## Understanding in MathematicsThe concept of understanding in mathematics with regard to mathematics education is considered in this volume. The main problem for mathematics teachers being how to facilitate their students' understanding of the mathematics being taught. In combining elements of maths, philosophy, logic, linguistics and the psychology of maths education from her own and European research, Dr Sierpinska considers the contributions of the social and cultural contexts to understanding. The outcome is an insight into both mathematics and understanding. |

### Contents

1 | |

Components and Conditions of an Act of Understanding | 27 |

Processes of Understanding | 72 |

Good Understanding | 112 |

Developmental and Cultural Contraints of Understanding | 138 |

170 | |

183 | |

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able abstract accepted act of understanding action activity algebra already approach asked awareness basis become called child cognitive communication complex concept concrete considered consist construction continuous course culture defined definition difficulties domain elements epistemological obstacles equal example existence experience explain expressions fact Figure formal function given ibidem idea identification important kind knowledge language later learning limit linear logical mathematics mathematics education meaning mental metaphor mind natural notion numbers object obstacles operations particular person philosophers possible problem proof question reasoning refer relations representations result role rules scientific seems sense sequence Sierpinska situation social solving speak stage standing starts statement structure symbolic teacher teaching theorem theory things thinking thought tion understood values variable various vectors Vygotski whole