ABSTRACT

Creative thinking and problem solving are higher-order epistemological activities of humans, which play also a major role as educational objectives in our schooling system. We consider thinking and problem solving as creative if they go beyond the reproductive application of previously learned routines. International assessment studies in learning mathematics and science education such as TIMSS or PISA have emphasised the relevance of flexible thinking and problem solving for education and for living in a complex society. We consider flexibility in thinking and problem solving as the amount of different views and approaches an individual can create to solve a task or a problem. Although the relevance of flexibility in thinking and problem solving is widely acknowledged, not very much is known yet about the nature of this flexibility and how it may be improved. We will analyse in this chapter the role of representations in flexible thinking and problem solving. More specifically, we will investigate how the construction, manipulation and usage of different forms of external and internal (i.e., mental) representations, and the interaction of these representations, can contribute to these higher-order cognitive processes. First, we will describe different views on creative thinking and problem solv-

ing in psychology. Second, we will analyse more deeply two basic kinds of representations, which we will call descriptive and depictive representations. Third, we will investigate the functionality of these different kinds of representations in terms of their representational and inferential attributes. Fourth, we will focus on the interplay between external representations and internal (mental) representations in thinking and problem solving and we will differentiate between different kinds of mental representations. Fifth, we will analyse the role of different representations in thinking and problem solving, with examples from science education and mathematics. Finally, we will draw some conclusions for the process of teaching in order to foster creative thinking and problem solving.