(51) Thus, to understand how people do mathematics, we must understand the cognitive origin of this experience, that is, we must work to understand the cognitive mechanisms that allow for the reification of abstract ideas. Most writing about this phenomenon has been of a philosophical nature, but what is needed now is a cognitive account of it. Natural category representation To develop a theory of how people might represent mathematical objects in the mind, we should look to theories of how they represent more familiar objects such as dogs or tomatoes. What of this mathematics as tools?
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