ABSTRACT
This chapter explores the idea of mediated action in the context of mathematical problem solving and its implications for our understanding of the development of mathematical concepts in educational settings. The chapter discusses different studies which highlight how systems of signs affect pupils' problem-solving activity. It suggests some of the educational implications of this theory and further steps in the investigation of the way systems of signs affect mathematical reasoning and learning in school. Children can draw on different tools to mediate their problem-solving activity; in other words, the same concept might be represented in different ways. The chapter discusses some evidence for the need to understand mathematical signs in the context of particular mathematical practices. It deals with the process of compressing representations and also deals with the question of partial versus complete representation. The chapter explores variations in children's performance that relate to the issue of compressed representations in different types of problem.
