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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.

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.

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. ©

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.

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.