DIGITAL RESOURCES AND MATHEMATICS TEACHERS PROFESSIONAL DEVELOPMENT AT UNIVERSITY

International audienceFor university mathematics as for other levels, a profusion of digital resources is available for teachers. This evolution impacts the teacher's practices, and contributes to teachers' professional development. Retaining here a focus on the interactions between teachers and resources, I study the use of digital resources for the teaching of mathematics at university, and how this use articulates with teachers' professional knowledge and its evolution. I also investigate the consequences of digital resources for teachers' collective work. I consider these issues, drawing on a case study concerning a mathematics lecturer working with computer science students

Travail collectif des professeurs et démarches d'investigation dans l'enseignement des sciences

National audienceDans un contexte d'incitations institutionnelles à la mise en place, dans les classes, de démarches d'investigation dans l'enseignement des sciences (DIES), nous étudions la question des collectifs, impliquant des professeurs, et susceptibles de contribuer à cette mise en place. Ces collectifs peuvent être de différentes natures : constitués spontanément ou délibérément ; associant seulement des professeurs, ou impliquant également des formateurs, des chercheurs, ou des élèves ; fondés sur un projet commun à leurs membres, ou simplement liés par un intérêt partagé. Nous nous centrons ici sur des collectifs qui poursuivent un objectif de formation de leurs membres aux DIES. En nous appuyant sur deux exemples de recherches récentes en didactique des mathématiques, nous nous penchons sur les questions suivantes : - quels types de collectifs peuvent contribuer à des évolutions de pratique, en direction des DIES ? Au sein de quels dispositifs de formation ? - quelles évolutions peut apporter le numérique, dans le développement de communautés de professeurs en formation, comme dans le développement professionnel de ces professeurs

Technology and resources use by university teachers

International audienceIn this paper we introduce the study of the use of resources by mathematics teachers at university. The available resources evolve, in particular concerning Open Educational Resources offered on the Internet. Studying the consequences of these evolutions for the teaching and learning practices requires to introduce a comprehensive concept of resource. A resource for the teacher is defined here as anything likely to resource the teacher's practice: technologies, but also traditional textbooks on paper, or even discussions with colleagues. Teachers look for resources, transform them: we call this the documentation work of a teacher. Along this work, teachers develop documents, which associate resources and professional knowledge. The structured set of all these documents, developed along the years by a teacher is called his/her documentation system. Understanding the evolutions resulting from the use of different kinds of resources requires to study the teachers' documentation systems. We set up a study of these systems in the context of a university in France, investigating the work of six teachers with different profiles for their teaching in the first and second year of university with scientific students

Geometric thinking in a n-space

International audienceWhat does “thinking geometrically” mean in a n-dimensional vector space, with n>3?According to several authors, like Fischbein, or Harel, a productive reasoning in mathematics always relies upon an intuitively accepted model. A first possibility of model in dimension n is provided by the use of coordinates; the use of that model can be called “analytic thinking”. But other possibilities exist, related with synthetic geometry; in that case the expression “geometric thinking” applies. I will display some of these possibilities here, and show on a particular example how they can intervene in students problem solving processes in linear algebra

Resources, at the core of mathematics teachers' work

International audienceMathematics teachers work with resources in class and out of class. Textbooks, in particular, hold a central place in this material. Nevertheless, the available resources evolve, with an increasing amount of online resources: software, lesson plans, classroom videos etc. This important change led us to propose a study of mathematics teachers documentation. Mathematics teachers select resources, combine them, use them, revise them, amongst others. Teachers' documentation is both this work and its outcome. Teachers' documentation work is central to their professional activity; it influences the professional activity, which evolves along what we call professional geneses. In this conference, I introduce a specific perspective on teachers resources, which enlightens in particular the changes caused by digitalization, and in particular Internet resources

Mathematics teacher education advanced methods: an example in dynamic geometry

International audienceWe present a research work about an innovative national teacher training program in France: the Pairform@nce program, designed to sustain ICT integration. The Pairform@nce trainings are grounded in a principle of collective lesson design by teams of trainees; they associate face-to-face and distant training. We study here a training for secondary school teachers, whose objective is to foster the development of an inquiry-based approach in the teaching of mathematics, using investigative potentialities of dynamic geometry environments (DGE). We adopt the theoretical background of the documentational approach to didactics for studying how a training organizing the design of lessons by teachers teams can contribute to teacher professional development, directed in particular towards more inquiry in the classroom supported by DGE. This approach conceptualizes the interactions between teachers and resources as geneses: complex, long-term processes, associating evolutions and stability. In the frame of this approach, for studying these geneses, we develop a specific methodology: we organize a follow-up of teachers during several weeks; during this period, the teachers fill a logbook describing their activity; they answer to questionnaires and interviews; we also collect as completely as possible the material resources involved in their work. We followed in particular the work of a team of trainees; drawing on the data collected, we analyse their professional development, related with the training. We discuss on a more general level, the consequences of a training based on collective documentation work for the integration of technology by mathematics teachers

Ressources en ligne et enseignement des mathématiques

National audienceLes ressources en ligne accessibles pour les professeurs, les élèves et les autres acteurs du système éducatif sont de plus en plus nombreuses. En mathématiques, alors que l'intégration des logiciels de calcul formel ou de géométrie dynamique se heurte encore à des résistances importantes, certaines ressources en ligne sont massivement utilisées par les enseignants, dans la préparation de leurs cours comme en classe avec les élèves. La recherche en didactique des mathématiques s'est donc intéressée à ces ressources, et aux conséquences de leur emploi pour l'apprentissage, l'enseignement, et le développement professionnel des enseignants. Dans cette conférence, nous présentons certains des résultats que nous avons pu établir, et nous évoquons pour les mettre en perspective un panorama de travaux internationaux

Démarches d'investigation : exemples avec le boulier virtuel, la calculatrice et le TBI.

Le groupe TREMA-1 s'intéresse aux usages de ressources numériques au premier degré pour l'enseignement des mathématiques. Nous présentons et analysons ici deux séances suivies cette année : en CE1 avec le boulier virtuel et en CM1/CM2 avec la calculatrice. Nous montrons que dans les deux cas, ces ressources ont permis aux élèves de développer une démarche d'investigation. De plus, les enseignants étaient munis de tableaux blancs interactifs (TBI), qui ont joué un rôle essentiel pour les mises en œuvre en classe, en lien avec ces démarches d'investigation. Au cours de l'année 2009-2010, le groupe TREMA-1 a poursuivi son objectif d'accompagnement de l'intégration d'outils TICE au premier degré, en s 'attachant particulièrement à des usages relevant d'une démarche d'investigation, à des titres divers. Nous présentons d'abord le questionnement général auquel se rattachent ces travaux ; puis les spécificités du travail mené cette année. Nous développons ensuite deux exemples de séquences, en cycle 2 et en cycle 3

Didactic contract and secondary-tertiary transition: a focus on resources and their use

International audienceIn this article we claim that the concept of didactic contract can help to develop a deeper understanding of the secondary-tertiary transition, in particular by showing changes at three different levels: at the general, institutional level; at the level of the discipline concerning mathematical practices; and at the level of a given mathematical content. In fact, we argue that the didactic contract is linked to the use of and interaction with different resources, by teachers and students, in the sense that their use is shaped by the contract; and at the same time the available resources shape the mathematics taught. We draw here on two studies, one in the UK and one in France, to illustrate how a focus on resources can inform us about contract rules at the different levels