Examining Students’ Algebraic Thinking in a Curricular Context: A Longitudinal Study

Abstract

This chapter highlights findings from the LieCal Project, a longitudinal project in which we investigated the effects of a Standards-based middle school mathematics curriculum (CMP) on students’ algebraic development and compared them to the effects of other middle school mathematics curricula (non-CMP). We found that the CMP curriculum takes a functional approach to the teaching of algebra while non-CMP curricula take a structural approach. The teachers who used the CMP curriculum emphasized conceptual understanding more than did those who used the non-CMP curricula. On the other hand, the teachers who used non-CMP curricula emphasized procedural knowledge more than did those who used the CMP curriculum. When we examined the development of students’ algebraic thinking related to representing situations, equation solving, and making generalizations, we found that CMP students had a significantly higher growth rate on representing-situations tasks than did non-CMP students, but both CMP and non-CMP students had an almost identical growth in their ability to solve equations. We also found that CMP students demonstrated greater generalization abilities than did non-CMP students over the three middle school years.