Abstract:

The percentage of high school students experiencing frustration due to failing a math course can be quite significant, even leading them to the extreme of dropping out of high school. The reason could be that failing a course triggers negative feelings and a sense of personal failure, further hindering their learning. Statistics from the National Institute for the Evaluation of Education (INEE) and other studies show that approximately 14.9% of upper secondary education students in Mexico drop out of school, and among them, 30% to 40% face serious difficulties in mathematics. Although not all these students drop out exclusively due to this subject, it is a significant factor. That´s why it is important to design strategies that aid and motivate meaningful learning, especially for students who have not had positive experiences with mathematics. We believe that a practical approach, where the student identifies and defines the elements of a structure they have built, can help knowledge be more easily acquired. Conic functions, in particular, are difficult to visualize and understand when taught exclusively theoretically. The proposed activity aims to reinforce the content of conic functions in students who have previously failed and have a sense of self-failure, through a practical and enjoyable learning experience.

The activity was implemented from January to May 2024 with a group of 30 repeater students at PrepaTec campus Morelia in the Algebraic and Transcendental Functions course. It consists of constructing a movable hyperboloid structure using toothpicks and rubber bands, based on an instructional video. Each student adjusted the structure according to their choice, and subsequently, the mathematical software Desmos was used to analyze and define the main elements of the obtained hyperbola: equation, coordinates of the center, vertices, foci, focal length, equations of the directrix, eccentricity, transverse axis, and conjugate axis.

After completing the activity, an identical quiz to the one they took the first time they took the course was administered, resulting in an average score of 56 initially and 87 on the second occasion. Additionally, a satisfaction survey was conducted where 100% of the students expressed that the approach to the topic made the content much clearer compared to the first time, and they felt very proud of their work.

The activity not only allowed students to build a physical model of a mathematical structure but also helped them better understand its properties and applications. The combination of hands-on activity with digital analysis in Desmos made learning more dynamic and accessible, increasing students' interest and participation in the study of conic functions. Achieving positive results on the exam after completing the activity was crucial for the students as it reinforced their confidence in their abilities and demonstrated that they could overcome previous difficulties with the subject. Since these are repeating students, achieving a personal success when they hadn't been able to before involves a significant effort in breaking down emotional barriers and could potentially make a difference in future experiences, thereby completely changing their relationship with mathematics.

Keywords:

Education, mathematics, tec21, achievement.