Abstract
The article begins with a brief overview of the situation throughout the world regarding problem solving. The activities of the ProMath group are then described, as the purpose of this international research group is to improve mathematics teaching in school. One mathematics teaching method that seems to be functioning in school is the use of open problems(i.e., problem fields). Next we discuss the objectives of the Finnish curriculum that are connected with problem solving. Some examples and research results are taken from a Finnish–Chilean research project that monitors the development of problem-solving skills in third grade pupils. Finally, some ideas on “teacher change” are put forward. It is not possible to change teachers, but only to provide hints for possible change routes: the teachers themselves should work out the ideas and their implementation.
Highlights
The Finnish curriculum demands that, in addition to calculation skills, problem solving and mathematical thinking should be taught in school (NBE, 2004)
This does not seem to occur within ordinary mathematics teaching, where the teacher is too eager to use the textbook and its tasks
New elements should be connected in instruction: open problem tasks with which the teacher can develop the pupils’ problem solving and thinking skills
Summary
The article begins with a brief overview of the situation throughout the world regarding problem solving. In the last ten years, a number of overview papers have been published in which the situation of problem solving has been described in several countries. When the constructivist view of learning was accepted in mathematics education about 30 years ago, there was a need to develop teaching methods that corresponded to the challenges set by constructivism. One such solution was the open approach (or the use of open problems) in Japan. Some ten years ago, Pehkonen (2004) wrote an overview on the situation of open problem solving. Zimmermann (2010) described the development of open problem solving over the previous 20 years in Germany, while ProMath meetings have produced research results on the use of open problems for approximately 15 years (e.g., Bergqvist, 2012)
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