…Inexactly.

When I was at school, there was this time period when I found physics incredibly fun and interesting, and a time period when I found it painful and dull. Of course, the moments with experiments were by far more engaging than the moments with mathematics and equations, but I’m actually just thinking at the latter part — there were times when the formulas were beautifully simple and the results satisfying, and times when the calculations felt like drudgery, there were a plethora of formulae which I couldn’t intuit, and even the result didn’t “click” with me intuitively.

I attribute a large part of this lack of excitement over physics to excessive focus on algebra and symbolic manipulations. I consider myself fairly good at algebra, but I feel that even I would have benefited more from my physics tuition if I had thought of it less as an exercise pure math and more as a systemization of the physical world. I am not advocating for making physics less conceptual — quite the opposite — I want kids to understand that all things are connected, and that there are really very few rules that govern the world; that there is a kind of beauty to physics. I just don’t want to conflate this with a college dose of pure mathematics.

What is it precisely that I am advocating for?

What if we change the way we teach physics (and, while we’re at it, all exact sciences) to focus not on forcing kids to memorize all the formulas, which end up being derivatives of one another (but we don’t have the tools or the sophistication to know it), but on having them answer questions about the physical world by teaching them the few simple rules and equipping them with the tools to compute the answer, sacrificing the symbols along the way? In other words, I want to teach kids as few formulas as possible, instead showing them how they can transform these formulas numerically and compute the answer.

What I am proposing is no small matter. It means teaching the kids the concept of calculus (but without the heavy algebra behind it), and having them apply it in problems. Yes, they would be able to (numerically) integrate before they learned about exact solutions to quadratic equations, but why is this necessarily something to avoid?

I believe this would work for a number of reasons. First, while in the absence of sophisticated tools, checking the algebra was really the only fair way to evaluate students, these days we can follow the kids’ thought process even without any symbols. It is also satisfying to arrive at a tangible answer as both an apt metaphor for physics as a way to answer questions about the world, and something one can have an intuitive reaction to (“5″ is a much better answer to have an intuitive reaction to than “x^2+1, at 2″). It also decouples physics as an experimental science where theories are put in place and tested, from the mathematics behind the theories that can be daunting and distracting from the main point. And while I believe that symbolic manipulation is a great skill that drastically improves ones cognitive abilities, we still have mathematics that will teach it to the kids. And imagine the “aha” moment that kids will have once they realize that what they have been doing in math, transforming all these expressions, coming up with closed form solutions and exact answers, can enrich everything they have been doing in physics — using numerical calculus in application of a few very simple rules to arrive at the answers to problems.

By the way — it would be a sin to not recommend what I believe to be by far the most engaging, satisfying, and challenging physics textbook I have ever read: Motion Mountain. I wish I had had read it much earlier than I did (at 25). Motion Mountain is epic, in all the possible meanings of this word. Instead of focusing on hard math, it does its best to show me what physics is all about — the side of it that I was never shown in class. Its problems make me think (never recall), and, while you need to have a degree to take full advantage of it, I believe you can reach for it at an early age. In fact, it’s these “layers” that make the book so fascinating.