## Abstract

This chapter discusses both the challenges that students face when working within the representation system of mathematical proof and the affordances it offers. It reviews G. A. Goldin’s description of a representation system, including what constitutes syntactic and semantic reasoning within a representation system. The chapter describes what it convey by the representation system of proof and also discusses syntactic and semantic reasoning within this system. Proof is fundamental to mathematics and students should be engaged in the activity of proving throughout their mathematics education. In advanced mathematics courses, students are expected to produce mathematical proofs, or arguments that obey well-defined conventions that are agreed on by contemporary mathematicians. A growing body of research in mathematics education demonstrates that undergraduate students find the character of mathematical proof to be deeply perplexing and that this confusion can inhibit them from successfully constructing proofs.

Original language | American English |
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Title of host publication | Teaching and Learning Proof Across the Grades |

Subtitle of host publication | A K-16 Perspective |

Publisher | Taylor and Francis |

Pages | 323-338 |

Number of pages | 16 |

ISBN (Electronic) | 9781135856755 |

ISBN (Print) | 9780415989848 |

DOIs | |

State | Published - Jan 1 2010 |

Externally published | Yes |

## ASJC Scopus subject areas

- Social Sciences(all)
- Mathematics(all)