The purpose of this paper is to contribute to the debate about how to tackle the issue of ‘the teacher in the teaching/learning process’, and to propose a methodology for analysing the teacher’s activity in the classroom, based on concepts used in the fields of the didactics of mathematics as well as in cognitive ergonomics. This methodology studies the mathematical activity the teacher organises for students during classroom sessions and the way he manages1 the relationship between students and mathematical tasks in two approaches: a didactical one [Robert, A., Recherches en Didactique des Mathematiques 21(1/2), 2001, 7–56] and a psychological one [Rogalski, J., Recherches en Didactique des Mathematiques 23(3), 2003, 343–388]. Articulating the two perspectives permits a twofold analysis of the classroom session dynamics: the “cognitive route” students are engaged in—through teacher’s decisions—and the mediation of the teacher for controlling students’ involvement in the process of acquiring the mathematical concepts being taught. The authors present an example of this cross-analysis of mathematics teachers’ activity, based on the observation of a lesson composed of exercises given to 10th grade students in a French ‘ordinary’ classroom. Each author made an analysis from her viewpoint, the results are confronted and two types of inferences are made: one on potential students’ learning and another on the freedom of action the teacher may have to modify his activity. The paper also places this study in the context of previous contributions made by others in the same field.

A Cross-Analysis of the Mathematics Teacher’s Activity. An Example in a French 10th-Grade Class

European Perspectives on Learning at Work: The Acquisition of Work Process Knowledge

Les rapports produits sur les SAS2 sont verses a la bibliotheque afin de mettre rapidement l’information a la disposition des chercheurs interesses. Afin d’en assurer l’exactitude et la qualite, ce rapport a ete soumis a un processus d’examen interne.

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Les outils de la recherche participative

We examine teachers’ classroom activities with the spreadsheet, focusing especially on episodes marked by improvisation and uncertainty. The framework is based on Saxe’s cultural approach to cognitive development. The study considers two teachers, one positively disposed towards classroom use of technology, and the other not, both of them experienced and in a context in which spreadsheet use was compulsory: a new curriculum in France for upper secondary non-scientific classes. The paper presents and contrasts the two teachers in view of Saxe’s parameters, and analyzes their activity in two similar lessons. Goals emerging in these lessons show how teachers deal with instrumented techniques and the milieu under the influence of cultural representations. The conclusion examines the contribution that the approach and the findings can bring to understanding technology integration in other contexts, especially teacher education.

Teachers’ emergent goals in spreadsheet-based lessons: analyzing the complexity of technology integration

In this paper, we address the issue of problem solving in classrooms in France through two different and complementary approaches: didactic research and curricular choices. These two approaches correspond to two different, but not independent perspectives on problem solving and we investigate the existing links between them. We show that in France, the solving of problems is given a central role both in didactic research and curricular choices and that problem solving, as generally understood, is an object taking controversial positions, and we try to elucidate the rationale behind such positions. This paper is structured into two main parts: the first part devoted to didactic research, the second part to curricula, and one last part, discussion, wherein we question didactic research and curricula as regards their potential for influencing the reality of problem solving in classroom practices.

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Problem solving in France: didactic and curricular perspectives

Resume Cet article presente des objectifs et une methodologie pour analyser les pratiques des enseignants et des enseignantes de mathematiques a partir de deroulements de seances en classe. Les transcriptions recueillies sont etudiees de deux points de vue complementaires: les premieres analyses sont liees aux apprentissages potentiels des eleves, reconstitues a partir des activites des eleves et de l'itineraire mathematique que l'enseignant ou l'enseignante a propose en classe, les autres analyses s'appuient sur le point de vue de l'enseignant ou de l'enseignante exercant son metier dans une institution, parmi des collegues, et en faisant jouer sa personnalite. Le travail de synthese mene a partir de ces analyses, conformement a notre hypothese de complexite et de coherence des pratiques, doit permettre de degager a la fois des contraintes communes a tous les enseignants et enseignantes d'un meme niveau et des marges de manœuvre au niveau de la classe, investies de maniere differente par chacun. On propo...

Le système complexe et cohérent des pratiques des enseignants de mathématiques: Une double approche

In this paper, we present how trainers and teachers activity can be analysed through articulating concepts and methods of cognitive ergonomics with notions and tools of discourse analysis. The aim is a better understanding of the determinants and the properties of their activities in order to contribute to improve the initial and on the job training of the training staffs, and to design useful trainers' support systems. Similarities and differences with approaches of other human-centred domains are presented. It is proposed to consider training as a case of open dynamic environment management, where the object of action is trainees' knowledge or competence. A key component of the trainer's activity is the control of how trainees go through the didactical process designed for trainees' learning. For this, the trainer uses discourse in face-to-face interaction as a crucial instrument for his/her action. Concepts issued from the pragmatics are used for analysing some dimensions of analysis of trainer's discourse, using examples from mathematics teaching and professional training. We discuss the differences related to the trainees: young children, adolescent and adults students, professionals, and to the type of training target: generic 'theoretical' knowledge, specific professional competence). In the conclusion, we will sketch some consequences for trainers' training and support.

Cognitive ergonomics, didactics and discourse analysis for the analysis of teachers' and trainers' activity

Les didactiques disciplinaires et professionnelles participent, au cote de l’ergonomie, de la sociologie et de la psychologie du travail, au developpement des connaissances concernant l’analyse de l’activite reelle en situation a l’ecole et au travail. Les chercheurs du domaine, peut-etre parce que la constitution de leur champ d’investigation est recent, precisent assez rarement l’origine de leurs sources. Dans cet article, nous nous efforcons de resituer ce qu’ils doivent a un chercheur don...

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Didactique psychologique. Application à la didactique de la psychologie de Jean Piaget de Aebli

A comprehensive approach is proposed for analysing interactions between organizational setting, task complexity, and individual cognitive activities. A triadic relationship ”actors-task-operational system” enables to take into account the ”vertical” and the ”hoizontal” dimension involved in collective work, through considering a task as a node in a network. Actors are defined as (system of) prescribers and (system of) operators linked by a ”contract” about the task. A task may be analyzed along three components: a target-state to be reached (a goal related to higher level purposes), a set of criteria for evaluation (related to more general values), and a set of resources and constraints. The notion of ”virtual operator” allows to use this framework for analysing individual or collective activities as well as for designing operational devices (including human-machine interaction). Examples are given for open dynamic environment management.

Janine Rogalski

Papers

Le système complexe et cohérent des pratiques des enseignants de mathématiques: Une double approche

Cognitive ergonomics, didactics and discourse analysis for the analysis of teachers' and trainers' activity

Didactique psychologique. Application à la didactique de la psychologie de Jean Piaget de Aebli

Organizational Setting and Task Complexity: Interactions with Collective and Individual Cognitive Activities