Элементарная математика
Математика
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AMS, 2010. - 293 pages.

From the Preface: This book is an attempt to look at mathematics from a new and somewhat unusual point of view. I have started to systematically record and analyze from a mathematical point of view various dif?culties experiencing by children in their early leaing of mathematics. I hope that my approach will eventually allow me to gain a better understanding of how we—not only children, but adults, too — do mathematics. This explains the title of the book:
metamathematics is mathematics applied to study of mathematics. I chase shadows: I am trying to identify and clearly describe hidden structures of elementary mathematics which may intrigue, puzzle, and — like shadows in the night — sometimes scare an inquisitive child.

The real life material in my research is limited to stories that my fellow mathematicians have chosen to tell me; they represent tiny but personally signi?cant episodes from their childhood. I directed my inquiries to mathematicians for an obvious reason: only mathematicians possess an adequate language which allows themto describe in some depths their experiences of leaing mathematics. So far my approach is justi?ed by the warm welcome it found among my mathematician friends, and I am most grateful to them for their support. For some reason (and the reason deserves a study on its own) my colleagues know what I am talking about!
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