Teaching Badly

January 7, 2019

I'd like to demonstrate three widespread flaws in education today, through a few little narratives.

The first stems from an early gifted-ed teacher of mine; I had the naive view that my teacher could provide insight on any problem I posed to him. And usually this was the truth; he often could help.

But on matters of mathematics, he knew very little. Unfortunately, this did not stop my teacher from providing advice on these topics, and he did so with his usual degree of confidence. I'd take him at his word and resultantly spend many hours barking up the wrong, impossible tree.

That's not to say that spinning your tires on a problem is necessarily a bad thing, but it's frustrating when you've been lead by a trusted adviser that a bad approach is in fact a good one.

This leads us to our first insight: be knowledgeable in your topic, or at least in your ignorance. If you are teaching, ensure you know what it is that you're trying to teach. This problem is particularly prevalent in North American schooling, where teachers are often treated as being fungible---the typical example is enlisting the gym teacher to teach science class.

Kids aren't stupid, and it quickly becomes evident that the person responsible for teaching a subject knows as much about it as they do. I would suggest that this teaches the wrong lesson; that it's OK to boldly not know what you're talking about because you have vested authority.

The second flaw in education I've seen comes from a more topical experience. A few months ago, I started taking piano lessons again. It was mostly an accident---a piano teacher got in touch wondering if I could tutor her daughter in computer science. We decided on a quid-pro-quo agreement where I'd trade CS lessons for piano lessons.

The lessons started with an exceptionally high learning curve. My new teacher had expectations about where I should be in terms of piano, and set her lessons accordingly. Needless to say, these expectations of hers were significantly above where I actually was in skill level.

Now, I'm not one to shy away from a challenge, so I duly gave it the old college try. My teacher would give me a piece to sight read (play without having seen before) that was in a key signature I wasn't familiar with, making sure I played every note for the exact correct duration of time, while asking me to perform an analysis of the chords as I went, and expecting me to notice repeating patterns in the music.

Any one, or possibly even two of these tasks, would have been possible for me given serious, concerted effort. But attempting to simultaneously juggle five difficult tasks in real-time is not a recipe for success. I'd play the piece attempting to focus on all of my goals, and inevitably drop one or two. My teacher would immediately stop me and point out the mistake.

Frustrating, concentration-breaking, and actively unhelpful. If you're having a hard time focusing on a single challenge, your performance isn't going to improve by instead focusing on two challenges.

This is our second insight, and it's one of methodology---focus on doing only one thing at a time, and on doing it well. Practice a skill until it becomes instinctive, then---and only then---tackle the next piece of the overall problem. In other words, decompose a hard problem into easier sub-problems and conquer them individually.

My third example comes from an improv class I took a few months back. Despite having taken about a year's worth of improv, I decided to sign up for the beginner's class. This was a mistake on my part, but gave me a better context in which to evaluate the teaching.

After each class, I'd conduct an informal little straw poll among the other students---"how are you liking improv so far?"---that kind of thing. The response was always lukewarm. "It doesn't really feel like we're learning anything."

Somehow learning wasn't happening, despite us doing three hours of exercises per week. The problem, I think, was that the instructor never impressed upon us why we were doing the exercises. Exercises that are not themselves the eventual end-goal are helpful insofar as they build related skills. However, if you don't know what the exercise is trying to teach, it's hard to extract value from it.

That's not to say it's impossible, per se, merely that it's an inefficient way of learning. It feels like the equivalent of listening to foreign-language tapes while you sleep, hoping that they'll sink in through osmosis. While this may or may not be true, it's certainly less effective than saying "I reliably mess up the subjunctive tense in French; I'm going to go practice that and pay attention to it for a little while."

There is a related failure mode here, which I've often noticed from musicians. They'll play something that I like and I'll ask "what did you just do?" And more often than not, they won't know how to articulate it. "I was just screwing around." It's not that they've forgotten, it's that they don't have the awareness of why something works. It just does. They've learned it instinctually through brute force, and subsequently lack the tools to analyze or articulate it.

And so we make our way to the third insight---exercises are most valuable when you understand what they're trying to teach you. To the instructor, it's probably obvious what the goal is, but this is only through the lens of hindsight bias. The beginner doesn't have enough knowledge to identify specific sub-skills or, relatedly, their value.

The takeaway is obvious: if you're responsible for providing examples to students, take a moment to explicitly tell them what to focus on while doing it. Provide a high-level description of why this is a valuable thing and how it relates to the bigger skill at large. And it should go without saying that if you're only recommending an exercise because your teacher recommended it to you, maybe you should take a moment before passing on that particular torch.

Not only does knowledge of the immediate goal help motivate the students, but it helps train them in the more immediate skill of "how do I know if I'm doing this thing well?" Fast feedback cycles are key to fast learning. It's hard enough throwing a basketball into the hoop---imagine if you had to learn how to do it while blind.

My claim is that these three points are crucial in the pursuit of good education. Know what you're talking about, and if you don't, be clear about it. Subdivide problems into easier ones, and ensure mastery of the essentials before attempting to synthesize them together. Finally, provide guidance on what these sub-skills are, how they relate to the bigger picture, and how to go about learning them.

When put this way, my ideal educator is less of a grade-school teacher and more of a mentor. Someone whose responsibility is to show you the right direction, to keep you from going off into the weeds, and to suggest a training regimen to help. In short, the mentor isn't responsible for your success, only for giving you the best possible chance at it.

I can only show you the door. You're the one that has to walk through it.

Morpheus, The Matrix