This article deals with peer-assessment in the context of higher education teaching in mathematics, and examines the nature of student activity when assessing work produced by peers. After an overview of research on peer assessment, we propose an experiment with students in a specific post-secondary scientific class, and analyze the activity of the students involved. Our analyses are based on a priori analyses of the proposed tasks and tools from research on students personal mathematical work. We base on written notes of assessments, observations of pairs in assessment situations, and answers to a questionnaire on the perception of their activity. We have identified some specific student activities during the peer assessment process, in particular related to the analysis and correction of proofs, but also to the awareness of the issues associated with evaluation. This enables us to argue for the potential of peer assessment in higher mathematics education.

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 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.

An emphasis on integrating learning in the disciplines of science, technology, engineering and mathematics (STEM) brings into focus specific examples of more general questions of coherence and relevance in relation to mathematics and other disciplines. By considering several dimensions both of relevance and of coherence in a range of reforms, this chapter describes the central role that mathematical modelling plays in transdisciplinary approaches to school curricula. It goes on to identify both the opportunities and the challenges that emerge in these reforms.

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. THE APPEARANCE OF ALGORITHMS IN CURRICULA A NEW OPPORTUNITY TO DEAL WITH PROOF? Simon Modeste, Cécile Ouvrier-Buffet

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 for collaborative problem solving between classes, and facilitates collaboration between teachers.

Nous presentons l'analyse de preuves de chercheurs sur l'equivalence de deux definitions du concept d'arbre en theorie des graphes, l'une des deux definitions etant de type recursif et l'autre non. L'analyse vise a mettre en lumiere la relation entre les notions de recurrence et de recursivite, telle qu'elle est percue par les experts, afin d'eclairer les questions didactiques que souleve leur apprentissage.

espanolPresentamos un analisis epistemologico del concepto de algoritmo que nos permite estudiar el proceso de transposicion didactica. Proponemos un modelo basado en la nocion de concepcion del modelo cK¢ y, mas precisamente en la nocion de concepcion Cµ, que apunta a representar la concepcion desde el punto de vista del saber sabio. Mostramos como esta nocion, con una definicion de problema adaptada, permite describir concepciones tomando en cuenta la diversidad de las representaciones del concepto algoritmo y tambien su dialectica herramienta-objeto. Al final, presentamos resultados obtenidos sobre la transposicion didactica en el instituto en Francia (lycee). EnglishWe present an epistemological analysis of the concept of algorithm that permits us to study the didactic transposition. We propose a model based on the notion of conception from the cK¢ model, more precisely on the notion of conception Cµ that aims to represent the conception from the point of view of the academic knowledge. We show how this notion, with an adapted definition of problem, allows us to describe conceptions, taking into account the diversity of representations of the concept algorithm and also its tool-object dialectic. Finally, we present some results we obtained about the didactic transposition in the French high school (lycee). francaisNous presentons ici une analyse epistemologique du concept d’algorithme permettant l'etude de la transposition didactique. Le modele est base sur la notion de conception du modele cK¢, plus precisement sur la notion de conception Cµ qui pretend a representer la conception du point de vue du savoir savant. Nous montrons comment cette notion, avec une definition de probleme adaptee, nous permet de decrire des conceptions qui prennent en compte la diversite des representations du concept d’algorithme ainsi que sa dialectique outil-objet. Enfin, nous presentons les resultats obtenus concernant la transposition didactique au lycee en France.

Cédric Fluckiger est maître de conférences au CIREL (Centre Interuniversitaire de Recherche en Éducation de Lille) en sciences de l’éducation et didactique de l’informatique. Il vient de publier aux Presses universitaires de Rennes un ouvrage intitulé « Une approche didactique de l’informatique scolaire », issu de ses recherches et adapté de sa note d’habilitation à diriger des recherches (HDR) éponyme.

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

. This paper questions the teaching and learning of mathematical modeling. We develop an epistemological study of the mathematization in the practices of experts in two fields: life sciences and industrial sciences. We use the results of this contemporary epistemological study to analyze and support the relevance of some problems designed to foster the devolution of the mathematical modeling process to the students. Then, we present our choices for implementing these problems in the classroom in link with this objective, and compare the students’ productions with the results of the epistemological analysis. Résumé