## Building up mathematics |

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### Contents

A Survey of the Present Position | 1 |

A Theory of MathematicsLearning | 19 |

Arithmetical Concepts | 37 |

Copyright | |

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24-house village 6-house abstract Adelaide algebra applied arithmetic base blocks blue circle blue squares bus routes C-set child circular tour classes of numbers commutative law constructive corresponding cube Cuisenaire rods cycle Diagonal distributive law equation equivalence classes equivalence relation equivalent example experiences fact flats flip Floorboard function hook number insight kind Klein group learning-situation less logical logical disjunction mathematical concepts mathematical learning mathematics-learning matical means move multiplication narrow natural numbers negative numbers neutral element number of rings number of rows objects pegboard pegs perceptual pieces pile play position possible predicate problem properties reader realize rectangle red circles red square relation relationships rotations rules scalars shape and colour shuttle situation solution stage structure subtraction suburb symbols task teacher teaching techniques tetrahedron thinking tion tower triangles triple units universe of discourse University of Sherbrooke Variability Principle vector vector-space