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This contribution takes place in the context of a research project 1 on the epistemological and didactical issues of interactions between mathematics and computer science. We make the hypothesis that, with the introduction of digital tools and computer science content in most curricula, significantly taking into account the epistemology of mathematics, computer science and their interactions is essential in order to tackle the challenges of mathematics and computer science education in the digital era. In view of this, addressing the question of proof in mathematics and computer science is a central didactical issue, which we examine in this contribution. We will elaborate on the links between the concepts of algorithm, proof, and program, and will argue for their significance in a general reflection on didactical issues in mathematics and computer science, in their teaching at high school and undergraduate levels.

The purpose of this work is to take a didactic look at a learning situation located at the interface between mathematics and computer science. This situation offers a first approach to the concept of artificial intelligence through the study of a reinforcement learning device. The learning situation, inspired by the Computer Science Unplugged approach, is based on a combinatorial game, along with a device that learns how to play this game. We studied the learning potential when the human players face the machine. After an a priori analysis using the Theory of Didactic Situations (TDS), we conducted a pre-experiment in order to strengthen our hypotheses. In this article, we will focus on the analysis of the didactic variables, the values we have chosen for these variables and their effects on students' strategies.

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