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Introduction to the virtual special issue: Mathematics that underpins social issues 虚拟特刊简介：支撑社会问题的数学
IF 1
Journal of Mathematical Behavior Pub Date : 2024-07-17 DOI: 10.1016/j.jmathb.2024.101176
Eva Thanheiser , Ami Mamolo
{"title":"Introduction to the virtual special issue: Mathematics that underpins social issues","authors":"Eva Thanheiser ,&nbsp;Ami Mamolo","doi":"10.1016/j.jmathb.2024.101176","DOIUrl":"10.1016/j.jmathb.2024.101176","url":null,"abstract":"<div><p>This Virtual Special Issue on <em>Mathematics in Society: Exploring the Mathematics that Underpins Social Issues</em> features 13 articles which expand our understanding of how people build, retain, communicate, apply, and comprehend mathematical ideas as they relate to social and societal issues. The focus is on education research that explores the ways in which mathematics and a mathematical worldview can influence choices, on educational, personal and societal levels. We take a broad view and raise questions about what it means to be mathematical in society, and we consider the multifaceted ways in which abilities to derive and interpret information presented mathematically are also necessary in and for society.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"75 ","pages":"Article 101176"},"PeriodicalIF":1.0,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0732312324000531/pdfft?md5=4975a2f50fd35144526bbe438543d68c&pid=1-s2.0-S0732312324000531-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141638374","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
Preparing elementary pre-service teachers to teach early algebra: A conceptual replication study 培养小学职前教师教授早期代数：概念复制研究
IF 1
Journal of Mathematical Behavior Pub Date : 2024-06-28 DOI: 10.1016/j.jmathb.2024.101174
Charles Hohensee , Vahid Borji
{"title":"Preparing elementary pre-service teachers to teach early algebra: A conceptual replication study","authors":"Charles Hohensee ,&nbsp;Vahid Borji","doi":"10.1016/j.jmathb.2024.101174","DOIUrl":"https://doi.org/10.1016/j.jmathb.2024.101174","url":null,"abstract":"<div><p>Early algebra can prepare elementary students for the transition they will need to make from arithmetic and algebra. Although teacher preparation programs emphasize the teaching of early algebra, research on how to prepare elementary pre-service teachers (PSTs) to teach early algebra is still scarce. The replication study reported in this article was a conceptual replication study designed to examine Iranian PSTs’ reasoning about pre-symbolic early algebra by looking at what was more, somewhat, and less challenging. The aims of the replication study aligned with the original study (Hohensee, 2017). Results from the replication study show that participating PSTs (<em>N</em> = 15) found the early algebra approach to variables and functions more challenging, indeterminable unknowns somewhat challenging, and equivalence and equations less challenging. We make comparisons with the original study, as well as offer implications and suggestions for preparing PSTs to teach early algebra.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"75 ","pages":"Article 101174"},"PeriodicalIF":1.0,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141479173","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
New kinds of embodied interactions that arise in augmented reality dynamic geometry software 增强现实动态几何软件中出现的新型体现式互动
IF 1
Journal of Mathematical Behavior Pub Date : 2024-06-25 DOI: 10.1016/j.jmathb.2024.101175
Candace Walkington , Mitchell J. Nathan , Jonathan Hunnicutt , Julianna Washington , Monique Zhou
{"title":"New kinds of embodied interactions that arise in augmented reality dynamic geometry software","authors":"Candace Walkington ,&nbsp;Mitchell J. Nathan ,&nbsp;Jonathan Hunnicutt ,&nbsp;Julianna Washington ,&nbsp;Monique Zhou","doi":"10.1016/j.jmathb.2024.101175","DOIUrl":"https://doi.org/10.1016/j.jmathb.2024.101175","url":null,"abstract":"<div><p>Dynamic geometry software (DGS) has long been studied in mathematics education as a way for students to explore and interact with geometric objects and figures. Recent advances in Augmented Reality (AR) technologies that allow dynamic three-dimensional mathematical objects to appear in students’ environment as holograms have changed the nature of what is possible for a DGS, particularly with respect to embodiment. New forms of embodied interactions may arise in AR-based DGS, as students gesture and move their bodies through their environment, taking different perspectives to interact with these immersive shapes projected in three dimensions. In the present study, we examine videos of 28 high school students interacting with an AR-based version of the DGS GeoGebra, while wearing the Microsoft HoloLens 2 headsets. We document the novel kinds of embodied interactions that the AR environment affords, relating to (1) perspective and orientation, (2) scale, (3) three dimensions. Based on our analysis, we give important directions for future research on DGS and implications for the design of the next generation of holographic DGS.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"75 ","pages":"Article 101175"},"PeriodicalIF":1.0,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S073231232400052X/pdfft?md5=52834f5c84f9c81469fd3a2de5c68290&pid=1-s2.0-S073231232400052X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141479172","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
Abstract algebra students’ conceptual metaphors for isomorphism and homomorphism 抽象代数学生对同构和同态的概念隐喻
IF 1
Journal of Mathematical Behavior Pub Date : 2024-06-20 DOI: 10.1016/j.jmathb.2024.101173
Rachel Rupnow , Brooke Randazzo
{"title":"Abstract algebra students’ conceptual metaphors for isomorphism and homomorphism","authors":"Rachel Rupnow ,&nbsp;Brooke Randazzo","doi":"10.1016/j.jmathb.2024.101173","DOIUrl":"https://doi.org/10.1016/j.jmathb.2024.101173","url":null,"abstract":"<div><p>Group isomorphism and homomorphism are core concepts in abstract algebra, and student understanding of isomorphism has received extensive attention in line with the centrality of this topic. However, limited work has directly examined student conceptions of homomorphism or what metaphors students use to express their thought processes while problem solving. Based on interviews with four students, we contrast two students who used predominantly formal definition and mapping-centered metaphors for homomorphism with two who additionally used sameness-centered metaphors and note that the usage or non-usage of sameness-centered metaphors was not indicative of successful problem solving. Implications include the alignment between students’ metaphors and those used in instruction, indicating the importance of attending to metaphors when teaching, and the importance of discussing what is intended by some sameness-based metaphors, such as operation-preservation.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"75 ","pages":"Article 101173"},"PeriodicalIF":1.0,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141434861","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
From knowledge acquired at academic mathematics courses to significant changes in instructional practices 从数学学术课程中获得的知识到教学实践中的重大变化
IF 1
Journal of Mathematical Behavior Pub Date : 2024-06-20 DOI: 10.1016/j.jmathb.2024.101172
Ruhama Even , Yocheved Mytlis
{"title":"From knowledge acquired at academic mathematics courses to significant changes in instructional practices","authors":"Ruhama Even ,&nbsp;Yocheved Mytlis","doi":"10.1016/j.jmathb.2024.101172","DOIUrl":"https://doi.org/10.1016/j.jmathb.2024.101172","url":null,"abstract":"<div><p>This non-interventional study investigates the contribution of university mathematics to teaching high-school mathematics. Data sources included interviews with five teachers who taught high-school mathematics before, during, and after their academic mathematics studies. All teachers provided tangible examples of fundamental changes in instructional practices that they explicitly linked to new knowledge acquired in the academic mathematics courses. The domain of analysis in general, and the topics of integrals and derivatives in particular, were central in the teachers’ illustrations of changes they made in their teaching, although other mathematical topics and domains were also mentioned. The reported changes were mostly associated with emphasis on mathematical explanations, exposition of two key elements of the deductive structure of mathematics: definition and proof, an increased focus on formal mathematics, and portrayal of mathematics as a wide and varied discipline. The study results are discussed in light of the relevant literature.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"75 ","pages":"Article 101172"},"PeriodicalIF":1.0,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141434862","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
Seeing mathematics together: A comparative case study of youths and facilitators collaborating to learn mathematics in informal settings 一起看数学：青少年与辅导员在非正式环境中合作学习数学的比较案例研究
IF 1.7
Journal of Mathematical Behavior Pub Date : 2024-06-19 DOI: 10.1016/j.jmathb.2024.101171
Marc T. Sager , Maximilian K. Sherard , Candace Walkington , Saki Milton , Anthony J. Petrosino
{"title":"Seeing mathematics together: A comparative case study of youths and facilitators collaborating to learn mathematics in informal settings","authors":"Marc T. Sager ,&nbsp;Maximilian K. Sherard ,&nbsp;Candace Walkington ,&nbsp;Saki Milton ,&nbsp;Anthony J. Petrosino","doi":"10.1016/j.jmathb.2024.101171","DOIUrl":"https://doi.org/10.1016/j.jmathb.2024.101171","url":null,"abstract":"<div><h3>Background</h3><p>This comparative case study examined the use of math walks with middle grade youths and adult facilitators in an informal STEM learning space. Math walks are place-based walking tours where youths and facilitators critically examine and ask math-related questions about their environment.</p></div><div><h3>Method</h3><p>Drawing on situated theories of learning and frameworks for understanding group participation, we examined how facilitators constrained or supported youths’ mathematical thinking as they participated in math walks at the local zoo.</p></div><div><h3>Results</h3><p>Using interaction and stance analysis, we identified, analyzed, and compared three contrasting cases: In the first case, the facilitator may have overly constrained youths’ mathematical thinking by asking leading questions and not providing time for youths to discuss their personal interests. In the second case, the facilitator may have underly constrained youths’ mathematical thinking by allowing youths to ask too many new questions without refining or developing any one specific question. In the third case, the facilitator supported mathematical thinking by praising youths’ work, layering on mathematical terminology, and providing clear and actionable instructions for how youths could refine their mathematical questions.</p></div><div><h3>Conclusions</h3><p>Findings support efforts to understand how adult facilitators can support youths in seeing mathematics within and asking mathematical questions about the world around them.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"75 ","pages":"Article 101171"},"PeriodicalIF":1.7,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0732312324000488/pdfft?md5=3b96c08b00e0bf0a482a419169dbe013&pid=1-s2.0-S0732312324000488-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141429580","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
Pre-service mathematics teachers’ discourse: Differences between defining in task situations involving prototypical and non-prototypical solids 职前数学教师的话语：在涉及原型和非原型固体的任务情境中进行定义的差异
IF 1.7
Journal of Mathematical Behavior Pub Date : 2024-06-18 DOI: 10.1016/j.jmathb.2024.101170
Rocío Toscano , Aurora Fernández-León , José María Gavilán-Izquierdo , Alfonso J. González-Regaña , Verónica Martín-Molina
{"title":"Pre-service mathematics teachers’ discourse: Differences between defining in task situations involving prototypical and non-prototypical solids","authors":"Rocío Toscano ,&nbsp;Aurora Fernández-León ,&nbsp;José María Gavilán-Izquierdo ,&nbsp;Alfonso J. González-Regaña ,&nbsp;Verónica Martín-Molina","doi":"10.1016/j.jmathb.2024.101170","DOIUrl":"https://doi.org/10.1016/j.jmathb.2024.101170","url":null,"abstract":"<div><p>The literature has highlighted the significant role of definitions and defining in mathematics learning and teaching. Furthermore, non-prototypical figures are particularly important when teaching geometry, but teachers and pre-service teachers still have problems defining them. For these reasons, we investigated whether there were differences in the way that pre-service mathematics teachers constructed and selected definitions for prototypical and non-prototypical solids. In particular, the commognitive framework was employed to investigate the differences in the discourse of 33 pre-service secondary-school teachers when constructing and selecting definitions in task situations that involved prototypical and non-prototypical solids. Moreover, we studied if some commognitive conflicts appeared in task situations involving non-prototypical solids but not in similar task situations involving prototypical solids. The findings show some differences between the pre-service teachers’ discourses in both types of task situations. Additionally, some commognitive conflicts appeared only in task situations with non-prototypical solids. Lastly, we classified those commognitive conflicts.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"75 ","pages":"Article 101170"},"PeriodicalIF":1.7,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0732312324000476/pdfft?md5=02bccb14ff2fe7c2ef9abd84783f1247&pid=1-s2.0-S0732312324000476-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141423150","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
The emotions lived in mathematics classes and their reflection outside the school context: A case study of Manuel 数学课上的情绪及其在校外的反映：曼努埃尔的案例研究
IF 1.7
Journal of Mathematical Behavior Pub Date : 2024-06-17 DOI: 10.1016/j.jmathb.2024.101168
Valentina Souza , Isaias Miranda , Alejandro Coca
{"title":"The emotions lived in mathematics classes and their reflection outside the school context: A case study of Manuel","authors":"Valentina Souza ,&nbsp;Isaias Miranda ,&nbsp;Alejandro Coca","doi":"10.1016/j.jmathb.2024.101168","DOIUrl":"https://doi.org/10.1016/j.jmathb.2024.101168","url":null,"abstract":"<div><p>Based on the theory of the Cognitive Structure of the Emotions (OCC), this article has a dual objective: 1) to document negative attitudes toward mathematics generated during the academic formation of Manuel, an adult who ended his school education 15 years before this investigation and today is a professional voice-over actor; and 2) to analyze the reflection of those attitudes in the emotions that emerged during the process of solving mathematical problems related to his work. Manuel was chosen from among ten voice-over professionals who, before the study began, manifested a strong aversion toward mathematics. Manuel was interviewed twice: once before, and then after solving the mathematical problems posed. Results indicate that his negative attitude toward mathematics was reflected in the emotions — frustration, fear, anger, and nervousness — he experienced while solving the problems.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"75 ","pages":"Article 101168"},"PeriodicalIF":1.7,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0732312324000452/pdfft?md5=a0d0bd3dcf9c36deeaf44f9a1740d6a2&pid=1-s2.0-S0732312324000452-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141423152","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
Disrupting racial storylines about black girls in mathematics through teaching content and building relationships 通过教学内容和建立关系，打破数学领域关于黑人女孩的种族故事情节
IF 1.7
Journal of Mathematical Behavior Pub Date : 2024-06-15 DOI: 10.1016/j.jmathb.2024.101167
Charles E. Wilkes II , Dan Battey
{"title":"Disrupting racial storylines about black girls in mathematics through teaching content and building relationships","authors":"Charles E. Wilkes II ,&nbsp;Dan Battey","doi":"10.1016/j.jmathb.2024.101167","DOIUrl":"https://doi.org/10.1016/j.jmathb.2024.101167","url":null,"abstract":"<div><p>This study is a qualitative case study that focuses on the instructional practice of a white woman teacher with three Black girls. We draw upon literature that describes racial storylines for Black girls to focus on how a white Woman teacher navigates racial storylines to enact instructional practices that are humanzing for Black girls. Specifically, we show how interactions the teacher has with three Black girls disrupt racial storylines about invisibility/hypervisibility, behavior, and ability. Implications of this work pushes back against the idea that Black girls are monolithic and illustrate practices in mathematics that support the success of Black girls.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"75 ","pages":"Article 101167"},"PeriodicalIF":1.7,"publicationDate":"2024-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0732312324000440/pdfft?md5=606d16a90b2c4b9e79e6a03a705b3db1&pid=1-s2.0-S0732312324000440-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141328316","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
Effects of domain-specific linguistic factors on the difficulty of mathematics tasks 特定领域的语言因素对数学任务难度的影响
IF 1.7
Journal of Mathematical Behavior Pub Date : 2024-06-14 DOI: 10.1016/j.jmathb.2024.101169
David Bednorz , Michael Kleine , Rudolf vom Hofe
{"title":"Effects of domain-specific linguistic factors on the difficulty of mathematics tasks","authors":"David Bednorz ,&nbsp;Michael Kleine ,&nbsp;Rudolf vom Hofe","doi":"10.1016/j.jmathb.2024.101169","DOIUrl":"https://doi.org/10.1016/j.jmathb.2024.101169","url":null,"abstract":"<div><p>Linguistic features as a task-related feature influence the difficulty of mathematical tasks. To reduce this influence (e.g., in testing situations), studies on linguistic simplification focus on modifying linguistic features. These studies show little or no effect on increasing test performance. An open question is whether a quantitative–exploratory approach with texts from a specific domain can be an additional model for reducing the linguistic influence on mathematical tasks. To answer this question, generalized linear mixed models were used to determine the effects of linguistic factors, the requirements of the items, and the effects of linguistic factors when differentiating the requirements of the items, while controlling for further person- and item-related effects. The results show that linguistic factors can have either a negative or positive influence on test performance. The findings indicate that for mathematics assessments and teaching, it might be essential to consider the influence of language factors and task requirements.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"75 ","pages":"Article 101169"},"PeriodicalIF":1.7,"publicationDate":"2024-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0732312324000464/pdfft?md5=c79a22fd375cbd2eed86754934ef27e6&pid=1-s2.0-S0732312324000464-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141324346","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
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