The analogy of a chess player has been very aptly used to illustrate the various mental attitudes towards the acquisition of mathematical knowledge. One who simply reads understandingly a mathematical text, or hears understandingly a mathematical lecture or explanation, is like an onlooker at a game of chess, who sees that each move is made in accordance with the rules, and that finally one player or the other wins. It is a great step in advance when the player sees also why these moves were made rather than some others, that are also in accord with the rules. This likewise has its evident analogy in mathematics. But to get the real exhilaration of the game of chess one must play one's self. To watch others play, to analyze the motives of their moves, is essential to mastery of the game, but is effective only as it finds application in actual play. It is actual play, begun as soon as the moves of the pieces are known, that develops the need for theoretic study of the game. It would be a very tedious way of making a good chess player to require him simply to follow the play of others, and never to permit him to play himself.
Teaching of Mathematics in the Elementary and Secondary School, 1906