## Thinking MathematicallyThinking Mathematically unfolds the processes which lie at the heart of mathematics. It demonstrates how to encourage, develop, and foster the processes which seem to come naturally to mathematicians. In this way, a deep seated awareness of the nature of mathematical thinking can grow. The book is increasingly used to provide students at a tertiary level with some experience of mathematical thinking processes. |

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### Contents

a Everyone can start | 3 |

P4HR SIHP | 9 |

Review and preview | 29 |

Copyright | |

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activity advice answer argument articulate aware become black Fridays chapter CHECK CHESSBOARD SQUARES coins colours confidence conjecture consecutive numbers consecutive positive numbers CONSECUTIVE SUMS context counting cubes diagram divisor Entry phase ENTRY Specialize example experience feelings Fibonacci FLIPPING CUPS fold form 4M formula four digit palindrome GOLDBACH'S CONJECTURE greatest common divisor happens hidden assumptions important insight INTRODUCE justified KEEPING GOING key ideas key moments KNOW and WANT looking magic squares manipulating matches mathematical thinking means minimum number monitor mulling nice notation notice NULLARBOR PLAIN number of moves number of threads odd factor odd number order of calculation original question PAINTED TYRES PAPER STRIP PINS and GAP polygons possible problem recognize rectangle reflection regions resolution resolve result Review RUBRIC writing rule SCEPTICAL seesaws sense sequence someone structure STUCK suggested sum of consecutive Supporting Mathematical symbols tackling tension thinking mathematically total number