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Journal of Mathematical Behavior最新文献

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Theo’s reinvention of the logic of conditional statements’ proofs rooted in set-based reasoning 西奥对基于集合推理的条件语句证明逻辑的再创造
IF 1.7
Journal of Mathematical Behavior Pub Date : 2023-06-01 DOI: 10.1016/j.jmathb.2023.101043
Paul Christian Dawkins , Kyeong Hah Roh , Derek Eckman
{"title":"Theo’s reinvention of the logic of conditional statements’ proofs rooted in set-based reasoning","authors":"Paul Christian Dawkins ,&nbsp;Kyeong Hah Roh ,&nbsp;Derek Eckman","doi":"10.1016/j.jmathb.2023.101043","DOIUrl":"https://doi.org/10.1016/j.jmathb.2023.101043","url":null,"abstract":"<div><p>This report documents how one undergraduate student used set-based reasoning to reinvent logical principles related to conditional statements and their proofs. This learning occurred in a teaching experiment intended to foster abstraction of these logical relationships by comparing the relationships between predicates within the conditional statements and inference structures among various proofs (in number theory and geometry). We document the progression of Theo’s set-based emergent model (Gravemeijer, 1999) from a model-of the truth of statements to a model-for logical relationships. This constitutes some of the first evidence for how students can abstract such logical concepts in this way and provides evidence for the viability of the learning progression that guided the instructional design.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50177010","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: 1
A learning trajectory for university students regarding the concept of vector 大学生关于向量概念的学习轨迹
IF 1.7
Journal of Mathematical Behavior Pub Date : 2023-06-01 DOI: 10.1016/j.jmathb.2023.101044
Armando Cuevas-Vallejo , José Orozco-Santiago , Sofía Paz-Rodríguez
{"title":"A learning trajectory for university students regarding the concept of vector","authors":"Armando Cuevas-Vallejo ,&nbsp;José Orozco-Santiago ,&nbsp;Sofía Paz-Rodríguez","doi":"10.1016/j.jmathb.2023.101044","DOIUrl":"https://doi.org/10.1016/j.jmathb.2023.101044","url":null,"abstract":"<div><p>This paper presents and evaluates a hypothetical learning trajectory by which students bridge the transition from elementary to university-level instruction regarding the concept of vector. The trajectory consists of an instructional sequence of five tasks and begins with a problem in context. Each task is carried out with the support of a Virtual Interactive Didactic Scenario, accompanied by exploration and guided learning sheets, in which the problem is introduced through the simulation of the movement of a robotic arm. This proposal was implemented at the beginning of the SARS-CoV-2 pandemic using various digital media. Two teaching experiments were carried out with engineering students at a Mexican public university. We present the hypothetical learning trajectory that should be followed toward solving the task, and contrast it in each case with the students’ actual learning trajectory. The results show that more than 70 % of the students successfully transitioned from the geometrical vector representation of elementary physics to the algebraic one.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50177017","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: 1
Teachers creating mathematical models to fairly distribute school funding 教师创建数学模型以公平分配学校资金
IF 1.7
Journal of Mathematical Behavior Pub Date : 2023-06-01 DOI: 10.1016/j.jmathb.2023.101041
Hyunyi Jung , Megan H. Wickstrom
{"title":"Teachers creating mathematical models to fairly distribute school funding","authors":"Hyunyi Jung ,&nbsp;Megan H. Wickstrom","doi":"10.1016/j.jmathb.2023.101041","DOIUrl":"https://doi.org/10.1016/j.jmathb.2023.101041","url":null,"abstract":"<div><p>Our study aims to investigate what teachers do as they draw on their mathematical understanding and personal experiences to engage in social justice-oriented mathematical modeling. We analyze what ideas were expressed by teachers regarding their mathematical identities while they explore, wrestle with, and reconcile the underlying societal values that support mathematical models. We invited groups of teachers to make mathematical models for distributing school funding given real data from diverse, anonymized schools. Our results show that teachers created and refined diverse mathematical models to connect the mathematical world and societal space and these models reflected different societal values. Drawing on their own experiences, teachers expressed a sense of agency and critical consciousness while making decisions about school funding. This study delineates mathematical contents and processes necessary for advancing a societal goal of fairly distributing funds and we explore how teachers connect to this context as learners and members of society.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50176928","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: 2
Characterizing prospective secondary teachers’ foundation and contingency knowledge for definitions of transformations 描述未来中学教师的基础和转换定义的偶然性知识
IF 1.7
Journal of Mathematical Behavior Pub Date : 2023-06-01 DOI: 10.1016/j.jmathb.2022.101030
Yvonne Lai , Alyson E. Lischka , Jeremy F. Strayer , Kingsley Adamoah
{"title":"Characterizing prospective secondary teachers’ foundation and contingency knowledge for definitions of transformations","authors":"Yvonne Lai ,&nbsp;Alyson E. Lischka ,&nbsp;Jeremy F. Strayer ,&nbsp;Kingsley Adamoah","doi":"10.1016/j.jmathb.2022.101030","DOIUrl":"https://doi.org/10.1016/j.jmathb.2022.101030","url":null,"abstract":"<div><p>One promising approach for connecting undergraduate content coursework to secondary teaching is using teacher-created representations of practice. Using these representations effectively requires seeing teachers' use of mathematical knowledge in the work of teaching. We argue that the dimensions of Rowland's (2013) Knowledge Quartet, especially Foundation and Contingency, form a fruitful framework for this purpose. We contribute an analytic framework to characterize the quality of mathematical knowledge observed in the Foundation and Contingency dimensions, developed using a purposive sampling from over 300 representations. These representations all featured geometry teaching. We showcase the framework with examples of \"high\" and \"developing\" Foundation and Contingency.Then, we compare our coding along these dimensions with performance on a measure of mathematical knowledge for teaching geometry. Finally, we describe the potential for generalizing this framework to other domains, such as algebra and mathematical modeling.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50176938","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
Spatial visualization and measurement of area: A case study in spatialized mathematics instruction 面积的空间可视化与测量——以数学空间化教学为例
IF 1.7
Journal of Mathematical Behavior Pub Date : 2023-06-01 DOI: 10.1016/j.jmathb.2023.101038
Danielle Harris, Tracy Logan, Tom Lowrie
{"title":"Spatial visualization and measurement of area: A case study in spatialized mathematics instruction","authors":"Danielle Harris,&nbsp;Tracy Logan,&nbsp;Tom Lowrie","doi":"10.1016/j.jmathb.2023.101038","DOIUrl":"https://doi.org/10.1016/j.jmathb.2023.101038","url":null,"abstract":"<div><p>The purpose of this study was to explore the influence of spatial visualization skills when students solve area tasks. Spatial visualization is closely related to mathematics achievement, but little is known about how these skills link to task success. We examined middle school students’ representations and solutions to area problems (both non-metric and metric) through qualitative and quantitative task analysis. Task solutions were analyzed as a function of spatial visualization skills and links were made between student solutions on tasks with different goals (i.e., non-metric and metric). Findings suggest that strong spatial visualizers solved the tasks with relative ease, with evidence for conceptual and procedural understanding. By contrast, Low and Average Spatial students more frequently produced errors due to failure to correctly determine linear measurements or apply appropriate formula, despite adequate procedural knowledge. A novel finding was the facilitating role of spatial skills in the link between metric task representation and success in determining a solution. From a teaching and learning perspective, these results highlight the need to connect emergent spatial skills with mathematical content and support students to develop conceptual understanding in parallel with procedural competence.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50176953","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
Enhancing students’ fraction magnitude knowledge: A study with students in early elementary education 提高学生分数量级知识——以小学早期教育学生为对象的研究
IF 1.7
Journal of Mathematical Behavior Pub Date : 2023-06-01 DOI: 10.1016/j.jmathb.2023.101042
Arthur B. Powell
{"title":"Enhancing students’ fraction magnitude knowledge: A study with students in early elementary education","authors":"Arthur B. Powell","doi":"10.1016/j.jmathb.2023.101042","DOIUrl":"https://doi.org/10.1016/j.jmathb.2023.101042","url":null,"abstract":"<div><p>The idea of magnitude is central to understanding fractional numbers. To investigate this relationship, we implemented a design research project in an urban school in the northeast of the US to examine the potential of a measuring perspective and the mathematical notion of fraction-<em>of</em>-quantity to enhance second-grade students’ conceptual understanding of fraction magnitude. We used ideas from the history of mathematics and mathematics education within a cultural-historical framework to define fractions and construct tasks. The research team consisted of a university professor, two doctoral students, one of whom was an administrator of the municipal board of education, eight elementary school teachers, and a parent. The research sessions involved 35 students divided into two classes, meeting one hour per session twice a week for 12 weeks or 24 hours. The students manipulated non-symbolic or non-numeric manipulatives (Cuisenaire rods) and learned to talk about specific relations they perceived among them. Through physical manipulations and discourse, students developed the idea that a fraction reports a multiplicative comparison between two commensurable quantities of the same kind. Our results indicate that second-grade students appropriated the concept of the magnitude of fractions-<em>of</em>-quantity and, based on mental manipulations of evoked non-numeric images, constructed symbolic expressions involving fractional comparisons.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50177011","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: 3
Leveraging interdiscursivity to support elementary students in bridging the empirical-deductive gap: the case of parity 利用交叉演绎性支持小学生弥合经验演绎差距：以奇偶性为例
IF 1.7
Journal of Mathematical Behavior Pub Date : 2023-06-01 DOI: 10.1016/j.jmathb.2023.101052
Joanne Knox, Igor’ Kontorovich
{"title":"Leveraging interdiscursivity to support elementary students in bridging the empirical-deductive gap: the case of parity","authors":"Joanne Knox,&nbsp;Igor’ Kontorovich","doi":"10.1016/j.jmathb.2023.101052","DOIUrl":"https://doi.org/10.1016/j.jmathb.2023.101052","url":null,"abstract":"<div><p>Research has recognized deductive reasoning as challenging but not impossible for young mathematics learners. In this paper, we present a learning environment developed to assist elementary-school students to bridge the empirical-deductive gap in the context of parity of numbers. Using the commognitive framework, we construe the empirical-deductive gap as part of a broader divide between two discourses that abide by different rules of a “mathematical game”: a discourse on specific numbers and a discourse on numeric patterns. Interdiscursivity is leveraged as a mechanism for instructional design, where students’ familiar routines with specific numbers are teased out and advanced to make sense in the new discourse. We mobilize this mechanism to create opportunities for students to play an active role in recognizing issues with empirical reasoning and generating deductive arguments to establish the validity of universal statements. The environment is illustrated with a small group of 8-year-olds who learned to justify deductively that “odd + odd = even”.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50177012","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
Prospective teachers’ unified understandings of the structure of identities 未来教师对身份结构的统一理解
IF 1.7
Journal of Mathematical Behavior Pub Date : 2023-06-01 DOI: 10.1016/j.jmathb.2023.101066
Kaitlyn Stephens Serbin
{"title":"Prospective teachers’ unified understandings of the structure of identities","authors":"Kaitlyn Stephens Serbin","doi":"10.1016/j.jmathb.2023.101066","DOIUrl":"https://doi.org/10.1016/j.jmathb.2023.101066","url":null,"abstract":"<div><p>United States curriculum standards advise mathematics teachers to teach students to attend to structure and understand how mathematical concepts are related. This requires teachers to have a structural perspective and a coherent, unified understanding of mathematical structures that span curricula. This study explores Prospective Secondary Mathematics Teachers’ (PSMTs) unified understandings of identities and characterizes the structural features of identities that PSMTs attend to. I contribute a theoretical framework of three ways in which PSMTs reason about identities: a do-nothing element, a result of undoing something, and a coordination with inverse, binary operation, and set. I classify the level of coherence of their identity schemas demonstrated as they reasoned about the structural connections among additive, multiplicative, and compositional identities. I illustrate how having unified, coherent understandings of identities can lead PSMTs to reason productively about inverse and identity functions, while having incoherent understandings of identities can lead to inaccurate reasoning about inverse and identity functions. I conclude with teaching implications for fostering PSMTs’ unified understandings of algebraic concepts.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50177014","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
Describing critical statistical literacy habits of mind 描述批判性统计素养的思维习惯
IF 1.7
Journal of Mathematical Behavior Pub Date : 2023-06-01 DOI: 10.1016/j.jmathb.2023.101063
Nina G. Bailey , Allison W. McCulloch
{"title":"Describing critical statistical literacy habits of mind","authors":"Nina G. Bailey ,&nbsp;Allison W. McCulloch","doi":"10.1016/j.jmathb.2023.101063","DOIUrl":"https://doi.org/10.1016/j.jmathb.2023.101063","url":null,"abstract":"<div><p>Given the vast number of data representations that people encounter daily, it is imperative that people become critical consumers of the representations they will face. This requires the development of particular habits of mind. The purpose of this paper is to share the critical statistical literacy habits of mind framework. We articulate how we drew on the literature related to statistical literacy, critical mathematics, and critical statistical literacy to identify the habits of mind needed to enact critical statistical literacy in the context of consuming data representations. We describe the refinement process using qualitative interview data. To illustrate what each of the critical statistical literacy habits of mind looks like when enacted, we share examples from statistics teachers making sense of a data representation.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50177015","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
Making visible “the invisible”: Can mathematics embedded in work practices enable critical questioning? 让看得见的“看不见的”：工作实践中嵌入的数学能引发批判性提问吗？
IF 1.7
Journal of Mathematical Behavior Pub Date : 2023-06-01 DOI: 10.1016/j.jmathb.2022.101028
Arindam Bose , Danyal Farsani
{"title":"Making visible “the invisible”: Can mathematics embedded in work practices enable critical questioning?","authors":"Arindam Bose ,&nbsp;Danyal Farsani","doi":"10.1016/j.jmathb.2022.101028","DOIUrl":"https://doi.org/10.1016/j.jmathb.2022.101028","url":null,"abstract":"","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50176937","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
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