SOLVING PROBLEMS IN DIFFERENT WAYS: TEACHERS' KNOWLEDGE SITUATED IN PRACTICE

This study is part of a larger longitudinal research concerned with teachers' knowledge development in the context of connecting tasks. We find this study important in the view of the existing gap between practice and theory of employing connecting tasks in school mathematics. In this paper we focus on the development of teachers ' problem-solving performance as a result of systematic learning and their teaching practice associated with connecting tasks. This study is aimed to deepen our understanding of the role of both systematic (though learning) and craft (through teaching) teachers ' knowledge development. We argue for the necessity of combining systematic and craft modes of development in teacher education. THEORETICAL BACKGROUND Connecting tasks: The gap between theory and practice In this study a task is called a “multiple-solution connecting task ” (connecting task for short) when it can be solved in different ways using: (a) different definitions or representations of a mathematical concept; (b) hierarchy, which is expressed in seeing an idea as a special case of a more general idea; (c) different mathematic