Discovery and Delight

I’ve been thinking a lot about where one finds joy in a subject, and how the goal of educators should be to create situations in which this is most likely to happen. In particular, I’ve been reflecting on the way this is achieved in specific subjects during the likes of one’s elementary and secondary education, before choosing a career path to embark on. My question is simple. Are we doing all we can to deliver delight to students? Like always, I want to focus on my particular interests, which encompasses science and mathematics.

I think it’s fruitful to compare the two, because they both have a quantitative aspect to them, and a similar type of mindset is required for each.

From what I’ve observed, the science classes seem to produce much more delight in students than mathematics. I’m not saying that students chatter excitedly about their science classes, but what I’m saying is that there is a certain purpose to learning, where it makes sense to learn a particular example. Whether it’s learning about how machines are composed of simpler ones, or how the force of gravity creates parabolic trajectories for objects in free fall, the purpose is clear. It’s to explain the way the world works, and it’s not that difficult to get students on board with this goal and have them delight in the fact. After all, it’s quite fun being able to explain to one’s family why objects accelerate at the same rate, or why certain reactions occur faster than others. As such, I’d argue that there can be a delight in learning about science just from this one aspect, regardless of if the subject is physics, chemistry, biology, or the many other wonderful topics in science.

If I’m honest, I think this is why I pursued science in the first place, and in particular, physics. It was a subject in which I thought it was so cool to be able to understand the world with only a few principles such as Newton’s laws, and so I was motivated to continue learning. What I want to point out here is that, yes, I did have some good science teachers, but the school I went to didn’t have a bunch of resources, so it’s not like I was in a top-tier science program. Instead, it was more that the subject itself (and the way it was taught), allowed one to become interested without too much extra effort.

Mathematics, on the other hand, wasn’t something that many regarded as enjoyable. Even I, who did well in my mathematics classes, didn’t particularly love it. I thought it was an interesting subject, but I never thought I wanted to study it later on after secondary school. Instead, mathematics was something I did to get better at analyzing situations, but I wasn’t there to learn mathematics because I delighted in it.

So why was that? Why was mathematics not filled with as much delight as there was in my science classes?

I think the answer is simply, purpose.

I’ve worked with many secondary school students, and I’ve heard this over and over from them. “Why are we learning this?” They don’t understand why the things they are learning are required of them. The emphasis is important here, because it’s not that none of this is inherently uninteresting. Instead, it’s because there’s no reason why it should be required of the students to learn a lot of what is taught.

My perspective on this is as follows. I find that within mathematics, a little bit of everything gets taught, but there’s no theme or sense weaved in between the subjects. One goes from geometry to solving equations to proofs without there ever being a why. Instead, there’s always this underlying sense that there is more to learn, but without the motivation. As such, it becomes difficult for the students to latch on and take delight in the learning process, because they’re being told that all of this skill in mathematics that they are building up has a purpose and that it is applicable in the “real world”, but the truth is that mathematics isn’t about applications. It’s about the connections between structures, the creativity of the mind, and the consistency of starting with axioms and building those structures. In the end, that’s where the delight in mathematics comes from. It’s not from the “context” paragraphs that are slapped onto word problems to give them what is supposed to be real world application. The delight comes from the mathematics themselves, and this is the fact that needs to be realized by all of us who teach. There is a joy in the pure abstract world of mathematics, and that’s what we need to cultivate.

Every time I get on this train of thought, I think about Paul Lockhart’s, “A Mathematician’s Lament”. It’s a great read, and something I recommend to anyone who thinks about mathematics education. In particular, I find that his comparison between teaching random mathematical facts and forcing students to learn how to read sheet music to be particularly apt. As I said above, the real joy and delight of mathematics comes from the subject itself, not the applications to the outside world. It’s very similar to other forms of art. If you look at someone who plays music, they usually do it because they delight in the act of playing music itself, not because they want to make it big. They don’t become musicians only to impress others. It’s because they simply love music. Likewise for mathematics, the goal shouldn’t primarily be to get students “prepared” for real life after secondary school. Instead, it should be to show students how wonderful the connections in mathematics are.

I’m not saying that mathematics has nothing to say about a lot of problems. Of course it does, but if we emphasize those (or worse, only emphasize the methods without context at all), we send the message to students that mathematics is only a collection of facts. But that is doing such a disservice to mathematics that I can’t ignore it.

If we want students to find more joy and delight in mathematics, it’s up to us to foster the sense of wonder within its various subjects. This means taking the time to point out the many connections between ideas, and to shy away from merely showing how to calculate things. After all, the goal of mathematics is to solve the problem, not to repeatedly do it over and over again.

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