MCCME Open Environment for Worldwide Mathematical Education Moscow, April 8–11, 2015 1

Problem Solving Approach as a

Tradition in Russian Mathematical Education

Dr. Ivan Yashchenko,Director of MCCME

“If you can't solve a problem, then there is an easier problem you can solve: find it.” 

George Pólya, Mathematical Discovery on Understanding, Learning, and Teaching

Problem Solving

Problem books from 17th century to present days

MCCME Open Environment for Worldwide Mathematical Education Moscow, April 8–11, 2015 2

First regular math textbooks appear in Russian in 17th century

Right: The textbook on math by Leonard Euler

Left: Arithmetic (1703). Leontiy Magnitsky. The first math hand-book which was in use as a school textbook for handreds years

Problem books from 17th century to present days

MCCME Open Environment for Worldwide Mathematical Education Moscow, April 8–11, 2015 3

The first textbook on geometry (1709). The book was edited by Peter the Great

MCCME Open Environment for Worldwide Mathematical Education Moscow, April 8–11, 2015 4

Задачники как отдельный вид учебных материалов появляются в России в конце XVII – начале XVIII века.

Above: Initial base of a pure mathematics by Nikolay Fuss (1820)Left: Initial base of mathematics by Nikolay Muravyov (1752)

Problem books from 17th century to present days

MCCME Open Environment for Worldwide Mathematical Education Moscow, April 8–11, 2015 5

Arithmetical problem books for technical schools and preliminary courses for gymnasiums. 1911(left), 1876 (right)

Problem books from 17th century to present days

MCCME Open Environment for Worldwide Mathematical Education Moscow, April 8–11, 2015 6

Anti-alcohol math problems. The book issued in 1914

Problem books can carry not only pure educational function

History knows cases when that genre had been used for many goals, particularly for a social propaganda

MCCME Open Environment for Worldwide Mathematical Education Moscow, April 8–11, 2015 7

Math Olympiads problem books of Soviet period

Problem books from 17th century to present days

MCCME Open Environment for Worldwide Mathematical Education Moscow, April 8–11, 2015 8

Famous geometry problems in books by V.Prasolov

Problem books from 17th century to present days

MCCME Open Environment for Worldwide Mathematical Education Moscow, April 8–11, 2015 9

Since 1935 starts the Moscow Mathematical Olympiad

Problem books from 17th century to present days

MCCME Open Environment for Worldwide Mathematical Education Moscow, April 8–11, 2015 10

Problem books from 17th century to present days

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Mathematical feast – a real opportunity to find future mathematicians and inspire their mathematical thinking and activity

Left: MF problem bookRight: the same

Problem books from 17th century to present days

MCCME Open Environment for Worldwide Mathematical Education Moscow, April 8–11, 2015 12

Задачники как отдельный вид учебных материалов появляются в России в конце XVII века.

Problem books from 17th century to present days

Regular school textbooks traditionally contain large amount of problems in the course and

extra curriculum

MCCME Open Environment for Worldwide Mathematical Education Moscow, April 8–11, 2015 13

Learning complex by N.Vilenkin for grades 5-6

1816 problems 1578 problems

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Learning complex by Yu.Makarychev for grades 7-9

1410 problems 1503problems1351problems

Regular school textbooks traditionally contain large amount of problems in the course and

extra curriculum

MCCME Open Environment for Worldwide Mathematical Education Moscow, April 8–11, 2015 15

The most common textbook by N.Kolmogorov for grades 10-11

1451 problems

Regular school textbooks traditionally contain large amount of problems in the course and

extra curriculum

Solving problems in Russian schools is not just

that a problem must be solved

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There might be a serious dialogue

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And there might be mistakes from the both sides

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Free database for Olympiad problems http://www.problems.ru

Nowadays the Internet access to databases of math problems becomes a

common practice

MCCME Open Environment for Worldwide Mathematical Education Moscow, April 8–11, 2015 19

zadachi.mccme.ruFree database of geometrical problems by R.Gordin

Nowadays the Internet access to databases of math problems becomes a

common practice

MCCME Open Environment for Worldwide Mathematical Education Moscow, April 8–11, 2015 20

Nowadays the Internet access to databases of math problems becomes a

common practice

http://mathege.ru

Free database of problems for the Unified state exam in mathematics

Now we can talk about the new type of learning materials: problem-bases are gradually replacing traditional problem-books

We feel like there came a time to think about an International bank of math

problems

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That’s why we have gathered here. Thank you for this