ABSTRACT
Although it is often neeessary to start off by giving definitions of some of the terms that will be used in a ehapter, this is not an easy matter. Most theoretieal definitions of terms such as knowledge, social interaction, and learning are based on epistemological presuppositions, and the title of this chapter is no exception. Thus, trying to make my presuppositions clear, I first describe the constructivist (mainly Piagetian) conception of knowledge. In a second part, I discuss personal (and then wider societal) interaction within the constructivist framework, and in the last part I reflect on the learning of mathematics in very young children from the constructivist, interactive perspective. My remarks on this point are necessarily both personal and psychological (because I am not a teacher), as well as sketchy. As Steffe remarked, though learning is at the heart of our business in mathematics education, few attempts have been made to study learning, primarily because it is so very difficult. The difficulty of studying learning—and teaching—lies, in my view, in the fact that it demands the study of the processes by which children come to know in a short time basic principles (in mathematics, but also in other scientific disciplines) that took humanity thousands of years to construct. This view of learning constitutes the main leitmotiv of this chapter.
