Abductive Arguments Supporting Students’ Construction of Proofs

Research studies show that it is not easy for the instructor to modify students’ argumentations based on conceptions that hardly evolve into theorems. Extending these studies, this chapter shows that abductive arguments can be effectively used by the instructor to support students in completing their argumentations, when they are struggling in solving a problem or they are using incorrect rules to solve it. Test results drawn from 60 undergraduate students who solved two algebraic problems, a factorization problem and a system of linear equations, are presented. Students who provided incomplete or incorrect solutions to one of these problems were selected for a one-on-one meeting with the instructor. The analysis of three cases shows how an instructor’s abductive argument can help students recognize their mistakes and modify their argumentations in solving these problems. Toulmin’s model is used to analyze the interaction between a student’s argumentation and an instructor’s intervention to show that instructors’ abductive arguments should be appropriately constructed in ways that support cognitive unity between students’ argumentation and proof.