Moscow Center for Continuous Math education education - keeping ...
Moscow Center for Continuous Math education education - keeping ...
Moscow Center for Continuous Math education education - keeping ...
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<strong>Moscow</strong> <strong>Center</strong> <strong>for</strong> <strong>Continuous</strong> <strong>Math</strong><br />
<strong>education</strong> - <strong>keeping</strong> traditions of Russian<br />
math <strong>education</strong>
Co-founders of MCCME<br />
MCCME was founded (1994)<br />
by<br />
• <strong>Moscow</strong> Government<br />
• <strong>Math</strong>ematical<br />
section of the<br />
Russian academy of sciences<br />
• Steklov <strong>Math</strong>ematical Institute<br />
• <strong>Moscow</strong> State University<br />
• Independent University of <strong>Moscow</strong>.
Objectives<br />
• Improving level of math <strong>education</strong> in<br />
Russia<br />
• finding mathematically gifted children;<br />
• teaching not only high level math, but<br />
math in the context of world culture;<br />
• educating not only the mind but the spirit.
Ways and means<br />
• Improving teachers qualification<br />
• creating a favorable environment <strong>for</strong> the<br />
development of the intellect and creativity of<br />
gifted school children;<br />
• enhancing the inner motivation <strong>for</strong> the study of<br />
mathematics;<br />
• maintaining a high level of <strong>education</strong>;<br />
• bringing up children by teaching;<br />
• maintaining the continuity of math <strong>education</strong>:<br />
math circle high h school university;
Important aspects<br />
• individual approach<br />
to each pupil;<br />
• involving research<br />
mathematicians ti i and<br />
university students<br />
in the <strong>education</strong>al process;<br />
• famous mathematicians involved in<br />
teaching create a special atmosphere;<br />
• best university students enthusiastically<br />
teach gifted high school students
Training future research<br />
mathematicians is not the main<br />
purpose.<br />
The most important is<br />
to teach children<br />
to work hard and honestly and<br />
to enjoy this process.
Elements of the system<br />
• math circles;<br />
• well-organized wide spectrum of math<br />
competitions.<br />
• network of math schools and specialized<br />
math classes;<br />
• lectures <strong>for</strong> pupils and teachers;<br />
• summer camps;<br />
• community of math teachers and working<br />
mathematicians;<br />
ti i<br />
• publishing and internet projects.
<strong>Math</strong> circles<br />
• Saturday club <strong>for</strong> high school<br />
students interested in math;<br />
• conducted by research<br />
mathematicians and best<br />
university students;<br />
• lectures on interesting topics;<br />
• solving series of interrelated<br />
problems;<br />
• very in<strong>for</strong>mal atmosphere;<br />
• very strong feedback<br />
expected.
Summer schools<br />
• two aspects:<br />
competition and<br />
learning;<br />
• <strong>education</strong> is indivisible<br />
from communication;<br />
• students acquire the<br />
very spirit of<br />
mathematics;<br />
• what is mathematics<br />
and who are the<br />
mathematicians
<strong>Math</strong> competitions – not a main<br />
goal but a tool<br />
• Olympiads<br />
• Tournament of towns<br />
• Team competitions<br />
<strong>Math</strong>ematical<br />
“battles”<br />
• …<br />
<strong>Math</strong>ematical “regattas”<br />
<strong>Math</strong>ematical ti “feast”
Research projects and summer<br />
conferences<br />
• Tournament of towns summer conference<br />
–One problem <strong>for</strong> a week, not 50 <strong>for</strong> 4 hours ,<br />
or 6 <strong>for</strong> 5 hours<br />
– Possible cooperation<br />
– Awards<br />
• Partial success in a problem<br />
• Full success in a problem
Some figures<br />
• 100 000 pupils in <strong>Moscow</strong> in each <strong>for</strong>m<br />
• 15000 participants in math competitions<br />
• 1000 attends math circles<br />
• 100 pupils in high level specialized math<br />
schools and classes
In our opinion,<br />
studying math is<br />
an excellent tool in<br />
<strong>education</strong> and upbringing,<br />
in the creation of a balanced<br />
personality
Main focus: math teacher<br />
MCCME develop active communication with<br />
<strong>Moscow</strong> and all-Russia school math teachers:<br />
• Improvement of teachers qualification<br />
(More than 15 special courses yearly)<br />
• Involving colleagues in olimpiads<br />
• Special math contest <strong>for</strong> teachers<br />
• Conferences and meetings<br />
• Publishing and internet activities<br />
• Internet site to answer teachers questions
High and middle school<br />
students<br />
• ”Kruzhoks” and Correspondence<br />
shool of MCCME<br />
– All materials are available at<br />
http://www.mccme.ru/circles/mccme/<br />
• <strong>Math</strong> comptetitions<br />
• <strong>Moscow</strong> math conference of school<br />
students<br />
• Summer Schools
Distant “kruzhoks”<br />
• <strong>Math</strong>ematical internet-kruzhok<br />
• Correspondence probability theory and<br />
statistics school<br />
• Distant collective internet-kruzhok<br />
k
Examples<br />
• Cut A and B figures<br />
into “T” figures:<br />
«»<br />
. <br />
. <br />
• Cut each figure into<br />
two equal parts:<br />
) )<br />
) )<br />
• The box contains 10 sweets. Peter and Mary are playing<br />
the game: every minute one of them can take one, two<br />
or three sweets from the box and eat them. The person<br />
who will eat the last sweet will win. Mary takes sweets<br />
first. Who will win and what is the best strategy?
Example of Olympiad:<br />
<strong>Moscow</strong> mathematical Olympiad<br />
• One of the most known Olympiads in<br />
the world<br />
• Everybody is eligible to participate<br />
• More that 5000 students participated<br />
in 2008
Creative contest<br />
• Teachers solve problems and “check” students’ papers<br />
• Participation in the contest is fully voluntary and<br />
anonymous<br />
– Only names of winners are announced<br />
• Winners of the contest are awarded by diplomas,<br />
premiums and valuable prizes<br />
• Receiving of the diploma may serve as the basis <strong>for</strong> the<br />
increase of the qualification category
Methodological support of<br />
“kruzhoks”<br />
• The process:<br />
–the school subscribes and receivesan entrance test<br />
– the school receives the tasks, extra tasks,<br />
methodological recommendations<br />
– ateacherconducts conducts the “kruzhok”<br />
–a teacher sends resultsand obtains specific detailed<br />
recommendations and appropriate tasks<br />
• Hotline works<br />
• Form of qualification improvement<br />
• Certificate – <strong>for</strong> students
Distant “kruzhok” teacher’s<br />
materials. Structure<br />
• Tasks<br />
• Methodological recommendations:<br />
–Timing<br />
–What to solve first<br />
– Ideas<br />
–Hints<br />
– Solutions and tricks<br />
–How to give the summary<br />
– How to make it look like a game<br />
How to make it look like a game<br />
• Detailed solutions
Teachers’ materials collection<br />
• Materials of best<br />
teachers are<br />
collected<br />
• Teachers share<br />
their methodology
Working with university<br />
students<br />
• Independent University and project<br />
with Higher School of Economics<br />
• Summer schools<br />
• Involving students s into the work<br />
with schoolchildren
Internet-attestation of schools<br />
• Publicity and transparency<br />
• Approved database of tasks<br />
• independent system of content knowledge<br />
check
Internet-projects<br />
• MCCME.ru<br />
• <strong>Math</strong>.ru<br />
• Problems.ru<br />
• olimpiada.ru<br />
• System of internet-attestation<br />
• Internet-Olympiads
CREATIVE CONTEST FOR<br />
TEACHERS OF MATHEMATICS<br />
Two-step Olympiad. (First stage is online.)<br />
Aims of the contest:<br />
Measuring content and pedagogical knowledge. This will<br />
help to identify practices that lead to high mathematical<br />
knowledge among teachers.<br />
Motivation of school teachers to improve their skills in<br />
mathematics.<br />
Rewarding good specialists.<br />
Important:<br />
Anonymity. Every person will be able to know only about<br />
his results. Only names of the winners will be published.<br />
Prizes (such as invitation to workshop, conference or just<br />
cash prize)<br />
Acknowledgement of colleagues
TRANLSATION OF MCCME<br />
MATERIALS<br />
Existing materials<br />
Huge database of various mathematical problems<br />
(Olympiads, contests, etc.)<br />
Materials of different courses (E.g. summer schools<br />
materials, materials of “kruzhoks<br />
kruzhoks”, Independent University<br />
courses materials, etc.)<br />
Partner’s projects (like etudes.ru)<br />
Current materials<br />
Tasks of different contests, t that t are going now<br />
(mathematical battles, regattas, tournaments etc.)<br />
Materials of present-day “Kruzhoks”<br />
Permanent support and renewal<br />
Some videos (e.g. per<strong>for</strong>mances of famous mathematicians)<br />
can also be translated
TRANSLATION OF<br />
RUSSIAN TEXTBOOKS<br />
Possible projects:<br />
• Textbook “<strong>Math</strong>ematics” written by B. P. Geidman -<br />
text book <strong>for</strong> the elementary school.<br />
• “Probability”. bilit It combines practicality with the<br />
clearness and contains a lot of important tasks and<br />
their solutions.<br />
• The books published in MCCME, containing<br />
materials of prominent Russian teachers. For<br />
example, the textbooks based on mathematical<br />
<strong>education</strong> in one of the best <strong>Moscow</strong> 57 school.
Summer workshop <strong>for</strong> teachers (in<br />
<strong>Moscow</strong>)<br />
• Ability to share best practices between Russian<br />
and American teachers<br />
• Invitation to a conference as a reward <strong>for</strong><br />
winners of the Creative Contest<br />
• Brilliant Russian teachers methodologists could<br />
be invited