Abstract
In this chapter, we examine the relevance of and interest in including some instruction in logic in order to foster competence with proof in the mathematics classroom. In several countries, educators have questioned of whether to include explicit instruction in the principles of logical reasoning as part of mathematics courses since about the 1980s. Some of that discussion was motivated by psychological studies that seemed to show that "formal logic ... is not a model for how people make inferences" (Johnson-Laird 1975 ). At the same time, university and college faculty commonly complain that many tertiary students lack the logical competence to learn advanced mathematics, especially proof and other mathematical activities that require deductive reasoning. This complaint contradicts the view that simply doing mathematics at the secondary level in itself suffices to develop logical abilities. In addition, in many countries prospective elementary and secondary teachers arrive at university with poor logical reasoning abilities. One questions whether, if they do not learn basic logical principles, these candidates will graduate as teachers able to guide their own students' reasoning. Enhancing the teaching of mathematics thus calls for increasing teachers' awareness of crucial logical aspects of proof. The question is how best to achieve this aim. We discuss this question and offer some examples intended to provide ideas about how to develop teachers' and students' logical competence and how to modify curricula to foster development of these abilities. First, we review various positions on the role of logic in argumentation and proof; we then discuss them from an educational perspective; and finally, we offer suggestions that emerged from the contributions of the members of our working group.