Simon Modeste’s research while affiliated with French National Centre for Scientific Research and other places

This chapter deals with the recent development of computational thinking (CT) in the curricula of many countries, principally in mathematics. It aims at discussing, broadly, how CT changes the mathematical activity and impacts mathematical contents. More precisely, we study the relations between mathematics, computer science, mathematical thinking, and computational thinking, and discuss new content at the interface of computer science and mathematics as well as the transformation of mathematical content due to the integration of CT. We ground our discussions on examples of integration of CT and computer science in various countries; we further discuss the origins of CT in mathematics education and offer an epistemological reflection on the disciplines of mathematics and computer science. Finally, we discuss related issues for classroom implementation, teaching resources, and teacher development.

In this paper, we present an activity to introduce the idea of public-key cryptography and to make pre-service STEM teachers explore fundamental informatics and mathematical concepts and methods. We follow the Theory of Didactical Situations within the Didactical Engineering methodology (both widely used in mathematics education research) to design and analyse a didactical situation about asymmetric cryptography using graphs. Following the phases of Didactical Engineering, after the preliminary analysis of the content, the constraints and conditions of the teaching context, we conceived and analysed the situation a priori, with a particular focus on the milieu (the set of elements students can interact with) and on the choices for the didactical variables. We discuss their impact on the problem-solving strategies the participants need to elaborate to decrypt an encrypted message. We implemented our situation and collected qualitative data. We then analysed a posteriori the different stategies that participants used. The comparison of the a posteriori analysis with the a priori analysis showed the learning potential of the activity. To elaborate on different problem-solving strategies, the participants need to explore and understand several concepts and methods from mathematics, informatics, and the frontier of the two disciplines, also moving between different semiotic registers.

This chapter focuses on the relations between mathematics and other disciplines through the lens of school curricula. The debates between teaching mathematics as a 'service' discipline and per se is old. In mandatory curricula, it is generally mentioned that mathematics is useful and serves valuable purposes in everyday life, other disciplines and for future study and vocational pathways of the students. Despite this, designing a mathematics curriculum that takes into account the relation with other disciplines, with applications and with the future needs of students is a hard task, and the balance between these aspects and the mathematical work itself has to be found.

In CERME12, our working group “Algorithmics” started its work as a newly established TWG. Since algorithms have always been at the heart of mathematics and their importance has been steadily in- creasing since the beginnings of theoretical computer science, the design and analysis of algorithms – called algorithmics (Traub 1964, Knuth 1985) – lies at the intersection of mathematics and computer science. For this reason, on the one hand, various algorithms and algorithmic activities have their traditional place in mathematics curricula at all levels. At the school level, mathematics and computer science have interacted since the 1980s, when many schools set up labs with computers equipped with programming software. On the other hand, many questions arise in the context of teaching and learning algorithms: a first, more applied group of questions aims at algorithms in mathematics education and curricula, a second, more theoretical group of questions seeks to clarify the concepts of algorithm and algorithmic thinking.

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. Subject Classification: 97D99, 97K99, 97P80

The IREMs are a French experience of sustainable collaborative work between teachers and with academics started 50 years ago. We investigate this experience through the study of the collaborative work developed in an IREM group in Montpellier (ResCo), which provides a device or collaborative problem solving between classes, and facilitates collaboration between teachers.

This contribution takes place in the context of a research project 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.

This article is devoted to the teaching and learning of Algorithmics, discipline at the intersection of Informatics and Mathematics. We focus on the didactic transposition of Algorithmics in secondary school in France and Ukraine. Based on epistemological and didactical frameworks, we identify the general characteristics of the approaches in the two countries, taking into account the organization of the contents and the national contexts (in the course of Mathematics in France and in the course of Informatics in Ukraine). Our results give perspectives to understand the place that Algorithmics can hold in the teaching and learning of Mathematics and Informatics.

–We are interested in the pupils’ and students’ conception of main notions of Algorithmics in the transition “secondary school-university” in France. Using an elaborated questionnaire and an analysis grid based on an epistemological model, we show how this conception evolves with time, in particular developing the object dimension of the notion “algorithm” in the students’ conception during the first years of university.