I wasn’t great in maths during my institutional education period. I never connected with maths, until I started realizing it as a useful tool during my doctoral research work. But still the connection was weak, I did only that amount of work on math as much was absolutely necessary. I used numerical methods because it was a tool that helped me process my experimental test bench data during my PhD. I had no attachment to the tool. I experienced fear.
Fast forward to today. I am a part-time math teacher and hoping I am not too bad at it (fingers crossed). I am hoping I also improve my skills. But the pertaining challenge is – I am afraid of maths. In the introductory class on calculus which I am teaching to undergrads, we talked a bit about the experience of math with the students. And almost everyone expressed their fear of maths. And as i realize more and more, almost everyone around says they fear math. Many have expressed that they didn’t take up studying sciences because of the requirement of maths to be studied along with. In a course on ecology in which I am participating as a student, whenever the teacher throws in some mathematical formulations, I can sense my fellow participants taking a back step, or looking at each other with sad eyes and pathological fear. I would have done that too, had I not had some confidence built up in math over the years. Before every math class I go to teach, I experience many hours of anxiety and self-doubt. I prepare my lecture fighting the thought – “Oh shit, I don’t know if I know this shit myself, what will I even explain to my students?”. I fear my students might see through this fear and judge me, or feel similar, and actually suffer, partly due to their own fears of the subject and partly due to a teacher who himself fears the subject. Imagine a classroom full of fear and anxiety, and if this ever happens, how can learning exist in such a situation, ever? So my question is, why this fear of math? I wonder how many of our teachers of math are also suffering from this alleged fear? How many students would have dropped engaging with mathematics altogether over such a traumatic fear of numbers and functions and relationships?
If this fear were true across the world, I am sure it must have been addressed and studied before? Yes. There is a nice Wikipedia article titled ‘Mathematical anxiety‘. It talks about this distress and how it affects performance of children and how people have tried to tackle it, contain it by improving the pedagogy. It talks of how it was measured and found to be a significant problem. I am sure following the links and papers mentioned in this Wiki article and elsewhere, one can come up with a more thorough and through understanding of the issue. But let me take a step aside from all the academically sound and proven literature about it, and instead express some of my naive thoughts on this issues.
2 thoughts. The first one being the nature of math seems to be quite different from the natural working of our brains. and secondly, math anxiety may be related to our deeply ingrained lasting fear of exclusion from our social group.
Relationships – our core nature
To discuss the first point, imagine a subject which triggers emotions and sensations within us. Examples could be literature, films, music, dialogs between people or living beings or with inanimate things. Math is not such a subject, normally. To realize such levels of emotional or sensory upsurge while dealing with math is a gift of the very few, who are able to associate sensibilities to mathematical forms. It is at beast an acquired taste. Paul Dirac, if I remember from my physics courses, could and wished for such a deep connection. Checkout “Mathematical Beauty” – an article talking about the aesthetics of mathematical formulae and Dirac’s idea that a physical hypothesis is true if its mathematics is beautiful. However valid such associations may be, it may not be accessible to the most of us. The super abstract nature of mathematics requires significant amounts of dedication, focused and single minded mastery of the subject before aesthetic senses (may) kick in. Such is true for any subject, be it physics, carpentry, literature, or any other. However, it seems the ability to sustain the abstract quest, in order to secure some mastery, but without the aid of emotional or sensory feedback is the key difference in what separates math from other subjects. It is obvious that every subject requires some set of elementary skills so as to connect and engage with. And acquiring these skills takes much time and effort. For math, it seems it takes significantly more time and effort and a certain non-dependence on immediate emotional and sensory returns.
Coming back to our initial experience with mathematics, a lot of people seem to ask the question – why? Why learn surds, complex numbers, algebra, trigonometry and so on? How does this knowledge help me with my current problems and desires, which mostly deal with my abilities/challenges to connect with the world around me? How does math help in me relating to my needs? Answering such questions could probably help build trust and buy some time to help keep a student’s openness to the math. But if we may enquire further, why do we have such a significant desire of dealing with the world via connections in the first place? I know it sounds like a stupid question, but quite revealing for me! I think due to our evolution as physically weak creatures, our social structure and inclusion with our peers seems to be the most fundamental medium to survive. Groups survive better than an individual. We may be intrinsically programmed to have this fear, without conscious thought, so that our body/mind automatically seeks inclusion by approval and valuation from our peers. The deepest insecurity in ourselves is thus the chance that we might be rejected from a group on some mysterious grounds. We also project relationships with non-human beings as well as objects (Gollum’s “My Prescious” could be a reference). Thus, it seems the humanities could be the subjects which deal most directly with our very core human nature, or this obsession with rejection/devaluation of any sort. However, it is unfortunate why humanities is not the dominant popular subject in the modern human world. I wonder why?
Abstraction – the killer idea
When we began to find and develop tools, we also naturally associated relationships with those tools. We do it even now, I think, all the time! My car, my home, my keys, my computer, my cellphone, etc. However, when our ancestors began making more sophisticated tools from rocks and wood and fire, they probably realized, as we do now, emotional attachments are not helping in making better tools. The quest for a better tool essentially requires a letting go of formed relationships, even if they are powerful and deeply of value. Modern science has taken this ‘abstraction’ to a new high. We have realized our tools to be distant unnamed servants, not friends. Well, for most of the tools. But we still do have our cars and homes and gadgets with overriding ‘relational’ and emotional value to us, even if they don’t serve the utilitarian purposes they once did or promised. The abstraction abilities help us extract simpler utilitarian relationships between objects which have non-human tendencies. Like in physics, if an apple falls from the sky, its not my apple which fell from the sky as ‘gods’ would have wished for, it is a phenomenon that seems to occur millions and millions of times every day, irrespective of who observes it or triggers it. Such an act of removing the human being from the scene has helped blast out the powers of scientific thought from the confines of human emotional/relational chains. We now do a lot of science where a significant amount of time is invested to remove the artifacts of the experimenter or the biases of the theorist from the work. When we do a survey we try to remove the biases of the surveyor’s nature and character from the work, so that it may be replicated across the world. Even in the humanities this phenomenon can be observed, for example in the modern method of historiography where historians study multiple accounts of the same era/events to remove the biases of the individual history chroniclers, thus leading to a more ‘factual’ understanding of the world. Replication, yes that’s the amazing power of abstraction. Once a complex situation is simplified enough by abstraction, a simple model of the phenomenon is formed, which is called a pattern. The idea of this pattern is perfected, and now such patterns in nature could be observed, and predicted. We can also modify some key parameters to influence the very nature of the pattern and as a consequence form newer patterns!
The language of abstraction is math. Math has become the most powerful tool in the hands of scientists, economists, planners, industries, etc. Expressing things in mathematical form is the basis of our industrial world today, of human behavior today. Money is directly math, and it matters like blood would to a body. Math is just everywhere and directly linked to survival, even if most of us would not like to practice math. The outcomes of math are too utilitarian and loud than its intrinsic aesthetic value and beauty. The tool has become the tool of the masters, but it also has a heart and beauty which is drowned by the pressure to learn and use the tools in this practical world. What we teach in school about math seems to give out a confused message to the kids, are we teaching math as a tool of survival or are we teaching how to appreciate the beauty of abstraction? In fact what is education by itself, should be reconsidered deeply. Is it a tool to learn about and value life and relationships around us or is it so that we serve as mere pawns in the practical world of large organizations (including the idea of nations)?
Not being able to abstract well is now judged as not being intelligent, or versatile. The central theme of school and education and social life is – Are you intelligent enough that one must include you in the group? We fear this and everyone knows, but no one acknowledges. Isn’t it an irony that while we humans dominate the world in numbers and we have more peers around us than ever, and yet we feel so scared of rejection? And ‘intelligence’ has been narrowed down to the ability to live and talk and walk in this artificial disabled state of abstraction, unconnected to the people and places around us, unconnected to the self that is full of relationship seeking and sensory activities. It seems to me that abstraction, despite its value in increasing the scales of human collaboration and civilization, it kills the need for a heart and the need to form emotional connects. Therefore, I believe that such a habit of unchecked abstraction may also be responsible for deteriorating the planet, while allowing a fraction of the human population to experience the adrenaline rush which comes from technology driven change.
Conclusion
Given these challenges, naturally why should one participate in a subject that is so removed from reality, and within which so easy to be judged as inadequate? Why risk social connections and value when it is already too much to handle anyways? Some people don’t mind being a recluse or away from the mainstream, for various reasons. We are called ‘nerds’. We like to spend more time with non-human subjects than in the overwhelming world of relationships, which feels like an alien planet altogether. An interesting example is Sheldon from the Big Bang Theory. It wont be too wrong if I say the modern world of science and technology has been designed and built by nerds, and thus is the modern meaning of intelligence fashioned upon qualities that promote abstract thinking. The destruction and inhuman nature of the world is also in front of us, probably brought to us by the same disconnected thinking that we consider as intelligence today.
Given this realization, I wish to convey to myself and my students that its OK to not ‘get’ math. It’s a great subject, and one can love it and see through it a glimpse of the vast universe, and even dare to comprehend an infinitesimally small fraction of it. But to not get it in everyday of our lives is perfectly alright. Some people connect to the world better in abstract forms, whereas some need relational, emotional and sensory connect. The common truth is – we all hold the same desire of connecting, just the paths may be different. The math and physics and the sciences are just one of the many ways to connect to this mystery that we call the universe. If we are unburdened about paths in general, then maybe we will be kinder to those who travel different paths.