Sense making through algebraic activities: A case study

This article presents 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 occurred in the context of two-month-long student research project. The data analysis was aimed at identification and characterization of the activities in which the students were engaged and the processes involved in the students’ self-imposed sense-making quest. We found that the sensemaking process consisted of a sequence of generational and transformational algebraic activities in the context of a global, meta-level activity, long-term problem solving. In this process, the students: (1) formulated and justified claims; (2) made generalizations, (3) found the mechanisms behind the algebraic objects; and (4) established coherence among the explored objects. The article is concluded by a proposal for a four-component decomposition of algebraic sense
making.