Friday, February 19, 2010

Does Learning/Playing Chess Develop The 'Mathematical Mind'?

Nothing revolutionary about this question but it's been on my mind for some time and, now, that I have a six-year old grandson who seems to be analytical like me (we speak the same language!), I've decided to introduce him to chess via chess puzzles.

I'm not writing this because I believe one should develop a math curriculum around chess! I'm simply suggesting that any activity which requires problem-solving, analysis and creativity develops the mind. Chess is only one of many such vehicles which drive the student toward deeper thought processes. I could make a similar argument for writing and other artistic activities, but I chose chess because it's a game I love even though I'm still a novice.

Perhaps the most important aspect of all of this for children is that learning chess can be fun provided it is introduced properly. I believe many young children would quickly become frustrated and bored if they begin by learning proper openings and the concepts of positional play in the beginning stages.

There are well-known analogies between playing chess and mathematical problem-solving so I will only mention a few that occurred to me a priori, some of which have been validated by the writings of the brilliant mathematician, Paul Halmos:

  • Chess has an elaborate technical language and is completely deterministic.
  • Chess - like mathematics - requires problem solving, evaluation, critical thinking, intuition and planning

Halmos also believed, as I do, that mathematics is a creative art
"because mathematicians create beautiful new concepts; it is a creative art because mathematicians live, act, and think like artists; and it is a creative art because mathematicians regard it so.”

A New Jersey senator introduced and helped to pass bills in the Senate regarding chess instruction in schools, declaring:
"Chess increase strategic thinking skills, stimulates intellectual activity and improves problem-solving ability."

For learning how individual pieces moves and for experiencing more immediate feedback and satisfaction, I recommend Chess Puzzles, which involve contrived board positions requiring the solver to find a mate in one or more moves. Starting with Mate in One Puzzles seems developmentally appropriate in the Piagetian sense, although I would introduce Mate in Two early on as an extra challenge. That is, I wouldn't spend two weeks on Mate in One to the exclusion of other puzzles. For me, the best online site for doing these puzzles on a daily basis is the Mate in Two Chess Puzzles website developed by John Bain, MS Education, a special education teacher, certified USCF tournament director, and a specialist in textbook and materials modification. John is a teacher in the truest sense of the word!

 I'm not suggesting that children should not also be allowed to try a full game with a parent, instructor or with peers. I would allow the child free exploratory play when starting a game, correcting only invalid moves. This is not a purely constructivist approach however -- I do not expect students to invent the the theory of positional play and the deeper aspects of the game! Guided instruction must be introduced strategically just as it is with mathematics instruction, and, as with math, there is never a substitute for repetition and practice!

I'm opening the "board" for you to jump in. Do you agree with some of my thoughts about chess and math? Do you see other analogies I've missed? Have you personally used chess as a way to develop thinking in elementary, middle or secondary schools? Please share!!

"All Truth passes through Three Stages: First, it is Ridiculed...
Second, it is Violently Opposed...
Third, it is Accepted as being Self-Evident."
- Arthur Schopenhauer (1778-1860)

You've got to be taught
To hate and fear,
You've got to be taught
From year to year,
It's got to be drummed
In your dear little ear
You've got to be carefully taught.
--from South Pacific

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