In mathematics, notation is simultaneously everything and nothing. It isn’t difficult to imagine another alien species havig the same notions of calculus as we do, but without the symbols of integration or differentiation. It might seem so natural now to see the expression $\partial x$, but that’s only because we’ve spent years working with these symbols, forging a connection between concepts and notation. Due to this, it can seem entirely natural to look at notation and instantly understand what it’s about as a concept, rather than just symbols. This is quite similar to our experience with foreign languages, where the words and characters look alien to us, yet our own languages seem so obvious.

When you’re trying to solve a simple algebraic expression like $ab = 5b$ for the variable $a$, it quickly becomes second-nature to divide both sides of the equation by $b$, yielding $a = 5$. This makes complete sense, and it’s what most people would do right off, without even thinking. I mean, look at both sides of that equation! If there’s a $b$ on both sides, then the other value on each side of the equation should be equal to each other, giving us $a = 5$.

As a student in both mathematics and physics, I often see the differences in mindset between the two fields, and how these mindsets change the way classes are taught. The former is usually about structure and patters, while the latter is about modeling the world using mathematics. The problem is that belonging only in the camp of physics seems to be a dangerous thing to do, in terms of building one’s foundational understanding.

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.