FORMALISM AND INTUITION IN MATHEMATICS: THE ROLE OF THE PROBLEM

A main characteristic of the intuitive – inductive philosophy of mathematics is the attention given to the problem – solving processes, in contrast to the formalistic – productive philosophy where emphasis is given to the content. Therefore a crucial question is what is actually the role that problem plays for the learning of mathematics. The aim of the present paper is to give an answer to the above question. For this a review of the evolution of the problem – solving process in mathematical education is attempted – from the time that Polya presented his first ideas on the subject until today- in contrast to other existing views giving emphasis to other factors of the learning process like the acquisition of the proper schemas, the automation of rules, etc and our personal conclusions and beliefs are stated