Pub Date : 2025-03-25DOI: 10.1016/j.jmathb.2025.101240
Sophie Marchand , Dirk Schlimm
Notations are essential for mathematics, mathematical logic, and many other disciplines. In order for them to be used, they have to be learned and understood, which is relative to the perceptual and cognitive resources of their users. However, most reflections about the design of notations have not taken into consideration the diversity of possible users. In recent years, various groups of people have been identified who exhibit specific strengths and challenges with regard to the reading and processing of written information. This gives us the opportunity to reflect on how particular choices in the design of mathematical and logical notations can hinder and support the ease of reading and understanding for neurodiverse groups of students.
{"title":"Notations for neurodiverse learners","authors":"Sophie Marchand , Dirk Schlimm","doi":"10.1016/j.jmathb.2025.101240","DOIUrl":"10.1016/j.jmathb.2025.101240","url":null,"abstract":"<div><div>Notations are essential for mathematics, mathematical logic, and many other disciplines. In order for them to be used, they have to be learned and understood, which is relative to the perceptual and cognitive resources of their users. However, most reflections about the design of notations have not taken into consideration the diversity of possible users. In recent years, various groups of people have been identified who exhibit specific strengths and challenges with regard to the reading and processing of written information. This gives us the opportunity to reflect on how particular choices in the design of mathematical and logical notations can hinder and support the ease of reading and understanding for neurodiverse groups of students.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"79 ","pages":"Article 101240"},"PeriodicalIF":1.0,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143696996","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 : 2025-03-21DOI: 10.1016/j.jmathb.2025.101253
Anderson Norton , Joseph Antonides , Rachel Arnold , Vladislav Kokushkin
Understanding the cognitive challenges students experience in proofs-based mathematics courses is a necessary precursor for supporting them in meeting those challenges. We report on results from a pair of clinical interviews with each of seven STEM majors enrolled in an introductory proofs course. We investigate the epistemological obstacles they experienced in interaction with the interviewer and how those experiences might relate to their treatment of logical implications as actions, objects, or pseudo-objects. We share profiles for each of the seven students, characterizing their treatment of logical implications and their experiences of related epistemological obstacles. These profiles indicate marked differences between epistemological obstacles experienced during interactions with students who treat logical implications as objects, versus actions or pseudo-objects. Results suggest that proof-based mathematics courses should focus centrally on supporting students’ constructions of logical implications as mathematical objects.
{"title":"Logical implications as mathematical objects: Characterizing epistemological obstacles experienced in introductory proofs courses","authors":"Anderson Norton , Joseph Antonides , Rachel Arnold , Vladislav Kokushkin","doi":"10.1016/j.jmathb.2025.101253","DOIUrl":"10.1016/j.jmathb.2025.101253","url":null,"abstract":"<div><div>Understanding the cognitive challenges students experience in proofs-based mathematics courses is a necessary precursor for supporting them in meeting those challenges. We report on results from a pair of clinical interviews with each of seven STEM majors enrolled in an introductory proofs course. We investigate the epistemological obstacles they experienced in interaction with the interviewer and how those experiences might relate to their treatment of logical implications as actions, objects, or pseudo-objects. We share profiles for each of the seven students, characterizing their treatment of logical implications and their experiences of related epistemological obstacles. These profiles indicate marked differences between epistemological obstacles experienced during interactions with students who treat logical implications as objects, versus actions or pseudo-objects. Results suggest that proof-based mathematics courses should focus centrally on supporting students’ constructions of logical implications as mathematical objects.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"79 ","pages":"Article 101253"},"PeriodicalIF":1.0,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143680519","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 : 2025-03-06DOI: 10.1016/j.jmathb.2025.101243
Karolina Karpińska
This paper aims to describe mathematics teaching at the Victoriaschule in Gdańsk during the second half of the 19th century and the early 20th century. Although Gdańsk is currently located in Poland, during the period under consideration it was part of Prussian Poland, which refers to the Polish lands under Prussian rule, and it was formerly known as Danzig. The Victoriaschule was established in 1818 and, three years later, became the first public secondary school for girls in Gdańsk. In the latter half of the 19th century, a teachers’ seminary was also opened there. By the early 20th century, due to the efforts of the then-director, a real gymnasium for girls began operation, allowing students to take matriculation exams and pursue university studies. It became one of the best educational institutions for girls in Prussian Poland. This paper will compare mathematics teaching at the Victoriaschule with that in similar schools for boys and other selected girls’ schools operating at the same time in Prussian Poland, including institutions in Bydgoszcz, Grudziądz, Toruń, Malbork, and Kwidzyn. The analysis will focus on curricula, ministerial orders, school textbooks, and the initiatives of individual school reformers.
{"title":"Mathematics teaching at girls’ Victoriaschule in Gdańsk from the mid-19th century until World War I","authors":"Karolina Karpińska","doi":"10.1016/j.jmathb.2025.101243","DOIUrl":"10.1016/j.jmathb.2025.101243","url":null,"abstract":"<div><div>This paper aims to describe mathematics teaching at the <em>Victoriaschule</em> in Gdańsk during the second half of the 19th century and the early 20th century. Although Gdańsk is currently located in Poland, during the period under consideration it was part of Prussian Poland, which refers to the Polish lands under Prussian rule, and it was formerly known as Danzig. The <em>Victoriaschule</em> was established in 1818 and, three years later, became the first public secondary school for girls in Gdańsk. In the latter half of the 19th century, a teachers’ seminary was also opened there. By the early 20th century, due to the efforts of the then-director, a real gymnasium for girls began operation, allowing students to take matriculation exams and pursue university studies. It became one of the best educational institutions for girls in Prussian Poland. This paper will compare mathematics teaching at the <em>Victoriaschule</em> with that in similar schools for boys and other selected girls’ schools operating at the same time in Prussian Poland, including institutions in Bydgoszcz, Grudziądz, Toruń, Malbork, and Kwidzyn. The analysis will focus on curricula, ministerial orders, school textbooks, and the initiatives of individual school reformers.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"79 ","pages":"Article 101243"},"PeriodicalIF":1.0,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143562293","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 : 2025-03-04DOI: 10.1016/j.jmathb.2025.101242
Katja Krüger , Gerda Werth
This paper reviews the process of introducing mathematics education in girls’ secondary schools in Prussia, the largest German state at that time, from 1890 to 1925. This period of the German Empire and the subsequent Weimar Republic is known for its various educational reforms. Our historical analysis focuses on the purposes, new teaching tasks, and methods of mathematics education for girls in comparison with an extensive reform of mathematics education for boys, the so-called “Meran Reform” of 1905. Progress and obstacles on the way to equal educational opportunities for girls in mathematics are highlighted, including the development of new teaching methods and structural disadvantages.
{"title":"Mathematics education for girls in Prussia 1890–1925","authors":"Katja Krüger , Gerda Werth","doi":"10.1016/j.jmathb.2025.101242","DOIUrl":"10.1016/j.jmathb.2025.101242","url":null,"abstract":"<div><div>This paper reviews the process of introducing mathematics education in girls’ secondary schools in Prussia, the largest German state at that time, from 1890 to 1925. This period of the German Empire and the subsequent Weimar Republic is known for its various educational reforms. Our historical analysis focuses on the purposes, new teaching tasks, and methods of mathematics education for girls in comparison with an extensive reform of mathematics education for boys, the so-called “Meran Reform” of 1905. Progress and obstacles on the way to equal educational opportunities for girls in mathematics are highlighted, including the development of new teaching methods and structural disadvantages.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"79 ","pages":"Article 101242"},"PeriodicalIF":1.0,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143535170","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 : 2025-02-19DOI: 10.1016/j.jmathb.2025.101241
Fulvia Furinghetti , Alexander Karp
This article is the introduction to a special issue of the journal dedicated to the history of mathematics education of girls and young women. The article analyzes possible directions for research in this history. The authors discuss the general problematics of such research and briefly introduce the articles published in the special issue.
{"title":"The history of women’s mathematics education: Forming a research program","authors":"Fulvia Furinghetti , Alexander Karp","doi":"10.1016/j.jmathb.2025.101241","DOIUrl":"10.1016/j.jmathb.2025.101241","url":null,"abstract":"<div><div>This article is the introduction to a special issue of the journal dedicated to the history of mathematics education of girls and young women. The article analyzes possible directions for research in this history. The authors discuss the general problematics of such research and briefly introduce the articles published in the special issue.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"78 ","pages":"Article 101241"},"PeriodicalIF":1.0,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143438279","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 : 2025-02-06DOI: 10.1016/j.jmathb.2025.101239
Elisabete Zardo Búrigo
Throughout the 19th century in southern Brazil, as in the whole country, girls received a poorer mathematical education than boys. Historical records of this education are scarce. The first systematic opportunity for girls to progress beyond basic arithmetic was by pursuing training as elementary school teachers. In the 20th century, several movements converged to reduce inequalities: coeducation became standard in primary schools, secondary education was standardized, and both coeducational and girls’ secondary schools expanded rapidly. The first part of this text presents a systematic review of the sparse records found on mathematical education for girls until 1930. The second part compares school notebooks and the existing curriculum to examine traces of the mathematics studied in a girls' secondary school created in 1948. The regulation and expansion of secondary education allowed girls to study mathematical topics in algebra, deductive geometry, problem-solving, and introductory functions.
{"title":"From oral counting to plotting graphs: Advances in girls' math education in the South of Brazil","authors":"Elisabete Zardo Búrigo","doi":"10.1016/j.jmathb.2025.101239","DOIUrl":"10.1016/j.jmathb.2025.101239","url":null,"abstract":"<div><div>Throughout the 19th century in southern Brazil, as in the whole country, girls received a poorer mathematical education than boys. Historical records of this education are scarce. The first systematic opportunity for girls to progress beyond basic arithmetic was by pursuing training as elementary school teachers. In the 20th century, several movements converged to reduce inequalities: coeducation became standard in primary schools, secondary education was standardized, and both coeducational and girls’ secondary schools expanded rapidly. The first part of this text presents a systematic review of the sparse records found on mathematical education for girls until 1930. The second part compares school notebooks and the existing curriculum to examine traces of the mathematics studied in a girls' secondary school created in 1948. The regulation and expansion of secondary education allowed girls to study mathematical topics in algebra, deductive geometry, problem-solving, and introductory functions.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"78 ","pages":"Article 101239"},"PeriodicalIF":1.0,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143316515","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 : 2025-01-20DOI: 10.1016/j.jmathb.2025.101238
Jenneke H.J. Krüger
In 1863 the Dutch government introduced subsidized secondary schools, meant for boys, with an emphasis on sciences and mathematics. The question of the need and suitability of mathematics for girls was much debated. Co-education was seen as undesirable, nevertheless, a minority of girls received permission to enroll at the boys' schools. Secondary schools for girls became popular, mostly with a curriculum that emphasized languages and no national examinations. Some girls' schools offered the same curriculum as those of the boys, with the same diploma. After standardization of co-education in 1968, girls came to be perceived as a problem, for not choosing mathematics and sciences. Female mathematics teachers pointed out that probably, the girls were not the problem, but the mathematics curriculum and the way it was taught. This point of view was one of many factors increasing the participation of girls in mathematics.
{"title":"History of mathematics education for girls in the Netherlands","authors":"Jenneke H.J. Krüger","doi":"10.1016/j.jmathb.2025.101238","DOIUrl":"10.1016/j.jmathb.2025.101238","url":null,"abstract":"<div><div>In 1863 the Dutch government introduced subsidized secondary schools, meant for boys, with an emphasis on sciences and mathematics. The question of the need and suitability of mathematics for girls was much debated. Co-education was seen as undesirable, nevertheless, a minority of girls received permission to enroll at the boys' schools. Secondary schools for girls became popular, mostly with a curriculum that emphasized languages and no national examinations. Some girls' schools offered the same curriculum as those of the boys, with the same diploma. After standardization of co-education in 1968, girls came to be perceived as a problem, for not choosing mathematics and sciences. Female mathematics teachers pointed out that probably, the girls were not the problem, but the mathematics curriculum and the way it was taught. This point of view was one of many factors increasing the participation of girls in mathematics.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"78 ","pages":"Article 101238"},"PeriodicalIF":1.0,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143132403","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 : 2025-01-18DOI: 10.1016/j.jmathb.2025.101237
Yana Shvartsberg
This paper offers comparative analysis of mathematics education for girls in two New York City schools during the time from 1890 to 1920, known as the Progressive Era in the United States. During this time, secondary education transitioned from being mostly accessible through private and religious institutions to becoming widely available through public high schools. This expansion led to an unprecedented increase in enrollment and brought several challenges, including the need to adapt curricula to meet the diverse needs of students. Concurrently, changes in labor market demands, particularly in urban areas, underscored the varying educational objectives for girls and boys, driven by the belief that they would have distinct career paths upon graduation. As a result, many educators and policymakers viewed curriculum differentiation as a necessary tool to accommodate students from varied backgrounds. Curriculum differentiation enabled students to choose classes they considered essential, a trend particularly prominent in public schools. In contrast, private schools continued to enroll students who planned to pursue further education after graduation, and therefore, these schools had to maintain their curricular rigor. Wadleigh Public School and Brearley Private School, both girls-only institutions, provide a snapshot of this complexity by highlighting how distinct goals in mathematics education coexisted within the same city at the same time. This paper explores the strengths and challenges faced by both schools, focusing on the purpose of mathematics education, curricular differentiation, and demographic factors affecting girls' enrollment in mathematics classes.
{"title":"A comparative study of the Brearley School and Wadleigh High School in early 20th century New York City","authors":"Yana Shvartsberg","doi":"10.1016/j.jmathb.2025.101237","DOIUrl":"10.1016/j.jmathb.2025.101237","url":null,"abstract":"<div><div>This paper offers comparative analysis of mathematics education for girls in two New York City schools during the time from 1890 to 1920, known as the Progressive Era in the United States. During this time, secondary education transitioned from being mostly accessible through private and religious institutions to becoming widely available through public high schools. This expansion led to an unprecedented increase in enrollment and brought several challenges, including the need to adapt curricula to meet the diverse needs of students. Concurrently, changes in labor market demands, particularly in urban areas, underscored the varying educational objectives for girls and boys, driven by the belief that they would have distinct career paths upon graduation. As a result, many educators and policymakers viewed curriculum differentiation as a necessary tool to accommodate students from varied backgrounds. Curriculum differentiation enabled students to choose classes they considered essential, a trend particularly prominent in public schools. In contrast, private schools continued to enroll students who planned to pursue further education after graduation, and therefore, these schools had to maintain their curricular rigor. Wadleigh Public School and Brearley Private School, both girls-only institutions, provide a snapshot of this complexity by highlighting how distinct goals in mathematics education coexisted within the same city at the same time. This paper explores the strengths and challenges faced by both schools, focusing on the purpose of mathematics education, curricular differentiation, and demographic factors affecting girls' enrollment in mathematics classes.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"78 ","pages":"Article 101237"},"PeriodicalIF":1.0,"publicationDate":"2025-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143132407","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 : 2025-01-16DOI: 10.1016/j.jmathb.2024.101236
Joanna Debney Mobley
This article explores how the mathematics education and educators at the New York, USA women’s college, Barnard College, during its early years approached the issue of equal study on separate campuses as well as how some of the female students of Barnard with a mathematics focus in their studies utilized their knowledge of this male-dominated field to pursue careers following their graduation. Women in the 19th century struggled to earn a degree of equal value to what was available to men, especially when they were excluded from sharing a campus and classes with their male counterparts. When Barnard was founded, higher education for women was a highly controversial issue, especially for institutions with rigorous academic demands. This paper uses archival material from both Barnard and Columbia to explore the mathematics curriculum required of Barnard’s students, why that particular curriculum was selected, and selected faculty and alumnae active in the department during its first 25 years.
{"title":"Development and change in mathematics education for undergraduate women: An examination of the early years of Barnard College","authors":"Joanna Debney Mobley","doi":"10.1016/j.jmathb.2024.101236","DOIUrl":"10.1016/j.jmathb.2024.101236","url":null,"abstract":"<div><div>This article explores how the mathematics education and educators at the New York, USA women’s college, Barnard College, during its early years approached the issue of equal study on separate campuses as well as how some of the female students of Barnard with a mathematics focus in their studies utilized their knowledge of this male-dominated field to pursue careers following their graduation. Women in the 19th century struggled to earn a degree of equal value to what was available to men, especially when they were excluded from sharing a campus and classes with their male counterparts. When Barnard was founded, higher education for women was a highly controversial issue, especially for institutions with rigorous academic demands. This paper uses archival material from both Barnard and Columbia to explore the mathematics curriculum required of Barnard’s students, why that particular curriculum was selected, and selected faculty and alumnae active in the department during its first 25 years.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"78 ","pages":"Article 101236"},"PeriodicalIF":1.0,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143132406","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 : 2025-01-13DOI: 10.1016/j.jmathb.2024.101235
Amy B. Ellis , Dru Horne , Anna Bloodworth , Robert Ely
Mathematical play can support student agency and engagement, offer learning benefits, and foster productive mathematical dispositions. However, the bulk of research on mathematical play investigates the mathematics that emerges in young children’s natural play or in students’ play in informal spaces such as video games. We introduce the term “playful math” to describe the activities and features of an instructional environment that can facilitate mathematical play, and we investigate the efficacy of incorporating playful task design elements into algebra activities. Drawing on two small-group teaching experiments with middle-school students, the first with two participants and the second with three participants, we identified 13 phenomena characterizing students’ mathematical play activity: Competitive Fun, Feeling Proud, Enjoyment, Wonderment, Taking on Authority, Perturbation, Investment, Immersion, Agency, Perseverance, Creative/Unusual, Harder Math, and Laughter. We found that all phenomena except Wonderment and Perturbation occurred more during playful math tasks. We describe two vignettes exemplifying the mathematical play phenomena and discuss implications for task design and instruction.
{"title":"From mathematical play to playful math","authors":"Amy B. Ellis , Dru Horne , Anna Bloodworth , Robert Ely","doi":"10.1016/j.jmathb.2024.101235","DOIUrl":"10.1016/j.jmathb.2024.101235","url":null,"abstract":"<div><div>Mathematical play can support student agency and engagement, offer learning benefits, and foster productive mathematical dispositions. However, the bulk of research on mathematical play investigates the mathematics that emerges in young children’s natural play or in students’ play in informal spaces such as video games. We introduce the term “playful math” to describe the activities and features of an instructional environment that can facilitate mathematical play, and we investigate the efficacy of incorporating playful task design elements into algebra activities. Drawing on two small-group teaching experiments with middle-school students, the first with two participants and the second with three participants, we identified 13 phenomena characterizing students’ mathematical play activity: Competitive Fun, Feeling Proud, Enjoyment, Wonderment, Taking on Authority, Perturbation, Investment, Immersion, Agency, Perseverance, Creative/Unusual, Harder Math, and Laughter. We found that all phenomena except Wonderment and Perturbation occurred more during playful math tasks. We describe two vignettes exemplifying the mathematical play phenomena and discuss implications for task design and instruction.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"78 ","pages":"Article 101235"},"PeriodicalIF":1.0,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143132405","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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