## Abstract

This article concerns student sense making in the context of algebraic activities. We present a case in which a pair of middle-school students attempts to make sense of a previously obtained by them position formula for a particular numerical sequence. The exploration of the sequence occurred in the context of two-month-long student research project. The data were collected from the students’ drafts, audiotaped meetings of the students with the teacher and a follow-up interview. The data analysis was aimed at identification and characterization of the algebraic activities in which the students were engaged and the processes involved in the students’ sense-making quest. We found that sense-making process consisted of a sequence of generational and transformational algebraic activities in the overarching context of a global, meta-level activity, long-term problem solving. In this sense-making process, the students: (1) formulated and justified claims; (2) made generalizations, (3) found the mechanisms behind the algebraic objects (i.e., answered why-questions); and (4) established coherence among the explored objects. The findings are summarized as a suggestion for a four component decomposition of algebraic sense making.

Original language | English |
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Pages (from-to) | 245-262 |

Number of pages | 18 |

Journal | Educational Studies in Mathematics |

Volume | 95 |

Issue number | 3 |

DOIs | |

State | Published - 1 Jul 2017 |

Externally published | Yes |

### Bibliographical note

Publisher Copyright:© 2017, Springer Science+Business Media Dordrecht.

## Keywords

- Algebraic activities
- Coherence
- Integer sequences
- Project-based learning
- Sense-making