Pub Date : 2022-03-26DOI: 10.1080/10986065.2022.2058160
L. Sumpter, A. Löwenhielm
{"title":"Differences in grade 7 students’ understanding of the equal sign","authors":"L. Sumpter, A. Löwenhielm","doi":"10.1080/10986065.2022.2058160","DOIUrl":"https://doi.org/10.1080/10986065.2022.2058160","url":null,"abstract":"","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2022-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42311444","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 : 2022-03-25DOI: 10.1080/10986065.2022.2056676
Michael N. Fried
The word “modeling” is key (in developing mathematical concepts in the contexts in which they are actually used). Real problems do not come at the end of chapters. Real problems do not look like mathematical problems. Real problems are messy. Real problems ask questions such as: How do we create computer animation? How do we effectively control an animal population? What is the best location of a fire station? What do we mean by “best”? (From Solomon Garfunkel’s introduction to Mathematics Modeling Our World (COMAP, 1998) as cited in Niss and Blum, pp. 184–5).
{"title":"Models and Modelling: The Fine Balance between Mathematics, Practice, and Research","authors":"Michael N. Fried","doi":"10.1080/10986065.2022.2056676","DOIUrl":"https://doi.org/10.1080/10986065.2022.2056676","url":null,"abstract":"The word “modeling” is key (in developing mathematical concepts in the contexts in which they are actually used). Real problems do not come at the end of chapters. Real problems do not look like mathematical problems. Real problems are messy. Real problems ask questions such as: How do we create computer animation? How do we effectively control an animal population? What is the best location of a fire station? What do we mean by “best”? (From Solomon Garfunkel’s introduction to Mathematics Modeling Our World (COMAP, 1998) as cited in Niss and Blum, pp. 184–5).","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2022-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46683677","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 : 2022-02-16DOI: 10.1080/10986065.2022.2037043
Charles Hohensee, Laura Willoughby, S. Gartland
{"title":"Backward transfer, the relationship between new learning and prior ways of reasoning, and action versus process views of linear functions","authors":"Charles Hohensee, Laura Willoughby, S. Gartland","doi":"10.1080/10986065.2022.2037043","DOIUrl":"https://doi.org/10.1080/10986065.2022.2037043","url":null,"abstract":"","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2022-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48619788","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 : 2022-01-20DOI: 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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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}
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