Didactical Phenomenology of Mathematical Structures

Abstract

Didactical phenomenology has played an important part in Freudenthal's earlier work. In this book, which also explores the theory and practice of mathematics education, he goes on to stress one feature more explicitly: mental objects versus concept attainment. Thus the didactical scope of mental objects and activities and the onset of conscious conceptualization, if didactically possible, is the main theme of this phenomenology. Mathematical ideas are a means of organizing phenomena of the physical, social and mental worlds. The phenomenology of a mathematical idea is its description in relation to the phenomena of which it was created, and to which it has been extended in the learning processes of children, it becomes didactical phenomenology. Concept attainment is preceded by grasping mathematical ideas as mental objects. This stage, often neglected in mathematics education, is given in this work the badly needed attention it deserves