Pub Date : 2024-12-09DOI: 10.1016/j.jmathb.2024.101208
Yacin Hamami
Mathematics education and the philosophy of mathematical practice are two fields of research whose domains of investigation overlap in a striking way. And yet, interactions between the two fields have been very limited so far, research being mostly conducted in parallel, sometimes on the very same issues. As a consequence, the potential for interaction and cross-fertilization between the two fields remains largely under-explored and under-exploited. The aim of this article is to encourage these interactions by indicating a number of concrete research opportunities where existing contributions in one field may lead to original developments in the other.
{"title":"Philosophy of mathematical practice and mathematics education: Cross-fertilization, dialogue and prospects","authors":"Yacin Hamami","doi":"10.1016/j.jmathb.2024.101208","DOIUrl":"10.1016/j.jmathb.2024.101208","url":null,"abstract":"<div><div>Mathematics education and the philosophy of mathematical practice are two fields of research whose domains of investigation overlap in a striking way. And yet, interactions between the two fields have been very limited so far, research being mostly conducted in parallel, sometimes on the very same issues. As a consequence, the potential for interaction and cross-fertilization between the two fields remains largely under-explored and under-exploited. The aim of this article is to encourage these interactions by indicating a number of concrete research opportunities where existing contributions in one field may lead to original developments in the other.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"78 ","pages":"Article 101208"},"PeriodicalIF":1.0,"publicationDate":"2024-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143132652","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 : 2024-12-01DOI: 10.1016/j.jmathb.2024.101186
Jinfa Cai , Boris Koichu , Benjamin Rott , Chunlian Jiang
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?
{"title":"Advances in research on mathematical problem posing: Focus on task variables","authors":"Jinfa Cai , Boris Koichu , Benjamin Rott , 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}
Pub Date : 2024-11-28DOI: 10.1016/j.jmathb.2024.101211
Yaomingxin Lu
Research has shown that many undergraduate students struggle to learn to prove, including those who major in mathematics (Moore, 1994; Selden, 2012). While studies have explored how expert mathematicians construct proofs to inform teaching practices, expert strategies might not be equally beneficial to novice provers with limited abilities in proving. Novice provers often face difficulties and impasses when engaged in problem-solving or proving tasks. Looking through the lenses of impasses, this study provides a more fine-grained account by characterizing novice provers’ navigating actions when they encounter impasses to better support them in their proving processes. This research draws on task-based interviews conducted with undergraduates enrolled in a transition-to-proof course. A framework was developed to identify productive actions students took when navigating stuck points in the proving process. The result of this study shows that productive actions around stuck points can develop important proof skills in students, even if the student did not ultimately complete the proof successfully. Therefore, instructors are encouraged to recognize and support these productive actions, prioritizing them over mere proof completion when guiding students in their proving processes.
{"title":"Overcoming impasses in proving processes: Novice provers’ productive actions when encountering stuck points","authors":"Yaomingxin Lu","doi":"10.1016/j.jmathb.2024.101211","DOIUrl":"10.1016/j.jmathb.2024.101211","url":null,"abstract":"<div><div>Research has shown that many undergraduate students struggle to learn to prove, including those who major in mathematics (Moore, 1994; Selden, 2012). While studies have explored how expert mathematicians construct proofs to inform teaching practices, expert strategies might not be equally beneficial to novice provers with limited abilities in proving. Novice provers often face difficulties and impasses when engaged in problem-solving or proving tasks. Looking through the lenses of impasses, this study provides a more fine-grained account by characterizing novice provers’ navigating actions when they encounter impasses to better support them in their proving processes. This research draws on task-based interviews conducted with undergraduates enrolled in a transition-to-proof course. A framework was developed to identify productive actions students took when navigating stuck points in the proving process. The result of this study shows that productive actions around stuck points can develop important proof skills in students, even if the student did not ultimately complete the proof successfully. Therefore, instructors are encouraged to recognize and support these productive actions, prioritizing them over mere proof completion when guiding students in their proving processes.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"77 ","pages":"Article 101211"},"PeriodicalIF":1.0,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142748741","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 : 2024-11-28DOI: 10.1016/j.jmathb.2024.101205
Amy J. Hackenberg , Fetiye Aydeniz Temizer , Rebecca S. Borowski
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.
以18名七年级学生为研究对象，在第一作者与班主任共同授课的比例推理单元中，进行了单元协调三个阶段的课堂研究，以了解如何进行响应式教学。在本单元中，学生们努力使两辆汽车以相同的速度行驶。根据其他地方的报道，在单元协调的所有三个阶段的学生都学会了这样做（Hackenberg et al., 2023）。本文的研究重点是在小组教学中进行响应式探究的实践。我们发现，教师-研究人员的去中心化是这种做法背后的一种机制。去中心化包括采用另一个人的观点，把自己的观点放在一边，把别人的观点作为互动的基础。我们发现，两种分散行动模式和一种问题类型，即利用问题，支持学生跨单元协调的各个阶段，以维持挑战和学习。
{"title":"Decentering to support responsive teaching for middle school students","authors":"Amy J. Hackenberg , Fetiye Aydeniz Temizer , 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":"2024-11-28","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}
Pub Date : 2024-11-25DOI: 10.1016/j.jmathb.2024.101212
Beth L. MacDonald , Allison M. Kroesch , Neet Priya Bajwa , Jeffrey Barrett , Jessica H. Hunt , Jennifer Tobias
We examined how whole number knowledge and fraction knowledge may interact, conducting task-based interviews with two third-grade children with ISM.2 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.
{"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 , Allison M. Kroesch , Neet Priya Bajwa , Jeffrey Barrett , Jessica H. Hunt , 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":"2024-11-25","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}
Pub Date : 2024-11-21DOI: 10.1016/j.jmathb.2024.101207
Lisnet Mwadzaangati , Jill Adler
Our study focuses on teachers’ engagement with language practices through their participation in an adapted lesson study (LS) focusing on introduction to the concept of similarity and the meaning of ‘similar’ in a lesson on similar triangles. We use data from textbook analysis, lesson planning, lessons and lesson reflection sessions to explore teachers’ engagement with language practices and how these evolved over a LS cycle. Working with the notion of dilemmas in teaching as ‘sources of praxis’ (Adler, 1998), we identified inter-connected teaching dilemmas, engagement with which led to a wider use of language registers and representations in the second lesson and with these, opening opportunities for elaborating the meaning of similar triangles. We describe the dilemmas that emerged and their related language practices, evidence teachers’ engagement with these in their talk and their teaching, and argue that LS can create conditions for teachers’ learning about language practices in teaching.
我们的研究侧重于教师通过参与改编课程研究（LS）参与语言实践的情况，该课程研究的重点是在一堂关于相似三角形的课上介绍相似性的概念和 "相似 "的含义。我们利用课本分析、备课、上课和课后反思环节的数据，探讨教师参与语言实践的情况，以及这些实践在 LS 周期中的演变情况。教学中的困境是 "实践的源泉"（Adler，1998 年），根据这一概念，我们确定了相互关联的教学困境，这些困境导致教师在第二节课上更广泛地使用语言语域和表述方式，并为阐述相似三角形的含义提供了机会。我们描述了出现的困境及其相关的语言实践，证明了教师在谈话和教学中对这些困境的参与，并认为通识教育可以为教师学习教学中的语言实践创造条件。
{"title":"Teachers’ engagement with language practices through a geometry lesson study","authors":"Lisnet Mwadzaangati , Jill Adler","doi":"10.1016/j.jmathb.2024.101207","DOIUrl":"10.1016/j.jmathb.2024.101207","url":null,"abstract":"<div><div>Our study focuses on teachers’ engagement with language practices through their participation in an adapted lesson study (LS) focusing on introduction to the concept of similarity and the meaning of ‘similar’ in a lesson on similar triangles. We use data from textbook analysis, lesson planning, lessons and lesson reflection sessions to explore teachers’ engagement with language practices and how these evolved over a LS cycle. Working with the notion of dilemmas in teaching as ‘sources of praxis’ (Adler, 1998), we identified inter-connected teaching dilemmas, engagement with which led to a wider use of language registers and representations in the second lesson and with these, opening opportunities for elaborating the meaning of similar triangles. We describe the dilemmas that emerged and their related language practices, evidence teachers’ engagement with these in their talk and their teaching, and argue that LS can create conditions for teachers’ learning about language practices in teaching.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"76 ","pages":"Article 101207"},"PeriodicalIF":1.0,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142704873","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 : 2024-11-21DOI: 10.1016/j.jmathb.2024.101194
Heidi Strømskag
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.
本研究探讨了数学教学情境理论（TDS）和社会互动理论（TSI），采用了理论网络图式的策略来揭示它们之间潜在的互补性。这些理论为数学课堂互动提供了不同的先验视角：TDS 侧重于数学知识在说教情境中的运作，而 TSI 则侧重于通过主体间性的互动成就数学意义的产生。本研究提出了一个关于理论框架互补层面的假设，特别是关于社会互动和相关课堂规则的假设。通过对数学课堂数据集的理论三角分析，这一假设得到了实证。考虑到相关数学知识，TDS 分析确定了数据集中的 Topaze 效应，而 TSI 分析则将经验事实解释为呈现出漏斗状的互动模式。本文认为，这两种解释相互增强了对方的解释力。
{"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}
Pub Date : 2024-11-20DOI: 10.1016/j.jmathb.2024.101204
Dov Zazkis , Andre Rouhani
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.
{"title":"A lens for exploring which dimensions contribute to a justification’s proofiness","authors":"Dov Zazkis , 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}
Pub Date : 2024-11-18DOI: 10.1016/j.jmathb.2024.101203
William D'Alessandro , Irma Stevens
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 epistemicism, 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 adding imagery, developing associations, establishing confidence and generalizing concepts.
{"title":"Mature intuition and mathematical understanding","authors":"William D'Alessandro , 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}
Pub Date : 2024-11-17DOI: 10.1016/j.jmathb.2024.101209
Polly Thanailaki
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 Philekpedeutiki Etaireia provide this research with a rich source of information regarding female schooling in 19th century.
{"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}
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