One of the most frustrating things that I regularly encounter is clearly intelligent people demeaning themselves. One of the most tragic is seeing clearly intelligent children told they are not good at something. In The Geography of Thought Richard Nesbit highlights the particularly western perception that people have certain fixed attributes and competencies whether they be sociability, musicality, writing ability, mathematics or any number of other things. This is for the most part just wrong. Many fail to appreciate the degree to which people able to change themselves; our personalities and aptitudes are constantly developing. Once we acknowledge that we are inherently changeable we are able to see that what is more important than talent is just plain work. No one wakes up one day able to play piano, solve differential calculus equations or paint, or write poetry. People are able to do these things because they devote a huge amount of time and effort to them. It’s horrendously unfair to attribute these achievements merely to talent.
As someone with eclectic interests, a principle that I live my life by is that with some effort I can generally achieve a reasonable degree of proficiency in most things. This is how, after struggling through mathematics in high school and generally considering myself of at best average ability, I was able to complete two university courses in pure mathematics with relative success.
So what turned things around? I think I owe a large part of my success to my father’s ceaseless, to the point of being infuriating, insistence that I was good at maths despite my bad results in school. At the time I thought of a number of reasons why he would say this. Principally I thought he was just assuming that because he was good at maths that I would be too. Whatever the reason, he said it enough that even though I achieved mediocre results in school I eventually believed him.
In addition to giving me the confidence to attempt mathematics at a later stage this forced me to locate the reason for my poor results somewhere other than an innate lack of talent. And there was only one thing to blame, really. I was lazy. From then on I had the belief that I was probably okay at maths as long as I applied myself. Still I held this belief for almost two years before I did anything about it.
A semester before I started studying mathematics again I took a course in introductory logic under the philosophy department. It was a difficult course but I assumed that I would do well because I “knew” I was good at philosophy. As it turned out, I did excel, but at the same time I realised that what I was doing was essentially mathematics. And I loved it. The surprise of finding hidden contradictions and unexpected but irrefutable conclusions from seemingly innocuous premises was intoxicating. I realised this by approaching the subject with confidence and positive belief. This is what finally prompted me to take up mathematics for the first time since high school.
Now I don’t want to give the impression that it was smooth sailing from there on out, because it certainly wasn’t. I wasn’t able to pick a course out of nowhere, in a field that was for the most part foreign to me, and succeed just because I was “clever”. Truth be told the first course I took in Discrete mathematics (not discreet) was worth 3 out of 24 credit points for the semester and it probably took up about half of my time. I remember spending a disproportionately large number of hours on an assignment that was only worth 5% of my total mark for the course only to get 2/5 for it. That was definitely discouraging but I found consolation in the fact that I had lost one mark out of sheer carelessness (I had erroneously written in my last line of working that 2^8 equals 64) and I persevered to pass the course comfortably.
Even now I don’t see myself as particularly exceptional in mathematics but I’m also aware that the people I am comparing myself to have spent an inordinately greater amount of time and effort on the subject than I have. Two semesters at university is really not that much. Nevertheless this was a life changing experience, I had turned what I considered a great weakness into a strength, and now I’m able to help others achieve the same thing.
The benefits of this experience reach far beyond proficiency in mathematics. Since then I’ve never limited myself to anything. Just this year I’ve taken up piano and learning German, both of which I am now competent in to a degree that I honestly never expected. Learning a foreign language especially was something that I had given up on in high school after lacklustre experiences in German and Japanese (which were mostly my fault).
Having said all this, I do not wish to imply that a struggling student struggles simply because she does not try hard enough. Effort directed towards the wrong area is practically useless. Often it is harder to determine where and how effort should be applied than to spend hours aimlessly slaving over a text-book. The point is that for the majority of students a lack of talent is not what is holding them back, and the more that they believe that it is, the more they allow themselves to be lazy. But this is a good thing! It’s easy to address. Hard work and a positive attitude may seem like tired advice to give but it is inevitably overlooked.
I also don’t want to lead anyone to believe that it is necessary to set ones goals at the same level as I do. I set my goals at the level I do because I know what motivations me. I know that I’m not discouraged by striving for things which I’m unsure of whether I can achieve. But I also know that there are many people for whom this is not the case. Indeed some people are more productive with sequential easily achievable goals. To set a highly challenging goal at the outset would paralyse them. Despite this, what I do want to get across is that most students are capable of far more than they believe or are told, and for this reason they should set their goals accordingly, even if it is just a little higher. If we work towards being fearless of failure, soon it becomes clear that the higher we set our goals, the more we allow ourselves to achieve, regardless of whether we reach our goal or not.
It would be naive to assert that talent doesn’t exist. But by definition, it’s innate and unchangeable, so it’s useless to concern ourselves with it. We are much better of focussing on what we can achieve, which for most of us is a very great deal. Even for those who might be called talented, they didn’t get to where they are by talent alone. Setting challenging goals and positively pursuing them is the best way to become more competent, regardless of talent.
Norman Doidge – The Brain That Changes Itself
Richard Nesbit – The Geography of Thought
Judy Willis – Learning to Love Math