Abstract

Mathematical theories ¹ and the theoretical aspects of mathematics ² represent a challenge for mathematics educators all over the world. Neither abandoning them in favour of curricula designed to work with the average student, nor insisting on the traditional methods for teaching of them are good solutions. Indeed, the former represents negligence of on the part of the school in passing scientific culture to new generations; the latter is hardly productive and impossible in today’s school systems. This represents an interesting and important area of investigation to mathematics education research, but on what theoretical aspects of mathematics should the effort be concentrated? Why must they be implemented in curricula? How can we ensure reasonable success with them in classroom activities?