About my teaching skills

Mathematics is one of the sciences whose relevance is undeniable, whether it is seen as an intellectual work or if we look at its many applications to everyday life. Precisely, the research I do in mathematics tries to understand how the world works and to respond to the needs of today’s society. I believe that it is necessary to create opportunities to bring young people and adults closer to scientific knowledge, and numerical analysis is an area with potential for this. The above is related to the constant reflection that as a teacher I have made in recent years on the teaching and learning of mathematics. From what I have observed in some school institutions, mathematics is taught from a traditional perspective which has caused fear, rejection and anxiety of students towards mathematics. This happens in schools as well as in undergraduate and graduate courses. Going deeper into these ideas, I present below the bases on which I promote the learning processes of mathematics in my teaching practices:

Always start with a motivation

It is usual to start my classes by promoting the students’ interest in the topic to be addressed. This motivation may be related to a current research problem, or simply to my curiosity about how the world works. I always show this motivation to my students, in order to transmit them my enthusiasm towards the teaching of the content to be presented in the class and the advantages that their learning will have for them. On many occasions, I randomly ask a student about some detail of his or her life related to the goals of the class, allowing the group to question their own environment through mathematics. Because of the abstraction that exists in mathematics, it is essential to maintain this motivation throughout the classes, either through questions or particular examples that connect to reality. I am careful in the choice of examples and questions that I present in class, and although my position is linked to applications, I maintain rigor and emphasize the importance of logical-mathematical thinking, which will allow students to have an alternative perspective on many aspects of reality.

An approach to the use of ICTs

With the pandemic as the main scenario these last two years, communication and information technologies have become a major component in teaching. As a specialist in the area of numerical analysis, I have a strong conviction that the use of computational tools for teaching mathematics is necessary in today’s society. Being an avid programmer of languages such as Matlab, Python, or C++, I can promote the use of these languages, either through software or a virtual platform. Students can have access to the codes that I implement, or a cloud where we can share programs that they can manipulate and test under their conditions. The above, always focused on the subject of study. This will undoubtedly promote in the students an interest in group research and the proposal of ideas to solve a problem using computational tools.

The importance of developing mathematical skills

The diversity of students present in the classroom requires that basic foundations be clearly established so that knowledge can be built in a solid and well-ordered manner. By possessing this knowledge, it is possible to develop different skills that are at the heart of mathematical practice. However, sometimes students think that mathematics is about calculating and repeating, so in every class I make sure to show that mathematics is not about memorizing theorems, exercises, or techniques to answer a certain type of problem, but about using creativity, intuition, and various ways of thinking, which allow them to approach the possible solution to a problem.

In addition to the above, the development of these mathematical skills is achieved through the inclusion of specially designed tasks in the teaching process. Solving problems with the tools given in class will allow students to share their mathematical experience with their classmates and with me. I consider it important that students understand their individual and group role in the construction of mathematical knowledge, so the presentation and discussion of the results of their homework and research is a constant in my classes.

My contribution as a mathematics teacher

With my teaching experience over the years, I have taught different courses, from basic mathematics in sixth grade in high schools, to advanced numerical analysis to undergraduate students. This has allowed me to learn how to adapt to different teaching contexts, which makes it easier for me to design classes according to the level of complexity of the knowledge and the goals of the course. In all cases, I look for students to question the way they develop mathematical activity, particularly the strategies they use to solve different types of tasks and how they communicate their mathematical ideas in a rigorous and precise form.

With my knowledge in numerical analysis, numerical methods and numerical algebra, I can contribute to the strengthening of different university programs that require the inclusion of computational tools in the training of their students. I can work in teams with other professors to provide mathematical and computational ideas in the development of programs, or directly with a view to solving a local, national, or international problem.

The fact that I have lived abroad for several years and have had the opportunity to work with students from different parts of the world has helped me to relate to my students in a more empathetic and respectful way. At the same time, I will always be willing to discuss with my colleagues our ideas about teaching and learning mathematics in order to maximize the strengths and minimize the weaknesses that may arise in the training of my students according to what is established by the university.

Finally, I can develop academic curriculum that adapts to the vision of the university, without losing focus on the formation of high quality students. Multidisciplinarity is an essential component of this aspect, whereby the relationship between mathematics and other areas of science is considered as a common point for the development of activities.