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Lecturers' use of questions in undergraduate mathematics lectures 讲师在本科数学授课中使用问题的情况
IF 1
Journal of Mathematical Behavior Pub Date : 2024-09-18 DOI: 10.1016/j.jmathb.2024.101190
{"title":"Lecturers' use of questions in undergraduate mathematics lectures","authors":"","doi":"10.1016/j.jmathb.2024.101190","DOIUrl":"10.1016/j.jmathb.2024.101190","url":null,"abstract":"<div><p>Mathematics lecturers frequently ask questions in their lectures, and these questions presumably play an important role in students’ thinking about and learning of the lecture content. We replicated and developed a coding scheme used in previous research in the US to categorise lecturers’ questions in a sample of 136 lectures given by 24 lecturers at a research-intensive UK university. We found that the coding scheme could be applied reliably, and that factual questions were predominant (as in previous research). We explore differences in the lecturers’ use of questions – both between our UK sample and the previous US work, and between individual lecturers in our sample. We note the presence of strings of related successive questions from the lecturer, which we term ‘question chains’. We explore the nature of these, examine their prevalence, and seek to account for them in terms of the lecturers’ possible intentions.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0732312324000671/pdfft?md5=eed3542583cd33645c2f09865c9e4dd8&pid=1-s2.0-S0732312324000671-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142238787","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
Creating and sharing linear algebra metaphors as an assessment for engaging students beyond the cognitive domain 创建和分享线性代数隐喻，将其作为吸引学生参与认知领域以外活动的一种评估方法
IF 1
Journal of Mathematical Behavior Pub Date : 2024-09-11 DOI: 10.1016/j.jmathb.2024.101189
{"title":"Creating and sharing linear algebra metaphors as an assessment for engaging students beyond the cognitive domain","authors":"","doi":"10.1016/j.jmathb.2024.101189","DOIUrl":"10.1016/j.jmathb.2024.101189","url":null,"abstract":"<div><p>In this research, we investigated how a summative assessment of creating and sharing metaphors for linear algebra concepts supported undergraduate students’ affective, behavioral, and cognitive engagement. All seven research participants were enrolled in an introductory linear algebra course designed to develop students’ geometric understanding of linear algebra concepts in <em>R</em><sup><em>2</em></sup> and <em>R</em><sup><em>3</em></sup>. Using embodied cognition and an engagement framework, we analyzed students’ written responses and video-taped their focus group discussion. Our findings suggest that this summative assessment (a) privileged mathematical aesthetics and the affective domain of learning, (b) engaged students in binding formal aspects of linear algebra concepts with metaphors that they enacted via embodiment, and (c) was an opportunity to demonstrate learning and higher-order cognition. Thus, illustrating that assessments can focus on aesthetic and affective domains of mathematics while simultaneously integrating serious mathematical cognition. We conclude by offering adaptations of this assessment for other mathematics courses.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142167340","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
Secondary teachers’ guided reinvention of the definitions of reducible and irreducible elements 中学教师在指导下重塑可还原和不可还原元素的定义
IF 1
Journal of Mathematical Behavior Pub Date : 2024-09-11 DOI: 10.1016/j.jmathb.2024.101188
{"title":"Secondary teachers’ guided reinvention of the definitions of reducible and irreducible elements","authors":"","doi":"10.1016/j.jmathb.2024.101188","DOIUrl":"10.1016/j.jmathb.2024.101188","url":null,"abstract":"<div><p>Informed by Realistic Mathematics Education, we designed a hypothetical learning trajectory on graduate students’ guided reinvention of reducible and irreducible elements in rings. We created experientially real context problems for use in a teaching experiment, in which secondary in-service and pre-service teachers used algebra tiles as an emergent model of factoring integers and quadratics in <span><math><mrow><mi>Z</mi><mrow><mfenced><mrow><mi>x</mi></mrow></mfenced></mrow></mrow></math></span>. In their mathematical activity, this became the teachers’ model for abstracting the shared structure of (ir)reducible elements in <span><math><mi>Z</mi></math></span> and <span><math><mrow><mi>Z</mi><mo>[</mo><mi>x</mi><mo>]</mo></mrow></math></span>, which they used to formally define (ir)reducible elements. In this paper, we discuss the progression of the teachers’ reasoning and defining activities that were evident as they reinvented the definitions of reducible and irreducible elements of integral domains.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142167339","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
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
IF 1
Journal of Mathematical Behavior Pub Date : 2024-09-05 DOI: 10.1016/j.jmathb.2024.101187
{"title":"Engagement with student written work as an instantiation of and proxy for how college calculus instructors engage with student thinking","authors":"","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":null,"pages":null},"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
IF 1
Journal of Mathematical Behavior Pub Date : 2024-08-31 DOI: 10.1016/j.jmathb.2024.101179
{"title":"Developing (Pedagogical) content knowledge of constant rate of change: The case of Samantha","authors":"","doi":"10.1016/j.jmathb.2024.101179","DOIUrl":"10.1016/j.jmathb.2024.101179","url":null,"abstract":"<div><p>We present the results of a teaching experiment designed to foster a pre-service secondary teacher’s construction of a quantitative scheme for constant rate of change. Although the research participant developed a productive conception of constant rate of change as an interiorized ratio, images of chunky continuous covariation constrained her ability to reason efficiently across a variety of applied contexts. The participant constructed a scheme for constant rate of change at the reflected level of thought, which enabled her to become cognizant of its essential aspects and to appreciate its general applicability. Our results suggest that engaging in reflected abstraction is critical for supporting pre-service teachers’ construction of coherent and refined mathematical schemes.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142097020","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
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
{"title":"Use of mathematical problems rooted in primary historical sources to reveal preservice teachers’ mathematical content knowledge","authors":"","doi":"10.1016/j.jmathb.2024.101177","DOIUrl":"10.1016/j.jmathb.2024.101177","url":null,"abstract":"<div><p>In this paper, the use of mathematical problems rooted in primary historical sources as a diagnostic tool for identifying learners’ understanding about area and volume is examined. The study follows preservice teachers in the context of a compulsory course in mathematics education while dealing with such problems embedding errors and challenging mistaken beliefs about the area of quadrilaterals and the volume of the cube. Although the initial aim was to involve the participants in inquiry-based activities, in the end, the history of mathematics served as a means to reveal the complete or partial understanding of the concepts making evident at the same time the participants’ misconceptions such as the overgeneralization of the rule ‘length times breadth’ and the confusion between area and perimeter concerning the area of the quadrilaterals task, and the illusion of linearity and the confusion between volume and surface area concerning the volume of the cube task.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142058328","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
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
{"title":"Does use of a hypothetical learning progression promote learning of the cardinal-count concept and give-n performance?","authors":"","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":null,"pages":null},"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
IF 1
Journal of Mathematical Behavior Pub Date : 2024-07-17 DOI: 10.1016/j.jmathb.2024.101176
{"title":"Introduction to the virtual special issue: Mathematics that underpins social issues","authors":"","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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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
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