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Tasks in mathematics textbooks: teaching intentions and separating problem-solving tasks from exercises
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.ORCID iD: 0000-0001-5259-2712
(English)Manuscript (preprint) (Other academic)
Abstract [en]

In this article, an analytical tool for distinguishing between exercises and mathematical problems in textbooks is presented and elaborated on. This elaboration then lays the foundation for a discussion of plausible teaching intentions of different types of tasks in the textbook. The discussion is based on a task’s feasible teaching function according to its placement, context, and level of difficulty. Five examples of tasks are discussed, and eight plausible teaching intentions based on these examples are described. From the discussion, it is concluded that the compilation of teaching intentions together constitutes an overarching teaching intention. This overarching intention conveys a picture of learning mathematics by solving exercising tasks (following solved examples) as a means to be able to solve (future) mathematical problem tasks – learning mathematics for, rather than through, problem solving. Implications are discussed.

National Category
Didactics
Identifiers
URN: urn:nbn:se:mdh:diva-45359OAI: oai:DiVA.org:mdh-45359DiVA, id: diva2:1356932
Available from: 2019-10-02 Created: 2019-10-02 Last updated: 2019-10-11Bibliographically approved
In thesis
1. Support for mathematics teachers’ change: Examining catalysts for teacher learning and role of the teacher in professional development programmes
Open this publication in new window or tab >>Support for mathematics teachers’ change: Examining catalysts for teacher learning and role of the teacher in professional development programmes
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

When the perception changes regarding what mathematics students should be able to manage, this is typically addressed through a new national curriculum. To establish and implement this new curriculum in practice, teachers must be given the opportunity to change according to it. For such change, they need support in interpreting and implementing the new curriculum. Typically, there are two common ways to support teacher change: (1) developing and launching curriculum materials that correspond to the national curriculum; and (2) implementing professional development programmes (PDPs) that correspond to the new national curriculum. This thesis includes both aspects and aims to contribute to research on support for mathematics teachers’ change. This aim is operationalized by: (1) studying mathematics textbooks in which tasks and plausible teaching intentions are analysed; (2) studying teacher agency in collegial discussions in relation to the design of a PDP; and (3) mapping and describing catalysts for teacher learning from PDPs in research literature. These studies resulted in five papers, which are included in this thesis. The main results of the papers cover: the distribution of types of tasks in Swedish mathematics textbooks; the type of learning approach advocated in these textbooks; how different types of texts in PDPs relate to teacher agency in collegial discussions; and an identification and description of catalysts for teacher learning from PDPs for mathematics teachers. In the kappa1 of this thesis, these results are merged and discussed in relation to different models of teacher change. The focus in the kappa is on examining catalysts for teacher learning from such initiatives and the role of the teacher in PDPs. This examination suggests elaborations on parts of a conceptual framework for effective PDPs (Desimone, 2009). More precisely, the elaborations concern core critical features for effective PDPs, presented in this framework: Content Focus, Active Learning, Collective Participation, Duration, and Coherence. The main contributions of this thesis concern: a tool for analysing tasks in textbooks with respect to problem-solving tasks; an organizing frame for mapping learning catalysts from articles describing PDPs; a description of catalysts for teacher learning from PDPs as specifications of core critical features for effective PDPs; and the role of the teacher in PDPs as a catalyst for learning. Implications and suggestions for future research are discussed.

___________________________

1The Swedish term kappa will be used in this thesis in the absence of an equivalent English term for the introductory chapters of an aggregation dissertation

Place, publisher, year, edition, pages
Västerås: Mälardalen University, 2019
Series
Mälardalen University Press Dissertations, ISSN 1651-4238 ; 298
National Category
Didactics
Research subject
Didactics
Identifiers
urn:nbn:se:mdh:diva-45360 (URN)978-91-7485-442-8 (ISBN)
Public defence
2019-11-13, Kappa, Mälardalens högskola, Västerås, 13:15 (Swedish)
Opponent
Supervisors
Available from: 2019-10-04 Created: 2019-10-02 Last updated: 2019-10-14Bibliographically approved
2.
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Brehmer, Daniel

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