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.
Bibliographical noteFunding Information:
This research was supported by Grant No. 1596/13 from the Israel Science Foundation. In addition, the first author wishes to express his gratitude to the Technion Graduate School and Mandel Leadership Institute. We also wish to thank the anonymous reviewers for their valuable suggestions on the previous versions of this article.
© 2017, Springer Science+Business Media Dordrecht.
- Algebraic activities
- Integer sequences
- Project-based learning