Now we may ask:

Is this kind of pedagogy really possible to realize within the math subject ?

Yes, at least up to a certain degree. Of course, we cannot apply this intuitive, creative comprehension in higher, very abstract maths, this is impossible. But I have made some effort to show that theorems, algebra, analysis, etc., up to the college-level is possible to teach by an alternative, visual way that supports and calls for a direct comprehension with the characteristics of seeing. (You can click on the different mathematical topics in the frame-bar to experience some examples of this!)

What then are the benefits?

The pupils will be truly interested and engaged because all is learned with the fundament of direct and creative comprehension. The keyword is comprehension, not memorization. True comprehension is a pleasure for the Human Mind.

But is it really enough to prove a mathematical statement by visual, geometrical means?

What is a proof? The best proof, I think, is when we comprehend something directly and fully, in the moment. Such proof will last and it is not subjected to the poor faculty of memory. For instance, if a pupil forgets Pythagoras Theorem he can easily recollect the process of his creative comprehension and derive the theorem once again.