Mathematical Thinking and Learning最新文献_第9页

Informal statistical models and modeling 非正式统计模型和建模

IF 1.6 4区教育学

Mathematical Thinking and Learning Pub Date : 2021-05-15 DOI: 10.1080/10986065.2021.1925842

Michal Dvir, D. Ben-Zvi

{"title":"Informal statistical models and modeling","authors":"Michal Dvir, D. Ben-Zvi","doi":"10.1080/10986065.2021.1925842","DOIUrl":"https://doi.org/10.1080/10986065.2021.1925842","url":null,"abstract":"ABSTRACT Growing scholarship on the pedagogical applications of statistical modeling is currently taking place to create adaptations of this practice to introduce novices to statistics. These are intended to promote novices’ reasoning, and are typically void of formal mathematical procedures and calculations. In this article, we define the potential product that novices can create as they engage in such informal implementations, Informal Statistical Models (ISM), as purposeful representations – with both deterministic and stochastic components – of how observed variability in data is generated. This definition reflects the potential connection between informal constructs that novices and young students can create and the formal view of statistical models, thereby suggesting how informal insights may be later cultivated into more mature understandings. We illustrate the usefulness of this definition by providing an in-depth account of the reasoning that a pair of sixth-grade students employed through their informal statistical modeling process. The findings illustrate a four-episode sequence where students created and developed an initial deterministic model before extending it with an informal stochastic component. This shows how starting with deterministic models can be a valuable precursor to develop initial ISMs.","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":"25 1","pages":"79 - 99"},"PeriodicalIF":1.6,"publicationDate":"2021-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/10986065.2021.1925842","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42313618","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 7

The process of actively building a model for a randomization test – insights into learners’ modeling activities based on a case study 主动为随机测试建立模型的过程-基于案例研究洞察学习者的建模活动

IF 1.6 4区教育学

Mathematical Thinking and Learning Pub Date : 2021-05-06 DOI: 10.1080/10986065.2021.1922837

Susanne Podworny, Rolf Biehler

{"title":"The process of actively building a model for a randomization test – insights into learners’ modeling activities based on a case study","authors":"Susanne Podworny, Rolf Biehler","doi":"10.1080/10986065.2021.1922837","DOIUrl":"https://doi.org/10.1080/10986065.2021.1922837","url":null,"abstract":"ABSTRACT Inferential reasoning is an integral part of science and civic society, but research shows that it is a problematic domain for many people. One possibility for a more accessible approach to inferential reasoning is to use randomization tests via computer simulations. A case study was conducted with primary preservice teachers after they had passed a course module that introduced inferential reasoning with randomization tests. The study examines how three pairs of primary preservice teachers construct models in a randomization test task with both hands-on and computer-supported components. Our findings suggest that there is a common sequence in the model building process: planning, modeling the random assignment, setting sample size and replacement, and running the simulation. Our findings show in depth how TinkerPlots can be a supportive and constraining medium in the modeling process, building on experiences with physical simulations of a randomization test. These insights can be used for redesigning technology-supported learning trajectories for randomization tests. Together with other case studies our findings provide a good sense of university students’ modeling processes.","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":"24 1","pages":"291 - 311"},"PeriodicalIF":1.6,"publicationDate":"2021-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/10986065.2021.1922837","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43540000","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 2

Statistical modeling in teacher education 教师教育中的统计建模

IF 1.6 4区教育学

Mathematical Thinking and Learning Pub Date : 2021-05-06 DOI: 10.1080/10986065.2021.1922859

Lucía Zapata-Cardona, C. Martínez-Castro

{"title":"Statistical modeling in teacher education","authors":"Lucía Zapata-Cardona, C. Martínez-Castro","doi":"10.1080/10986065.2021.1922859","DOIUrl":"https://doi.org/10.1080/10986065.2021.1922859","url":null,"abstract":"ABSTRACT The purpose of this research is to investigate prospective teachers’ learning in the statistical modeling process. To reach this goal, we position the study in a socio-critical perspective of modeling that informed the design of a statistical investigation. Participants were 10 prospective teachers from a state university in northwestern Colombia who were taking a methods course in statistics. They worked out a statistical investigation inspired by a news article on global warming. The main source of data was fragments from prospective teachers’ speech while working out the statistical investigation. The information was complemented with prospective teachers’ narratives in which they reflected on their experience with statistics. The results reveal that the prospective teachers’ discourse offers indications to suggest that the participants were in the process of developing statistical knowledge as well as developing awareness as critical citizens. Prospective teachers used statistics tools to (1) make sense of a crisis of society while progressing in the development of their statistical knowledge and (2) reflect on the critical issue while showing signs of social awareness development.","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":"25 1","pages":"64 - 78"},"PeriodicalIF":1.6,"publicationDate":"2021-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/10986065.2021.1922859","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43862461","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 4

Decentering framework: A characterization of graduate student instructors’ actions to understand and act on student thinking 欺骗框架：研究生导师理解学生思维并对其采取行动的特征

IF 1.6 4区教育学

Mathematical Thinking and Learning Pub Date : 2021-04-09 DOI: 10.1080/10986065.2020.1844608

Sinem Bas-Ader, M. Carlson

引用次数: 4

About time: Syntactically-guided reasoning with analog and digital clocks 关于时间：使用模拟和数字时钟进行语法引导的推理

IF 1.6 4区教育学

Mathematical Thinking and Learning Pub Date : 2021-03-04 DOI: 10.1080/10986065.2021.1881703

D. Earnest

引用次数: 3

Exploring the nature of math anxiety in young children: Intensity, prevalence, reasons 探索幼儿数学焦虑的本质:强度、流行程度和原因

IF 1.6 4区教育学

Mathematical Thinking and Learning Pub Date : 2021-02-11 DOI: 10.1080/10986065.2021.1882363

Monika Szczygieł, Barbara Pieronkiewicz

{"title":"Exploring the nature of math anxiety in young children: Intensity, prevalence, reasons","authors":"Monika Szczygieł, Barbara Pieronkiewicz","doi":"10.1080/10986065.2021.1882363","DOIUrl":"https://doi.org/10.1080/10986065.2021.1882363","url":null,"abstract":"ABSTRACT According to previous findings, math anxiety already occurs at early school age and is negatively correlated with math achievement. So far, however, little is known about the nature of math anxiety in young children. To fill this gap, we present the results of a longitudinal study on the math anxiety of children that were followed in the first year of elementary school. We tested the level of math anxiety and its prevalence. We also investigated the reasons for math anxiety that were reported by the children at the beginning of elementary education. For this purpose, we adopted both individual-difference and developmental perspectives. The results show that first-grade students experienced mild math anxiety that peaked at the beginning of the school year. Most children experienced a low level of math anxiety; some of them were not anxious at all or experienced moderate anxiety, while only a few children were highly math anxious. The reasons for math anxiety that were most frequently reported by the students were associated with risk of failure, task difficulty, time pressure, and fear of receiving a bad grade. We discuss the obtained results in the context of actions aimed at improving the mathematical achievement of students.","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":"24 1","pages":"248 - 266"},"PeriodicalIF":1.6,"publicationDate":"2021-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/10986065.2021.1882363","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47077194","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 21

Profiles in understanding operations with rational numbers 了解有理数运算的概况

IF 1.6 4区教育学

Mathematical Thinking and Learning Pub Date : 2021-02-04 DOI: 10.1080/10986065.2021.1882287

Juan Manuel González-forte, C. Fernández, Joris J. van Hoof, W. Van Dooren

{"title":"Profiles in understanding operations with rational numbers","authors":"Juan Manuel González-forte, C. Fernández, Joris J. van Hoof, W. Van Dooren","doi":"10.1080/10986065.2021.1882287","DOIUrl":"https://doi.org/10.1080/10986065.2021.1882287","url":null,"abstract":"ABSTRACT Students often show difficulties in understanding rational numbers. Often, these are related to the natural number bias, that is, the tendency to apply the properties of natural numbers to rational number tasks. Although this phenomenon has received a lot of research interest over the last two decades, research on the existence of qualitatively different profiles regarding students’ understanding is scarce. The current study investigated the different ways students reasoned in arithmetic operation items with fractions and decimals. A cross-sectional study with 1,262 participants from 5th to 10th grade was performed. A TwoStep Cluster Analysis revealed eight different student reasoning profiles. We found that the natural number bias is first overcome in addition and subtraction, and later in multiplication and division. Moreover, differences regarding representation were only found in addition and subtraction items, indicating that natural numbers interfered more strongly in fractions than in decimal numbers. Finally, results showed that some students’ difficulties with rational number multiplications and divisions had other explanations than the natural number bias.","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":"24 1","pages":"230 - 247"},"PeriodicalIF":1.6,"publicationDate":"2021-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/10986065.2021.1882287","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42016023","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 3

Length measurement in the early years: teaching and learning with learning trajectories 早期的长度测量：带学习轨迹的教学

IF 1.6 4区教育学

Mathematical Thinking and Learning Pub Date : 2021-01-15 DOI: 10.1080/10986065.2020.1858245

J. Sarama, D. Clements, Jeffrey E. Barrett, C. Cullen, A. Hudyma, Y. Vanegas

{"title":"Length measurement in the early years: teaching and learning with learning trajectories","authors":"J. Sarama, D. Clements, Jeffrey E. Barrett, C. Cullen, A. Hudyma, Y. Vanegas","doi":"10.1080/10986065.2020.1858245","DOIUrl":"https://doi.org/10.1080/10986065.2020.1858245","url":null,"abstract":"ABSTRACT Measurement is a critical component of mathematics education, but research on the learning and teaching of measurement is limited. We previously introduced, refined, and validated a developmental progression – the cognitive core of a learning trajectory – for length measurement in the early years. A complete learning trajectory includes instructional activities and pedagogical strategies, correlated with each level of the developmental progression. This study evaluated a portion of our learning trajectory, focusing on the instructional component. We found that the instruction was successful in promoting a progression from one level to the next for 40% of the children, with others developing positive new behaviors (but not sufficient to progress to a new level). We identified specific characteristics of the interventions’ tasks and teacher–child interactions that engendered learning. The use of standard or multiple nonstandard units may play different roles at different points in the learning trajectory.","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":"24 1","pages":"267 - 290"},"PeriodicalIF":1.6,"publicationDate":"2021-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/10986065.2020.1858245","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49342893","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 10

Exploring undergraduate engineering students’ mathematical problem-posing: the case of integral-area relationships in integral calculus 探讨工科本科生的数学问题:以积分学中的积分-面积关系为例

IF 1.6 4区教育学

Mathematical Thinking and Learning Pub Date : 2021-01-03 DOI: 10.1080/10986065.2020.1858516

Mahboubeh Nedaei, Farzad Radmehr, Michael Drake

{"title":"Exploring undergraduate engineering students’ mathematical problem-posing: the case of integral-area relationships in integral calculus","authors":"Mahboubeh Nedaei, Farzad Radmehr, Michael Drake","doi":"10.1080/10986065.2020.1858516","DOIUrl":"https://doi.org/10.1080/10986065.2020.1858516","url":null,"abstract":"ABSTRACT Previous studies have suggested that problem-posing activities could be used to improve the teaching, learning, and assessment of mathematics. The purpose of this study is to explore undergraduate engineering students’ problem posing in relation to the integral-area relationship. The goal is to help fill a gap in tertiary level research about students’ mathematical problem posing, particularly of engineering students. The mathematical problem posing of 135 undergraduate engineering students was explored using four problem-posing tasks and semi-structured interviews. The findings indicate that many of the problems the students posed were solvable and in a pure mathematics context, while those problems students attempted to set in a real-world setting did not provide a realistic situation. In addition, students faced a number of difficulties when posing problems related to the integral-area relationship and mathematics in general, and several students had a limited understanding of the applications and uses of the integral-area relationship in the real-world. This study suggests that using problem-posing activities in teaching and assessment can help identify engineering students’ mathematical understanding and misunderstanding. Furthermore, using problem-posing tasks can help developing engineering students’ understanding of the applications of integral calculus. More broadly, the findings suggest that problem-posing tasks could be used more often, alongside problem-solving tasks, as part of the teaching and assessment of mathematics at the university level.","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":"24 1","pages":"149 - 175"},"PeriodicalIF":1.6,"publicationDate":"2021-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/10986065.2020.1858516","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45188935","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 9

Gestures, embodiment, and learning the rate of change 手势、体现和学习变化率

IF 1.6 4区教育学

Mathematical Thinking and Learning Pub Date : 2020-12-17 DOI: 10.1080/10986065.2020.1864574

Yanning Yu, D. Uttal

{"title":"Gestures, embodiment, and learning the rate of change","authors":"Yanning Yu, D. Uttal","doi":"10.1080/10986065.2020.1864574","DOIUrl":"https://doi.org/10.1080/10986065.2020.1864574","url":null,"abstract":"ABSTRACT Many researchers have stressed the embodied nature of mathematical understanding. Here we explore how embodied knowledge may evolve as students learn a basic calculus concept: the rate of change. We examined undergraduate students with different levels of calculus knowledge working in pairs to model the rate of change in an everyday phenomenon. Our findings revealed substantial differences between advanced and introductory students in how they represented rate of change with their speech and gestures. In particular, the advanced students’ embodied representations showed alignment with the formal symbolic process of integration and reflected more advanced ways to coordinate the relation between multiple changing variables. For example, advanced students often made gestures that represented a “disk” when explaining how the rate at which water rose in a bottle was related to the change in height. Thus, both introductory and advanced students demonstrated embodied knowledge through speech and gestures, but the advanced students constructed different concrete representations that reflected an advancement in their embodied knowledge. Our findings are relevant to calculus education and to the study of gestures in mathematics learning.","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":"24 1","pages":"203 - 229"},"PeriodicalIF":1.6,"publicationDate":"2020-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/10986065.2020.1864574","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49331460","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 1