Étude fonctionnelle-structurelle de deux extraits de manuels anciens de géométrie

Cet article vise à montrer l’utilité d’une approche fonctionnelle-structurelle pour l’étude des manuels scolaires en mathématiques. L’approche s’inspire de trois sources : la théorie des fonctions du langage de Duval, le modèle des fonctions du langage dans la communication de Jakobson et le modèle des structures sémiotiques développé par Richard. Après avoir présenté l’approche dans la première partie, nous l’appliquons ensuite à l’analyse de deux courts textes, tirés des manuels de géométrie qui ont été en usage au Québec, dans les écoles secondaires de langue française. L’intention adidactique qui se dégage des deux textes montre comment les moyens sémiotiques mobilisés sont mis au sevice de la qualité de la communication avec l’éventuel lecteur.The objective of this article is to show the pertinence of a functional-structural approach to the study of mathematics school texts. This approach is based on three sources : Duval’s theory of language functions, Jakobson’s model of language functions in communication, and the model of semiotic structures developed by Richard. Following the presentation of the approach in the first part, the authors apply this to an analysis of two short texts taken from a geometry text used in French secondary schools in Québec. The adidactic objective that can be derived from these two texts shows how the semiotic means used can serve to improve the quality of communication with the future reader.Este artículo tiene por obetivo demostrar la utilidad de un enfoque funcional-estructural para el estudio de los libros de texto en matemáticas. El enfoque origina de tres fuentes : la teoría de las funciones del lenguaje de Duval, el modelo de las funciones del lenguaje en la comunicación de Jakobson y el modelo de las estructuras semióticas desarrollado por Richard. Una vez presentado el enfoque en la primera parte, lo aplicaremos luego al análisis de dos breves textos que proceden de libros de geometría que han sido utilizados en Québec, en escuelas secundarias de lengua francesa. La intención adidáctica que resalta de los dos textos demuestra cómo los medios semióticos movilizados sirven la calidad de la comunicación con el eventual lector.Dieser Beitrag hat sich zum Ziel gesetzt, die Nützlichkeit einer funktionell-strukturellen Methode für die Untersuchung von Mathematiklehrbüchern zu beweisen. Die Grundlage dazu bilden drei Quellen : Die Theorie der Sprachfunktionen von Duval, das Sprachfunktionsmodell von Jakobson sowie das Modell der semiotischen Strukturen von Richard. Nach Erläuterung unserer Ausgangsquellen bringen wir diese bei der Analyse zweier kurzer Texte aus Geometrielehrbüchern, wie sie an französischen Sekundarschulen in Québec in Gebrauch sind, zur Anwendung. Trotz der in beiden Texten enthaltenen undidaktischen Intention wird deutlich, wie die eingesetzten semiotischen Mittel für die Kommunikationsqualität mit dem potentiellen Leser eingesetzt werden

Reforms in education through the lens of Transactional Analysis theory

The question posed in this paper is why education reform movements don’t seem to bring the expected improvements and lead only to calls for new reforms. The paper seeks answers to this question by interpreting (a) teacher-students classroom interactions, and (b) interactions between ideologues of school reform movements and the public, in terms of certain concepts from Transactional Analysis theory, particularly the notion of Rescue Game. The focus is on reform movements in North America since early nineteenth century. Particular attention is paid to the writings of the main ideologue of the Common School Movement, Horace Mann, and to the phenomenon of survival until today of the bureaucratic public school system whose foundations were laid during this movement

A History of the Master in the Teaching of Mathematics (MTM) Program 1967 – 2018

The MTM – Master in the Teaching of Mathematics – program has been the oldest graduate program in the Department of Mathematics and Statistics of Concordia University, established in 1967, when Concordia was still the Sir George Williams University. Very quickly, however, the Department developed a Master of Science/Master of Arts in Mathematics program and, later, a PhD program in Mathematics. MTM survived about 50 years, until 2016 when admissions to the program were suspended, or until 2019 when the last MTM student graduated. In this document, we describe the program, its mission, degree requirements and courses. We present the context of the program’s creation in 1967 and the reasons for its suspension 50 years later. We present also the people – faculty and students – who made the program what it was: a lively space for critical reflection on mathematics education research and practice, always open to trying novel approaches to teaching mathematics. The tradition of critical reflection and trying different approaches to teaching mathematics has a chance to survive in the department after the suspension of the MTM program; MSc/MA students have the option of doing their research in the area of mathematics education. The purpose of writing this historical piece is to keep the memory of the MTM program at Concordia alive, and to create an easily accessible reference for graduates of the program when they apply for jobs or further graduate studies. The document has been written by the last director of the MTM program, Anna Sierpinska, with editorial help of her former student, Carol Beddard, an MTM 2012 graduate

Teaching absolute value inequalities to mature students

This paper gives an account of a teaching experiment on absolute value inequalities, whose aim was to identify characteristics of an approach that would realize the potential of the topic to develop theoretical thinking in students enrolled in prerequisite mathematics courses at a large, urban North American university. The potential is demonstrated in an epistemological analysis of the topic. It is also shown that this potential is not realized in the way the topic is presently taught in prerequisite mathematics courses. Three groups of students enrolled in such courses were each exposed to one of three approaches we conceived for teaching the topic, labeled the procedural (PA), the theoretical (TA), and the visual (VA) approaches. The design of the three lectures was constrained by institutional characteristics of college-level courses, and informed by epistemological and didactical analyses of the topic. It was found that following the VA lecture, which proposed two equally valid mathematical techniques (graphical and analytic), one of which could be used to test the validity of results obtained by the other, students were more likely to engage in some aspects of theoretical thinking. They displayed more reflective and systemic thinking than other groups, and dealt more effectively with the logical intricacies of absolute value inequalities. VA students appeared to have a synthetic grasp of the inequalities, and a flexibility of thought not displayed by PA and TA students. However, without sufficient attention to tasks not easily solved by graphical means, VA approach provided students with a way to avoid the challenges of systemic and analytic thinking, some of which were more apparent in TA students. PA students expectedly behaved more as procedural knowers, but we saw interesting examples of engagement with theoretical thinking while dealing with the procedures proposed in the PA lecture

6. Interaction des perspectives épistémologique, cognitive et didactique

Le problème central de la didactique des mathématiques est parfois formulé comme la recherche des conditions de la compréhension en mathématiques (Duval, 1996 ; Sierpinska, 1995a). Cette question peut être étudiée d’au moins trois points de vue : didactique, épistémologique, cognitif. Le point de vue didactique prend comme objet d’étude les conditions institutionnelles, liées à l’organisation des curricula, à la préparation des contenus en vue de l’enseignement, au temps de l’enseignement et ..

Quelques idées sur la méthodologie de la recherche en didactique des mathématiques liée à la notion d'obstacle épistémologique /

Septembre 1990Bibliogr.: f. 2

Research into the teaching and learning of linear algebra

It is commonly claimed in the discussions about the teaching and learning of linear algebra that linear algebra courses are badly designed and badly taught, and that no matter how it is taught, linear algebra remains a cognitively and conceptually difficult subject. This leads to (a) curricular reform actions, (b) analyzing the sources of students' difficulties and their nature, as well as (c) research based and controlled teaching experiments. This chapter is organized along these three axes of action and research. The chapter does not claim the title of an exhaustive review of research on the teaching and learning of linear algebra at the undergraduate level. All omissions should be blamed on the authors' ignorance rather than their bad will