1,721,001 research outputs found
La validation dans l'enseignement des probabilités au niveau secondaire
Get PDFOur research is concerned with the question of validation in the teaching of probabilities for Grade 9 and 10 students (age 14 and 15). We adopted the theoretical and methodological model of Mathematic Working Spaces associate to notion of probabilistic paradigm is used to characterize validation in the teaching of probability. The research is based on three successive studies. The first one is exploratory and aims at comparing both the validation practiced in probability and geometry. It showed that semiotics registers are favored to validate in probability and are more used than in geometry. Through the analysis of various tasks implemented at various school levels and related to three categories of tasks (simple, complex, rich) the second study shows highlights different forms of validation depending on the category of the task and the class level considered. The last study, based on interviews with teachers, leads to define the various types of validation adopted by teachers. As findings of the research and based on the data coming the three studies, some characteristics of validation in probability are given and show the specific originality of the teaching of probability in France.Notre recherche porte sur la question de la validation dans l’enseignement des probabilités en classe de 3e et de 2nde. Nous avons adopté le modèle des Espaces de Travail Mathématique et la notion de paradigme probabiliste pour caractériser la validation dans l’enseignement des probabilités. Nous avons mené notre recherche en suivant trois sortes d’enquête. La première est exploratoire, elle vise à comparer la validation pratiquée dans les deux domaines, probabilités et géométrie. Elle a permis de mettre en évidence la place privilégiée des registres sémiotiques dans le discours de la validation en probabilités par rapport à la géométrie. La deuxième enquête s'appuie sur l’étude de tâches mises en oeuvres dans différents niveaux de classe et relevant de différentes catégories de tâches (simple, complexe, riche). Elle met en évidence l’existence de différentes formes de validation, qui dépendent de la catégorie de la tâche et du niveau de classe considéré. Enfin, une dernière enquête, sous forme d'entretien auprès des enseignants, a permis de dégager plusieurs styles de validation adoptés par les enseignants. L’étude de l'ensemble des données de ces trois enquêtes donne une caractérisation de la validation probabiliste et de sa singularité dans l’enseignement probabiliste en Franc
Signs and validation in the teaching of geometry at the end of compulsory schooling in France: A case analysis
No full textInternational audienceIn the first part of the communication, we present the research question, as well as the theoretical framework and methodology used to answer this question. In the second part, we describe a task given to students and provide a detailed analysis of some extracts from the session we observed. Based on the results obtained from the analysis, the last part provides a practical answer to our research question
On forms of geometric work: a study with pre-service teachers based on the theory of Mathematical Working Spaces
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La pratique de la polyvalence vécue par les professeurs des écoles débutants en France
No full textInternational audienceIn this paper, we present a study of interdisciplinarity (polyvalence) by pre-service trainee teachers (PES in french) is observed in the context of a training course that focus on school subjects. The training design allows PES to discover the theoretical foundations of interdisciplinary teaching are acquired through research articles. It also helps them to design and practice a session based on interdisciplinarity, in a collaborative and iterative way follows the principles of "MicroTeaching Lesson Studies". The results of this study show the existence of two main forms of interdisciplinary in the practices reported by PES.Dans le cadre de cette contribution, nous présentons une étude portant sur la pratique de la polyvalence par des professeurs des écoles stagiaires (PES), dans le contexte d’un dispositif de formation centré sur la polyvalence disciplinaire. Ce dispositif permet aux PES de découvrir les fondements théoriques de la polyvalence disciplinaire à travers des articles de recherche. Il les aide également à concevoir et à mettre en pratique une séance de polyvalence, de façon collaborative et itérative selon le principe des « MicroTeaching Lesson Studies ». Les résultats de cette étude montrent l’existence de deux principales formes de pratique de polyvalence dans les pratiques déclarées par les PES
Methodological Aspects in the Theory of Mathematical Working Spaces
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Personal geometrical work of pre-service teachers: a case study based on the theory of Mathematical Working Spaces
No full textInternational audienceIn this contribution, we intend to revisit the interplay between geometrical paradigms GI and GII in the context of the current French curriculum, which gives an important place to modelling activities in mathematics learning. We asked master students to perform a geometric modelling task on the estimation of the area of a field. The resolution of the task requires an articulation between GI and GII by considering measurement and approximation. From this first study, it results that the vast majority of students have developed a geometric work in the GI paradigm by mobilizing a low use of the classical property-based proof discourse. These results question teacher training and, more broadly, the today's mathematics teaching in France
On dialectic and dynamic links between the Mathematical Working Space model and practice in the teaching and learning of mathematics
No full textInternational audienceIn this communication, we address the specific relationships between the Mathematical Working Space model (MWS model) and practice in the teaching and learning of mathematics. The strong and positive interactions existing between these two aspects are illustrated with two examples from geometry and probability teaching. They show how some theoretical constructs as MWS diagram can enlighten practice and, conversely, how studies on practice nourish the model with new tools such as "comics", "complete mathematical work" or "emblematic tasks". A decade ago, the Mathematical Working Space (MWS) model has been introduced as a theoretical and methodological framework dedicated to identify and shape the mathematical work in schooling. Developed by researchers working collaboratively in various countries with, sometimes, very different educational approaches in Europe (France, Spain, Cyprus), Latin America (Chile, Mexico…) and North America (Canada), the model is deeply rooted in the teaching of mathematics in real classrooms. This communication aims at showing dynamics and dialectics between the MWS model and relevant questions to education practice. After a short presentation of the MWS model, we show first how it can be used to deal with the question of planning series of tasks in the teaching and learning of geometry. That leads us to introduce two new constructs: the methodological tool of "comics" used to describe the evolution and circulation of the mathematical work and the more theoretical idea of "complete mathematical work" which allows qualifying the final nature of this circulation within the diagram. Then, these two new tools are used for the study of the teaching of probability and statistics. In France, this teaching is relatively new and it is now initiated on modeling tasks with use of technological tools. This leads us to check the relevance of the above constructs and identify two kinds of incompleteness of mathematical work and, in addition, to draw out certain specific tasks, named "emblematic tasks". Designed on these former results, our present research aims at tracking transformations made by teachers when they adapt these "emblematic tasks" to their classrooms. A short insight in the MWS model Extending the research work developed by Houdement and Kuzniak (2006) in didactics of geometry, the MWS model emerged during the last decade. The model, especially in geometry, had already been presented during former CERME meetings (Kuzniak and Nechache, 2015). A recent issue of ZDM-Mathematics Education (48-6, 2016) is devoted to this model and we refer the reader to this issue for further details and discussions about the MWS model. Some elements of the introduction (Kuzniak, Tanguay and Elia, 2016) to this issue are used to present the framework
Personal geometrical work of pre-service teachers: a case study based on the theory of Mathematical Working Spaces
No full textInternational audienceIn this contribution, we intend to revisit the interplay between geometrical paradigms GI and GII in the context of the current French curriculum, which gives an important place to modelling activities in mathematics learning. We asked master students to perform a geometric modelling task on the estimation of the area of a field. The resolution of the task requires an articulation between GI and GII by considering measurement and approximation. From this first study, it results that the vast majority of students have developed a geometric work in the GI paradigm by mobilizing a low use of the classical property-based proof discourse. These results question teacher training and, more broadly, the today's mathematics teaching in France
Personal geometrical work of pre-service teachers: a case study based on the theory of Mathematical Working Spaces
No full textInternational audienceIn this contribution, we intend to revisit the interplay between geometrical paradigms GI and GII in the context of the current French curriculum, which gives an important place to modelling activities in mathematics learning. We asked master students to perform a geometric modelling task on the estimation of the area of a field. The resolution of the task requires an articulation between GI and GII by considering measurement and approximation. From this first study, it results that the vast majority of students have developed a geometric work in the GI paradigm by mobilizing a low use of the classical property-based proof discourse. These results question teacher training and, more broadly, the today's mathematics teaching in France
On dialectic and dynamic links between the Mathematical Working Space model and practice in the teaching and learning of mathematics
No full textInternational audienceIn this communication, we address the specific relationships between the Mathematical Working Space model (MWS model) and practice in the teaching and learning of mathematics. The strong and positive interactions existing between these two aspects are illustrated with two examples from geometry and probability teaching. They show how some theoretical constructs as MWS diagram can enlighten practice and, conversely, how studies on practice nourish the model with new tools such as "comics", "complete mathematical work" or "emblematic tasks". A decade ago, the Mathematical Working Space (MWS) model has been introduced as a theoretical and methodological framework dedicated to identify and shape the mathematical work in schooling. Developed by researchers working collaboratively in various countries with, sometimes, very different educational approaches in Europe (France, Spain, Cyprus), Latin America (Chile, Mexico…) and North America (Canada), the model is deeply rooted in the teaching of mathematics in real classrooms. This communication aims at showing dynamics and dialectics between the MWS model and relevant questions to education practice. After a short presentation of the MWS model, we show first how it can be used to deal with the question of planning series of tasks in the teaching and learning of geometry. That leads us to introduce two new constructs: the methodological tool of "comics" used to describe the evolution and circulation of the mathematical work and the more theoretical idea of "complete mathematical work" which allows qualifying the final nature of this circulation within the diagram. Then, these two new tools are used for the study of the teaching of probability and statistics. In France, this teaching is relatively new and it is now initiated on modeling tasks with use of technological tools. This leads us to check the relevance of the above constructs and identify two kinds of incompleteness of mathematical work and, in addition, to draw out certain specific tasks, named "emblematic tasks". Designed on these former results, our present research aims at tracking transformations made by teachers when they adapt these "emblematic tasks" to their classrooms. A short insight in the MWS model Extending the research work developed by Houdement and Kuzniak (2006) in didactics of geometry, the MWS model emerged during the last decade. The model, especially in geometry, had already been presented during former CERME meetings (Kuzniak and Nechache, 2015). A recent issue of ZDM-Mathematics Education (48-6, 2016) is devoted to this model and we refer the reader to this issue for further details and discussions about the MWS model. Some elements of the introduction (Kuzniak, Tanguay and Elia, 2016) to this issue are used to present the framework
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