"One makes sense of , whether fictional or factual, by a mental construction that is sometimes called the world of story ...[T]he imaginative effort is a standard way of understanding what people say... In order to understand connected speech about concrete things, one imagines them. ...The capacity to do this... encourages empathy, but it also allows one to do mathematics. ...This is often fun, and it is a form of playing with ideas. ...This ludic aspect of mathematics is emphasized by in his semiotic analysis of mathematics and acknowledged by David Wells in his comparison of mathematics and games. ...The ludic aspect is something that undergraduates, many of whom have decided that mathematics is either a guessing game... or the execution of rigidly defined procedures, need to be encouraged to do when they are learning new ideas. They need to fool around with them to become familiar... Changing the s and seeing what a function looks like... to learn how the function behaves. ...Mathematical research involves a good deal of fooling around, which is part of why it is a pleasurable activity... This is not competitive..."
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Mathematics education
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