Looking at the world through Mathematics


A formal and rigorous vision of Mathematics should be accompanied by an instrumental or practical vision. Teachers must model real-life phenomena and allow students to not only learn and pass their Mathematics courses, but to value and appreciate the potential of this knowledge in their personal and professional environment.

By Ruth Rodríguez Gallegos

Whenever I tell people that I am a math teacher, their reaction is nearly always practically the same: “I hated math at school,” “I had a terrible match teacher in elementary/middle school,” or, even worse, “I wasn’t a good student. In fact, I was awful. I’m better at art, the humanities, etc.” Interestingly, what these people are really sharing is the way in which they recall the experience they had as children or teens, rather than their capacity, or lack thereof, to understand mathematics. Something that worries me as a math teacher and enthusiast is precisely that these perceptions can become transferable, to the extent that those who are now parents usually transmit to their children (perhaps unconsciously) this idea about how difficult it is to learn and understand this so-called “hard” science.

When Mexico “fails” international tests, such as PISA, in reality this shows that our students have not developed the capacity to use and apply mathematical knowledge in their daily lives.

Ever since I was a little girl, I found it easy to learn the logical and then formal mechanisms of this science. However, as a math teacher of future engineers, I have now come to realize that this formal rigorous vision should be accompanied by an instrumental or practical vision of mathematics, since my target audience in each class are future users of the same. When Mexico “fails” international tests, such as PISA, in reality this shows that our fifteen-year-olds have not developed the capacity to use and apply mathematical knowledge in their daily lives. This has been named by the OECD  as mathematical literacy, which has been established as a competency for 21st-century citizens. This partially explains the “failed” math education, which is not exclusive to our country, but rather a reality in the large majority of nations, even in the first world, except, of course, for the well-known success stories of Finland or the Asian countries that have performed outstandingly in the last PISA tests.

Mathematics can be linked to physical experiments such as the cooling phenomenon of a cup with boiling water, the flash of a cell phone or a cardiac defibrillator to restore the heart’s normal rhythm.

One of the possible routes to improvement is to show our students, at every educational level, a process that links their reality to what they have learned in a math class, where abstract topics, such as functions, derivatives, integrals, etc., acquire a new perception when students discover that an algebraic expression, a graph or a table of values in reality shows them how the temperature changes as the day goes by, how much money they have in the bank and how much they will have for their retirement, or allows them to predict the exact day and time when natural phenomena will occur, such as eclipses, etc. The capacity to describe the world, to predict it and, ultimately, to explain it, strengthens and prioritizes learning mathematics from very early on until university education. Several research undertakings demonstrate the advantages of this modeling-based approach for children and young people, and how motivation and performance usually increase when they realize how useful it is in their daily lives.

Since 2010, a community of teachers and researchers, who are experts in teaching mathematics in Mexico, has begun talks to first learn and then visualize new meanings in the actual use of knowledge. Our common topic has been, on the one hand, an interest in modeling real-life phenomena and, on the other, a concern not only for enabling students to learn and pass their math courses, but also to value and appreciate the potentiality of this knowledge in their personal and professional settings.

To relate mathematical knowledge teachers can implement teaching based on mathematical modeling to solve problems based on natural phenomena.

In my experience as a teacher, I have conducted in the classroom physics experiments that link what students have learned about mathematics from a theoretical perspective with what they observe in their daily lives. For example, studying the cooling phenomenon of a cup of boiling water or the behavior of a Resistance-Capacitor (RC) electrical circuit, which, in turn, makes it possible to understand how a camera or mobile phone flash works or how a cardiac defibrillator helps to reestablish a normal heartbeat. This teaching method, based on mathematical modeling, has been defined as the cyclical process consisting of the creation or use of mathematical models to solve issues based on phenomena of a physical or social nature with the reality of students’ professional activities (Rodríguez and Quiroz, 2016). Some research work also considers mathematical modeling as a didactic strategy.

The efforts and participation of all those interested in the educational system will be fundamental to the success of building dialogue bridges between communities, thus enabling our students to learn more and better the beautiful science of mathematics. Please feel free to join in these initiatives by contributing your expertise and your diverse perspective in these collaborations with the Latin American Group for Training Engineers in Mathematics Education.

About the author
Ruth Rodríguez Gallegos is a research professor in Educational Mathematics. Her interests lie in studying the use of mathematics in the areas of engineering through computer modeling and simulation.