In Latin America, it is very common to hear the phrase "I don't have talent in math" or some variation of this message. The underlying issue is simple: math is perceived as difficult because a high percentage of people encountered a stressful learning environment when they were taught.
The consequence is that most people believe they do not have what it takes to succeed in mathematics and miss out on the opportunity to use it in their daily lives to more effectively navigate professional, personal, political, and social spheres. Math is feared, hated, felt to be tedious, boring, or stressful by the vast majority, and this leaves us in a vulnerable position as a society, because a mathematically incompetent population is more vulnerable.
For example, in Latin America, the number of people accessing higher education has grown steadily, but very few pursue science or engineering careers due to fear of mathematics. And although the region has observed an interest in science and engineering among young students, few people pursue careers in these fields, leaving the region behind in scientific and technological advancement. (OEI, 2019)
Worse yet, the lack of competent people in science and technology negatively affects the adoption of processes and technologies that increase industrial productivity, as there is little qualified labor for the use of new tools and technologies. (Stiglitz, 2016). Having more people with mathematical skills and mathematical thinking increases the development of individuals and communities, protecting us as Latin Americans from the harms caused by misinformation and manipulation, aiding us in decision-making, and I dare to think it could even strengthen democratic processes because a mathematically thinking society is more critical and better judges the performance of its political representatives.
Many factors contribute to the lack of mathematical competence in the region, but it seems to me that the math teaching method in Latin American educational systems is a key part of the problem. If we are not enabling the general population to achieve numerical competence, the systems designed for that purpose are not working.
I believe there is a way to improve this condition, but it requires changing the pedagogy of mathematics in the region.
In basic, secondary, and upper secondary education levels, mathematics is a subject, and a common factor is that it prioritizes learning rote calculation or "computation", such as finding an unknown X from known values, solving formulas to find the perimeter of a figure, etc.
The focus on mathematical processes for operating equations creates a perception that learning math means following steps so that a formula allows us to calculate a variable—which is true, but it is only a small part of mathematical thinking.
Under the described view, schools continue to force students to perform exercises with pencil and paper, in many cases prohibiting the use of calculators. If the student makes a mistake while solving an exercise, such as omitting a minus sign ("-") that alters the result or making an error in the hierarchy of parentheses, the entire exercise is marked incorrect, and the student receives a numerical grade that tells them nothing but reinforces the feeling of "not having talent for math." In many cases, a parenthetical error can mean failing an exam, irremediably affecting the student's academic trajectory.
This seems serious and sad to me because that is not learning mathematics. Those who do pass math under this method do not necessarily have the capacity to use what they learned in a context outside the classroom or for their own creative purposes. The current educational model is not helping most students develop mathematical thinking nor is it offering them numerical tools and the mental structure to face problems and seize opportunities in a non-academic setting.
We need to change the way mathematics is taught, and this requires changing the culture behind the teaching and experience of mathematics. To this end, I propose three pillars for pedagogical transformation:
Three Pillars for Pedagogical Transformation
1. Understanding that mathematics is a language.
A distinctive human characteristic is the use of language. We have hundreds of languages we use in different contexts and media to express our ideas; mathematics is an example of this.
Learning a new language is useful because it allows expressing ideas creatively that will be interpreted by those who know it. An analogy is that learning to play the piano and compose music is useful because it allows expressing ideas in musical language. It is the same with mathematics; its usefulness lies in allowing us to express creative ideas to describe the world around us.
An example of this is Richard Feynman, a celebrated 20th-century physicist whose contributions to quantum physics shaped the contemporary world. In his lectures on quantum electrodynamics, Feynman uses the Mayas to exemplify how advanced mathematics are "convenient" shortcuts and solutions for calculating very large or microscopic magnitudes.
“We could count one by one thousands of times, but that is a lot of work, so we have these shortcuts to save time,” the physicist explained. Watch Feynman’s video here
Learning mathematics, understanding its concepts in a narrative and discursive way, allows us to find relationships and applications of that mathematical concept in our environment. Mathematics as a language becomes a tool to face the world; it is a new piano with which to compose symphonies.
2. Errors in mathematics should not be penalized.
In mathematics, it is necessary to make mistakes and iterate on the method to get closer to the desired result (Papert, 1980). Exams and assignments should not be limited to evaluating the final result, but rather the thinking process used to reach a solution. Helping the student structure logical processes where mathematical ideas are used to find solutions to problems or leverage daily opportunities must be the objective of mathematics education. This structuring process is learned and requires feedback, reflection, and practice to perfect. However, when an exercise is only graded as correct or incorrect, we disregard the thought process and sow a mistaken idea of the learning objective.
Seymour Papert, a great learning theorist and one of the pioneers in educational technology, explained that the construction of learning requires designing environments that allow the student to make mistakes and iterate to build knowledge. We need students to have the opportunity to make mistakes, err, and be given the time to explore and reflect on their thinking processes to develop the critical and methodical capacity necessary to master the application and use of mathematical concepts.
3. Learning mathematics in context.
Every field of study in the Latin American educational system has a space to incorporate mathematical thinking; not doing so is wasting the opportunity to explore the expression of mathematical ideas in a useful and relevant context. In social sciences, exact and natural sciences, arts, and even sports, it is possible to apply and express mathematical ideas. It requires teaching creativity and educational leadership to ensure that all subjects and classes open space for the expression of mathematical thinking.
Just as truly bilingual schools are those where, beyond having a foreign language class a week, all subjects are taught in English (and thus students learn the language by applying it in a context), schools seeking to teach mathematics must incorporate mathematical thinking into all subjects and programs.
Having a math class a week is useful for learning certain methods or "techniques," but it is in the integration with other subjects that mathematics gains relevance. It is not the same to talk about the number line as it is to understand a timeline and put historical events that shaped contemporary society into perspective, but it is the same mathematical concept, and the integration of fields gives it life.
Implementation Strategies and Call to Action
Having explored the three ideas that will allow us to transform the culture of mathematics in education, we must explore which strategies would allow us to work on the skills necessary to develop the ability to express creative ideas in a mathematical language. For this, students and teachers can do specific things:
Contemporary teaching involves designing learning experiences. This implies setting learning objectives and activities, but also entails creating environments and settings conducive to learning.
From this perspective, the math learning space must allow dialogue, research, as well as creative and collaborative creation. This is impossible to achieve if we do not provide a basic resource: time. Some students will have a predisposition and innate ability to learn math faster, but that does not mean the rest lack the capacity; it just takes them more time. It is the job of teachers to create the temporal window for each student to explore and delve into questions and problems that lead them to express their creative ideas in mathematical language.
A tool that could generate the necessary scaffolding for this immersion would be programming languages and computers. Programming a computer requires expressing abstract ideas in a logical order to achieve a desired result. Regardless of whether they are letters or numbers, computers allow us to simulate situations and create models of reality.
The (almost) infinite versatility of computers makes the behavior of an idea or process visible in a simulated environment. In this way, a mathematical equation, which is nothing more than the description of some phenomenon, can be "made visible" to those who wish to learn. The equation, an abstraction of reality, is difficult to understand for someone with little experience in mathematics, but manipulating an equation on a computer makes its manifestation, behavior, or effects visible. In short, the meaning of that message is understood.
Language is the door to thought, and under that logic, using mathematics to express ideas allows us to think differently and helps us discover how we think.
What can anyone who wants to learn mathematics do?
My recommendation is to learn to program. It might seem like a distraction, but it is actually approaching the mathematical language from an easier route, one whose origin is the manifestation of a phenomenon and whose destination is the discovery of the language that will allow you to express your ideas and projects with all the power of the mathematical world as another tool at your disposal.
References
- OEI (2019): Organization of Ibero-American States. The text refers to reports on the lack of interest in Science, Technology, Engineering, and Mathematics (STEM) careers in Latin America.
- Stiglitz, J. E. (2016): Joseph Stiglitz's work on inequality, economic development, and the need for skilled labor for productivity.
- Papert, S. (1980): Mindstorms: Children, Computers, and Powerful Ideas. Seymour Papert's central work on constructivist learning, the use of technology, and the culture of error.
- Feynman, R. (Video): Quantum Electrodynamics Lecture. https://www.youtube.com/watch?v=KdE6uHM1eIw
This essay is part of a series of reflections on learning. If you are interested in learning more about me, you can contact me on my website hoppenstedt.mx
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