### Abstract

Although mathematics educators seem to agree on the importance of teaching

mathematics for understanding, what they mean by understanding varies greatly.

In this article, I elaborate and exemplify the construct of key developmental understanding

to emphasize a particular aspect of teaching for understanding and to

offer a construct that could be used to frame the ideniification of conceptual learning

goals in mathematics. The key developmental understanding construct is based

on extant empirical and theoretical work. The construct can be used in the context

of research and curriculum development. Using a classroom example involving

fractions, I illustrate how focusing on key developmental understandings leads

to particular, potentially useful types of pedagogical thinking and directions for

inquiry.

mathematics for understanding, what they mean by understanding varies greatly.

In this article, I elaborate and exemplify the construct of key developmental understanding

to emphasize a particular aspect of teaching for understanding and to

offer a construct that could be used to frame the ideniification of conceptual learning

goals in mathematics. The key developmental understanding construct is based

on extant empirical and theoretical work. The construct can be used in the context

of research and curriculum development. Using a classroom example involving

fractions, I illustrate how focusing on key developmental understandings leads

to particular, potentially useful types of pedagogical thinking and directions for

inquiry.

Original language | English (US) |
---|---|

Pages (from-to) | 359-371 |

Number of pages | 13 |

Journal | Mathematical Thinking and Learning |

Volume | 8 |

Issue number | 4 |

State | Published - 2006 |

### Keywords

- Mathematical concept
- Instructional goals
- Reflective abstraction