Abstract:

In the context of mathematics education, the first lesson serves as a gateway to the rest of the course. It is during this initial meeting that students form their first impressions of the course content, the instructor, and the approach to teaching. The beginning of a mathematics course often carries the weight of preconceived expectations and attitudes about the subject. Many students approach mathematics with a sense of apprehension, believing it to be difficult, abstract, or irrelevant to their everyday lives.

A typical first lesson might consist of an overview of the syllabus, introductory concepts, or the procedural aspects of the subject. However, this standard approach can often fail to inspire students or challenge their existing assumptions. Instead, beginning with an unexpected or unusual lesson can break through the barriers of preconceived notions and provoke students' curiosity. Moreover, these activities help create a sense of wonder, reducing anxiety and promoting a growth mindset.

In this article, we describe and discuss several activities designed by the authors with this perspective, which were tested during the first lessons of mathematics courses for first-year students of the Bachelor's degree in Agricultural Sciences. Some of the activities aim to surprise students, showing unexpected sides of math and sparking their curiosity and engagement, while others are more focused on working on emotional aspects to help them feel at ease.

In particular, we present two activities of the first type, designed to show students that mathematics is not just about doing calculations or memorizing formulas, but also has surprising and unexpected aspects. In the first activity, students must predict the shape that will emerge when a folded sheet of paper, prepared according to specific folding rules demonstrated by the instructor, is cut with a single scissor stroke. The unexpected outcome challenges their intuition and highlights the beauty of mathematical reasoning. In the second activity, students receive a sheet displaying a seemingly disorganized image and must fold it correctly to reconstruct a coherent picture. This exercise serves as a metaphor for the learning process in mathematics, where seemingly fragmented concepts come together to form a meaningful whole. Both activities aim to make the first lesson an engaging and thought-provoking experience, setting the stage for an explorative and dynamic approach to the subject.

Moreover, we present two activities of the second type focusing on students’ emotional approach to the course. In the first one, students were asked to anonymously share a word or an image on a Padlet to express how they perceive mathematics. This activity encouraged self-reflection and helped students see that their feelings—whether excitement, anxiety, or curiosity—are shared by others. In the second activity, students wrote a piece of advice on a small sheet of paper, either for themselves or for their peers, on how to "survive" the mathematics course. This exercise promoted a supportive classroom environment and encouraged students to adopt a proactive approach to learning. Both activities aimed to reduce anxiety and help students embrace the course with a more open and constructive mindset.

Keywords:

Mathematics education, students engagement, lessons' plan.