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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 : 2024-11-21 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":"2024-11-21","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
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 : 2024-11-20 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":"2024-11-20","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
Mature intuition and mathematical understanding 成熟的直觉和数学理解力
IF 1
Journal of Mathematical Behavior Pub Date : 2024-11-18 DOI: 10.1016/j.jmathb.2024.101203
William D'Alessandro , Irma Stevens
{"title":"Mature intuition and mathematical understanding","authors":"William D'Alessandro ,&nbsp;Irma Stevens","doi":"10.1016/j.jmathb.2024.101203","DOIUrl":"10.1016/j.jmathb.2024.101203","url":null,"abstract":"<div><div>Mathematicians often describe the importance of well-developed intuition to productive research and successful learning. But neither education researchers nor philosophers interested in epistemic dimensions of mathematical practice have yet given the topic the sustained attention it deserves. The trouble is partly that intuition in the relevant sense lacks a usefully clear characterization, so we begin by offering one: mature intuition, we say, is the capacity for fast, fluent, reliable and insightful inference with respect to some subject matter. We illustrate the role of mature intuition in mathematical practice with an assortment of examples, including data from a sequence of clinical interviews in which a student improves upon initially misleading covariational intuitions. Finally, we show how the study of intuition can yield insights for philosophers and education theorists. First, it contributes to a longstanding debate in epistemology by undermining <em>epistemicism</em>, the view that an agent’s degree of objectual understanding is determined exclusively by their knowledge, beliefs and credences. We argue on the contrary that intuition can contribute directly and independently to understanding. Second, we identify potential pedagogical avenues towards the development of mature intuition, highlighting strategies including <em>adding imagery</em>, <em>developing associations</em>, <em>establishing confidence</em> and <em>generalizing concepts</em>.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"76 ","pages":"Article 101203"},"PeriodicalIF":1.0,"publicationDate":"2024-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142704875","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
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 : 2024-11-17 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":"2024-11-17","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
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 : 2024-11-16 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":"2024-11-16","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
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 : 2024-11-07 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":"2024-11-07","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
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 : 2024-11-05 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":"2024-11-05","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
Undergraduate students’ collaboration on homework problems in advanced mathematics courses 本科生在高等数学课程作业问题上的合作
IF 1
Journal of Mathematical Behavior Pub Date : 2024-11-04 DOI: 10.1016/j.jmathb.2024.101200
Ciara Murphy, Maria Meehan
{"title":"Undergraduate students’ collaboration on homework problems in advanced mathematics courses","authors":"Ciara Murphy,&nbsp;Maria Meehan","doi":"10.1016/j.jmathb.2024.101200","DOIUrl":"10.1016/j.jmathb.2024.101200","url":null,"abstract":"<div><div>While mathematicians and mathematics education researchers have acknowledged the importance of undergraduate mathematics students’ learning outside of class time, little is known about what students actually do. The aim of this study is to examine one aspect of students’ out-of-class learning: their collaboration with peers on homework problems. Ten interviews with recent graduates of mathematics degrees were conducted and analyzed using reflexive thematic analysis. We examine participants’ descriptions of how they collaborated on homework problems and with whom. Additionally, we explore their perceptions of the affordances of collaborating on homework, as well as the factors they perceive as constraining their engagement in the practice. Our study is an initial step towards developing a more complete understanding of undergraduate mathematics students’ engagement with homework problems and out-of-class learning practices more generally. We discuss the implications of our findings in terms of guiding future research.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"76 ","pages":"Article 101200"},"PeriodicalIF":1.0,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142578129","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
Quantitative operators as an analytical tool for explaining differential equation students’ construction of new quantities during modeling 数量运算符是解释微分方程学生在建模过程中构建新数量的分析工具
IF 1
Journal of Mathematical Behavior Pub Date : 2024-10-30 DOI: 10.1016/j.jmathb.2024.101198
Sindura Kularajan , Jennifer Czocher , Elizabeth Roan
{"title":"Quantitative operators as an analytical tool for explaining differential equation students’ construction of new quantities during modeling","authors":"Sindura Kularajan ,&nbsp;Jennifer Czocher ,&nbsp;Elizabeth Roan","doi":"10.1016/j.jmathb.2024.101198","DOIUrl":"10.1016/j.jmathb.2024.101198","url":null,"abstract":"<div><div>Theories of quantitative reasoning have taken precedence as an analytical tool to interpret and describe students’ mathematical reasonings, especially as students engage in mathematical modeling tasks. These theories are particularly useful to describe how students construct new quantities as they model. However, while using this lens to analyze Differential Equations students’ construction of mathematical models of dynamic situations, we found cases of quantity construction that were not fully characterized by extant concepts. In this theory-building paper, we present five examples of such cases. Additionally, we introduce a new construct—quantitative operators—as an extended analytical tool to characterize those cases. Our findings suggest that quantitative operators may be viewed as an extension for theories of quantity construction and complementary to symbolic forms, when localizing theories of quantity construction <em>for</em> mathematical modeling, especially at the undergraduate differential equation level.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"76 ","pages":"Article 101198"},"PeriodicalIF":1.0,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142553299","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 : 2024-10-22 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":"2024-10-22","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
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