### Abstract

The purpose of this article is to contribute to the dialogue about the notion of a d van c ed m a thematical thinking by offering an alternative characterization for this idea, namely advancing mathematical activity. We use the term advancing (versus a d van c ed) because we emphasize the progression and evolution of students’ reasoning in relation to their previous activity. We also use the term a c tiv ity, rather than thinking. This shift in language reflects our characterization of progression in mathematical thinking as acts of participation in a variety of different socially or culturally situated mathematical practices. For these practices, we emphasize the changing nature of students’ mathematical activity and frame the process of progression in terms of multiple layers of horizontal and vertical mathematizing.

Original language | English (US) |
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Title of host publication | Advanced Mathematical Thinking |

Subtitle of host publication | A Special Issue of Mathematical Thinking and Learning |

Publisher | Taylor and Francis |

Pages | 51-73 |

Number of pages | 23 |

ISBN (Print) | 9781315045955 |

DOIs | |

State | Published - Jan 1 2013 |

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### ASJC Scopus subject areas

- Social Sciences(all)

### Cite this

*Advanced Mathematical Thinking: A Special Issue of Mathematical Thinking and Learning*(pp. 51-73). Taylor and Francis. https://doi.org/10.4324/9781315045955