Being Smart Doesn’t Have to be About Mathematics or Science
Pretty much anywhere I go in the region that I live, people will react to me saying that I’m going to be a scientist with this: “Of course, you have to be smart if you’re a scientist.”
This is the refrain that I hear all too often amongst my friends. While I’m getting my physics degree, they’re busy becoming nurses, learning the trade of construction, or looking to work in agriculture. They all have different lives, yet they all seem to agree that being a scientist requires you to be smart in a way that the others don’t.
As you may have imagined, I wholeheartedly disagree with this.
We assume a hierarchy of information, as if some information is more important than others. Or rather, understanding the information is only available to those who are intelligent. While this can be reasonably accepted, actually classifying said knowledge is more than a little difficult. It’s frankly a ridiculous proposition, and creates this implicit agreement where being a scientist means you’re smarter than the rest of the population. This isn’t true, and diminishes the way we think of other professions, because, if being a scientist or doctor requires you to be amazingly smart, it implies the reverse for other careers.
But this is simply not true. If it were so, then being smart would automatically mean you’d be a scientist or thereabouts. Why can’t we have incredibly intelligent people in other domains of life? If I were to go on a farm, I’d know little about what is actually happening there, yet many of my friends could explain this with ease. Learning about science and mathematics hasn’t helped me in that regard.
It’s the same story for many other walks of life. I don’t know much about law, history, or even literature. I doubt people would call me stupid because of this since I’m educated in science, but these other areas of life can be just as vital to humanity (and even more) than a lot of science. And I can guarantee you that there are plenty of smart people in those domains. Being smart does not necessarily equal being good at mathematics or science.
What I hope for is a larger acceptance of being smart. There are incredibly smart people who don’t need to be involved in mathematics or science, and that’s perfectly fine. If all the intelligent people group up into one domain, what’s going to happen to the others?
As many people have said before me, the idea of “multiple intelligences” seems to be correct. People can be incredibly smart in different aspects of their lives, which ultimately translates to being good at different things.
Let’s push back on classifying someone that does science as smart, as if anything else means one is not.
As a runner, I’m expected to give myself goals. It’s the thing that runners do. We set goals, train hard to get enough fitness to achieve them (usually in the form of some sort of race time), and then we evaluate and set new ones. This cycle is familiar to anyone who is a runner.
However, there are some people who are exceptions, and I happen to be one of them. I’m someone who hasn’t set any “real” goals in running for over a year now. An injury was certainly part of the problem, but there was (and still is) something else: paralysis.
When you’re working in a field, you usually want to look at others to know what they are up to. This helps inspire us to keep chugging along and grinding away at our work. Unfortunately, I’ve found that looking at others’ goals paralyzes me. An easy example is the past Olympics. During this time, I watched as some of the fastest in the world gutted it out on the track and On the roads. This got me all ready to once again train for some faster races. However, my goal at the time was not to do that. I was thinking about other races.
Fast forward to now, and I’m torn between what I want to do. I think I really want to see what I’m made of in a long trail race, but then I’ll watch or hear about another runner who has made a breakthrough in their training for a short and fast race, and suddenly my goals go out the window as their kind of racing seems more appealing. Instead of sticking with my goal, it’s as if I get lured away by the next shiny thing. I say this with no small amount of irony as I type away while facing my wall with race bibs that aren’t the kind of race I want to run next season.
There’s always the null solution: ignore everyone else. But that’s no fun, so I’m in a spot where I want to lock down on a goal but not feel like I’m a slave to it. At the same time, I’m trying to convince myself that I don’t need to do what everyone else is doing. We all live our own lives, and it’s okay if I don’t follow the path everyone else does.
I can extend this to other areas of life in general. I’ve found that it’s alluring to chase the new thing that others are doing, but it’s much more difficult to buckle down and do the work that I need to do. I’m getting better at it – my writing here is a testament to that – but I regularly need a reminder. Don’t let yourself be derailed by the goals of others. Pick something, and work towards it. And most important of all: remember that you aren’t tied to this goal for the rest of your life.
The Little Frustrations
I had the interesting realization recently while tutoring one of my students. As he worked on his solution for solving a system of equations, I suggested that his work would be much more clear if he outlined what he was doing and showed steps to his process instead of simply writing a bunch of equations and having the answer pop out at the end.
He bemoaned having to be so complete with the work, not seeing the point of having to add these small elements to his solution, but I held my viewpoint. I knew it was important for him to write the entire solution in a clear manner, but he didn’t seem to care about achieving this level of perfection. He thought the elements I suggested were more or less superfluous, since the core of his solution was correct.
So what was my realization?
It was that, ironically, I do the same thing as he does in my own mathematics classes.
The quest for one hundred
As I’ve mentioned a few times in my writing, I’ve had the same professor for all of my mathematics courses in CÉGEP. During this time, I had a bit of a personal goal: get a perfect score on one of my tests.
Unfortunately, I never met this goal, though I did get close. My best mark was 69.5/70, which is over 99%. Other than that, my tests usually hovered around the lower nineties.
What becomes clear though as you look at my exams is that, apart from silly errors, most of my work is correct, but is lacking a small clarification or a point of completion. As you can probably see (and like I said, I only just made the connection), my situation is remarkably close to that of my student who I tutor.
Every time I saw this kind of error on my exam, I’d shake my head, not really even knowing how I could have been expected to write that anyway. I took solace in the fact that almost no one in my classes ever included the little things, and so I was just like the rest of the class.
In regards to my own performance, I didn’t fully appreciate what these little clarifications for completeness would do to my solution. Instead, I told myself to be happy that I got the core part of the problem and just forgot a little thing of almost no consequence. This is obviously the wrong view to take, but I didn’t make the connection.
The reality is that mathematics is a sort of logic. Therefore, all parts of a solution to a problem are important if the final answer is to be believed. Whether or not the final answer works is entirely dependent on the small and big details of the solution. Omitting a detail means the foundation isn’t rock solid. Sure, it might happen to be the correct answer now, but it is only in spite of the lack of detail, not because of it.
For example, I lost points on one of my tests because I failed to identify the curve I was using as a cylinder. I was dealing with the classic $x^2+y^2=1$ representation of the cylinder, but I failed to mention that the previous equation was for all z values. I thought this was an implicit assumption from the equation, but it’s actually important to explicitly declare it. This is because the equation I wrote is actually a circle in two dimensions, yet is a sphere or solid in three dimensions.
Therefore, what I thought was a harmless extra point of completeness was actually very relevant to the solution. It was the difference between a circle and a cylinder. Consequently, I now fully understand why my professor took away points in the question. Of course she knew I was talking about a cylinder, but the equation I wrote was really that of a circle, so further clarification was needed,
What I’ve learned from this is that there is no small detail that you should leave out from a mathematics problem. Simply put, it’s much more advantageous to be explicit about the work you’re doing than to make a bunch of implicit assumptions and hope everyone gets it. You will rarely lose points for being complete, but you definitely will on the other side.
I’ve found that this occurs for me just as it does others. Even with over a decade of doing mathematics in class, I struggle to be perfectly complete. However, it does give me a bit of inspiration to include all the important points of a solution as they come up.
Remember: the little frustrations are annoying, yet they will instruct one to be more complete in their mathematical pursuits.
The Last-Minute Rush
Everyone is pooled outside of the classroom, anxiously waiting for the room to vacate so we can sit down. There’s a nervous energy in the air, permeating through even the most calm person. Many have their class notes out, mumbling about various facts and concepts. Others quiz each other, reciting definitions that I could say word for word, instead of giving their own “version” of the answer.
Every few minutes, my eyes drift to the clock. Two minutes left.
The door opens, and the time to check one’s notes evaporates. We all file in, and the exam begins.
I’m fairly certain you’ve had such an experience before. Depending on the type of person you are, this may have affected you more or less than it did I. Still, the last minutes before an exam are fairly similar for everyone. The age-old wisdom is still followed: study until the final minute.
I won’t lie: I do this all the time as well, and I don’t think it’s necessarily a bad thing. However, there’s a difference between looking something up just before an exam, and planning to remember new things right before you write the exam.
I’m reminded of a saying that, as runners, we use a certain expression: the hay is in the barn. This saying is supposed to calm one’s nerves before a race, where one might be doubting their training and preparation for the race at hand.
In the same way, this is how I try to position myself mentally before a test. I tell myself that I’ve done everything I could to prepare myself for the test, and that now I simply have to write it. Sure, I might be exaggerating in the sense that one could always do more, but I make sure to do the best I can before a test, and I tell myself that it’s enough.
What is my best? Well, in my science tests that means I will generally do all the practice problems suggested for me, plus I will go over all the content I’ve seen in class. In this sense, I feel as if I’m prepared, since I did everything suggested to do before the exam. And, it’s all optional, so I didn’t have to do it, but I chose to.
Getting ready for an exam is a stressful affair. I know some people who don’t or barely even study before an exam, and only start on the morning of, meaning they are trying to fill their heads with knowledge with only hours to go. This, I believe, is a losing strategy, because it means you aren’t familiar with the concepts at hand. In contrast, I usually enter exams confident that I know the material. I may have trouble on a question, but I know what I have to do.
Don’t fall prey to the rush of the last minute. By working on the material throughout your time, you’ll become much more familiar with it than if you worked on it for a day.