Pub Date : 2022-01-20DOI: 10.1080/10986065.2022.2028225
Erin E. Turner, A. Bennett, Monica Granillo, Nishaan Ponnuru, Amy Roth Mcduffie, Mary Q. Foote, J. Aguirre, Elzena McVicar
{"title":"Authenticity of elementary teacher designed and implemented mathematical modeling tasks","authors":"Erin E. Turner, A. Bennett, Monica Granillo, Nishaan Ponnuru, Amy Roth Mcduffie, Mary Q. Foote, J. Aguirre, Elzena McVicar","doi":"10.1080/10986065.2022.2028225","DOIUrl":"https://doi.org/10.1080/10986065.2022.2028225","url":null,"abstract":"","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47937413","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}
Pub Date : 2022-01-10DOI: 10.1080/10986065.2022.2025639
Sheunghyun Yeo, Corey Webel
{"title":"Elementary students’ fraction reasoning: a measurement approach to fractions in a dynamic environment","authors":"Sheunghyun Yeo, Corey Webel","doi":"10.1080/10986065.2022.2025639","DOIUrl":"https://doi.org/10.1080/10986065.2022.2025639","url":null,"abstract":"","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44896540","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}
Pub Date : 2022-01-06DOI: 10.1080/10986065.2021.2016029
Jenni Ingram
ABSTRACT
Understanding randomness is essential for modern life, as it underpins decisions under uncertainty. It is also an essential part of both the mathematics and science curricula in schools. Yet, research has shown that many people consider randomness difficult to perceive and argue about, with a number of different and contradictory views on the nature of randomness prevailing. This study explores beginning mathematics and science teachers’ understanding of randomness. A questionnaire was used with student teachers in an initial teacher-education course to explore their understanding of and reasoning about randomness and random events. Results suggest that mathematics and science student teachers conceptualize and argue about randomness in a variety of ways. Furthermore, these different conceptualizations affect how they respond to both common classroom tasks and everyday contexts involving randomness. This raises important implications for the education of teachers who will themselves be teaching probability and statistical inference.
{"title":"Randomness and probability: exploring student teachers’ conceptions","authors":"Jenni Ingram","doi":"10.1080/10986065.2021.2016029","DOIUrl":"https://doi.org/10.1080/10986065.2021.2016029","url":null,"abstract":"<p><b>ABSTRACT</b></p><p>Understanding randomness is essential for modern life, as it underpins decisions under uncertainty. It is also an essential part of both the mathematics and science curricula in schools. Yet, research has shown that many people consider randomness difficult to perceive and argue about, with a number of different and contradictory views on the nature of randomness prevailing. This study explores beginning mathematics and science teachers’ understanding of randomness. A questionnaire was used with student teachers in an initial teacher-education course to explore their understanding of and reasoning about randomness and random events. Results suggest that mathematics and science student teachers conceptualize and argue about randomness in a variety of ways. Furthermore, these different conceptualizations affect how they respond to both common classroom tasks and everyday contexts involving randomness. This raises important implications for the education of teachers who will themselves be teaching probability and statistical inference.</p>","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":"19 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138516039","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}
Pub Date : 2022-01-01DOI: 10.1007/978-3-031-04075-7
{"title":"Thinking: Bioengineering of Science and Art","authors":"","doi":"10.1007/978-3-031-04075-7","DOIUrl":"https://doi.org/10.1007/978-3-031-04075-7","url":null,"abstract":"","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":"15 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81683344","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}
Pub Date : 2021-12-31DOI: 10.1080/10986065.2021.1993035
T. Rowland
{"title":"Care in mathematics education: alternative educational spaces and practices","authors":"T. Rowland","doi":"10.1080/10986065.2021.1993035","DOIUrl":"https://doi.org/10.1080/10986065.2021.1993035","url":null,"abstract":"","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":"1 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43143998","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}
Pub Date : 2021-12-28DOI: 10.1080/10986065.2021.2013144
G. Stillman, Jill P. Brown
ABSTRACT This paper investigates students’ mathematical modeling activity in data-rich modeling tasks. It aims at gaining insight into how students develop meaning when modeling data-rich situations and the mathematical models produced. A tendency to model a particular dataset, rather than the phenomenon that the dataset is a particular instance of, has been observed previously. Students concentrate on fitting mathematical objects such as functions to data, rather than using domain knowledge about the situation being modeled, mapping this to the data so as to capture the phenomenon as a whole. In other instances, students find functions that simply linearly interpolate the data and do not consider key features of the phenomenon, particularly when they have access to technological tools. The extent to which students’ reasoning indicated awareness of their taking either approach was investigated in a qualitative study with Year 10/11 students. How the approach taken affected the processes students engage in whilst modeling was also investigated. The paper contributes to our currently limited literature on research into this issue and how it affects the outcome of students learning to model in classrooms at this level of schooling.
{"title":"Modeling the phenomenon versus modeling the data set","authors":"G. Stillman, Jill P. Brown","doi":"10.1080/10986065.2021.2013144","DOIUrl":"https://doi.org/10.1080/10986065.2021.2013144","url":null,"abstract":"ABSTRACT This paper investigates students’ mathematical modeling activity in data-rich modeling tasks. It aims at gaining insight into how students develop meaning when modeling data-rich situations and the mathematical models produced. A tendency to model a particular dataset, rather than the phenomenon that the dataset is a particular instance of, has been observed previously. Students concentrate on fitting mathematical objects such as functions to data, rather than using domain knowledge about the situation being modeled, mapping this to the data so as to capture the phenomenon as a whole. In other instances, students find functions that simply linearly interpolate the data and do not consider key features of the phenomenon, particularly when they have access to technological tools. The extent to which students’ reasoning indicated awareness of their taking either approach was investigated in a qualitative study with Year 10/11 students. How the approach taken affected the processes students engage in whilst modeling was also investigated. The paper contributes to our currently limited literature on research into this issue and how it affects the outcome of students learning to model in classrooms at this level of schooling.","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":"25 1","pages":"270 - 295"},"PeriodicalIF":1.6,"publicationDate":"2021-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45062098","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}
Pub Date : 2021-12-28DOI: 10.1080/10986065.2021.2012741
Johanna Rellensmann, S. Schukajlow, Judith Blomberg, Claudia Leopold
ABSTRACT We investigated how students’ strategic knowledge about situational (pictorial) drawings and mathematical (schematic) drawings affects drawing accuracy and modeling competencies in the domain of geometry. We conducted a pre-posttest experimental study with 473 students in grade 9. Students were randomly assigned to one of three treatment conditions in which we used a 90-minute intervention to promote strategic knowledge about situational drawing (EG1), strategic knowledge about mathematical drawing (EG2), or strategic knowledge about situational and mathematical drawing (EG3). We also used a control group in which we did not promote any knowledge about drawing (CG). Results of a multilevel path analysis did not show a total effect of the strategic knowledge treatments on students’ modeling competencies. However, the results indicated an indirect effect: Students who participated in the treatments demonstrated higher modeling competencies than students in the control condition, and strategic knowledge and drawing accuracy were mediating variables. Moreover, students who constructed a more accurate situational or mathematical drawing for a modeling problem were more likely to solve this problem adequately. Our findings indicate that strategic knowledge is a necessary but not sufficient precondition for the construction of high-quality drawings and high modeling competencies in geometry.
{"title":"Does strategic knowledge matter? Effects of strategic knowledge about drawing on students’ modeling competencies in the domain of geometry","authors":"Johanna Rellensmann, S. Schukajlow, Judith Blomberg, Claudia Leopold","doi":"10.1080/10986065.2021.2012741","DOIUrl":"https://doi.org/10.1080/10986065.2021.2012741","url":null,"abstract":"ABSTRACT We investigated how students’ strategic knowledge about situational (pictorial) drawings and mathematical (schematic) drawings affects drawing accuracy and modeling competencies in the domain of geometry. We conducted a pre-posttest experimental study with 473 students in grade 9. Students were randomly assigned to one of three treatment conditions in which we used a 90-minute intervention to promote strategic knowledge about situational drawing (EG1), strategic knowledge about mathematical drawing (EG2), or strategic knowledge about situational and mathematical drawing (EG3). We also used a control group in which we did not promote any knowledge about drawing (CG). Results of a multilevel path analysis did not show a total effect of the strategic knowledge treatments on students’ modeling competencies. However, the results indicated an indirect effect: Students who participated in the treatments demonstrated higher modeling competencies than students in the control condition, and strategic knowledge and drawing accuracy were mediating variables. Moreover, students who constructed a more accurate situational or mathematical drawing for a modeling problem were more likely to solve this problem adequately. Our findings indicate that strategic knowledge is a necessary but not sufficient precondition for the construction of high-quality drawings and high modeling competencies in geometry.","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":"25 1","pages":"296 - 316"},"PeriodicalIF":1.6,"publicationDate":"2021-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45796475","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}
Pub Date : 2021-12-09DOI: 10.1080/10986065.2021.2012740
Katrin Vorhölter
ABSTRACT There are several conceptualizations of modeling competencies, including among others on the one hand so-called sub-competencies, which are required to progress from one step of a modeling process to the next, and metacognitive individual and group strategies. However, the relationship between metacognitive strategies and modeling sub-competencies remains unclear, as does the influence of metacognitive strategies on the development of modeling competencies. The current paper presents the results of a study conducted with 170 students in grades nine and ten. This intervention study concerns the relationships between metacognitive strategies and the development of these strategies and modeling sub-competencies over the course of the study. The results illustrate that metacognitive individual strategies are highly correlated with each other, and metacognitive group strategies are highly correlated with each other, but metacognitive individual strategies are not correlated with metacognitive group strategies. Analysis of the development of metacognitive strategies and modeling sub-competencies within the intervention study reveals that not all of these developed as expected. Additionally, the factors of metacognitive strategies that were measured within the study allow for limited conclusions about the development of students’ modeling sub-competencies. These results have implications for further research.
{"title":"Metacognition in mathematical modeling: the connection between metacognitive individual strategies, metacognitive group strategies and modeling competencies","authors":"Katrin Vorhölter","doi":"10.1080/10986065.2021.2012740","DOIUrl":"https://doi.org/10.1080/10986065.2021.2012740","url":null,"abstract":"ABSTRACT There are several conceptualizations of modeling competencies, including among others on the one hand so-called sub-competencies, which are required to progress from one step of a modeling process to the next, and metacognitive individual and group strategies. However, the relationship between metacognitive strategies and modeling sub-competencies remains unclear, as does the influence of metacognitive strategies on the development of modeling competencies. The current paper presents the results of a study conducted with 170 students in grades nine and ten. This intervention study concerns the relationships between metacognitive strategies and the development of these strategies and modeling sub-competencies over the course of the study. The results illustrate that metacognitive individual strategies are highly correlated with each other, and metacognitive group strategies are highly correlated with each other, but metacognitive individual strategies are not correlated with metacognitive group strategies. Analysis of the development of metacognitive strategies and modeling sub-competencies within the intervention study reveals that not all of these developed as expected. Additionally, the factors of metacognitive strategies that were measured within the study allow for limited conclusions about the development of students’ modeling sub-competencies. These results have implications for further research.","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":"25 1","pages":"317 - 334"},"PeriodicalIF":1.6,"publicationDate":"2021-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44580757","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}
Pub Date : 2021-12-08DOI: 10.1080/10986065.2021.2012736
Ana Margarida Baioa, S. Carreira
ABSTRACT The aim of this study is to understand how students’ mathematical thinking is activated and nurtured in solving a modeling problem, where the problem situation involves the design of a system. From a STEM integrated perspective, 9th grade students worked on a modeling task aiming to create an identification system based on hand biometrics. The theoretical framework proposes a conceptualization of the interplay between the mathematical modeling process, from a cognitive perspective, and the engineering design process. Central ideas refer to the cyclical nature of both processes and to the sub-processes involved in them. The empirical data were collected in two design-based research cycles with different 9th grade classes. The data from the groups’ audio and video recording and the students’ productions were analyzed under a directed qualitative content analysis informed by theory. The results showed a global pattern in the students’ thinking in solving a design system problem. The overlapping and interplay between the mathematical modeling and the design process was a prominent characteristic of students’ thinking. The modeling cycle was mirrored by a design cycle, with both running in parallel. System thinking pushed and drove students’ mathematical thinking, from the system requirements to the prototype validation.
{"title":"Mathematical thinking about systems – students modeling a biometrics identity verification system","authors":"Ana Margarida Baioa, S. Carreira","doi":"10.1080/10986065.2021.2012736","DOIUrl":"https://doi.org/10.1080/10986065.2021.2012736","url":null,"abstract":"ABSTRACT The aim of this study is to understand how students’ mathematical thinking is activated and nurtured in solving a modeling problem, where the problem situation involves the design of a system. From a STEM integrated perspective, 9th grade students worked on a modeling task aiming to create an identification system based on hand biometrics. The theoretical framework proposes a conceptualization of the interplay between the mathematical modeling process, from a cognitive perspective, and the engineering design process. Central ideas refer to the cyclical nature of both processes and to the sub-processes involved in them. The empirical data were collected in two design-based research cycles with different 9th grade classes. The data from the groups’ audio and video recording and the students’ productions were analyzed under a directed qualitative content analysis informed by theory. The results showed a global pattern in the students’ thinking in solving a design system problem. The overlapping and interplay between the mathematical modeling and the design process was a prominent characteristic of students’ thinking. The modeling cycle was mirrored by a design cycle, with both running in parallel. System thinking pushed and drove students’ mathematical thinking, from the system requirements to the prototype validation.","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":"7 2","pages":"335 - 360"},"PeriodicalIF":1.6,"publicationDate":"2021-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41264120","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}
Pub Date : 2021-12-04DOI: 10.1080/10986065.2021.2012631
S. Schukajlow, G. Kaiser, G. Stillman
ABSTRACT Mathematical modeling and applications are an important part of curriculum and considered to be important for students’ current and future lives. In this contribution, we focus on mathematical modeling from a cognitive prospective. Following embedding the cognitive perspective within the discourse of mathematical modeling, we describe some of the current thinking on modeling activities and review empirical results. Subsequently, new findings and implications for research offered by the contributions of the current special issue are described. The contributions of this special issue refer to the relation between cognitive and metacognitive modeling activities to (a) mathematical thinking during building a modeling example, (b) strategic knowledge within modeling activities, (c) solving of data-rich modeling problems and their status from a meta-perspective and (d) individual and social metacognition.
{"title":"Modeling from a cognitive perspective: theoretical considerations and empirical contributions","authors":"S. Schukajlow, G. Kaiser, G. Stillman","doi":"10.1080/10986065.2021.2012631","DOIUrl":"https://doi.org/10.1080/10986065.2021.2012631","url":null,"abstract":"ABSTRACT Mathematical modeling and applications are an important part of curriculum and considered to be important for students’ current and future lives. In this contribution, we focus on mathematical modeling from a cognitive prospective. Following embedding the cognitive perspective within the discourse of mathematical modeling, we describe some of the current thinking on modeling activities and review empirical results. Subsequently, new findings and implications for research offered by the contributions of the current special issue are described. The contributions of this special issue refer to the relation between cognitive and metacognitive modeling activities to (a) mathematical thinking during building a modeling example, (b) strategic knowledge within modeling activities, (c) solving of data-rich modeling problems and their status from a meta-perspective and (d) individual and social metacognition.","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":"25 1","pages":"259 - 269"},"PeriodicalIF":1.6,"publicationDate":"2021-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45696921","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}
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