Pub Date : 2024-11-16DOI: 10.1016/j.jmathb.2024.101206
Maria Larsson , Hanna Fredriksdotter , Nina Klang
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.
{"title":"Different types of talk in mixed-attainment problem-solving groups: Contributions to individual students’ combinatorial thinking","authors":"Maria Larsson , Hanna Fredriksdotter , 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}
Pub Date : 2024-11-07DOI: 10.1016/j.jmathb.2024.101202
Jessica Carter
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.
{"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}
Pub Date : 2024-11-05DOI: 10.1016/j.jmathb.2024.101201
Alexander Karp
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.
{"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}
Pub Date : 2024-11-04DOI: 10.1016/j.jmathb.2024.101200
Ciara Murphy, Maria Meehan
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.
{"title":"Undergraduate students’ collaboration on homework problems in advanced mathematics courses","authors":"Ciara Murphy, 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}
Pub Date : 2024-10-30DOI: 10.1016/j.jmathb.2024.101198
Sindura Kularajan , Jennifer Czocher , Elizabeth Roan
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 for mathematical modeling, especially at the undergraduate differential equation level.
{"title":"Quantitative operators as an analytical tool for explaining differential equation students’ construction of new quantities during modeling","authors":"Sindura Kularajan , Jennifer Czocher , 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}
Pub Date : 2024-10-22DOI: 10.1016/j.jmathb.2024.101196
Julia M. Aguirre , Erin E. Turner , Elzena McVicar , Amy Roth McDuffie , Mary Q. Foote , Erin Carll
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.
{"title":"Mathematizing the world: A routine to advance mathematizing in the elementary classroom","authors":"Julia M. Aguirre , Erin E. Turner , Elzena McVicar , Amy Roth McDuffie , Mary Q. Foote , 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}
Pub Date : 2024-10-22DOI: 10.1016/j.jmathb.2024.101197
Jungeun Park , Jason Martin , Michael Oehrtman , Douglas Rizzolo
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.
通过将学生的定义学习视为对有关定义的元话语规则以及如何在定义活动中运用这些规则的学习，我们通过分析微积分 II 学生重塑极限的正式定义的教学实验，研究了旨在促进这种学习的教学实践。我们所确定的教学实践通过提供一种方法来检查学生的叙述是否符合他们所要遵循的元规则，并指导学生如何修改他们的定义以符合这些元规则，从而解决了学生如何看待定义任务的问题。我们的结果为教学实践提供了一个范例，促进学生学习和参与现有文献普遍呼吁的新的元辨析规则，特别是在他们重塑数学对象的形式定义时。
{"title":"Teaching practice aimed at promoting student engagement with metarules of defining","authors":"Jungeun Park , Jason Martin , Michael Oehrtman , 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":"2024-10-22","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}
Pub Date : 2024-10-21DOI: 10.1016/j.jmathb.2024.101199
Eirin Stenberg , Per Haavold , Bharath Sriraman
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- (1) Spontaneous insight, (2) Passive gradual insight, (3) Sudden insight, and (4) Active gradual insight. 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.
{"title":"What types of insight do expert students gain during work with ill-structured problems in mathematics?","authors":"Eirin Stenberg , Per Haavold , 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":"2024-10-21","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}
For teaching mathematical modeling in schools, teachers need to create suitable problems for their students to deal with. Despite an emphasis on teaching approaches for mathematical modeling, little is known about the processes involved in posing problems based on real-world situations, referred to as modeling-related problem posing, and specifically about what has been termed “implemented anticipation” as a metacognitive process variable. To contribute to filling this research gap, this study analyzed the nature and presence of implemented anticipation among preservice teachers as they posed problems based on real-world situations. The study was conducted through qualitative research with seven preservice teachers and revealed that the decision-making process in modeling-related problem posing involves different processes of implemented anticipation, depending on the role the preservice teacher takes on. The paper discusses the implications for preparing preservice teachers to pose problems for teaching mathematical modeling.
{"title":"Preservice teachers’ metacognitive process variables in modeling-related problem posing","authors":"Luisa-Marie Hartmann , Stanislaw Schukajlow , Mogens Niss , Uffe Thomas Jankvist","doi":"10.1016/j.jmathb.2024.101195","DOIUrl":"10.1016/j.jmathb.2024.101195","url":null,"abstract":"<div><div>For teaching mathematical modeling in schools, teachers need to create suitable problems for their students to deal with. Despite an emphasis on teaching approaches for mathematical modeling, little is known about the processes involved in posing problems based on real-world situations, referred to as modeling-related problem posing, and specifically about what has been termed “implemented anticipation” as a metacognitive process variable. To contribute to filling this research gap, this study analyzed the nature and presence of implemented anticipation among preservice teachers as they posed problems based on real-world situations. The study was conducted through qualitative research with seven preservice teachers and revealed that the decision-making process in modeling-related problem posing involves different processes of implemented anticipation, depending on the role the preservice teacher takes on. The paper discusses the implications for preparing preservice teachers to pose problems for teaching mathematical modeling.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"76 ","pages":"Article 101195"},"PeriodicalIF":1.0,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142428274","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}
Pub Date : 2024-10-03DOI: 10.1016/j.jmathb.2024.101193
Rachel Rupnow , Rosaura Uscanga , Anna Marie Bergman , Cassandra Mohr
Sameness is foundational to mathematics but has only recently become an area of focus in mathematics education research. In this paper, we describe characterizations of sameness generated by four student groups: discrete mathematics students, linear algebra students, abstract algebra students, and graduate students. Based on qualitative analysis of open response surveys, we compare these groups’ characterizations of sameness; note the subcomponents discussed and variation within each dimension; and highlight experiences influential to students’ perceptions of sameness. Findings include interpretability of sameness as a big idea, nascent development of thematic connections across courses, emphases on current course material rather than connections to prior courses for students solicited from a particular course, greater reflectiveness from the graduate student group, and abstract algebra as an impactful course. Implications include a need for thoughtful examinations of how “big ideas” develop among students and what experiences might support such development.
{"title":"Snapshots of sameness: Characterizations of mathematical sameness across student groups","authors":"Rachel Rupnow , Rosaura Uscanga , Anna Marie Bergman , Cassandra Mohr","doi":"10.1016/j.jmathb.2024.101193","DOIUrl":"10.1016/j.jmathb.2024.101193","url":null,"abstract":"<div><div>Sameness is foundational to mathematics but has only recently become an area of focus in mathematics education research. In this paper, we describe characterizations of sameness generated by four student groups: discrete mathematics students, linear algebra students, abstract algebra students, and graduate students. Based on qualitative analysis of open response surveys, we compare these groups’ characterizations of sameness; note the subcomponents discussed and variation within each dimension; and highlight experiences influential to students’ perceptions of sameness. Findings include interpretability of sameness as a big idea, nascent development of thematic connections across courses, emphases on current course material rather than connections to prior courses for students solicited from a particular course, greater reflectiveness from the graduate student group, and abstract algebra as an impactful course. Implications include a need for thoughtful examinations of how “big ideas” develop among students and what experiences might support such development.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"76 ","pages":"Article 101193"},"PeriodicalIF":1.0,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142428275","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}
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