Froebel and Montessori are compared in their approaches for teaching preschool children the concept of number, numerical calculation, vulgar fraction and geometrical concepts. Froebel`s approach is largely metaphysical whereas Montessori`s is largely sensorial. But their approaches are not diametrically opposed to each other but rather complementary to each other from the educational view point. Their different claims or views should be closely studied and objectively evaluated through various experiments, before any of them are seriously incorporated in our educational practices.