Pupils, who had not been exposed to proof, were interviewed and their responses were analyzed. The research attempted to determine whether pupils were convinced about explored geometric statements and their level of conviction. It also attempted to establish whether pupils exhibited an independent desire for why the result, they obtained, is true and if they did, could they construct an explanation, albeit a guided one, on their own. The reader will discover a rather quick answer to a complex question, but many links to follow and pages to explore. This special issue of the Math Forum's weekly newsletter highlights interesting conversations taking place during December of 1998 on Internet math discussion groups.
Proofs are simply too long and too overwhelming for students.
My piano teacher always amazed me by playing complicated Bach pieces at sight. Whereas when I played at sight, each note involved finger juggling and thinking. Polya wrote about the value of teaching mathematical ideas using repetition but with variation, and pointed to the composers for examples. Perhaps sight-reading is another example where we could learn from the composers.