Pub Date : 2023-02-22DOI: 10.1080/10986065.2023.2172617
G. Stylianides, Andreas J. Stylianides
{"title":"Promoting elements of mathematical knowledge for teaching related to the notion of assumptions","authors":"G. Stylianides, Andreas J. Stylianides","doi":"10.1080/10986065.2023.2172617","DOIUrl":"https://doi.org/10.1080/10986065.2023.2172617","url":null,"abstract":"","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44511355","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 : 2023-02-20DOI: 10.1080/10986065.2023.2180849
Hyunyi Jung, C. Brady
{"title":"Modeling Actions Foregrounded in Whole-Class Modeling Discourse: A Case Study of a Model-Eliciting Activity and a Three-Act Task","authors":"Hyunyi Jung, C. Brady","doi":"10.1080/10986065.2023.2180849","DOIUrl":"https://doi.org/10.1080/10986065.2023.2180849","url":null,"abstract":"","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46451826","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 : 2023-02-20DOI: 10.1080/10986065.2023.2177818
J. McMullen, Antti Koskinen, Tomi Kärki, Antero Lindstedt, Saku Määttä, Hilma Halme, E. Lehtinen, M. Hannula-Sormunen, K. Kiili
Adaptive expertise is a highly sought after, but difficult to achieve, outcome of mathematics education. Many teaching methods appear to support the development of adaptive expertise only in a small proportion of students. Game-based learning environments may be useful for supporting adaptive expertise. Therefore, we carried out a quasi-experimental classroom intervention to examine the possibility of using a game-based learning environ- ment to promote adaptive rational number knowledge, a potential indicator of adaptive expertise in the domain of rational numbers. The Number Line Elaboration and Exploration learning environment relied on the increasing elaboration of the number line analogy as a means for students to explore connections between multiple aspects of rational number knowledge. Our results show the game-based learning environment was successful in promoting adaptive rational number knowledge. These results provide directions for the development and examination of how learning environments may be able to support adaptive expertise.
{"title":"A game-based approach to promoting adaptive rational number knowledge","authors":"J. McMullen, Antti Koskinen, Tomi Kärki, Antero Lindstedt, Saku Määttä, Hilma Halme, E. Lehtinen, M. Hannula-Sormunen, K. Kiili","doi":"10.1080/10986065.2023.2177818","DOIUrl":"https://doi.org/10.1080/10986065.2023.2177818","url":null,"abstract":"Adaptive expertise is a highly sought after, but difficult to achieve, outcome of mathematics education. Many teaching methods appear to support the development of adaptive expertise only in a small proportion of students. Game-based learning environments may be useful for supporting adaptive expertise. Therefore, we carried out a quasi-experimental classroom intervention to examine the possibility of using a game-based learning environ- ment to promote adaptive rational number knowledge, a potential indicator of adaptive expertise in the domain of rational numbers. The Number Line Elaboration and Exploration learning environment relied on the increasing elaboration of the number line analogy as a means for students to explore connections between multiple aspects of rational number knowledge. Our results show the game-based learning environment was successful in promoting adaptive rational number knowledge. These results provide directions for the development and examination of how learning environments may be able to support adaptive expertise.","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":"1 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41593142","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 : 2023-01-02DOI: 10.1080/10986065.2022.2161288
Per Nilsson, Andreas Eckert
{"title":"Design principles for simulation-based learning of hypothesis testing in secondary school","authors":"Per Nilsson, Andreas Eckert","doi":"10.1080/10986065.2022.2161288","DOIUrl":"https://doi.org/10.1080/10986065.2022.2161288","url":null,"abstract":"","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46298633","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 : 2022-12-01DOI: 10.1080/10986065.2022.2153970
Lyn D. English
With the commencement of MTL Volume 25, we will see an increased number of articles in each issue. This will enable us to clear some of our backlog as well as feature special issues in their entirety, rather than spread the articles across two issues. The latter occurred with the special issue on New ways of interacting with data, context, and chance in statistical modeling processes. Some of the articles appeared in the last MTL issue (volume 24, issue 4). Unfortunately, we had to omit the following four articles and carry them over to this first issue of Volume 25:
{"title":"Editorial","authors":"Lyn D. English","doi":"10.1080/10986065.2022.2153970","DOIUrl":"https://doi.org/10.1080/10986065.2022.2153970","url":null,"abstract":"With the commencement of MTL Volume 25, we will see an increased number of articles in each issue. This will enable us to clear some of our backlog as well as feature special issues in their entirety, rather than spread the articles across two issues. The latter occurred with the special issue on New ways of interacting with data, context, and chance in statistical modeling processes. Some of the articles appeared in the last MTL issue (volume 24, issue 4). Unfortunately, we had to omit the following four articles and carry them over to this first issue of Volume 25:","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":"25 1","pages":"1 - 1"},"PeriodicalIF":1.6,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47602638","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 : 2022-10-22DOI: 10.1080/10986065.2022.2139101
Martin A. Simon
{"title":"Understanding the nature of arithmetical concepts–important content for the education of primary mathematics teachers","authors":"Martin A. Simon","doi":"10.1080/10986065.2022.2139101","DOIUrl":"https://doi.org/10.1080/10986065.2022.2139101","url":null,"abstract":"","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44572346","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 : 2022-09-28DOI: 10.1080/10986065.2022.2129139
A. Baccaglini-Frank
As suggested by its title, this book takes the reader along paths in the “well-trodden” terrain of the learning and teaching of number, successfully guiding her through some less traveled paths. Right from the start, the authors point out the complexity of such a terrain, but they do so in a graceful and non-threatening way; they assign the reader a first task: “Give an example of number. And another, and another. Give an example of a number that is different from all the previous examples.” (p. 3). The authors then hint at the struggle of agreeing upon a definition of number. From there, they rapidly turn to the comforting and well-known solution in Mathematics of “defining by properties” (p. 4) and to the ways in which numbers are used: as labels, as count, as measure, as location, as multicultural artifact, as action, as abstract mathematical construct. The first chapter closes with a section on operations on numbers. Once the mathematical scene is set, the authors continue to prepare the reader for her journey with a second chapter, “Getting ready to act,” in which the authors act as the reader’s teachers, but also as teacher educators, imagining that she might find herself in the position of teaching students of her own about number. Hence, the authors explain many of the pedagogical moves that they, as educators, are prepared to make as their classes explore the terrain along the paths presented in the subsequent nine snapshots. Indeed, the tasks in each snapshot, as well as the comments and invitations to act between tasks, are built around the aspects introduced in this second chapter: mathematical themes (reversibility, invariance in the midst of change, freedom and constraint, presentation and re-representation), mathematical actions (discerning difference and seeking sameness, stressing and ignoring, specializing and generalizing, imagining and expressing, conjecturing and convincing, organizing and characterizing), actions to initiate and support activity (doing, talking and recording, say what you see, watch what you do, manipulating, “ – getting-a-sense-of – ” articulating, constructing personal narratives and explanations, scaffolding, and fading). Needless to say, they also provide advice on using tasks with learners. Instead of summarizing the content of each snapshot, I will touch on some of them in the following sections, where I highlight what I see as two great strengths of this book: it is a beautiful application of research to practice, and it offers pathways to inclusive approaches to the teaching of number for a broad spectrum of students.
{"title":"The learning and teaching of number. Paths less travelled through well-trodden terrain","authors":"A. Baccaglini-Frank","doi":"10.1080/10986065.2022.2129139","DOIUrl":"https://doi.org/10.1080/10986065.2022.2129139","url":null,"abstract":"As suggested by its title, this book takes the reader along paths in the “well-trodden” terrain of the learning and teaching of number, successfully guiding her through some less traveled paths. Right from the start, the authors point out the complexity of such a terrain, but they do so in a graceful and non-threatening way; they assign the reader a first task: “Give an example of number. And another, and another. Give an example of a number that is different from all the previous examples.” (p. 3). The authors then hint at the struggle of agreeing upon a definition of number. From there, they rapidly turn to the comforting and well-known solution in Mathematics of “defining by properties” (p. 4) and to the ways in which numbers are used: as labels, as count, as measure, as location, as multicultural artifact, as action, as abstract mathematical construct. The first chapter closes with a section on operations on numbers. Once the mathematical scene is set, the authors continue to prepare the reader for her journey with a second chapter, “Getting ready to act,” in which the authors act as the reader’s teachers, but also as teacher educators, imagining that she might find herself in the position of teaching students of her own about number. Hence, the authors explain many of the pedagogical moves that they, as educators, are prepared to make as their classes explore the terrain along the paths presented in the subsequent nine snapshots. Indeed, the tasks in each snapshot, as well as the comments and invitations to act between tasks, are built around the aspects introduced in this second chapter: mathematical themes (reversibility, invariance in the midst of change, freedom and constraint, presentation and re-representation), mathematical actions (discerning difference and seeking sameness, stressing and ignoring, specializing and generalizing, imagining and expressing, conjecturing and convincing, organizing and characterizing), actions to initiate and support activity (doing, talking and recording, say what you see, watch what you do, manipulating, “ – getting-a-sense-of – ” articulating, constructing personal narratives and explanations, scaffolding, and fading). Needless to say, they also provide advice on using tasks with learners. Instead of summarizing the content of each snapshot, I will touch on some of them in the following sections, where I highlight what I see as two great strengths of this book: it is a beautiful application of research to practice, and it offers pathways to inclusive approaches to the teaching of number for a broad spectrum of students.","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":"24 1","pages":"357 - 362"},"PeriodicalIF":1.6,"publicationDate":"2022-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47469100","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 : 2022-09-27DOI: 10.1080/10986065.2022.2128276
Konstantinos P. Christou, Despoina Ioanna Kyrvei, X. Vamvakoussi
{"title":"Interpreting literal symbols in algebra under the effects of the natural number bias","authors":"Konstantinos P. Christou, Despoina Ioanna Kyrvei, X. Vamvakoussi","doi":"10.1080/10986065.2022.2128276","DOIUrl":"https://doi.org/10.1080/10986065.2022.2128276","url":null,"abstract":"","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41912316","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 : 2022-09-06DOI: 10.1080/10986065.2022.2119497
R. Oughton, K. Nichols, David Bolden, Sarah Dixon-Jones, Sam Fearn, Sophia Darwin, Mrita Mistry, N. Peyerimhoff, Adam Townsend
{"title":"Developing ‘deep mathematical thinking’ in geometry with 3- and 4-year-olds: a collaborative study between early years teachers and university-based mathematicians","authors":"R. Oughton, K. Nichols, David Bolden, Sarah Dixon-Jones, Sam Fearn, Sophia Darwin, Mrita Mistry, N. Peyerimhoff, Adam Townsend","doi":"10.1080/10986065.2022.2119497","DOIUrl":"https://doi.org/10.1080/10986065.2022.2119497","url":null,"abstract":"","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44469913","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 : 2022-07-31DOI: 10.1080/10986065.2022.2105567
J. Olsson, C. Granberg
{"title":"Teacher-student interaction supporting students’ creative mathematical reasoning during problem solving using Scratch","authors":"J. Olsson, C. Granberg","doi":"10.1080/10986065.2022.2105567","DOIUrl":"https://doi.org/10.1080/10986065.2022.2105567","url":null,"abstract":"","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43167857","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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