Abstract
In the Netherlands, mathematics textbooks are a decisive influence on the enacted curriculum. About a decade ago, Dutch primary school mathematics textbooks provided hardly any opportunities to learn problem solving. In this study we investigated whether this provision has changed. In order to do so, we carried out a textbook analysis in which we established to what degree current textbooks provide non-routine problem-solving tasks for which students do not immediately have a particular solution strategy at their disposal. We also analyzed to what degree textbooks provide ‘gray-area’ tasks, which are not really non-routine problems, but are also not straightforwardly solvable. In addition, we inventoried other ways in which present textbooks facilitate the opportunity to learn problem solving. Finally, we researched how inclusive these textbooks are with respect to offering opportunities to learn problem solving for students with varying mathematical abilities. The results of our study show that the opportunities that the currently most widely used Dutch textbooks offer to learn problem solving are very limited, and these opportunities are mainly offered in materials meant for more able students. In this regard, Dutch mainstream textbooks have not changed compared to the situation a decade ago. A textbook that is the Dutch edition of a Singapore mathematics textbook stands out in offering the highest number of problem-solving tasks, and in offering these in the materials meant for all students. However, in the ways this textbook facilitates the opportunity to learn problem solving, sometimes a tension occurs concerning the creative character of genuine problem solving.
Highlights
Mathematics is inextricably linked with problem solving
In order to find out whether these present mathematics textbooks have changed with respect to the opportunity to learn problem solving, we carried out a replication study, in which we investigated to what degree current mathematics textbooks offer non-routine problems
The importance of problem solving together with the finding from a decade ago that Dutch primary school mathematics textbooks hardly included problem-solving tasks at that time, led us to investigate the opportunity to learn problem solving provided by current Dutch textbooks
Summary
Mathematics is inextricably linked with problem solving. Problem solving is even considered the heart of mathematics (Halmos 1980; Schoenfeld 1992; Dossey 2017). In the meaning of a mathematical task on which students have to work, the term problem can refer to all types of tasks regardless of their cognitive demands, but it is used for specific kinds of tasks, such as word problems in which previously learned mathematics has to be applied, or puzzle-like tasks which are new to the students and which they themselves have to figure out how to solve. The latter meaning is used in this study. By problems we mean non-routine mathematical tasks for which students do not immediately have a particular solution strategy at their disposal
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