### Abstract

By continuing a contrast with the DNR research program, begun in Harel and Koichu (2010), I discuss several important issues with respect to teaching and learning mathematics that have emerged from our research program which studies learning that occurs through students' mathematical activity and indicate issues of complementarity between DNR and our research program. I make distinctions about what we mean by inquiring into the mechanisms of conceptual learning and how it differs from work that elucidates steps in the development of a mathematical concept. I argue that the construct of disequilibrium is neither necessary nor sufficient to explain mathematics conceptual learning. I describe an emerging approach to instruction aimed at particular mathematical understandings that fosters reinvention of mathematical concepts without depending on students' success solving novel problems.

Original language | English (US) |
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Pages (from-to) | 281-294 |

Number of pages | 14 |

Journal | Journal of Mathematical Behavior |

Volume | 32 |

Issue number | 3 |

DOIs | |

State | Published - Sep 2013 |

### Keywords

- Abstraction
- Instructional design
- Learning theory
- Learning trajectory
- Mechanism of learning
- Task design

### ASJC Scopus subject areas

- Education
- Applied Psychology
- Applied Mathematics