Journal of Mathematical Behavior最新文献_第8页

Validating a measure of graph selection and graph reasoning for dynamic situations 验证动态情况下图形选择和图形推理的衡量标准

IF 1.7

Journal of Mathematical Behavior Pub Date : 2024-03-01 DOI: 10.1016/j.jmathb.2024.101137

Courtney Donovan , Heather Lynn Johnson , Robert Knurek , Kristin A. Whitmore , Livvia Bechtold

{"title":"Validating a measure of graph selection and graph reasoning for dynamic situations","authors":"Courtney Donovan , Heather Lynn Johnson , Robert Knurek , Kristin A. Whitmore , Livvia Bechtold","doi":"10.1016/j.jmathb.2024.101137","DOIUrl":"https://doi.org/10.1016/j.jmathb.2024.101137","url":null,"abstract":"<div><p>Using a mixed methods approach, we report results from the evaluation and validation stages of a fully online Measure of Graph Selection and Reasoning for Dynamic Situations, implemented with undergraduate college algebra students across three U.S universities. The measure contains six items; each includes a video animation of a dynamic situation (e.g., a fishbowl filling with water), a declaration of understanding, four Cartesian graphs from which to select, and a text box for explanation. In the evaluation stage, we demonstrate usability and content validity, drawing on individual cognitive interviews (n = 31 students). In the validation stage (n = 673 students), we use Rasch modeling to evidence reliability and internal structure, establishing a continuum of item difficulty and confirming the viability of a partial credit scoring approach for graph selection. Rasch results provide statistical support that the theorized graph reasoning framework (Iconic, Motion, Variation, Covariation) from Johnson et al. (2020) forms a hierarchical scale.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"73 ","pages":"Article 101137"},"PeriodicalIF":1.7,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0732312324000142/pdfft?md5=b5c87e78e611f37e30088a81c2c26173&pid=1-s2.0-S0732312324000142-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140062332","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

The influence of problem-posing task situation: Prospective primary teachers working with fractions 提出问题的任务情境的影响：从事分数教学的准小学教师

IF 1.7

Journal of Mathematical Behavior Pub Date : 2024-03-01 DOI: 10.1016/j.jmathb.2024.101139

Diana Sosa-Martín , Josefa Perdomo-Díaz , Alicia Bruno , Rut Almeida, Israel García-Alonso

{"title":"The influence of problem-posing task situation: Prospective primary teachers working with fractions","authors":"Diana Sosa-Martín , Josefa Perdomo-Díaz , Alicia Bruno , Rut Almeida, Israel García-Alonso","doi":"10.1016/j.jmathb.2024.101139","DOIUrl":"https://doi.org/10.1016/j.jmathb.2024.101139","url":null,"abstract":"<div><p>This research presents a study on the problems posed by pre-service primary school teachers by focusing on the problem-posing tasks situation as the research variable. The investigation was carried out with 205 students of a bachelor’s degree in Primary Education Teacher in Spain. They were asked to pose problems with fractions based on two given initial situations: numerical and contextualized. For each problem, we analyze its plausibility, the meanings of fractions, the mathematical structure, and the reasonability of the context. Results indicate that mostly posed problems use part-whole or operator meaning of fractions, as well as the additive or multiplicative structure. There are no differences between the plausibility and reasonability of the problems based on the initial situation, although it has shown better results when the given situation is contextualized. In addition, in contextualized situations, teachers show greater ability in formulating problems with a wide variety of structures and meanings of fractions.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"73 ","pages":"Article 101139"},"PeriodicalIF":1.7,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0732312324000166/pdfft?md5=e4d4a4cfb3243fa073b224aa6097a76d&pid=1-s2.0-S0732312324000166-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140030286","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

How mothers’ mathematical positioning relates to their images of mathematics and interactions with children 母亲的数学定位如何与她们的数学形象以及与孩子的互动相关联

IF 1.7

Journal of Mathematical Behavior Pub Date : 2024-03-01 DOI: 10.1016/j.jmathb.2024.101141

Sam Prough

引用次数: 0

Parental support for mathematical problem solving: Proximal and distal influences within the religious practice of tithing 父母对数学问题解决的支持：什一奉献宗教习俗中的近端和远端影响因素

IF 1.7

Journal of Mathematical Behavior Pub Date : 2024-02-23 DOI: 10.1016/j.jmathb.2023.101102

Edd V. Taylor , Tracy E. Dobie

引用次数: 0

Investigating boundaries and boundary crossing between mathematics and visual art teaching in a collaborative setting 在合作环境中探究数学与视觉艺术教学之间的界限和跨越界限问题

IF 1.7

Journal of Mathematical Behavior Pub Date : 2024-02-22 DOI: 10.1016/j.jmathb.2024.101138

Chrysoula Choutou, Despina Potari

引用次数: 0

Analogical structure sense: A case study of students’ analogical reasoning between groups and rings 类比结构感：学生在组与环之间进行类比推理的案例研究

IF 1.7

Journal of Mathematical Behavior Pub Date : 2024-02-15 DOI: 10.1016/j.jmathb.2024.101136

Michael D. Hicks , Kyle Flanagan

引用次数: 0

Teachers' mathematical problem posing: The role of processes and complexity levels in posing problems on the fraction part-whole concept 教师提出数学问题：过程和复杂程度在提出分数部分-整体概念问题中的作用

IF 1.7

Journal of Mathematical Behavior Pub Date : 2024-02-07 DOI: 10.1016/j.jmathb.2024.101134

Constantinos Christou, Demetra Pitta-Pantazi, Maria Chimoni

{"title":"Teachers' mathematical problem posing: The role of processes and complexity levels in posing problems on the fraction part-whole concept","authors":"Constantinos Christou, Demetra Pitta-Pantazi, Maria Chimoni","doi":"10.1016/j.jmathb.2024.101134","DOIUrl":"https://doi.org/10.1016/j.jmathb.2024.101134","url":null,"abstract":"<div><p>This study contributes to understanding the influence of different problem posing tasks on the performance of in-service teachers in posing important and worthwhile mathematical problems. The problem posing tasks pertain to the part-whole concept of fraction which presents ongoing challenges for teachers and students. The study sample was comprised of 40 in-service primary school teachers who completed an electronic problem posing test. The problem posing tasks included different problem situations and prompts that addressed: (a) four types of problem posing processes (editing, selecting, comprehending, and translating), and (b) four levels of complexity (uni-structural, multi-structural, relational, extended abstract). The results suggested that in-service teachers’ performance is mainly influenced by the process involved in a problem posing task, being higher in problem situations that are more closed structured compared to more open structured. The level of complexity was not found to influence in-service teachers’ performance.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"73 ","pages":"Article 101134"},"PeriodicalIF":1.7,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139699346","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

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