Chess is closely related to the concept of symmetry. To be a fair game, the positions of chess pieces must be placed in symmetry and so is the layout of a chessboard. Perhaps it is not coincidental that the play field of chess game is all about squares and the Chinese character of "rice field" is also a 2 by 2 square. The chessboard is a tessellation of 8 by 8 squares. Other than circle, no other regular polygons have so many symmetry lines as a square. Circle has infinite symmetry lines and it does not form tessellation so square becomes the battle ground for many board games.

To play a symmetric game the smallest board required is 5 by 5. Chess moves are closely related to geometry translation but with the current traditional way of teaching chess by introducing how each chess piece moves, the relationship between how each piece moves and its geometry meaning has totally lost and perhaps even causes confusion on how chess should be played. For example, the following is a typical description of how each chess piece moves in most chess books.

Chess pieces names and moves

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Symbol	Names of chess pieces	How does it move (If it is not blocked and is safe to move.)
q(Q)	Queen (major piece)	Up and down Left and right Diagonally   Any number of squares
k(K)	King	Up and down Left and right Diagonally   one square at a time
r(R)	Rook (major piece)	Up and down Left and right   Any number of squares
n(N)	Knight (minor piece)	L-shape or Y-shaped in 8 directions The only piece can jump over pieces.
b(B)	Bishop (minor piece)	Diagonally   Any number of squares
p	Pawn	One or two squares forward on the first move and only one square forward after first move. One square diagonally when take opponent's piece. When pawn reaches the other end of the board, pawn can be promoted to any pieces other than a king or a pawn.

I believe that the possible movements of each chess piece is originally intended to be a 360 degree circular movement – in any directions with the exception of pawn. So should rook be introduced as moving from side way and top/down or bottom/up? Should knight be introduced as moving in L shape or Y shape? 

I think that all pieces should be introduced with the view of moving in 360 degrees, the advantage being the young chess player would then play chess moves also in a 360 degree view which reflects how actually each move should be played.

How the Moves Chess Pieces Should be Taught?

Students should be reminded that in order to look for the "best" move, all possible directions of a chess piece should be considered, thus a chess move actually is moved with the view of 360 degree. This should be the main teaching concept of teaching how each chess piece moves.

For example, take a look at a chess diagram, if a chess piece is placed at c3, how many ways can this chess piece reach out to the side of a square to form a shape of inner circle (inscribed circle c2, b2, e4, d4) or outer circle (circumscribed circle c1, a3, e5, e3)? Depending how points are connected, a shape of square could also be formed.

The first "easy" way would be to move top-down or bottom-up and left-right or right-left, from c3 so as to reach the limit of a square and an inner circle is born and thus the move of rook is born. The motion of its move is called translation or slide. Connect the 4 out reached points with 4 straight lines, the shape is actually a square; but with contour curve then it forms a circle.

The second way of moving to the outer limit of a square and form a circle is to move in the directions of two main diagonals, thus an outer circle is produced and the movements of a bishop is born. Arguably, the four points also make a shape of a square. This motion from c3 to each of the 4 diagonal points is also a double-slide. The bishop can view in 360 degrees.

Combine the above two ways of rook and bishop moving, we have the most powerful move in all chess pieces that is a queen. King can only move in one square in each move and follows the moves of a queen.

In a 5 by 5 chessboard, we notice that all chess squares on each of 4 sides are covered by the moves of rook and bishop except a2, a4, b1, c5, d1, d5, e2, e4, so from a game point of attacking or defending view, this is a problem – there are 8 squares which are not covered. This is the reason of the birth of another chess piece called knight which covers the 8 squares by jumping to those 8 squares because it does not move by following the same moves of rook or bishop to reach the 8 squares. This perhaps is the reason why knight jumps since knight does not trace any squares in one straight line to reach any one of those eight unreachable squares. 

By using the moves of up/down, left-/right, diagonals, and diagonal jump, every square on a 5 by 5 chessboard is completely covered from c3.

Summary

 By introducing the moves with a view of a circle from one starting square, students could get the sense of how each piece moves and also understands deeply how each move should be made (played) – checking in circular motion of 360 degrees view of course. Further, how each chess piece's move linked to geometry transformation is also introduced to students in a sensible way.

This geometric view of teaching chess movement in 360-degree to form a complete square is much clearer than introducing knight moves in L shape and it also explains why knight jumps – to defend or attack 8 squares where all other chess pieces are not able to achieve.

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Comments on this article:

» left by dan from U.S. (363 days 4 hours ago.)

The content is good, but this article is in DIRE need of illustrations to support the text.

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» left by dan from U.S. (363 days 3 hours ago.)

I'm also not clear how this explains the initial point of why knights jump. It's clear that the movement pattern allows all squares of a 5x5 grid to be covered (assuming a rook, knight, and bishop at the center). But that has nothing to do with jumping.

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» left by Anonymous (363 days 2 hours ago.)

When rook or bishop moves, any squares on the path could be attacked or the rook or bishop could land on any squares of the path if it is safe to do so, but can knight do the same way i.e., attack or land on any squares of L shapled path? No! Knight can not even though it is often taught as a L shaped move. Clearly from this point, it is a "jump" move which is different from rook or bishop.

 

Chinese chess has a similar chess piece and it is called "horse" and when Chinese teach knight move, it is clearly called "jump" and kids were taught to remember it moves like a Chinese character "rice field", so it is interesting to know Chinese actaully clearly says it is a "jump" move.

 

By the way, there are many similarities between western chess (international chess) and Chinese chess and moves are the same for some chess pieces. I point out this is to show that knight "move" is actually a "jump".

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