Elementary methods

Initial situation

“Elementary Methods” is a course offered in the Faculty of Science in the Mathematics and Computer Science sections. Depending on the program, this course is offered at the Bachelor or Master level. This course is also open to college students as part of the Athena program.

The teacher’s objective was to offer students a different format than the traditional lecture followed by application sessions. The chosen approach is exactly the opposite, it is through problem solving before and during the course that students will discover the mathematical principles that will be presented afterwards.

Project implementation

For each new topic, students are presented with a set of problems. They will solve these problems either in small groups during the sessions or individually at home. At the pedagogical level, this problem-solving approach in mathematics allows students to focus not only on the solution and the tools, but rather on the reasoning and the methodology. The students are not in a situation of passive listening to the teaching team, but in an active process of autonomous reflection that will allow them to better integrate the theoretical concepts.

During the exercise sessions, each assistant follows a group of ten students who solve the proposed problems at their own pace. At the beginning, these problems are very simple and then increase in complexity. Very few indications are given for guidance, the objective being precisely that the students are in difficulty, ask themselves questions and actively look for solutions to move forward, clues are given to them in case they get stuck.

Each week, students are also required to solve problems at home and record their solutions. Some of these problems are also presented orally to the assistants.

This course is evaluated on a continuous basis, with students earning points each week through written and oral assignments they have prepared at home. Two sessions of problem-solving examinations are also organized. The evaluation considers the students’ approach and reasoning, not only the solution provided.

Thoughts and advice

This student problem-solving approach can easily be transferred to other scientific disciplines. It is important to be flexible, to allow students the freedom to seek their own way of solving problems without imposing a single “correct” solution. The teaching team in its guidance should make sure to keep in mind these multiple approaches without constraining.

Before starting, it is important for the teaching team to have a thorough knowledge of the different subjects covered. The challenge is then to find problems related to the mathematical concepts to be transmitted while ensuring that the difficulty is adapted to the students. There are databases where old problems can be used and modified.

This new approach can be confusing for students at first. The first exercises can be frustrating at first. But the exchanges emulsify, the feedback with the teaching team guides a little, the corrections made week after week allow to reveal in part the methodology of reasoning. The system allows to capture the essence of what mathematics is, a creative search for solutions and not a mountain of theories and theorems.

Student feedback

“The correction of some of the exercises is very helpful as well as the time provided in order to work on the exercises in small groups.”

“The exercises are challenging. Having homework to do keeps the focus on the course.”

“Blends theory and exercises, which helps assimilate and develop our way of thinking.”

“Give a minimum of reference material, not just the resolution of the exercises. It seems to me that the resolutions could be more detailed.”