“Students who define themselves as not being good at mathematics very often steal the limelight.”

If we ask people in a quick survey what comes to mind when they hear the word 'mathematics,' the answer would most likely be related to somewhat unpleasant feelings about and an aversion to the subject. Throughout my years as a teacher, I have used several strategies to teach mathematics but had never managed to get my students to engage voluntarily in the learning process, until now. I want to share my experience with you in this article.

This is a very simple initiative that everyone can replicate: teaching maths through problem-solving. Let me clarify that this proposal is not about fostering problem-solving in the classroom, but about teaching and captivating students with mathematical knowledge from a problem itself.

"If I were to be invited to a salsa club where all the guests were professional salsa dancers, I wouldn’t dare take a step... but if I were simply instructed to create a melody and a dance associated to the same, the result would be quite different."

**- Jorge Bozt – **

**How can we ‘enchant’ with mathematics?**

First of all, let’s agree on one fundamental question: What do we mean by "problem"?

According to the curricula and programs of the Ministry of Education in Chile, "solving a problem involves tapping into not only a broad set of skills, but also the creativity to find and test different solutions."

For our purpose, I would like to add three key aspects to this definition:

1. A problem should be challenging but doable. In other words, students must feel capable of finding a solution at all times. 2. A problematic situation is not a problem for every student. Therefore, a problem must necessarily possess a certain degree of flexibility, making it possible to reduce or expand its complexity, without changing its core objective. 3. A problem must have several strategies for reaching its solution and, ideally, more than one possible answer. A problem with these characteristics permits the social construction of knowledge, applying not only mathematical concepts but also strategies for tackling the problem.

**Methodology**

A good problem needs to be accompanied by a good methodology. In this case, I decided on group dynamics, with randomly selected participants. Not knowing with whom you will be working adds an element of excitement.

Diverse leadership, collaboration and teamwork, and communication skills should also be promoted. In my teaching dynamics, the problem is presented to the group and there is minimal teacher intervention since the members of the group have to resolve any doubts on their own. Afterward, a final plenary is held in which the different problem-solving strategies are exposed and discussed, thus generating an environment filled with optimism and mutual understanding of the concepts being addressed.

These dynamics have confirmed that students are capable of achieving the same learning objectives pursued through traditional teaching (in which the basic concepts and content are presented, followed by some applications and then an attempt at increasing complexity) while generating a passion and liking for mathematics.

This experience has undoubtedly shown me over the past few years that you can learn and 'enchant' with mathematics through problem-solving.

I have tested this methodology in a variety of contexts and with different types of students: maths, humanities, and general education electives, as well as courses and workshops for teachers. In every case, I have found a common pattern: time goes by very quickly and participants are euphoric from beginning to end; in fact, students who define themselves as not being good at mathematics very often steal the limelight.

In general, pages that focus on Math Olympics offer interesting materials but require just a small adjustment, so I want to invite all my colleagues to dare to be math-education innovators through the implementation of problem-solving.

**About the author**

Jorge Bozt (jabozt@uc.cl) holds a Master’s degree in Mathematics Education and is currently teaching mathematics for future educators at PUC, Campus Villarrica, in Chile. He has also participated in creating and executing workshops and programs to foster problem-solving and mathematical reasoning in the classroom.