Interaction between Knowledge and Contexts on Understanding Abstract Mathematical Concepts

The purpose of the present study was to investigate the effects of sparse vs real contexts on the understanding of abstract mathematical concepts regarding the interpretation of linear graphs. Four experiments addressed this issue: two focused on children's performance (N = 124 and 35, respectively; mean age about 12 years old) and two focused on adults (N = 165 and 169, respectively). In all four experiments subjects were asked to interpret isomorphic linear graphs. The tasks were embedded in sparse vs real contexts. Taken together, results of all four experiments showed that a sparse context facilitated understanding of abstract mathematical concepts more than real contexts. In addition, content analysis of students' responses showed that students activated different knowledge structures in solving the isomorphic tasks embedded in the various contexts. The theoretical and practical implications of the findings are discussed.