Intuitionist theory of mathematics education

Abstract

The development of constructivism as an important theory of mathematics education makes it appropriate to scrutinize the theory from both the conceptual and the historical points of view. The present work is an attempt to do just that. The conceptual critique is based on constructivism's response to the nature of mathematical objects (ontology), the nature of mathematical knowledge (epistemology), and the axiology of the classroom (ethics). The historical roots of constructivism go back as far as ancient skepticism and the theory itself may be classified as a modem form of Neo-Kantian idealism, consciously incorporating an ever more uncompromising empiricism. It is also shown that intuitionism is actually an early form of constructivism. N evertheless, intuitionism , despite being a major -- but implicit - influence in the educational thought of Z. P. Dienes, has not been explicitly developed as a theory about mathematics education. Thus, the foundational positions of intuitionism are examined from the ontological, epistemological, and ethical points of view in order to adduce the outlines of an intuitionist theory of mathematics education. Finally, the insights gained from the intuitionist theory are used in order to respond to certain criticisms of constructivism, as well as to suggest new directions for its development.