# Chess to built math capacity. John Kunz Started as a volunteer with Advantage Now Program Coordinator at LaFargeville & Theresa Works for Cornell Cooperative.

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Chess to built math capacity

John Kunz Started as a volunteer with Advantage Now Program Coordinator at LaFargeville & Theresa Works for Cornell Cooperative Extension of Jefferson County US Chess Federation rated tournament player

USCF Ratings History Graph

Sci-Tech Center Chess Chess Club started with two students Several cardboard Walmart Chess sets Enlisted the help of local Chess Club President The first “Simul” We lost every single game The Research began !!!

What to teach students about Chess The rules – pretty easy Strategy Tactics Opening Theory

Strategy – What you want to accomplish Play in the center of the board Use the Knights early Castle early Link the rooks Protect the pieces Always look for Checkmate

Tactics- How to implement strategy Pins Forks Skewers Discoveries Deflections Decoys Batteries Many other subtle devices

Opening Theory The Oxford Companion to Chess lists 1327 named openings and variants

Most Chess coaches will say that focusing on tactics is the best Most new Chess students are not very patient with the training component of a Chess program High quality miniatures are a good way to address many aspects of training Miniatures are Chess games that are completed in ~20 moves or less.

What does an academic Chess program look like? Meets on a regular basis Has an instructional component in every meeting Takes part in competitive event outside the Club

An Annotated Chessboard

Chess Clocks

Literature – Chess 5334

Each square on the board has its own coordinate location.

Chess pieces have a numerical value King is the object of the game – no value assigned Queen = 9 Rook = 5 Bishop = 3 Knight = 3 Pawn = 1

Algebraic Notation K = King Q = Queen B = Bishop N = Knight R = Rook Pawns are coordinate locations

Students are recording and reviewing data. 0-0 = castling kingside 0-0-0 = castling queenside x = capture + = check # = checkmate ! = good move ? = questionable move

Talk to the students in Algebraic Notation Be intentional with use of Geometric terms: Perimeter Diagonal Space Intersection Coordinates

It is easy to talk to students about rays, intersecting lines and vectors.

Knight’s Tour

The Knight hits each square only once.

Fractals A fractal is "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced- size copy of the whole.geometric shape

Fractals

Animation of a quadratic surface using fractalization.

Fractals like the Mandelbrot set give rise to some fantastic artwork.

Lyapunov fractal which derives from changes in population growth rates.

An 8x8 Chess board has 64 squares

By reconstructing the chessboard we can get a rectangle of 65 squares

How is this possible? Fibonacci Number Sequence Cassini Identity

An expanded version of the graph reveals a long parallelogram

Pattern Recognition

Checkmate patterns are very important to success in Chess.

Pattern Recognition in Mathematics. Quadratic Polynomials are an excellent example of pattern recognition in mathematics: The format of the equation is what matters. ax 2 + bx + c

Substituting Chess symbols for coefficients we still have ax 2 + bx + c x 2 + x +

Students can solve the polynomial Substitute the value of the chess piece for the symbol 5x 2 + 3x + 9 If x = 1 = 17

Gas chromatographs are studied for the patterns they reveal.

TSA personnel rely on pattern recognition.

Radiologists constantly work with pattern recognition.

What does the literature say about Chess and Math? About.com and Wereurope.org both credit Chess instruction in schools as the reason for Quebec being best in Math scores in Canada. The American Chess Foundation sponsored a Chess initiative in Harlem Schools. Student math scores improved by 17.3% compared to students taking part in other enrichment activities.

Other benefits of Chess Builds resilience Supports self esteem Improves decision making Provides an opportunity to apply knowledge Reinforces the link between actions and consequences Sharpens visualization and spatial awareness Fosters good sportsmanship

Internet Chess Resources Chessbase.com – International Chess News Web Page – Software manufacturer. ChessClub.com Chesscorner.com Chesstempo.com Susan Polgar’s Chess Blog Chessgames.com Wholesalechess.com

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