Educational Studies in Mathematics最新文献_第7页

Demonstrating mathematics learning as the emergence of eye–hand dynamic equilibrium 展示数学学习中出现的眼手动态平衡

IF 3.2 2区教育学

Educational Studies in Mathematics Pub Date : 2023-12-29 DOI: 10.1007/s10649-023-10279-0

Rotem Abdu, Sofia Tancredi, Dor Abrahamson, Ramesh Balasubramaniam

{"title":"Demonstrating mathematics learning as the emergence of eye–hand dynamic equilibrium","authors":"Rotem Abdu, Sofia Tancredi, Dor Abrahamson, Ramesh Balasubramaniam","doi":"10.1007/s10649-023-10279-0","DOIUrl":"https://doi.org/10.1007/s10649-023-10279-0","url":null,"abstract":"This paper combines recent developments in theories of knowledge (complex dynamic systems), technologies (embodied interactions), and research tools (multimodal data collection and analysis) to offer new insights into how conceptual mathematical understanding can emerge. A complex dynamic system view models mathematics learning in terms of a multimodal agent who encounters a set of task constraints. The learning process in this context includes destabilizing a systemic configuration (for example, coordination of eye and hand movements) and forming new dynamic stability adapted to the task constraints. To test this model empirically, we applied a method developed to study complex systems, recurrence quantification analysis (RQA), to investigate students’ eye–hand dynamics during a touchscreen mathematics activity for the concept of proportionality. We found that across participants (n = 32), fluently coordinated hand-movement solutions coincided with more stable and predictable gaze patterns. We present a case study of a prototypical participant’s hand–eye RQA and audio–video data to show how the student’s cognitive system transitioned out of prior coordination reflective of additive thinking into a new coordination that can ground multiplicative thinking. These findings constitute empirical substantiation in mathematics education research for cognition as a complex system transitioning among dynamic equilibria.","PeriodicalId":48107,"journal":{"name":"Educational Studies in Mathematics","volume":"217 1","pages":""},"PeriodicalIF":3.2,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139080240","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

How pedagogical content knowledge sharpens prospective teachers’ focus when judging mathematical tasks: an eye-tracking study 教学内容知识如何使准教师在判断数学任务时更加专注：一项眼动追踪研究

IF 3.2 2区教育学

Educational Studies in Mathematics Pub Date : 2023-12-19 DOI: 10.1007/s10649-023-10281-6

{"title":"How pedagogical content knowledge sharpens prospective teachers’ focus when judging mathematical tasks: an eye-tracking study","authors":"","doi":"10.1007/s10649-023-10281-6","DOIUrl":"https://doi.org/10.1007/s10649-023-10281-6","url":null,"abstract":"<h3>Abstract</h3> Teachers’ ability to accurately judge difficulties of mathematical tasks is an essential aspect of their diagnostic competencies. Although research has suggested that pedagogical content knowledge (PCK) is positively correlated with the accuracy of diagnostic judgments, experimental studies have not been conducted to investigate how PCK affects perception and interpretation of relevant task characteristics. In an intervention study with a control group, 49 prospective mathematics teachers judged the difficulty of 20 tasks involving functions and graphs while an eye tracker tracked their eye movements. Some of the tasks included characteristics well known to be difficult for students. Participants’ domain-specific PCK of typical student errors was manipulated through a three-hour intervention, during which they learned about the most common student errors in function and graph problems. We found that the process of perception (relative fixation duration on the relevant area in the tasks) was related to judgment accuracy. Pre-post comparisons revealed an effect of the intervention not only on participants’ domain-specific PCK of typical student errors but also on their perception and interpretation processes. This result suggests that domain-specific PCK of typical student errors allowed participants to focus more efficiently on relevant task characteristics when judging mathematical task difficulties. Our study contributes to our understanding of how professional knowledge makes teachers’ judgment processes of mathematical tasks more efficient.","PeriodicalId":48107,"journal":{"name":"Educational Studies in Mathematics","volume":"23 1","pages":""},"PeriodicalIF":3.2,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138742711","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Developing a diagnostic framework for primary and secondary students’ reasoning difficulties during mathematical problem solving 建立中小学生数学解题过程中推理困难的诊断框架

IF 3.2 2区教育学

Educational Studies in Mathematics Pub Date : 2023-12-19 DOI: 10.1007/s10649-023-10278-1

Anna Ida Säfström, Johan Lithner, Torulf Palm, Björn Palmberg, Johan Sidenvall, Catarina Andersson, Erika Boström, Carina Granberg

{"title":"Developing a diagnostic framework for primary and secondary students’ reasoning difficulties during mathematical problem solving","authors":"Anna Ida Säfström, Johan Lithner, Torulf Palm, Björn Palmberg, Johan Sidenvall, Catarina Andersson, Erika Boström, Carina Granberg","doi":"10.1007/s10649-023-10278-1","DOIUrl":"https://doi.org/10.1007/s10649-023-10278-1","url":null,"abstract":"It is well-known that a key to promoting students’ mathematics learning is to provide opportunities for problem solving and reasoning, but also that maintaining such opportunities in student–teacher interaction is challenging for teachers. In particular, teachers need support for identifying students’ specific difficulties, in order to select appropriate feedback that supports students’ mathematically founded reasoning without reducing students’ responsibility for solving the task. The aim of this study was to develop a diagnostic framework that is functional for identifying, characterising, and communicating about the difficulties students encounter when trying to solve a problem and needing help from the teacher to continue the construction of mathematically founded reasoning. We describe how we reached this aim by devising iterations of design experiments, including 285 examples of students’ difficulties from grades 1–12, related to 110 tasks, successively increasing the empirical grounding and theoretical refinement of the framework. The resulting framework includes diagnostic questions, definitions, and indicators for each diagnosis and structures the diagnostic process in two simpler steps with guidelines for difficult cases. The framework therefore has the potential to support teachers both in eliciting evidence about students’ reasoning during problem solving and in interpreting this evidence.","PeriodicalId":48107,"journal":{"name":"Educational Studies in Mathematics","volume":"9 1","pages":""},"PeriodicalIF":3.2,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138743082","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Extrema points: concept images, mis-in and mis-out examples 极值点：概念图像、误入和误出示例

IF 3.2 2区教育学

Educational Studies in Mathematics Pub Date : 2023-12-13 DOI: 10.1007/s10649-023-10273-6

Pessia Tsamir, Regina Ovodenko, Dina Tirosh

引用次数: 0

Teachers pose and design context-based mathematics tasks: what can be learned from product evolution? 教师提出并设计基于情境的数学任务：从产品演变中可以学到什么？

IF 3.2 2区教育学

Educational Studies in Mathematics Pub Date : 2023-12-13 DOI: 10.1007/s10649-023-10271-8

Nadav Marco, Alik Palatnik

{"title":"Teachers pose and design context-based mathematics tasks: what can be learned from product evolution?","authors":"Nadav Marco, Alik Palatnik","doi":"10.1007/s10649-023-10271-8","DOIUrl":"https://doi.org/10.1007/s10649-023-10271-8","url":null,"abstract":"This study proposes a model of several dimensions through which products of teachers’ context-based mathematics problem posing (PP) can be modified. The dimensions are Correctness, Authenticity, Task Assortment (consisting of Mathematical Diversity, Multiple Data Representations, Question–Answer Format, Precision-Approximation, and Generalization), Task Flow, and Student Involvement. A study was conducted in the context of a professional development (PD) program in which eight secondary school teachers iteratively designed 22 context-based mathematics tasks. Using the variation theory of learning as a theoretical framework and qualitative content analysis methodology, we compared different versions of the same tasks, focusing on items participants added or revised. To demonstrate the usability of the resulting semi-hierarchical model, we apply it to characterize the teachers’ final products of context-based PP. We found that most items teachers composed did not deviate from what we call the “common item form”—items that require numeric, exact, particular-case-related, and close-form answers without involving students in decision-making. Our findings may inform teacher educators and researchers on planning and implementing context-based mathematics task development by teachers in PD.","PeriodicalId":48107,"journal":{"name":"Educational Studies in Mathematics","volume":"234 1","pages":""},"PeriodicalIF":3.2,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138631569","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Mathematical modelling as a vehicle for eliciting algorithmic thinking 将数学建模作为激发算法思维的工具

IF 3.2 2区教育学

Educational Studies in Mathematics Pub Date : 2023-12-12 DOI: 10.1007/s10649-023-10275-4

Timothy H. Lehmann

{"title":"Mathematical modelling as a vehicle for eliciting algorithmic thinking","authors":"Timothy H. Lehmann","doi":"10.1007/s10649-023-10275-4","DOIUrl":"https://doi.org/10.1007/s10649-023-10275-4","url":null,"abstract":"Developing students’ competence in algorithmic thinking is emerging as an objective of mathematics education, but despite its inclusion in mathematics curricula around the world, research into students’ algorithmic thinking seems to be falling behind in this curriculum reform. The aim of this study was to investigate how the mathematical modelling process can be used as a vehicle for eliciting students’ algorithmic thinking. To achieve this aim, a generative study was conducted using task-based interviews with year 12 students (n = 8) to examine how they used the mathematical modelling process to design an algorithm that solved a minimum spanning tree problem. I observed each students’ modelling process and analysed how the task elicited the cognitive skills of algorithmic thinking. The findings showed that the students leveraged their mathematical modelling competencies to formulate a model of the problem using abstraction and decomposition, designed their algorithms by devising a fundamental operation to transform inputs into outputs during the working mathematically transition, and debugged their algorithms during the validating transition. Implications for practice are discussed.","PeriodicalId":48107,"journal":{"name":"Educational Studies in Mathematics","volume":"196 1","pages":""},"PeriodicalIF":3.2,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138573733","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Children’s subtraction by addition strategy use and their subtraction-related conceptual knowledge 儿童对加法减法策略的使用及其与减法有关的概念知识

IF 3.2 2区教育学

Educational Studies in Mathematics Pub Date : 2023-12-08 DOI: 10.1007/s10649-023-10276-3

Stijn Van Der Auwera, Bert De Smedt, Joke Torbeyns, Lieven Verschaffel

{"title":"Children’s subtraction by addition strategy use and their subtraction-related conceptual knowledge","authors":"Stijn Van Der Auwera, Bert De Smedt, Joke Torbeyns, Lieven Verschaffel","doi":"10.1007/s10649-023-10276-3","DOIUrl":"https://doi.org/10.1007/s10649-023-10276-3","url":null,"abstract":"This study is the first to examine the associations between the occurrence, frequency, and adaptivity of children’s subtraction by addition strategy use (SBA; e.g., 712 − 346 = ?; 346 + 54 = 400, 400 + 300 = 700, 700 + 12 = 712, and 54 + 300 + 12 = 366) and their underlying conceptual knowledge. Specifically, we focused on two rarely studied components of conceptual knowledge: children’s knowledge of the addition/subtraction complement principle (i.e., if a + b = c, then c − b = a and c − a = b) and their knowledge of different conceptual subtraction models (i.e., understanding that subtraction can be conceived not only as “taking away” but also as “determining the difference”). SBA occurrence was examined using a variability on demand task, in which children had to use multiple strategies to solve a subtraction. SBA frequency and strategy adaptivity were investigated with a task in which children could freely choose between SBA and direct subtraction (e.g., 712 − 346 = ?; 712 − 300 = 412, 412 − 40 = 372, and 372 − 6 = 366) to solve 15 subtractions. We measured both children’s knowledge of the addition/subtraction complement principle, and whether they understood subtraction also as “determining the difference.” SBA occurrence and frequency were not related to conceptual knowledge. However, strategy adaptivity was related to children’s knowledge of the addition/subtraction complement principle. Our findings highlight the importance of attention to conceptual knowledge when teaching multi-digit subtraction and expand the literature about the relation between procedural and conceptual knowledge.","PeriodicalId":48107,"journal":{"name":"Educational Studies in Mathematics","volume":"55 1","pages":""},"PeriodicalIF":3.2,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138562126","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Understanding the cognitive processes of mathematical problem posing: evidence from eye movements 理解数学问题提出的认知过程:来自眼球运动的证据

IF 3.2 2区教育学

Educational Studies in Mathematics Pub Date : 2023-11-23 DOI: 10.1007/s10649-023-10262-9

Ling Zhang, Naiqing Song, Guowei Wu, Jinfa Cai

{"title":"Understanding the cognitive processes of mathematical problem posing: evidence from eye movements","authors":"Ling Zhang, Naiqing Song, Guowei Wu, Jinfa Cai","doi":"10.1007/s10649-023-10262-9","DOIUrl":"https://doi.org/10.1007/s10649-023-10262-9","url":null,"abstract":"This study concerns the cognitive process of mathematical problem posing, conceptualized in three stages: understanding the task, constructing the problem, and expressing the problem. We used the eye tracker and think-aloud methods to deeply explore students’ behavior in these three stages of problem posing, especially focusing on investigating the influence of task situation format and mathematical maturity on students’ thinking. The study was conducted using a 2 × 2 mixed design: task situation format (with or without specific numerical information) × subject category (master’s students or sixth graders). Regarding the task situation format, students’ performance on tasks with numbers was found to be significantly better than that on tasks without numbers, which was reflected in the metrics of how well they understood the task and the complexity and clarity of the posed problems. In particular, students spent more fixation duration on understanding and processing the information in tasks without numbers; they had a longer fixation duration on parts involving presenting uncertain numerical information; in addition, the task situation format with or without numbers had an effect on students’ selection and processing of information related to the numbers, elements, and relationships rather than information regarding the context presented in the task. Regarding the subject category, we found that mathematical maturity did not predict the quantity of problems posed on either type of task. There was no significant main group difference found in the eye-movement metrics.","PeriodicalId":48107,"journal":{"name":"Educational Studies in Mathematics","volume":"314 ","pages":""},"PeriodicalIF":3.2,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138506244","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Book Review: The new mathematics education of new Europe. Alexander Karp (Ed.) (2020) Eastern European mathematics education in the decades of change 书评:新欧洲的新数学教育。亚历山大卡普(编)(2020)东欧数学教育在几十年的变化

2区教育学

Educational Studies in Mathematics Pub Date : 2023-11-06 DOI: 10.1007/s10649-023-10269-2

Snezana Lawrence

引用次数: 0

Correction to: Weaving together the threads of Indigenous knowledge and mathematics 更正:将本土知识和数学的线索编织在一起

2区教育学

Educational Studies in Mathematics Pub Date : 2023-10-24 DOI: 10.1007/s10649-023-10272-7

Jodie Hunter, Roberta Hunter

引用次数: 0