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Identifying competent problem posers and exploring their characteristics 识别有能力的问题提出者并探索他们的特点
IF 1.7
Journal of Mathematical Behavior Pub Date : 2023-09-01 DOI: 10.1016/j.jmathb.2023.101086
Ling Zhang , Andreas J. Stylianides , Gabriel J. Stylianides
{"title":"Identifying competent problem posers and exploring their characteristics","authors":"Ling Zhang ,&nbsp;Andreas J. Stylianides ,&nbsp;Gabriel J. Stylianides","doi":"10.1016/j.jmathb.2023.101086","DOIUrl":"https://doi.org/10.1016/j.jmathb.2023.101086","url":null,"abstract":"<div><p>In a study involving 66 masters and 60 sixth-grade students, we conducted Principal Component Analysis to identify more-and-less competent problem posers based on performance criteria rather than, as in prior research, relying on participants’ mathematical experience or background. Also, to cast light on characteristics of competent posers, we explored possible patterns in the problem-posing process based on the two identified groups’ self-reports and eye-movements. The results showed that: masters students had a significantly lower proportion of the more-competent group and a higher proportion of the less-competent group than sixth graders; more-competent posers perceived a better understanding of the problem-posing tasks than less-competent posers; more-competent posers exhibited significantly more fixation time on completing the entire problem-posing activities than less-competent posers, though this pattern disappeared across particular stages of the problem-posing process; and more-competent posers appeared to engage in a more purposeful search and processing to construct their problems than less-competent posers.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49875828","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
Exploring affordances and limitations of between-group movement in elementary mathematics classrooms 探究小学数学课堂小组间运动的可供性及其局限性
IF 1.7
Journal of Mathematical Behavior Pub Date : 2023-09-01 DOI: 10.1016/j.jmathb.2023.101083
Tye G. Campbell , Sheunghyun Yeo , Erin Rich , Mindy Green
{"title":"Exploring affordances and limitations of between-group movement in elementary mathematics classrooms","authors":"Tye G. Campbell ,&nbsp;Sheunghyun Yeo ,&nbsp;Erin Rich ,&nbsp;Mindy Green","doi":"10.1016/j.jmathb.2023.101083","DOIUrl":"https://doi.org/10.1016/j.jmathb.2023.101083","url":null,"abstract":"<div><p>In this exploratory study, we examine how between-group movement, as an autonomy-promoting practice, might incentivize or disincentivize sixth-grade students’ engagement in two mathematical practices: (1) making sense of problems and persevering in solving them; and (2) constructing viable arguments and critiquing the reasoning of others. Between-group movement refers to a pedagogical strategy wherein teachers allow groups to physically move within the classroom while problem-solving to discuss strategies, ask for help, or check their work with other groups. Exploring both the affordances and limitations of between-group movement, we found that between-group movement supported groups to construct viable justifications, among other sense-making mathematical practices. However, we also found that some groups over-scaffolded during between-group conversations which disincentivized meaningful engagement in mathematical practices. Furthermore, between-group movement revealed some equity concerns in relation to status-based privileges. The findings imply that between-group movement can be a constructive pedagogical practice under specific conditions.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50182193","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
An updated conceptualization of the intuition construct for mathematics education research 数学教育研究中直觉结构的更新概念
IF 1.7
Journal of Mathematical Behavior Pub Date : 2023-09-01 DOI: 10.1016/j.jmathb.2023.101080
Jessi Lajos
{"title":"An updated conceptualization of the intuition construct for mathematics education research","authors":"Jessi Lajos","doi":"10.1016/j.jmathb.2023.101080","DOIUrl":"https://doi.org/10.1016/j.jmathb.2023.101080","url":null,"abstract":"<div><p>To improve instruction, conduct communicable studies on student intuition, and provide an entry point for researchers interested in this area, the meaning of intuition in mathematics education needs to be addressed. This paper reviews 816 journal papers from top tier mathematics education journals to obtain an updated conceptualization of the intuition construct. Different research camps, such as a camp focused on instructional design that leverages learners’ primary intuitions in the classroom and a camp concerned with sources of errors through the lens of intuitive rules theory, emerged. A critical discussion of theoretical choices for intuition research will be followed by several directions for future research on intuition specific to university mathematics education.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50182191","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
Classroom interactions that shape the nature of students’ appropriation of a complex mathematical practice 课堂互动塑造了学生对复杂数学实践的挪用性质
IF 1.7
Journal of Mathematical Behavior Pub Date : 2023-09-01 DOI: 10.1016/j.jmathb.2023.101082
John Gruver , Casey Hawthorne
{"title":"Classroom interactions that shape the nature of students’ appropriation of a complex mathematical practice","authors":"John Gruver ,&nbsp;Casey Hawthorne","doi":"10.1016/j.jmathb.2023.101082","DOIUrl":"https://doi.org/10.1016/j.jmathb.2023.101082","url":null,"abstract":"<div><p>Scholars continue to emphasize the importance of fostering proficiency with mathematical practices as an educational outcome. As teachers attempt to support students in developing these practices, they communicate subtle messages about their nature. However, researchers lack a detailed understanding of the classroom interactions that communicate these messages. To begin to address this gap in the literature, we investigated the relationship between the types of classroom interactions around the mathematical practice of imposing structure and the ways students subsequently engaged in that practice. This led to the identification of three types of classroom interactions that shaped the nature of students’ appropriation of imposing structure: (a) engaging students in the practice, (b) providing different representations of the practice, and (c) reflecting on different instantiations of the practice. Our examination of the nature of these interactions suggests teachers must attend to details as they support students to appropriate mathematical practices in formal learning environments.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50182192","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
Examining and conceptualizing the relationship between teacher praise and the co-construction of mathematical competence in classrooms 教师表扬与课堂数学能力共建关系的考察与概念化
IF 1.7
Journal of Mathematical Behavior Pub Date : 2023-09-01 DOI: 10.1016/j.jmathb.2023.101065
Kathy Liu Sun , Jennifer L. Ruef
{"title":"Examining and conceptualizing the relationship between teacher praise and the co-construction of mathematical competence in classrooms","authors":"Kathy Liu Sun ,&nbsp;Jennifer L. Ruef","doi":"10.1016/j.jmathb.2023.101065","DOIUrl":"https://doi.org/10.1016/j.jmathb.2023.101065","url":null,"abstract":"<div><p>In this study we examined how teacher praise varies across and within four middle school mathematics classrooms in relationship to mathematical competence. We then conceptualized how teacher praise contributes to the co-construction of <em>normative identity</em>: the class’ shared understanding of what counts as being a competent learner in a mathematics classroom. Findings revealed teachers rarely used person-based praise (e.g., “you’re smart”) and frequently gave generic praise (e.g., “good”). Each teacher’s praise patterns supported different co-constructions of mathematical competence. Although some teachers taught the same lessons or ascribed to similar pedagogical approaches, findings suggest teachers’ praise patterns may contribute to the co-construction of different normative identities, some more exclusive and others more inclusive. Findings indicate praise may be a low-stakes and potentially impactful teacher practice with implications for students’ understanding of what it means to be good at math.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50182172","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
Using algorithmic thinking to design algorithms: The case of critical path analysis 运用算法思维设计算法——以关键路径分析为例
IF 1.7
Journal of Mathematical Behavior Pub Date : 2023-09-01 DOI: 10.1016/j.jmathb.2023.101079
Timothy H. Lehmann
{"title":"Using algorithmic thinking to design algorithms: The case of critical path analysis","authors":"Timothy H. Lehmann","doi":"10.1016/j.jmathb.2023.101079","DOIUrl":"https://doi.org/10.1016/j.jmathb.2023.101079","url":null,"abstract":"<div><p>Algorithmic thinking is emerging as an important competence in mathematics education, yet research appears to be lagging this shift in curricular focus. The aim of this generative study is to examine how students use the cognitive skills of algorithmic thinking to design algorithms. Task-based interviews were conducted with four pairs of Year 12 students (n = 8) to analyze how they used decomposition and abstraction to specify the projects, designed algorithms to solve scheduling problems by first devising fundamental operations and then using algorithmic concepts to account for complex and special cases of the problems, and tested and debugged their algorithms. A deductive-inductive analytical process was used to classify students’ responses according to the four cognitive skills to develop sets of subskills to describe how the students engaged these cognitive skills.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50182174","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
Validating a concept inventory for measuring students’ probabilistic reasoning: The case of reasoning within the context of a raffle 验证用于测量学生概率推理的概念清单：抽奖背景下的推理案例
IF 1.7
Journal of Mathematical Behavior Pub Date : 2023-09-01 DOI: 10.1016/j.jmathb.2023.101081
Hollylynne S. Lee , Hamid Sanei , Lisa Famularo , Jessica Masters , Laine Bradshaw , Madeline Schellman
{"title":"Validating a concept inventory for measuring students’ probabilistic reasoning: The case of reasoning within the context of a raffle","authors":"Hollylynne S. Lee ,&nbsp;Hamid Sanei ,&nbsp;Lisa Famularo ,&nbsp;Jessica Masters ,&nbsp;Laine Bradshaw ,&nbsp;Madeline Schellman","doi":"10.1016/j.jmathb.2023.101081","DOIUrl":"https://doi.org/10.1016/j.jmathb.2023.101081","url":null,"abstract":"<div><p>Assessing students’ conceptions related to independence of events and determining probabilities from a sample space has been the focus of research in probability education for over 40 years. While we know a lot from past studies about predictable ways students may reason with well-known tasks, developing a diagnostic assessment that can be used by teachers to inform instruction demands the use of familiar and unfamiliar contexts. This paper presents the current work of a research team whose aim is to create a formative concept inventory with strong evidence of validity that uses a psychometric model to confidently predict whether a student exhibits one or more misconception across many items. We illustrate this process in this paper using a particular item with a context of a raffle aimed to measure whether a student reasons with misconceptions related to independence or equiprobability. The results of two aspects of the validity process: cognitive interviews to assess response processes on individual items, and a large-scale administration to examine internal structure of the concept inventory revealed difficulties in assessing students’ reasoning about these key probability concepts and trends in the prevalence of misconceptions across grades. Results can provide guidance for others aiming to develop assessments in mathematics education and also support further possibilities for research into understanding students’ reasoning about independence and sample space.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50182310","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
Middle school students at three stages of units coordination learn to make same speeds 中学生在单位协调的三个阶段学习相同的速度
IF 1.7
Journal of Mathematical Behavior Pub Date : 2023-08-26 DOI: 10.1016/j.jmathb.2023.101085
Amy J. Hackenberg , Fetiye Aydeniz-Temizer , Rebecca S. Borowski
{"title":"Middle school students at three stages of units coordination learn to make same speeds","authors":"Amy J. Hackenberg ,&nbsp;Fetiye Aydeniz-Temizer ,&nbsp;Rebecca S. Borowski","doi":"10.1016/j.jmathb.2023.101085","DOIUrl":"https://doi.org/10.1016/j.jmathb.2023.101085","url":null,"abstract":"<div><p>A classroom study was conducted to understand how 18 seventh-grade students at three stages of units coordination constructed ways to make two cars travel the same speed as part of a unit on proportional reasoning co-taught by the first author and classroom teacher. Students at all three stages developed an understanding of how distance and time affected speed. However, when determining how to make two cars travel the same speed, students demonstrated differences related to their stages of units coordination. Three focus students show these differences. The student at stage 1 constructed doubled journeys as lengths with relative size. The student at stage 2 constructed same speeds by multiplying and by dividing but did not create a multiplicative structure with the results of division. The student at stage 3 constructed same speeds as multiples of the smallest distance-time pair. Comparisons with the other students in the class are made.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49875827","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
An inspiring career in mathematics education research: A tribute to Carolyn A. Maher 令人鼓舞的数学教育研究生涯：向卡罗琳-马赫致敬
IF 1.7
Journal of Mathematical Behavior Pub Date : 2023-07-27 DOI: 10.1016/j.jmathb.2023.101067
Gerald Goldin , Keith Weber , Elizabeth Uptegrove
{"title":"An inspiring career in mathematics education research: A tribute to Carolyn A. Maher","authors":"Gerald Goldin ,&nbsp;Keith Weber ,&nbsp;Elizabeth Uptegrove","doi":"10.1016/j.jmathb.2023.101067","DOIUrl":"10.1016/j.jmathb.2023.101067","url":null,"abstract":"","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0732312323000378/pdfft?md5=ce8c8382ee6987a8a755cefa2d872cf1&pid=1-s2.0-S0732312323000378-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121109475","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
Examining preservice teachers’ noticing of equity-based teaching practices to empower students engaging in productive struggle 考察职前教师对基于公平的教学实践的注意，以增强学生参与生产性斗争的能力
IF 1.7
Journal of Mathematical Behavior Pub Date : 2023-06-01 DOI: 10.1016/j.jmathb.2023.101045
Hiroko K. Warshauer , Christin Herrera , Shawnda Smith , Christina Starkey
{"title":"Examining preservice teachers’ noticing of equity-based teaching practices to empower students engaging in productive struggle","authors":"Hiroko K. Warshauer ,&nbsp;Christin Herrera ,&nbsp;Shawnda Smith ,&nbsp;Christina Starkey","doi":"10.1016/j.jmathb.2023.101045","DOIUrl":"https://doi.org/10.1016/j.jmathb.2023.101045","url":null,"abstract":"<div><p>Our study examined ways preservice teachers (PSTs) make connections between teaching practices and use of student resources that support productive struggle and promote equity. Our research questions are: (1) How do PSTs notice and describe the equity-based mathematics teaching practice of leveraging student resources to support student struggles? and (2) In what ways do PSTs make connections to and interpret the role student resources play in the resolution of students’ mathematical struggles? The qualitative study examined 39 PSTs in a mathematics content course for PSTs. Data come from a video analysis assignment where PSTs described their mathematical interpretations of the student struggle(s) and teacher’s use of student resources to support the struggle resolution. Findings show that PSTs noticed teacher moves that leveraged student’s mathematical thinking and linguistic funds of knowledge and based the productive level of the struggle on actions built upon peers, linguistic knowledge and prior mathematical knowledge.</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":"50177019","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
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