The relation between Riemann sums and double integrals: results of a second research cycle

Abstract

Following a first research cycle of student understanding of the relation between Riemann sums and double integrals, we proposed a model (genetic decomposition) of how students may construct their understanding of these notions. Didactical materials were designed and implemented in the classroom to help students do the proposed constructions. This is a report of a second research cycle in which the effectiveness of these materials was studied. The same interview instrument was used in both cycles. Interviews’ responses from eleven students who did not use the materials and eleven who did were analyzed. Results show that students using the proposed materials and a collaborative didactical strategy, constructed a deeper understanding of the intended relation than those attending a lecture-based course.