Fostering argumentation and proof competencies in the mathematics classroom.

Abstract

The authors' project aimed at answering the question of how students in grades 5 to 10 can learn mathematical reasoning and the understanding and construction of proofs. In order to empirically evaluate a theoretical competency model for mathematical proofs, the project investigated whether heuristic worked-out examples foster students' argumentation and proof competencies. The authors were able to show that particularly lower-achieving students profited a lot from the worked-out examples, whereas higher-achieving students benefited less. They also found some indication that the positive effects of heuristic worked-out examples on students' proving competencies can be enhanced by suitable teacher behaviour. (DIPF/Orig.).