Journal of Mathematical Behavior最新文献_第8页

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 : 2024-12-01 Epub 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":"2024-12-01","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

Mature intuition and mathematical understanding 成熟的直觉和数学理解力

IF 1

Journal of Mathematical Behavior Pub Date : 2024-12-01 Epub Date: 2024-11-18 DOI: 10.1016/j.jmathb.2024.101203

William D'Alessandro , Irma Stevens

{"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":"2024-12-01","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}

引用次数: 0

Preservice teachers’ metacognitive process variables in modeling-related problem posing 职前教师在与建模相关的问题假设中的元认知过程变量

IF 1

Journal of Mathematical Behavior Pub Date : 2024-12-01 Epub Date: 2024-10-09 DOI: 10.1016/j.jmathb.2024.101195

Luisa-Marie Hartmann , Stanislaw Schukajlow , Mogens Niss , Uffe Thomas Jankvist

引用次数: 0

Quantitative operators as an analytical tool for explaining differential equation students’ construction of new quantities during modeling 数量运算符是解释微分方程学生在建模过程中构建新数量的分析工具

IF 1

Journal of Mathematical Behavior Pub Date : 2024-12-01 Epub Date: 2024-10-30 DOI: 10.1016/j.jmathb.2024.101198

Sindura Kularajan , Jennifer Czocher , Elizabeth Roan

引用次数: 0

Teachers’ engagement with language practices through a geometry lesson study 教师通过几何课研究参与语言实践

IF 1

Journal of Mathematical Behavior Pub Date : 2024-12-01 Epub Date: 2024-11-21 DOI: 10.1016/j.jmathb.2024.101207

Lisnet Mwadzaangati , Jill Adler

引用次数: 0

Undergraduate students’ collaboration on homework problems in advanced mathematics courses 本科生在高等数学课程作业问题上的合作

IF 1

Journal of Mathematical Behavior Pub Date : 2024-12-01 Epub Date: 2024-11-04 DOI: 10.1016/j.jmathb.2024.101200

Ciara Murphy, Maria Meehan

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 : 2024-12-01 Epub Date: 2024-09-11 DOI: 10.1016/j.jmathb.2024.101188

Kaitlyn Stephens Serbin , Younggon Bae , Sthefanía Espinosa

引用次数: 0

Encouraging students to explain their ideas when learning mathematics: A psychological perspective 鼓励学生在学习数学时解释自己的想法：心理学视角

IF 1

Journal of Mathematical Behavior Pub Date : 2024-12-01 Epub Date: 2024-09-24 DOI: 10.1016/j.jmathb.2024.101192

Bethany Rittle-Johnson

{"title":"Encouraging students to explain their ideas when learning mathematics: A psychological perspective","authors":"Bethany Rittle-Johnson","doi":"10.1016/j.jmathb.2024.101192","DOIUrl":"10.1016/j.jmathb.2024.101192","url":null,"abstract":"<div><div>Children’s <em>self-explanations</em> are answers to voiced why and how questions that attempt to make sense of new information for oneself. They often are not sophisticated or generalizable. Despite this, prompting children to generate explanations often improves their learning. After providing examples of children’s explanations, this article summarizes empirical evidence for the learning benefits of prompting people to generate explanations when learning mathematics. There is strong evidence that prompting learners to explain leads to greater conceptual knowledge, procedural knowledge and procedural transfer when knowledge is assessed immediately after the learning session; there is limited evidence for greater procedural transfer after a delay. Scaffolding high-quality explanations via training or structured responses, designing prompts to carefully balance attention to important content, prompting learners to explain correct information, and prompting learners to explain why incorrect information is incorrect when appropriate, increases the benefits of prompts to generate explanations.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"76 ","pages":"Article 101192"},"PeriodicalIF":1.0,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0732312324000695/pdfft?md5=da899ecf252efeddeeea91ce27ec15c7&pid=1-s2.0-S0732312324000695-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142314687","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

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 : 2024-12-01 Epub 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":"2024-12-01","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

Snapshots of sameness: Characterizations of mathematical sameness across student groups 同一性的剪影：不同学生群体的数学同一性特征

IF 1

Journal of Mathematical Behavior Pub Date : 2024-12-01 Epub Date: 2024-10-03 DOI: 10.1016/j.jmathb.2024.101193

Rachel Rupnow , Rosaura Uscanga , Anna Marie Bergman , Cassandra Mohr

{"title":"Snapshots of sameness: Characterizations of mathematical sameness across student groups","authors":"Rachel Rupnow , Rosaura Uscanga , Anna Marie Bergman , Cassandra Mohr","doi":"10.1016/j.jmathb.2024.101193","DOIUrl":"10.1016/j.jmathb.2024.101193","url":null,"abstract":"<div><div>Sameness is foundational to mathematics but has only recently become an area of focus in mathematics education research. In this paper, we describe characterizations of sameness generated by four student groups: discrete mathematics students, linear algebra students, abstract algebra students, and graduate students. Based on qualitative analysis of open response surveys, we compare these groups’ characterizations of sameness; note the subcomponents discussed and variation within each dimension; and highlight experiences influential to students’ perceptions of sameness. Findings include interpretability of sameness as a big idea, nascent development of thematic connections across courses, emphases on current course material rather than connections to prior courses for students solicited from a particular course, greater reflectiveness from the graduate student group, and abstract algebra as an impactful course. Implications include a need for thoughtful examinations of how “big ideas” develop among students and what experiences might support such development.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"76 ","pages":"Article 101193"},"PeriodicalIF":1.0,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142428275","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