Learning outcomes

In connection with the teacher competency framework:

3° Competencies as a learning organizer and facilitator within an evolving dynamic

3.a. Master disciplinary content, its epistemological foundations, its scientific and technological developments, its didactics, and the methodology of its teaching.

4° Competencies as a reflective practitioner

4.a. Critically read the results of scientific research in education and didactics, and draw inspiration from them for teaching practice; also rely on various disciplines within the human sciences to analyze and act in professional situations.

Goals

The student will be able to:

  • Become aware of his own initial conceptions regarding mathematics teaching.
  • Develop these conceptions towards a position that aligns both with research findings and with current legal requirements in compulsory education.
  • Integrate into his practice the concepts and theoretical frameworks addressed in this course unit.
  • Implement and critically analyze the mathematics curricula and syllabi used in secondary education.


Content

In this course, students will be introduced to the foundational concepts of mathematics didactics, particularly the theory of didactic situations, the phenomenon of the didactic contract and its consequences, various types of obstacles (epistemological, didactic, ontogenetic...), and the process of didactic transposition and its implications.

These concepts will be explored through the discovery and discussion of selected readings in mathematics didactics. Highlighting these concepts will enable a critical and in-depth analysis of textbooks, curricula, official guidelines, and teaching sequences.

Table of contents

1 – Practical engagement based on a didactic sequence validated by research

2 – Presentation of the foundational concepts of mathematics didactics within the theory of didactic situations, through reflective reading of texts from the literature in mathematics and science didactics

3 – Analysis of the curricula and official guidelines for lower secondary education

Exercices

The exercise sessions will be dedicated to student-led presentations of classroom activities in a micro-teaching format.

Each presentation will be followed by a discussion with peers and the instructor to enhance its didactic effectiveness.

The didactic concepts covered in the course will be reinvested during these sessions.

Teaching methods

The course is based on interaction with students and is shaped by their reactions, questions, and reflections. Attendance at all sessions is therefore mandatory.

Most of the key concepts are presented visually, and this material is supplemented by critical readings, discussions, role-playing activities, and classroom observation of teaching sessions.

Assessment method

The final grade is based on three learning activities (LAs):

  • A written exam, with only a scientific calculator allowed, covering the entire secondary school mathematics curriculum (50% of the final grade)
  • Regular updates to the portfolio accompanying the various course sessions (10% of the final grade)
  • The preparation of a didactic sequence integrating the concepts covered during the course sessions and practiced during the exercise sessions (40% of the final grade)


Sources, references and any support material

Baruk S., "Si 7=0 - Quelles mathématiques pour l'école", Odile Jacob, Paris, 2004. 


Johsua S. - Dupin J.J., "Introduction à la didactique des sciences et des mathématiques", Presses Universitaires de France, Paris, 1993. 


Briand J. - Chevalier M.C., "Les enjeux didactiques dans l'enseignement des mathématiques", Hatier, Paris, 1995. 


Brousseau G., "Théorie des situations didactiques", La Pensée Sauvage, Grenoble, 1998. 

Language of instruction

French