Generalization: Strategies and representations used by sixth to eighth graders in a functional context

Abstract

We conducted a descriptive exploratory study in which we analyzed 313 sixth to eighth grade students’ answers to a word problem, accompanied by diagrams, involving generalization in an algebraic functional context. In this research we jointly addressed two objectives: (a) to determine the strategies deployed by students to generalize and (b) to identify the types of representation used to express their generalizations. We integrated how regularities are produced, evidenced in structures and represented by students. One of the most prominent findings was that functional strategy was used by almost all the students who generalized. They expressed the generalization using verbal, symbolical or multiple representations. Ways of expressing regularities that are not restricted to algebraic symbolism are also shown. Although the potential to identify functional relationships was observed in sixth graders, seventh and eighth school students were able to represent more varied and structurally complex relationships. However, no relevant differences in generalization strategies were found between students of different ages with and without previous algebraic training