Development of Symbolic Functions as the Basis for Learning of Mathematics at School: Continuation of the Dialogue Between Piaget and Vygotsky

This chapter compares the approaches of Vygotsky and Piaget in relation to the development of the symbolic function for learning mathematics. In the historical–cultural approach proposed by Vygotsky, the topic of acquisition of symbolic means is one of the central aspects of development in infancy. The use of symbolic means should become reflexive at the end of preschool age, as one of the indicators of readiness for school. The chapter considers the concept of orientation and gradual formation of symbolic functions on different levels as the principal differences between these approaches. The chapter analyzes the levels of formation of symbolic function as the level materialized actions, perceptive actions, and verbal actions with external mediatization and with the orientation of the adult. The analysis is provided on the basis of consideration of the practice of formation of symbolic function in the reality of child’s development. The chapter concludes that for Vygotsky’s followers, this concept became the key position for the whole development, including mathematical thinking.