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  • 1.
    Brehmer, Daniel
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    An analytical tool for separating mathematical problems from exercises in mathematics textbooksManuskript (preprint) (Annet vitenskapelig)
  • 2.
    Brehmer, Daniel
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Problem solving in mathematics textbooks2015Licentiatavhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    The aim of this study is to analyse how mathematical problem solving (MPS) is represented in mathematical textbooks for Swedish upper secondary school. The analysis comprises dominating Swedish textbook series, and relates to uncovering a) the quantity of tasks that are actually mathematical problems (MPs), b) their location in the chapter, c) their difficulty level, and d) their context. Based on an analysis of 5,722 tasks from the area of calculus, it is concluded that the textbooks themselves contain very few tasks that can be defined as MPs, and that those that are MPs are found at the end of a chapter at the most difficult level, and are presented in a pure mathematical context. Implications are discussed.

  • 3.
    Brehmer, Daniel
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
    Support for mathematics teachers’ change: Examining catalysts for teacher learning and role of the teacher in professional development programmes2019Doktoravhandling, med artikler (Annet vitenskapelig)
    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

  • 4.
    Brehmer, Daniel
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Tasks in mathematics textbooks: teaching intentions and separating problem-solving tasks from exercisesManuskript (preprint) (Annet vitenskapelig)
    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.

  • 5.
    Brehmer, Daniel
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Ryve, Andreas
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Catalysts for mathematics teachers’ learning from professional development programmes: a review of 64 journal articles in mathematics educationManuskript (preprint) (Annet vitenskapelig)
    Abstract [en]

    In their review, Goldsmith, Doerr and Lewis (2014) note that research on professional development programmes (PDPs) for mathematics teachers mostly concerns whether a programme has affected the teachers’ practice or student learning, while the teachers’ learning is treated as a black box. In light of this, they call for a ‘… shared body of knowledge about the nature of teachers’ learning and the catalysts that support it’ (p. 25). In this article, we examine and map 64 articles from mathematics education journals with respect to prerequisites for learning. From this mapping, we identify and describe catalysts for teacher learning from PDPs for mathematics teachers. These learning catalysts are then used to characterize two different types PDPs, based on which learning catalysts are used in them. Typical of PDPs targeting increased teacher knowledge is that they: emphasize knowledge of content and teaching and knowledge of content and students; manage this content through cooperation; and promote insight and/or body of knowledge as catalysts for learning. Typical of PDPs targeting changed instruction is that they: emphasize knowledge of content and teaching as well as following strategies by doing/experimenting when establishing it in the classroom as a catalyst for learning. Conclusions and implications are discussed.

  • 6.
    Brehmer, Daniel
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Ryve, Andreas
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Towards an organizing frame for mapping teachers' learning in professional development2018Inngår i: Nordic Research in Mathematics Education: Papers of NORMA17 / [ed] Eva Norén, Hanna Palmér, Audrey Cooke, Göteborg, 2018, s. 229-237Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In their claim that teachers’ learning is treated as a “black box” in research on

    professional development programs for mathematics teachers, Goldsmith, Doerr,

    & Lewis (2014) call for “an organizing framework that clearly distinguishes

    dimensions of teachers’ learning and identifies catalysts of teachers’ learning…”

    (p. 23). The aim of this study is to present initial efforts to construct a framework

    for categorizing descriptions of activities designed to support teachers’ learning

    as presented in research articles within mathematics education. Based on existing

    literature on professional development and examination of research articles, an

    organizing frame is constructed.

  • 7.
    Brehmer, Daniel
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Ryve, Andreas
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Van Steenbrugge, Hendrik
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Problem solving in Swedish mathematics textbooks for upper secondary school2016Inngår i: Scandinavian Journal of Educational Research, ISSN 0031-3831, E-ISSN 1470-1170, Vol. 60, nr 6, s. 577-593Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The aim of this study is to analyse how mathematical problem solving is represented in mathematical textbooks for Swedish upper secondary school. The analysis comprises dominating Swedish textbook series, and relates to uncovering (a) the quantity of tasks that are actually mathematical problems, (b) their location in the chapter, (c) their difficulty level, and (d) their context. Based on an analysis of 5,722 tasks from the area of calculus, it is concluded that the textbooks themselves contain very few tasks that can be defined as mathematical problems, and that those that are mathematical problems are found at the end of a chapter at the most difficult level, and are presented in a pure mathematical context. Implications are discussed.

  • 8.
    Insulander, E.
    et al.
    Stockholm University,.
    Brehmer, Daniel
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Ryve, Andreas
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Østfold University College, Norway.
    Teacher agency in professional development programmes – A case study of professional development material and collegial discussion2019Inngår i: Learning, Culture and Social Interaction, ISSN 2210-6561, E-ISSN 2210-657X, Vol. 23, artikkel-id 100330Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This article offers insight into teacher agency in professional development programmes, focusing on a national policy initiative in Sweden aiming to provide in-depth professional development for mathematics teachers. Data was produced from video observations from two collegial discussions with one group of teachers, during the professional development programme. We closely analyse forms of agency in the collegial discussions in relation to the affordances of the professional development materials. The analysis shows a complex relationship between possibilities for independent judgement as constructed in curriculum materials, teachers' agency, and the coach's role in collegial discussions. Contrary to previous research, the findings indicate that opportunities for facilitating enactment in professional development materials do not necessarily lead to teacher agency. The results of the study are discussed in relation to the Swedish educational context. ©

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