Date : 2024-12-01 Epub Date: 2024-08-31 DOI: 10.1016/j.jmathb.2024.101179
Michael A. Tallman , John Weaver , Taylor Johnson
{"title":"Developing (Pedagogical) content knowledge of constant rate of change: The case of Samantha","authors":"Michael A. Tallman ,&nbsp;John Weaver ,&nbsp;Taylor Johnson","doi":"10.1016/j.jmathb.2024.101179","DOIUrl":"10.1016/j.jmathb.2024.101179","url":null,"abstract":"<div><p>We present the results of a teaching experiment designed to foster a pre-service secondary teacher’s construction of a quantitative scheme for constant rate of change. Although the research participant developed a productive conception of constant rate of change as an interiorized ratio, images of chunky continuous covariation constrained her ability to reason efficiently across a variety of applied contexts. The participant constructed a scheme for constant rate of change at the reflected level of thought, which enabled her to become cognizant of its essential aspects and to appreciate its general applicability. Our results suggest that engaging in reflected abstraction is critical for supporting pre-service teachers’ construction of coherent and refined mathematical schemes.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"76 ","pages":"Article 101179"},"PeriodicalIF":1.0,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142097020","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 types of insight do expert students gain during work with ill-structured problems in mathematics? 专家型学生在处理数学中结构不严谨的问题时会获得哪些类型的洞察力？
IF 1
Journal of Mathematical Behavior Pub Date : 2024-12-01 Epub Date: 2024-10-21 DOI: 10.1016/j.jmathb.2024.101199
Eirin Stenberg , Per Haavold , Bharath Sriraman
{"title":"What types of insight do expert students gain during work with ill-structured problems in mathematics?","authors":"Eirin Stenberg ,&nbsp;Per Haavold ,&nbsp;Bharath Sriraman","doi":"10.1016/j.jmathb.2024.101199","DOIUrl":"10.1016/j.jmathb.2024.101199","url":null,"abstract":"<div><div>In our study, we explored how two high-performing mathematics students gained insight while working on ill-structured problems. We followed their problem-solving process through task-based interviews and observed a similar sequence of insights in both participants’ work- <em>(1) Spontaneous insight</em>, <em>(2) Passive gradual insight</em>, <em>(3) Sudden insight</em>, and <em>(4) Active gradual insight</em>. An impasse occurred in the intersection between the second and third insight and seemed to accelerate the progression toward solution. During this insight sequence, we observed emotional transitions that appeared to impact the process in a useful manner, especially due to the participant’s interpretation of uncertainty related to the impasse as a challenge and an inspiration. Future research is needed to study the observed sequence of insights and related affects in a larger data set and in a broader spectrum of problem solvers.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"76 ","pages":"Article 101199"},"PeriodicalIF":1.0,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142531529","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
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
IF 1
Journal of Mathematical Behavior Pub Date : 2024-12-01 Epub 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 ,&nbsp;Jessi Lajos ,&nbsp;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":"2024-12-01","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
A lens for exploring which dimensions contribute to a justification’s proofiness 探索哪些因素有助于证明理由的可证明性的视角
IF 1
Journal of Mathematical Behavior Pub Date : 2024-12-01 Epub Date: 2024-11-20 DOI: 10.1016/j.jmathb.2024.101204
Dov Zazkis , Andre Rouhani
{"title":"A lens for exploring which dimensions contribute to a justification’s proofiness","authors":"Dov Zazkis ,&nbsp;Andre Rouhani","doi":"10.1016/j.jmathb.2024.101204","DOIUrl":"10.1016/j.jmathb.2024.101204","url":null,"abstract":"<div><div>This study extends the investigation of students’ conceptions of what makes a written justification a proof by introducing a novel theoretical lens—the proofiness lens. Under a proofiness lens a justification is conceptualized as occurring in a multi-dimensional space with each dimension influencing the extent to which that justification is considered a proof. In this work, we target a single potential dimension, the proof-to-procedure continuum, although, other dimensions emerged from students’ work. Our data allows us to explore how sensitive students are to the proof-to-procedure dimension of proofiness. Additionally, all students in our study were attentive to writing style as an emergent dimension. We demonstrate that the proofiness lens and its associated methodology shed light on which dimensions of proofs students attend to and why.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"76 ","pages":"Article 101204"},"PeriodicalIF":1.0,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142704874","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
Advances in research on mathematical problem posing: Focus on task variables 数学问题的研究进展：关注任务变量
IF 1
Journal of Mathematical Behavior Pub Date : 2024-12-01 Epub Date: 2024-09-07 DOI: 10.1016/j.jmathb.2024.101186
Jinfa Cai , Boris Koichu , Benjamin Rott , Chunlian Jiang
{"title":"Advances in research on mathematical problem posing: Focus on task variables","authors":"Jinfa Cai ,&nbsp;Boris Koichu ,&nbsp;Benjamin Rott ,&nbsp;Chunlian Jiang","doi":"10.1016/j.jmathb.2024.101186","DOIUrl":"10.1016/j.jmathb.2024.101186","url":null,"abstract":"<div><div>In this paper, we aim to present an overarching picture of Mathematical Problem Posing (MPP) with a focus on the impact of task variables on MPP products and processes. Admittedly, there are many different settings with which to approach research related to task variables and their associated products and processes in MPP among mathematics students and teachers. In this paper, we approached related research in three kinds of settings: (1) the individual setting, (2) the group setting, and (3) the classroom setting. We then provide some theoretical considerations and literature review in examining task variables in MPP based on four questions: (1) What variables are considered in research on MPP? (2) What methods do researchers use to examine variables in MPP? (3) What do we learn from research on variables about MPP? (4) What might be future directions of research on MPP involving variables?</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"76 ","pages":"Article 101186"},"PeriodicalIF":1.0,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142748221","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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