Journal of Mathematical Behavior最新文献_第7页

Engagement with student written work as an instantiation of and proxy for how college calculus instructors engage with student thinking 参与学生的书面作业，作为大学微积分教师如何参与学生思维的实例和代表

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Journal of Mathematical Behavior Pub Date : 2024-09-05 DOI: 10.1016/j.jmathb.2024.101187

Jessica Gehrtz , Jess Ellis Hagman , Victoria Barron

{"title":"Engagement with student written work as an instantiation of and proxy for how college calculus instructors engage with student thinking","authors":"Jessica Gehrtz , Jess Ellis Hagman , Victoria Barron","doi":"10.1016/j.jmathb.2024.101187","DOIUrl":"10.1016/j.jmathb.2024.101187","url":null,"abstract":"<div><p>Teachers who use student thinking to make instructional decisions tend to create more positive learning experiences for students and support conceptual understanding. Looking at student work is one way college instructors learn about student thinking. We interviewed eight calculus instructors to investigate what they noticed when examining student work. Reflexive thematic analysis allowed us to classify instructors by the stance they adopted when looking at student work. Instructors who adopted an evaluative stance responded by providing examples or explaining how to solve the problem, often taking on the intellectual work of solving the problem. Instructors who adopted an interpretive stance responded by providing examples or asking guiding questions informed by the student’s thinking. We then extended our analyses to illustrate two instructional archetypes (Interpreter and Evaluator), to highlight how the stance taken when examining student work can serve as a proxy for how instructors engage with student thinking more broadly.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"76 ","pages":"Article 101187"},"PeriodicalIF":1.0,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0732312324000646/pdfft?md5=79808339f06402b0a6a1c331e5c9fa74&pid=1-s2.0-S0732312324000646-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142147683","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

Developing (Pedagogical) content knowledge of constant rate of change: The case of Samantha 发展有关恒定变化率的（教学）内容知识：萨曼莎的案例

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Journal of Mathematical Behavior Pub Date : 2024-08-31 DOI: 10.1016/j.jmathb.2024.101179

Michael A. Tallman , John Weaver , Taylor Johnson

引用次数: 0

Use of mathematical problems rooted in primary historical sources to reveal preservice teachers’ mathematical content knowledge 利用源于原始史料的数学问题揭示职前教师的数学内容知识

IF 1

Journal of Mathematical Behavior Pub Date : 2024-08-24 DOI: 10.1016/j.jmathb.2024.101177

Ioannis Papadopoulos

引用次数: 0

Does use of a hypothetical learning progression promote learning of the cardinal-count concept and give-n performance? 使用假定的学习进度是否能促进对心算概念的学习并提高学习成绩？

IF 1

Journal of Mathematical Behavior Pub Date : 2024-08-23 DOI: 10.1016/j.jmathb.2024.101178

Arthur J. Baroody , Douglas H. Clements , Julie Sarama

{"title":"Does use of a hypothetical learning progression promote learning of the cardinal-count concept and give-n performance?","authors":"Arthur J. Baroody , Douglas H. Clements , Julie Sarama","doi":"10.1016/j.jmathb.2024.101178","DOIUrl":"10.1016/j.jmathb.2024.101178","url":null,"abstract":"<div><p>The general aim of the research was to conduct a rare test of the efficacy of hypothetical learning progressions (HLPs) and a basic assumption of basing instruction on HLPs, namely teaching each successive level is more efficacious than skipping lower levels and teaching the target level directly. The specific aim was evaluating whether counting-based cardinality concepts unfold in a stepwise manner. The research involved a pretest—delayed-posttest design with random assignment of 14 preschoolers to two conditions. The experimental intervention was based on an HLP for cardinality development (first promoting levels that presumably support and are necessary for the target level and then the target knowledge). The active-control treatment entailed a Teach-to-Target approach (first promoting irrelevant cardinality knowledge about recognizing written numbers and then directly teaching the same target-level goals with the same explicit instruction and similar games). A mix of quantitative and qualitative analyses indicated HLP participants performed significantly and substantially better than Teach-to-Target participants on target-level concept and skill measures. Moreover, the former tended to make sensible errors, whereas the latter generally responded cluelessly.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"76 ","pages":"Article 101178"},"PeriodicalIF":1.0,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142058329","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

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

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Journal of Mathematical Behavior Pub Date : 2024-07-17 DOI: 10.1016/j.jmathb.2024.101176

Eva Thanheiser , Ami Mamolo

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

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 , Mitchell J. Nathan , Jonathan Hunnicutt , Julianna Washington , 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

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Journal of Mathematical Behavior Pub Date : 2024-06-20 DOI: 10.1016/j.jmathb.2024.101173

Rachel Rupnow , Brooke Randazzo

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

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Journal of Mathematical Behavior Pub Date : 2024-06-20 DOI: 10.1016/j.jmathb.2024.101172

Ruhama Even , Yocheved Mytlis

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 , Maximilian K. Sherard , Candace Walkington , Saki Milton , 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