Pehkonen: Problem solving (11.9.07) 1/5 WG2, Topic #8: Different conceptions of the mathematical knowledge needed for teaching and how it can be acquired, and its relation to pedagogical knowledge

The main content of the paper is to describe problem solving in Finnish school mathematics, since this is the picture of mathematics teaching that is convoyed to teacher students at universities. The description begins with considering Finnish mathematics curricula with the focus on the role of problem solving. Furthermore, different manifestations of problem solving in mathematics textbooks are discussed as well as how Finnish teachers implement problem solving in mathematics lessons. Additionally the way teachers use problem solving in assessment is discussed briefly. At the end of the paper, a new solution for teaching problem solving within the curriculum is dealt with. Such a reform is based on the use of problem solving as a teaching method that often is manifested by the use of open problems. The purpose of school education in each country is, more or less, to develop independent, self-confident, critically thinking, motivated and multitalented individuals who will manage in different societal settings that they will encounter later on in their life. The key question is what kind of school instruction is optimal for this goal. Problem solving in Finnish school mathematic