Constructive Aspects of Reflective Abstraction in Advanced Mathematics

Abstract

The notion of reflective abstraction was introduced by Piaget and, over a period of many years in a number of works, he expanded and elaborated this concept. He considered it to be the driving force of the (re-)constructions involved in the passage through the stages of sensori-motor actions, semiotic representations, concrete operations, and formal operations (Beth & Piaget, 1966, p. 245). But he also felt that reflective abstraction was critical for the development of more advanced concepts in mathematics. In his viewpoint, new mathematical constructions proceed by reflective abstraction (Beth & Piaget, p. 205). Indeed, it was for him the mechanism by which all logicomathematical structures are constructed (Piaget, 1971, p. 342), and he felt that “it alone supports and animates the immense edifice of logicomathematical construction” (Piaget, 1980a, p. 92).