Another my old post from my abandoned blog — I moved it here because of my recent exchanges with Scott Carter in which I mentioned Radzivilovsky’s name.
If I had not known some of his former pupils, I would treat Vladimir Radzivilovsky’s approach to teaching mathematics to very young children with great suspicion. The following two images are taken from his website: a worksheet of his pupil:
and a photograph of the pupil. Her name is Avital.
Radzivilovsky believes that teaching is an art, not a science. Moreover, teaching, in his opinion, is a performance art and therefore he, unfortunately, does not see the point in putting his ideas in writing. His rare comments can hardly be viewed as recipes. For example, he wrote to me recently:
I use this occasion to formulate some my pseudoscientific proposals for the methodology of mathematical teaching. We have difficulty remembering stuff we do not understand. But the reverse is also true — it is difficult to understand something which still has not settled in our heads. We have a vicious circle. The only way to break it is to repeat the same thing again and again: more we remember — easier to understand. Better we understand, more we remember. [...] To a five years old child I draw the unit circle [with formulae for sin and cos] about 20 times, and ask his or her Mom to draw it another 5o times. But the child will know [trigonometry] at the age of 5, not 15.
Please do not take that for a complete description of his method! As I said, I know some of his former pupils. If one uses the criterion set in Matthew 7:16 “Ye shall know them by their fruits. Do men gather grapes of thorns, or figs of thistles?“, Radzivilovsky is a fantastically successful teacher, and his work deserves a most careful study.