Didactique et épistémologie de la mathématique

Teacher(s)

Coyette Cécile; Ghorbal Sonia; Ninove Laure;

Language

French

Prerequisites

Basic training in mathematics (bachelor's level in mathematics).
Mastery of the discipline to be taught, i.e. 2nd and 3rd grade mathematics.
Clear and correct communication in the language of instruction both orally and in writing.
The interpersonal skills and professional postures normally expected of a teacher.

Main themes

Through the study of selected subjects in the high school curriculum, as well as various ways of approaching them, issues related to the construction of mathematical knowledge will be addressed. In particular:
- How to exploit, in order to teach the mathematical concepts and theories of the program, the everyday notions that prefigure them in students? The role of epistemological obstacles.
- How to foster a real capacity for reasoning and argumentation that is adapted to the level of the students? Levels of rigor. Need for correct expression in the French language.
- Identify difficulties and obstacles related to learning mathematics.
- Need to install a minimum of automatisms in students, without reducing their mathematical activities to routine.

Learning outcomes

At the end of this learning unit, the student is able to :

Contribution of the course to the learning outcomes of the master's program in mathematics. At the end of this activity, the student will have progressed in his/her ability to : - Communicate in a scientific manner. In particular, he/she will have developed the ability to:      - Structure an oral presentation by adapting it to the level of expertise of the interlocutors. - Mobilize the skills necessary to effectively enter the profession of upper secondary mathematics teacher and to evolve positively. In particular, the student will have developed the ability to:      - Teach in authentic and varied situations.      - Relate the mathematical content of the secondary school curriculum to that of university education.      - Compare and integrate different possible approaches to the main topics of the secondary school mathematics program, identify key steps and tricky points of the program.      - Implement learning devices that are appropriate, original, and relevant from both a rigorous and intuitive perspective.      - Formulate interdisciplinary examples in the form of problems to introduce, illustrate and implement mathematical concepts in the program.      - To exercise a reflexive look and to project oneself in a logic of continuous development. Course-specific learning outcomes. Upon completion of this activity, the student will be able to : - Produce instruction that is meaningful to students and promotes maximum real student activity. - Analyze existing textbooks and materials for students and teachers. - Analyze their own teaching practice and adapt it accordingly.

Content

This teaching unit consists of "equipping" students to become future teachers of mathematics in upper secondary schools. The aim is not only to present the elements of didactics and epistemology related to mathematics teaching but also to ensure the transfer and appropriation of these tools by future teachers.
We will deal with the construction of mathematical knowledge in students through the study of themes from the secondary school program, addressing, for example, questions such as :

•     How to exploit students' representations and errors to teach mathematical concepts and theories?
•     How to identify epistemological obstacles to learning?
•     What types of learning situations can be proposed in a mathematics course?
•     What is the role of the teacher in the context of a research activity on a problem?
•     How can we encourage students to develop a real capacity for reasoning and arguing?
•     What should we look for when evaluating students' learning?
•     ...

Teaching methods

The course is largely based on interactions with students.
Students will be actively involved, for example, in problem solving and in the research and analysis of teaching sequences.
Attendance is therefore essential and mandatory.
Readings will be offered to enrich and deepen the interactions between students and teachers. Preparations and assignments may be given, including in collaboration with students from non-French-speaking universities.

Evaluation methods

In this course, students are evaluated as follows :

• continuous assessment during the year (5% of the final grade): preparations, readings, active participation in the course; this part of the grade will be used for each session and may not be represented;
• a written exam in the January (and/or September) semester, open-ended and closed-book, on the learning of the first semester (40% of the final grade);
•  a written examination in the June (and/or September) semester, open-ended and closed-book, on the second quadrennial learning (40% of the final grade);
• an assignment, the instructions of which will be given during the year (15% of the final grade).

In order to pass this course, both the exam and the report must be passed.

• In the event of failure in at least one of these two parts, the overall grade for the unit will be calculated as the minimum between the weighted average of the different parts according to the coefficients indicated above and a 9/20.
• In the event of a serious deficiency (score less than or equal to 6/20) in at least one of these two parts, the overall score will be equal to the minimum of the scores of the different parts.

Course attendance is required. From the 3rd unjustified absence over the year or in the event of preparations not being made on time, the mark for the continuous evaluation part will be set to 0. Moreover, in accordance with article 72 of the General Regulations for Studies and Examinations, the course directors may propose to the jury that it refuse to register a student who has not attended at least 80% of the courses or who has not carried out a compulsory activity during the June and/or September session.
The use of generative AI as part of the work to be produced in this teaching unit is not authorized.

Other information

Complementary course to the general didactics course, to be taken preferably in parallel or after the latter.
This course is compulsory for students in the Aggregation program who are majoring in mathematics and for students in the Master's program in mathematics, didactics.

Online resources

The documents related to the courses are deposited on the online educational platform.

Bibliography

Faculty or entity

CAFC