Journal of Mathematical Behavior最新文献_第8页

Considering, piloting, scaling and sustaining a research-based precalculus curriculum and professional development innovation 考虑、试点、推广和维持基于研究的微积分先修课程和专业发展创新

IF 1.7

Journal of Mathematical Behavior Pub Date : 2024-02-07 DOI: 10.1016/j.jmathb.2024.101126

Marilyn P. Carlson , Alan E. O’Bryan , Jeremy F. Strayer , Timothy H. McNicholl , Jess E. Hagman

{"title":"Considering, piloting, scaling and sustaining a research-based precalculus curriculum and professional development innovation","authors":"Marilyn P. Carlson , Alan E. O’Bryan , Jeremy F. Strayer , Timothy H. McNicholl , Jess E. Hagman","doi":"10.1016/j.jmathb.2024.101126","DOIUrl":"https://doi.org/10.1016/j.jmathb.2024.101126","url":null,"abstract":"<div><p>We report a case study of scaling a <em>research-based curriculum and professional development innovation</em>. We describe the <em>Pathways Precalculus Curriculum and Professional Development</em> (PPCPD) project and provide an overview of its development and components. In doing so, we detail how research informed its development and refinement, illustrate why we claim the PPCPD innovation is research-based, and document ways in which it is educative for both instructors and students. We describe results from a case study in which the PPCPD scaled to 13 sites that piloted the innovation, 12 of which locally scaled the innovation and attempted to sustain its use. We report findings from survey and interview data that reveal key variables that led to the sites’ sustaining or not sustaining the PPCPD innovation. We further highlight the importance of conceptualizing curricular scaling as an opportunity for continuous learning among the project leaders, local leaders, and precalculus instructors during all phases (considering, piloting, locally scaling, and sustaining) of the PPCPD.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"73 ","pages":"Article 101126"},"PeriodicalIF":1.7,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139699347","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

The road to “good” problems goes through initial responses to stimulating socio-mathematical situations 通向 "好 "问题的道路要通过对激励性社会数学情境的初步反应来实现

IF 1.7

Journal of Mathematical Behavior Pub Date : 2024-02-06 DOI: 10.1016/j.jmathb.2024.101135

Igor’ Kontorovich

{"title":"The road to “good” problems goes through initial responses to stimulating socio-mathematical situations","authors":"Igor’ Kontorovich","doi":"10.1016/j.jmathb.2024.101135","DOIUrl":"https://doi.org/10.1016/j.jmathb.2024.101135","url":null,"abstract":"<div><p>Despite its almost four-decade history, research remains in the early stages of understanding the phenomenon of mathematical problem posing. In particular, the quality of problems created by beginning posers has been recognized as a persistent challenge. In this conceptual paper, I endorse an approach that identifies posing and solving as co-emergent components of steps learners take in a mathematically problematic situation. I further argue that some of the initial responses to the situation may constitute productive ingredients for creating problems that are personally meaningful and interesting to the learners. Drawing on the literature, I offer two principles through which the process of transitioning from initial responses to fully-fledged problems can be supported: making the didactical contract of the problem-posing activity transparent and immersing learners in socio-mathematical settings that are conducive to “good” problems. The approach is illustrated with fragments from a workshop for in-service teachers. The concluding discussion focuses on how the presented approach addresses some common issues in problem posing research.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"73 ","pages":"Article 101135"},"PeriodicalIF":1.7,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0732312324000129/pdfft?md5=6f7b2832ff36264620d46f3c40b96a07&pid=1-s2.0-S0732312324000129-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139694460","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

Combinatorial and quantitative reasoning: Stage 3 high school students’ reason about combinatorics problems and their representation as 3-D arrays 组合和定量推理：第三阶段高中生对组合问题的推理及其三维数组表示法

IF 1.7

Journal of Mathematical Behavior Pub Date : 2024-02-02 DOI: 10.1016/j.jmathb.2024.101125

Erik S. Tillema , Andrew M. Gatza , Weverton Ataide Pinheiro

{"title":"Combinatorial and quantitative reasoning: Stage 3 high school students’ reason about combinatorics problems and their representation as 3-D arrays","authors":"Erik S. Tillema , Andrew M. Gatza , Weverton Ataide Pinheiro","doi":"10.1016/j.jmathb.2024.101125","DOIUrl":"https://doi.org/10.1016/j.jmathb.2024.101125","url":null,"abstract":"<div><p>Researchers have identified three stages of units coordination that influence a range of domains of student reasoning. The primary foci of this research have been students’ reasoning in discrete, non-combinatorial whole number contexts, and with fractions, ratios, proportions, and rates represented using length quantities. This study extends this prior work by examining connections between eight high school students’ combinatorial reasoning and their representation of this reasoning using 3-D arrays. All students in the study were at stage 3 of units coordination. Findings include differentiation between two student groups: one group had interiorized three-levels-of-units, but had not interiorized four-levels-of-units; and the other group had interiorized four-levels-of-units. This differentiation was coordinated with differences in how they reasoned to produce 3-D arrays. The findings from the study indicate how combinatorics problems can support quantitative reasoning, where combinatorial and quantitative reasoning are framed as a foundation for algebraic reasoning.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"73 ","pages":"Article 101125"},"PeriodicalIF":1.7,"publicationDate":"2024-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139674665","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

“Guess what they would make you do on this one”: The discourse of a high-stakes exam in an AP Calculus classroom "猜猜他们会让你做什么？AP 微积分课堂上的高风险考试话语

IF 1.7

Journal of Mathematical Behavior Pub Date : 2024-02-02 DOI: 10.1016/j.jmathb.2024.101127

Sunghwan Byun , Beth Herbel-Eisenmann

引用次数: 0

Teaching mathematics through problem posing: Elements of the task 通过提出问题进行数学教学：任务要素

IF 1.7

Journal of Mathematical Behavior Pub Date : 2024-02-02 DOI: 10.1016/j.jmathb.2024.101133

Janaína Poffo Possamai , Norma Suely Gomes Allevato

引用次数: 0

Attending to task variables when engaging in group problem posing for elementary level mathematics 在小学数学小组讨论中关注任务变量

IF 1.7

Journal of Mathematical Behavior Pub Date : 2024-02-01 DOI: 10.1016/j.jmathb.2024.101128

Aisling Leavy, Mairéad Hourigan

{"title":"Attending to task variables when engaging in group problem posing for elementary level mathematics","authors":"Aisling Leavy, Mairéad Hourigan","doi":"10.1016/j.jmathb.2024.101128","DOIUrl":"https://doi.org/10.1016/j.jmathb.2024.101128","url":null,"abstract":"<div><p>In light of the growing interest in research examining problem posing, this study explores an under-researched aspect – group problem posing. It examines the role of problem situations and prompts, introduced within a problem posing intervention, on the nature of the problems posed by groups of pre-service elementary teachers for children in two 4th grade classes. The impact of the group on the problem posing process was also explored. The findings reveal improvements in the quality of the problems posed due to a number of factors including the use of textbook problems as initial problem situations that supported problem reformulation, the constructive role of prompts to focus attention on desirable problem features and the valuable role of feedback in determining problem aptness. A challenge when problem posing was difficulty coordinating attention to multiple problem features, however, this was mediated by the affordance of working in groups which served to share the responsibility for, and enhance, problem quality alongside the use of the F-PosE problem posing framework which focused attention on desirable problem features.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"73 ","pages":"Article 101128"},"PeriodicalIF":1.7,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0732312324000051/pdfft?md5=a4174bfa6bca3d3e97a11095ab27e051&pid=1-s2.0-S0732312324000051-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139675127","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

Problem-posing tasks and their influence on pre-service teachers’ creative problem-posing performance and self-efficacy 提出问题的任务及其对职前教师提出创造性问题的表现和自我效能感的影响

IF 1.7

Journal of Mathematical Behavior Pub Date : 2024-01-30 DOI: 10.1016/j.jmathb.2024.101130

Lukas Baumanns , Benjamin Rott

{"title":"Problem-posing tasks and their influence on pre-service teachers’ creative problem-posing performance and self-efficacy","authors":"Lukas Baumanns , Benjamin Rott","doi":"10.1016/j.jmathb.2024.101130","DOIUrl":"10.1016/j.jmathb.2024.101130","url":null,"abstract":"<div><p>In problem-posing research, the influence of task variables on problem-posing outcomes is a relatively new endeavor. To systematically vary task variables, we designed eight problem-posing tasks by crossing two problem-posing situations (unstructured vs. structured) with two problem-posing prompts (open vs. closed) and two mathematical contexts (patterns vs. geometry). Using this design, we investigated the influence of these task variables on (1) creative problem-posing performance, (2) problem-posing self-efficacy, and (3) the relationship between self-efficacy and creative problem-posing performance in 187 pre-service teachers. The analyses show that (1) the influence of the situation and prompt is small and topic-specific, (2) that self-efficacy is significantly lower in unstructured situations with an open prompt than in the other tasks, and (3) that creative problem-posing performance and self-efficacy are correlated negatively. The findings imply a need for more detailed investigations regarding the influence on creative problem-posing performance and for which subjects it is relevant.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"73 ","pages":"Article 101130"},"PeriodicalIF":1.7,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0732312324000075/pdfft?md5=970e182433cd5746789885155aca8ba3&pid=1-s2.0-S0732312324000075-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139648695","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

Variables in planning and carrying out a problem-posing task in early childhood education 幼儿教育中计划和执行提出问题任务的变量

IF 1.7

Journal of Mathematical Behavior Pub Date : 2024-01-25 DOI: 10.1016/j.jmathb.2024.101131

Enrique Carmona-Medeiro , Juan Pedro Martín-Díaz , Nuria Climent

{"title":"Variables in planning and carrying out a problem-posing task in early childhood education","authors":"Enrique Carmona-Medeiro , Juan Pedro Martín-Díaz , Nuria Climent","doi":"10.1016/j.jmathb.2024.101131","DOIUrl":"10.1016/j.jmathb.2024.101131","url":null,"abstract":"<div><p>This research focused on understanding the variables inherent in the design and implementation of a mathematical problem-posing task. We developed a single case study of a problem-posing lesson by an Early Childhood Education teacher in a classroom with 4- to 5-year-old children who were unfamiliar with such activities. The results of this study show the potential of considering five variables serving as critical points that pose dilemmas linked to the design and implementation of problem-posing tasks. We found that the task changed from its original design during implementation, implying that the choices the teacher made about the variables were not static and were strongly linked to the purpose of the problem-posing task as well as to the contextual characteristics of the early childhood classroom. This study provides a potentially useful framework for analyzing the design and implementation of problem-posing tasks as a dynamic process.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"73 ","pages":"Article 101131"},"PeriodicalIF":1.7,"publicationDate":"2024-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0732312324000087/pdfft?md5=0b76b7ff0271c2eacf5ca8c3f0c8f0ea&pid=1-s2.0-S0732312324000087-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139579380","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

Mathematics teachers’ specialized knowledge mobilized through problem transformation 通过问题转化调动数学教师的专业知识

IF 1.7

Journal of Mathematical Behavior Pub Date : 2024-01-25 DOI: 10.1016/j.jmathb.2024.101132

M. Montes , J. Chico , J.P. Martín-Díaz , E. Badillo

{"title":"Mathematics teachers’ specialized knowledge mobilized through problem transformation","authors":"M. Montes , J. Chico , J.P. Martín-Díaz , E. Badillo","doi":"10.1016/j.jmathb.2024.101132","DOIUrl":"10.1016/j.jmathb.2024.101132","url":null,"abstract":"<div><p>In this study we address two issues related to problem-posing tasks in teacher education: (i) the characterization of the specialized knowledge mobilized by prospective teachers when carrying out these tasks and (ii) the identification of the prospective teachers’ pedagogical intentions in making adaptations to textbook problems. We asked prospective teachers to outline their suggestions for transforming a multiplicative problem so as to “promote the understanding” of their potential pupils. We then carried out a content analysis of their responses using the Mathematics Teachers’ Specialized Knowledge model of teachers’ specialized knowledge and identified their pedagogical intentions by means of the constant comparison method. The results show that prospective primary teachers mobilized both mathematical and pedagogical content knowledge in their responses to the problem reformulation task. Further, four distinct pedagogical intentions emerged that drew on different interpretations of the task prompt, and this influenced the type of transformation the prospective primary teachers suggested and the knowledge they mobilized in their answers.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"73 ","pages":"Article 101132"},"PeriodicalIF":1.7,"publicationDate":"2024-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0732312324000099/pdfft?md5=68e09bf54f7b4e8af9310aee63c7220c&pid=1-s2.0-S0732312324000099-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139579777","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

Do task variables of self-generated problems influence interest? Authenticity, openness, complexity, and students’ interest in solving self-generated modelling problems 自创问题的任务变量会影响兴趣吗？真实性、开放性、复杂性与学生解决自创建模问题的兴趣

IF 1.7

Journal of Mathematical Behavior Pub Date : 2024-01-23 DOI: 10.1016/j.jmathb.2024.101129

Janina Krawitz , Luisa Hartmann , Stanislaw Schukajlow

{"title":"Do task variables of self-generated problems influence interest? Authenticity, openness, complexity, and students’ interest in solving self-generated modelling problems","authors":"Janina Krawitz , Luisa Hartmann , Stanislaw Schukajlow","doi":"10.1016/j.jmathb.2024.101129","DOIUrl":"https://doi.org/10.1016/j.jmathb.2024.101129","url":null,"abstract":"<div><p>Problem posing—generating one’s own problems—is considered a powerful teaching approach for fostering students’ motivation such as their interest. However, research investigating the effects of task variables of self-generated problems on students’ interest is largely missing. In this contribution, we present a study with 105 ninth- and tenth-graders to address the question of whether the task variables modelling potential, assessed by openness and authenticity, or complexity of self-generated problems have an impact on students’ interest in solving them. Further, we investigated whether the effect of task variables of self-generated problems on students’ interest differed among students with different levels of mathematical competence. High modelling potential had a positive effect on interest in solving the problem for students with low mathematical competence, whereas it had a negative effect for those with high mathematical competence. However, complexity of self-generated problems did not affect students’ interest in solving problems.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"73 ","pages":"Article 101129"},"PeriodicalIF":1.7,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0732312324000063/pdfft?md5=251ea0e01b6ed0b8168180abcd5f5419&pid=1-s2.0-S0732312324000063-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139549399","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