In my personal life, I have several different kinds of hobbies and interests. Obviously, you can see from my site that I love to write, and so it probably isn’t surprising that I enjoy reading as well. Additionally, I enjoy sports as a whole, but specifically I have a knack (and a love) for running, basketball, hockey, badminton, squash, and many other ones as well. However, if I had to choose which sports I participate on a serious basis, it would have to be solely running. I like all the other ones mentioned, but running is the one where I put a huge portion of my time and energy in. Likewise, I spend a good amount of effort writing and reading, so I would consider those my three big areas of my life.
But that’s just my personal life. Of course, my education is also extremely important to me, and in terms of my professional life, I’m working on becoming a better teacher. So that’s a quick list of the things that are important to me in my life, and they are what I spend most of my resources on.
Now, that’s not to say that I don’t have other interests. I’m the sort of person who is curious about many different fields. My interests include things like technology, AI and computer science, design, photography, typography, music, and video games. I imagine that I am like many others in the fact that I know a lot of geeky and seemingly random information concerning fields and areas of life that people would not expect me to have any knowledge about. I know a bit about the characteristics of type, the call-outs of many maps in Halo, principles of design, and many things about computers. Yet, my “big areas” are physics, mathematics, running, reading, and writing, not exactly applicable to the other things I listed above. But the point is that I have only dabbled in these other interests. I haven’t dug deep into them like I have with my core interests, and it makes all the difference.
Last year, I tried to learn a bit more on the guitar. This didn’t go so well. I learned some chords, but nothing came of it. Ultimately, I shelved this interest because I didn’t want to dedicate as much time to it as I did with my running. I saw that the two were competing for attention, and that I cared more about running, so I gave up my musical ambition.
Likewise, you cannot expect to simply add a new hobby into your life without encountering issues. More likely, you’ll have to make a decision between something you already do. The simple reality is that we have a limited time to do what we want each day, so we have to choose what to spend it on. That means making a difficult decision between things you enjoy. If you split your time, you’ll also split your focus. You can go that route, but you will always be limiting yourself.
There is always a juggling act going on in your life. Some things get more attention than others, and that’s alright. The important part is that you choose which things you want to be a focus in your life. Spend the time on things that interest you, and remember that it won’t be locked in stone forever.
One of the most hated things in all of school is the speech. Students hate talking by themselves in front of a room full of peers. This usually has something to do with students not wanting to look ridiculous in front of their peers. Personally, I never had too much of a problem with presenting in front of a bunch of others, but I wasn’t necessarily a natural either. My strategy consisted of trying to memorize my presentation as much as possible, but at the same time, I never fully had my presentation down. Therefore, I’d be walking a thin tightrope to not trip up on my presentation while still trying to sound natural.
Most of the time, it worked, but I knew that I was more or less faking it the entire time. I was trying to make it seem like I knew everything, though I didn’t. (To be fair, I was still good at presentations, but I always noticed this internally.)
I can’t help but notice the similarities between those presentations and how students need to approach tests at school. Whether it be in physics, chemistry, biology, or mathematics, students rarely go into a test feeling completely comfortable. Therefore, they are banking on the fact that the teacher will not ask difficult questions on the test that are in their “weak spot”.
Despite being pretty good at mathematics and physics, I’m frequently in this position. It’s not that I don’t know my material. It’s that there’s such a large amount of concepts that need to be known that it can be difficult to keep track of it in one’s head without forgetting a few things. Honestly, the only thing way I’ve found to permanently store concepts in my mind is through continued use over several semesters’ worth of classes, which is obviously too long to be useful for any specific test. I frequently catch myself in a new class and doing something that seemed so difficult just a few semesters ago and finding that it is straightforward now.
The problem is that there’s a tension between time and becoming comfortable with the material. Two and a half years after my first calculus course, I’m pretty comfortable with taking derivatives of most functions. But now, taking a derivative is supposed to be like doing simple arithmetic. New challenges have arisen in my courses, so those are what cause me trouble.
There’s no easy solution to this. The simplest solution is to do a lot of practice problems. Unfortunately, that takes a lot of time and so you are limited in what you can do. Therefore, the other strategy I take is to try and cover all my bases by doing problems that are vastly different in what they pose. Then, when I find one that I am struggling with, I focus on doing a few of those kinds of problems, and then I move on. This way, I’m not staying too narrowly focused on one topic.
The name of the game in school is to arrive on the test with as little need to “fake it” as possible. By exposing oneself to all the different scenarios and questions that can pop up, you’re giving yourself the best chance to be prepared to do well on the test.
Why Do I Need This?
The answer: you probably don’t.
The truth is that, because mathematics was deemed “important” early on in the history of public education, elementary and secondary students have to learn it. I can understand the argument for those in elementary school, since a lot of what they learn has to do with arithmetic and thinking about numbers in one’s mind. I think that’s a fairly useful skill that allows people to not need to pull out their calculators every time they have a small problem.
Once students get to secondary school, however, the actual usefulness of mathematics in every day life drops. I’m most definitely not saying that mathematics is useless and that nobody should learn it. On the contrary, I believe mathematics to be a wonderful subject to study. But we mustn’t kid ourselves that it often has limited use compared to something like learning a new language. Mathematics can help us answer serious questions and further our understanding of the universe, but the truth is that a good majority of people will most likely not be in that group of people who need to use mathematics.
The problem lies in how we frame mathematics. I constantly read and hear about people trying to make mathematics more relevant to a student’s every day lives. One only has to look at a textbook to see that this is true. Dan (link) even writes a weekly post where he shows his audience a picture of a textbook and asks us what we think the image is trying to convey. The idea he is trying to show is that we wrap up mathematics in a lot of “pseudocontext”, which isn’t really helpful to the student at all. This is exactly what I’m saying. Mathematics has its utility, but it isn’t necessarily useful for everything in our lives.
In my mind, core requirements in a curriculum should be there for a reason, which is that they are important to the education that a student is getting. Mathematics is one of those components that is required in every single year of secondary school education, so I think it is fair to assume that a class that takes up this volume of space should be absolutely critical to students. Unfortunately, this isn’t the case for mathematics. Those who enter the sciences will use mathematics, but there isn’t that much more application elsewhere (that I can think of). Therefore, is it really necessary to give students this much mathematics education when most of them will simply forget it all from lack of use?
I don’t have the full alternative solution to this problem, but I do think we could make a few changes. As mathematics is valuable in any career that involves the sciences (and here I mean both social science and natural science, so I am including the economic industry as well), we need to stress this importance at the beginning of secondary school. Since I know that people change their minds all the time with respect to their future (since they are young, after all), I think they should have mathematics classes until maximum secondary three. After that, we already have a fork in mathematics education as students must decide if they are going to take the “regular” mathematics course or what students like to call “high” mathematics, which is basically a more scientific and general mathematics course (a quick example is the students in the regular mathematics course learn about parabolas, but only fixed at the origin, while students in the other mathematics class have parabolas going everywhere). The same sort of decision is also made in secondary five.
Instead, of this, I can envision two options. On the one hand, those who want or need to take a mathematics course in order to go into higher education can take the scientific flavour of the course (which I don’t think is that much different than the regular one), and every one else can take a different course. Not a different mathematics course. A different subject entirely. As much as I love mathematics, there’s no hiding the fact that it has terrible reputation because so many students are taking it when they both hate mathematics and have no use for it. Should we really keep on giving them these classes when they aren’t helpful? Personally, I think the answer is “no”.
I don’t think the problem with mathematics is that it’s too abstract or that there aren’t enough relevant examples to pique the interest of students (though that may sometimes be the case to a small degree). I think the problem is that we expect too much of mathematics. It doesn’t need to be a subject that fits for everybody, just like fine arts or music or theatre aren’t for everyone. By removing the need for students to always take mathematics in order for them to graduate, we should set out the path for them for three out of their five years of education, let them decide, and teach those who want the mathematics education. That way, there will be a definite answer to why students need mathematics. It will be for their future career choice, as they themselves have chosen.
Finally, you might be thinking something along the lines of, “Art and physical education are mandatory for graduation, so why shouldn’t mathematics be as well?”
For physical education, I think the answer is simple enough. Even if students aren’t necessarily “getting” any skills from that class, it does provide one thing: a path for students to stay active and see that there are an enormous number of activities that one can do to stay healthy. To me, that’s reason enough to keep it as a mandatory requirement.
For art classes (I’m talking about all art, such as music and theatre), they are indeed mandatory to graduate, but it isn’t a requirement until a student’s fourth or fifth year. In this same way, I think it’s great to have students do some mathematics, but only enough to give them an idea of if they want to pursue it more. My point is that I don’t want it to be forced upon them for years and years.
Of course, I want to end by pointing out once again that I don’t know how reasonable this is, nor of all the factors at play. However, I can see that what we have now can be improved, so I’m hoping we can step up and do something about it.
Within One’s Expertise
Because I am a tutor for secondary students, most people assume that I know everything that needs to be known about those classes. However, that could not be further from the truth. In fact, I frequently encounter problems that the students I help have that I cannot answer. It’s not even that I don’t know the answer. Sometimes, it’s just so far back in my mind that I don’t remember what the exact steps are.
When this happens, I don’t beat around the bush and pretend I know the answer. I tell them I have no clue, and that we’ll work it out. The reason I do this is twofold. First, it’s probably true, since a lot of the secondary mathematics is straightforward after doing more advanced mathematics. But the second reason is that I want to show them that I am not a robot that knows all the answers to their questions. I’m a student just like them (even if I become a teacher as well), and I’m constantly learning. I want them to know that I am just like they are, expect a few years further down the line. That’s it. I’m not a mathematical prodigy or someone who can do all the calculations in their head. I’m just there to give them a hand when they need it.
This is why I’m not too scared of straying from my expertise. Yes, I may not have much experience in all the classes in secondary school (in fact, the majority of students I tutor this year are taking a class I’ve never taken), but there’s no harm in learning. Plus, learning this way also helps me become a better teacher in the future.
I’m definitely not advocating for you to proclaim expertise in every area of your life. I’m just saying that if you are willing to put in the hard work to learn, it’s entirely possible to become more knowledgeable at anything. Therefore, don’t restrict yourself to your personal expertise where you are comfortable. Experiment, and try to learn new things.