Problem Solving Approach
as a Tradition in Russian
Mathematical Education
“If you can't solve a problem, then there is an
easier problem you can solve: find it.”
Dr. Ivan Yashchenko,
Director of MCCME
George Pólya, Mathematical Discovery on
Understanding, Learning, and Teaching Problem
Solving
MCCME  Open Environment for Worldwide Mathematical Education  Moscow, April 8–11, 2015
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Problem books from 17th century to present days
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
MCCME  Open Environment for Worldwide Mathematical Education  Moscow, April 8–11, 2015
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Problem books from 17th century to present days
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
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Problem books from 17th century to present days
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)
MCCME  Open Environment for Worldwide Mathematical Education  Moscow, April 8–11, 2015
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Problem books from 17th century to present days
Arithmetical problem
books for technical
schools and preliminary
courses for gymnasiums.
1911(left),
1876 (right)
MCCME  Open Environment for Worldwide Mathematical Education  Moscow, April 8–11, 2015
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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
Anti-alcohol math problems. The book issued in 1914
MCCME  Open Environment for Worldwide Mathematical Education  Moscow, April 8–11, 2015
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Problem books from 17th century to present days
Math Olympiads problem books of Soviet
period
MCCME  Open Environment for Worldwide Mathematical Education  Moscow, April 8–11, 2015
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Problem books from 17th century to present days
Famous geometry problems in books by V.Prasolov
MCCME  Open Environment for Worldwide Mathematical Education  Moscow, April 8–11, 2015
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Problem books from 17th century to present days
Since 1935 starts the Moscow
Mathematical Olympiad
MCCME  Open Environment for Worldwide Mathematical Education  Moscow, April 8–11, 2015
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Problem books from 17th century to present days
MCCME  Open Environment for Worldwide Mathematical Education  Moscow, April 8–11, 2015
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Problem books from 17th century to present days
Mathematical feast – a real opportunity to find future mathematicians
and inspire their mathematical thinking and activity
Left: MF problem book
Right: the same
MCCME  Open Environment for Worldwide Mathematical Education  Moscow, April 8–11, 2015
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Problem books from 17th century to present days
Задачники
как
отдельный
вид
учебных
материало
в
появляютс
я в России
в конце
XVII века.
MCCME  Open Environment for Worldwide Mathematical Education  Moscow, April 8–11, 2015
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Regular school textbooks traditionally contain large
amount of problems in the course and extra curriculum
Learning complex by N.Vilenkin for grades 5-6
1816 problems
1578 problems
MCCME  Open Environment for Worldwide Mathematical Education  Moscow, April 8–11, 2015
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Regular school textbooks traditionally contain large
amount of problems in the course and extra curriculum
Learning complex by Yu.Makarychev for grades 7-9
1410 problems
1351problems
1503problems
MCCME  Open Environment for Worldwide Mathematical Education  Moscow, April 8–11, 2015
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Regular school textbooks traditionally contain large
amount of problems in the course and extra curriculum
The most common textbook by
N.Kolmogorov for grades 10-11
1451 problems
MCCME  Open Environment for Worldwide Mathematical Education  Moscow, April 8–11, 2015
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Solving problems in Russian schools is not just
that a problem must be solved
MCCME  Open Environment for Worldwide Mathematical Education  Moscow, April 8–11, 2015
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There might be a serious dialogue
And there might be mistakes from the both sides
MCCME  Open Environment for Worldwide Mathematical Education  Moscow, April 8–11, 2015
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Nowadays the Internet access to databases of
math problems becomes a common practice
Free database for Olympiad problems http://www.problems.ru
MCCME  Open Environment for Worldwide Mathematical Education  Moscow, April 8–11, 2015
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Nowadays the Internet access to databases of
math problems becomes a common practice
zadachi.mccme.ru
Free database of
geometrical problems
by R.Gordin
MCCME  Open Environment for Worldwide Mathematical Education  Moscow, April 8–11, 2015
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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 problembooks
MCCME  Open Environment for Worldwide Mathematical Education  Moscow, April 8–11, 2015
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We feel like there came a time to think about
an International bank of math problems
That’s why we have gathered here. Thank you for this
MCCME  Open Environment for Worldwide Mathematical Education  Moscow, April 8–11, 2015
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