Sophie Marques explains how exploring the usefulness of mathematics can benefit mental health.
How practical should mathematics be?
For many, the usefulness of mathematics is restricted to small day-to-day practicality such as counting change, computing monthly travel costs, or changes in loan repayments according to changes in the interest rate. The common definition of mathematics is mostly restricted to physical reality. On the other hand, we could also follow Plato and see parts of mathematics as more abstract – when the concept we consider cannot “be touched” anymore by our senses and seems to live somewhere else. For instance, the line between mathematics and somewhere else could lie in understanding that ‘one apple’ includes the abstract mathematical concept of ‘one’ which is not concrete or palpable in the real world. With such a vision of mathematics, mathematics becomes much broader and difficult to separate from other parts of our lives.
Exploring the universal values of mathematics
The limited perception of mathematics could be the result of our teaching methods. We often respond to the urge to make the content immediately practical to students and focus on creating procedures for the students to follow and directly practice. We create an algorithm that our students can follow like a good robot would.
I often compare sports with mathematics as the analogy works wonders in showing the usefulness of mathematics. Following this analogy, the urge of practicality would be like trying to convince someone to run by telling them that practicing running will make them get anywhere faster while most of us use a car. Instead, it is commonly accepted that running has general health benefits even when it does not mean competing to be the fastest or not using other modes of transport. This argument convinces more people to run regularly as they see the benefit for their day-to-day life. The same could be true for mathematics.
A popular meme says: “Why did I learn quadratic equations, it never helped me in life?”. The fact is that mathematics does not need to be practical in an everyday sense to help in life, but this is not a widely accepted notion. Many people do physical exercises to keep good physical health. Similarly, mathematics creates mental exercises that could allow us to keep good mental health, independent of the practical applications of its contents. Mathematics meets the ideal conditions for beneficial mental exercise when not associated with an overwhelming level of anxiety and stress, as evidence from neuroscience attests.
In the same way that overdoing physical exercise or doing it in a wrong way could create physical illness, applying mathematics for mental wellness needs to be done with awareness and vigilance. Also, in the same way that one can take any sport competitively to a higher level, one can do so with mathematics. But in both cases, this will apply to only a very small proportion of the population: does it make sense to push most our students to those extremities or is there a balanced way to make the mathematical experience beneficial for most? The reason I ask this difficult question is that it could be that our entire teaching could be aimed at this small proportion instead of the majority.
Mathematics serving mental well being
Let us now illustrate how mathematics could develop our mental health if we became consciously aware of it. When doing a computation, we often make what is referred to as silly mistakes. While these mistakes do not reveal that we are not understanding the material, they do reveal something about ourselves: we lost our focus along the way, we were not present in the moment, and most probably let our mechanical, autopilot side do the work for us without paying attention. So, even though silly mistakes do not mark a lack of understanding, they do tell us something important about ourselves. Improving our self-knowledge will make us work on our focus, awareness and conscious ability to be more present in the moment. It is undeniable that developing these skills is important in day-to-day life independent from any mathematical content involved.
Another example I like to use to show the usefulness of mathematics involves developing the art of writing an answer. It seems to me that we could be teaching our students to be selfish beings. When they write an answer to a problem, they mostly write it for themselves: if they understand, it should be good enough. Now, let us put the act of being asked a question in a day-to-day life context. The answer we give is not for us but for those we are speaking with. Learning how to write an answer conceived in our mind for others, whilst taking into consideration that the reader could have a different perspective on things, will develop empathy, compassion and essential communication skills. Mathematics creates the ideal framework to learn how to be precise, concise and well understood thanks to its more rigid and structured language.
Developing writing ability in mathematics consciously could makes us better at communicating with each other and more sensitive and empathetic to differences of perception. Unfortunately, since developing mathematics communication skills is often overlooked, and those with the ability to communicate mathematics effectively may come across as a bit selfish and proud, we lose out on the learning opportunity. The lack of group work in mathematics adds to this problem. Learning how to work in a group is difficult and could allow us to become better team players and collaborators in the workplace, for instance.
Mathematics also teaches us how to take a big problem, break it into manageable pieces (which have become manageable from experience) and put those pieces together as a puzzle to solve the big problem. Doing so teaches us tenacity and to have a good attitude when faced with an important challenge.
Showing the many benefits of mathematics to mental health can help students and teachers to connect humanly with mathematics by connecting their life experiences with mathematics. Too often mathematics objects seem cold and rigid while they are full of experience and memories. Mathematical objects are not necessarily fixed and absolute – as our understanding of them changes, our perception of the mathematical objects change in our mind. Developing a deeper and more flexible understanding of mathematics helps to develop our critical thinking.
Questioning, a pillar of mathematics
The way and the speed in which mathematics is often presented contributes to the disconnect between students and mathematics at a human level: a long succession of absolute truths that are rarely questioned, that we better accept as soon as possible so we can enter the practice ring. Even though time will always be a constraint in life and it is important to know how to work to a deadline, speed could be more balanced in our curriculum to give more space to deep understanding. Indeed, mathematics has been created through centuries of debate, changes, questions, controversy, inflexible minds. Can we learn from this that the human mind is not always ready to accept new ideas at first, and needs time to understand them? Can we learn from this that questions and changes made mathematicians stronger and wiser? I always wonder why the process of questioning the basic content and the history of unstable mathematical content is often omitted from our classrooms. The answer I gave myself was fear of being wrong, of struggle, or not possessing the answer. We want our students and ourselves not to struggle: to avoid more discomfort and uncertainty which would be not only time consuming but also stressful.
Struggle and failure as integral part of being a human and mathematics
Returning to my analogy with sport, let us imagine that we have just started doing a reasonable amount of exercise. The day after could be a day of aches – just climbing the stairs could be very painful. We could stop and give up. Alternatively, we could learn what we could have done better, improve our technique and notice that with time, the exercise brings us more well-being than pain if done properly and regularly.
In a mathematics class, the same struggle will occur, and it is part of the process. Teachers and students need to learn to perceive struggle as a challenge needed for growth. This includes not hiding the full story from the students. It is true that telling a student there is a correspondence between a procedure and a type of question can make them feel comfortable. But in a complex life, it is more complicated than that, and when they discover that the latter is not true, they become more frustrated and confused with mathematics. My belief is that hiding part of the truth not only brings long-term mathematics anxiety to the students, but also kills their critical thinking. I am convinced that we can find a truthful way to teach being okay with the possibility of being wrong, incomplete, or not having all the answers while still inspiring our students’ trust and critical thinking. I do not believe that being a “good teacher” is about making everything easy for the student or making them think they understand everything. Humans are not even able to understand clearly and completely the concept of ‘one’. Given those facts, it is improbable that one could understand everything.
Identifying and clearly expressing what we do not understand is also an essential step in learning mathematics. It also shows maturity and honesty. It makes us comfortable with not understanding everything – it makes us human. On a related note, mathematics should help us learn from any mistake and transform the frustration of making a mistake into an opportunity for growth. Mistakes and struggle are part of life and build experience. Mathematics itself is constantly evolving and growing, thanks to the many mistakes and struggles of the minds of those who contributed to its development. It is time to accept mistakes and struggles in a healthier way.
Embracing a multifaceted mathematics
Getting more insight into how mathematics could contribute to developing the mental health and mental agility of students shows the human side of mathematics, which I hope could make students realize how improving their relationship with the subject could make their life better. In doing so, they could also grow into more empathetic and compassionate critical thinkers who are able to see the bigger picture, and they could find a way to build a world better than the one we are proposing right now, kinder to differences and nature.
I want to finish this column by saying that every idea or practice can be taken to an unhealthy extreme. The side of mathematics explored above is only one of the multifaceted sides of mathematics. The practicality of mathematics and its applications in day-to-day life is amazing and important. Being able to extract a procedure to solve some problems is a good skill to have. The abstractness of pure mathematics, its rigor and precision are certainly the reasons why mathematics was constantly questioned and made stronger along the way. All these aspects coexist together in a balanced way and together build essential life skills for any human being.
My belief is that if we could bring more balance into our classrooms, including the human and emotional side of mathematics, this could help fight the stigma around mathematics. Finally, while teaching, it is important to realize how mathematics deeply shapes our reality, our students and us as human beings and therefore our impact into the world.
Dr. Sophie Marques
Department of Mathematical Sciences,
STELLENBOSCH UNIVERSITY, S.A.