## Learning and the nature of mathematics |

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### Contents

The Nature of Modern Mathematics | 35 |

Some Reflections on Learning | 49 |

Naive Foundations for a Theory | 77 |

Copyright | |

9 other sections not shown

### Common terms and phrases

abstract activity algebraic structures answer applied arithmetic axiomatic axiomatic method Babylonian mathematics basic behavior calculation child classical logic cognitive complex computation concepts concrete correspond course curriculum discussion elementary elements equation example fact formal function geometry given higher-order rule inference rules inverse investigation involved isomorphism Jean Piaget kind Klein group knowledge language learner learning mathematics logic material mathe mathematical structures mathematician mathematics education mathematics instruction mathematics learning matics means ment methods metic modern mathematics natural numbers nature of mathematics notion objects operations ordered pairs pairs paradigm paradigmatic experience particular patterns Piaget possible present problems procedure Professor psychological question relation result rules of inference school mathematics sender sequence seriation set theory simple situation statements symbols tasks teacher teaching theorems theory tion topics traditional mathematics two-cent pieces understanding University variables