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Being three years old my son asked me "Mammy, why there are interesting words and there are some uninteresting ones?"
In order to explain his question, he named things around and said that those words are interesting, while uninteresting words are "integral", "function" and some other words he heard from us.
Now he has PhD in Applied Mathematics and Computer Science.

All the time my son was surprising me by his smart behaviour and deep thoughts and interesting expressions.

I feel so sorry for children who are upset because of the problems caused by mathematics.
For some children these problems generate complexes, while others start to believe in the preconception that it is not possible to understand the mathematics without a special talent, and take this as the inevitable.

As a mathematician with a long teaching experience, and not only in Russia, I know very well about difficulties in mathematical training which originate from the problems of the mathematical education of kids from their early childhood.

I like to talk with children. Being of 3-5 years old they have so dynamical attitude. This is the time for them to discover new notions. Their mind is like a sponge, so it is better to fill it up looking into the future.
All the things which we have in our daily life since the childhood become more or less usual for us, so we become accustomed to deal with them.

Of course, parents of kids are busy enough with their daily duties and usually are unable to invent special ways to help to their children to develop the special ways of thinking, especially the mathematical ones. Very often I heard about this problems of parents, so they really need help.

A good special book could be a real helper in this case. Reading and discussing such a book together with a kid, is a real pleasure and a nice way to make the mathematical notions familiar to kid from the childhood.

I prepared a project of such a book, really aimed to help children to make their first steps in Mathematics and also to provide a support for their educators in giving such a help to children.
Very often from parents of children making their first steps in math I hear that they would like to help their children but they do not know how to do this. In fact, this was one of the reasons which prompted me to write this book.

The proposed book is conceived as a family book for reading to little ones at the age starting from 4-5 years old with the goal to form a special thinking mode which promotes a development of mathematical logic and stimulation of a permanent interest to a new knowledge.

The plot of the book is based on a journey of the main characters to the Islands of Mathematics, as I call them.
All the conversations of the characters happen in dialogs: a question is developed in a logical way and after that the reply is suggested with a clear logical explanation.

Intended for little ones, the book is rich illustrated and at the same time the presentation is based on a consistent and detailed treatment of basics of arithmetic and geometry.

This feature of the project may make the book also a family tutor for pupils of first classes of primary schools.

The book was written with love to children and inducement of their success in studying.
My approach is based on inspiration of the interest to new attainments and feeling of the victory as a result of comprehension of a new knowledge, which serves as a stimulus for a further studying.

The volume of my illustrated book is about 150 pages in MS Word (font Size 14).

In the book there are considered the following mathematical notions in detail:

• Structure of integers
• Inequalities between integers
• Addition, subtraction, multiplication and division within the integers 1-20
• Count till 100
• Count in terms of hundreds till one thousand
• Fractions with the same denominator
• Comparison of fractions, addition and subtraction of fractions
• Multiplication table is not suggested a priori, but the characters of the book naturally arrive at this table.
• There are also given the main ideas and some basic notions related to triangles, quadrangles and circles.

At the moment, the book together with all the illustrations exists in the electronic form, in Russian and Porguguese languages.

The project of the book was presented by me to the mathematical audience at the international conference FSORP-Madeira, 2002 (Factorization, Singular Operators and Related Problems, January 28 - February 1, 2002, Funchal, Madeira, http://fsorp.digiways.com.
It was highly appreciated by colleagues.

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