Linking Mathematical Praxeologies With an Epidemic Model

Introduction

In the last decades, profound changes have taken place at the global level that have led to the appearance of different points of view in relation to the educational sciences and, consequently, the emergence of didactic methodologies more appropriate to a student born in the era of the information technologies and of the economic globalization.

It is necessary to create didactic devices that are really capable of responding to the needs/preferences of the students by an online teaching and that, at the same time, they are susceptible to be used properly by teachers.

Nowadays there are currents questioning and highlighting the importance and functionality of the contents that are usually studied in the schools and, in addition, the way to address and teach that contents in the teaching-learning processes developed in different countries.

For example, in Mexico, in 2004, the following question was posed to 238 Computer Systems Engineers in service: “In your professional life do you use differential equations?” 96% responded “never” and 4% did not answer (none of them answered occasionally or frequently). This shows that what is done in the classrooms of differential equations does not make sense in the professional work of computer engineers in that country (Arrieta & Díaz, 2015). Recognizing the decoupling of the school practice, the daily life and professional practices, the concern of these authors lies in the separation of what is done in and out of school, in order to build bridges between the school and its environment.

According to Edgar Morin, the Western model of teaching separates artificially knowledge through closed disciplines that teach students to be individuals adapted to the society, but prevent them from understanding the problems of the world and of themselves. On the other hand, it is also discussed what should be the role of the teacher in the teaching process of students. The quoted author argued that the teacher should be the conductor of the orchestra, should observe the flow of knowledge, lead and elucidate the doubts of the students (Rangel, 2017).

In this way, we are aware that it is urgent to stimulate the curiosity, the critical spirit of the students in front of solutions found for a certain type of problem coming from, for example, the society. Dialectically, it is essential to develop competencies of creativity, of entrepreneurship, giving freedom, time and autonomy to the student to think for himself.

In particular, in solving problems which involving modelling, it is considered fundamental that the teacher provides tasks to the group of students that allow stimulating an analysis of the effectiveness and discussion of the economics of the techniques used to solve the same task. Also it is important to propose tasks that motivate a cooperative and collaborative work, the interdisciplinarity, and the connectivity with society and the world of work.

It is intended to give to the teaching in the schools a functional and immediate sense (from the point of view of the student) and thus increase the significance of the study. Based on the paradigm of questioning the world (Chevallard, 2012), we are looking for didactic devices that allow the development of the entire teaching-learning process around an open problematic issue of students' daily lives. This question must be sufficiently “provocative” and important for the student, by making him/her to feel the need to search and study certain contents (mathematical, biological, economical, geographical, philosophical, ethical, etc.) to get it solved as quickly as possible, using strategies with the minimum cost.

Thus, the present proposal arises from the need to adapt the curricular programs and the teaching methodologies to the type of students that we have nowadays, in the sense of taking advantage of their vision and more technological characteristics. In this way, we will try to emphasize the potential of the computer tool (in particular, of the GeoGebra software) in solving daily life problems with the aim of presenting a didactic proposal that contributes to the increase of the digital literacy both for students from secondary education as for university students.

Many researches in mathematics education, from different perspectives, advocate the need to teach mathematics as a modelling tool: