Abstract
Fresh university students face from the very beginning the need to study and develop by themselves more and more complex reasoning and proofs, which they had little opportunity to make in their secondary studies, including in the scientific tracks. In this article, we focus on the notion of implication. We first come back to the main known difficulties; then we present theoretical tools allowing to foresee and analyze these difficulties. Based on our practice as teachers in undergraduate mathematics and by research in didactics of mathematics, we consider that for the teaching of notions of logic it is necessary to find a balance between a formal approach, which is known to be not effective, and an approach that would eliminate the formal aspects which is also known to be not effective. Then, we will propose activities aiming explicitly to work on aspects related to the notion of implication, while mentioning opportunities for reinvest the knowledge developed during these activities in the teaching and learning of other concepts.