Potential application of fuzzy techniques to math education: Emphasizing paradoxes as a (seemingly paradoxical) way to enhance the learning of (strict) mathematics

Classes are often taught in an authoritarian way, when students do not understand the need to study the material. So, a key to success is for a teacher to make sure that the students understand this need - before explaining the material itself. In mathematics, this need sometimes comes from practice; sometimes, from the fact that common sense treatment of the topics leads to contradictions (paradoxes) and therefore, a more formal treatment is needed. Our experience shows that explaining paradoxes like the irrationality of square root of 2 or paradoxes of set theory indeed enhances learning.