The Philosophy of Mathematical Education Between Platonism and the Computer

Mathematics causes some specific epistemological and educational difficulties. On the one hand, it must accept the merely representational character of all knowledge. On the other hand, mathematical knowledge claims a special truth status, compared to other knowledge. The difference between a symbol and a thing is that symbols have meaning and that meaning is always something personal and thus subjectively biased. To counteract this fact, logic and mathematics have tried to formalize sense or meaning, reducing it to formal syntax, to sets of rules and recipes. Hence result specific educational difficulties. For example, difficulties to stimulate creativity and encourage insight.