Most people believe our education system is broken, but in my experience, it’s not common that two people actually have the same gripe with the system. Complaints vary from teacher pay to content practicality to poor standardized tests. I don’t think any of those are the main problem (although they may be upstream of my personal complaint). I think the core issue is the model in which we teach kids to think: we teach them to remember facts, not to understand systems.

My best example of this is the Kumon method of teaching. Kumon works by having students read some material about their next unit. After reading this material, they do worksheets in the classroom and at home. These worksheets are graded when they come in for their next session, and if they’re doing well enough, they get the opportunity to take a test and graduate to the next level. Students will learn arithmetic at a very young age and become proficient quite quickly. This makes for cosmetically impressive results - I’ve never seen anyone do multiplication faster than a 7-year-old who’s been doing Kumon for years.

I think these results are a mirage. While students are able to progress through the units, they do it by learning tricks. They learn the keep-change-flip method of dividing fractions, or they learn to solve quadratic equations by memorizing the quadratic formula. These tricks will get you the right answer, but they don’t help you build any deeper intuition about what’s going on. Learning the quadratic formula won’t help you understand differentiation better, but completing the square will! The keep-change-flip method won’t help you understand negative exponents, but splitting up the fractions into their component parts will. In both cases, the “trick” will get you to the right answer reliably and is fast to learn. It won’t, however, help you generalize onto future situations.

I’m picking on Kumon, but I don’t think the problem is exclusive to that system; they’re just the worst offenders that I know of (I was a Kumon tutor in a past life). I’ve had plenty of math teachers try to teach through these short-sighted tricks. I don’t blame them - their explicit reward system is only tied to standardized test results and students’ grades. In this system, I would also try to shuttle along kids so I could get along with my job. It’s only the best teachers, the ones truly in it for the love of the game, that put in the effort to teach differently. I’ve had a few of these kinds of teachers, and they changed my life.

The way we teach kids how to learn in school has ripple effects on the rest of their lives. In fact, I think this problem only rears its head in higher-level education or in the real world. In a real job, these tricks don’t exist in the same way: there’s no textbook with which to learn shortcuts to the “right answer” if such a provably right answer even exists. Instead, you’re forced to take in your surroundings and build a mental model for how your domain works. Building a strong understanding of your domain helps when doing routine tasks, and it’s literally required when trying to build something novel.

I’m particularly interested in this because so much of my “education” has happened outside the classroom. I’ve learned primarily through side projects and learning on the job. In either case, I didn’t read a book and memorize some tricks; nor did I just try to accomplish the task in the most expedient way. Instead, I’ve tried to focus on the process of building my DAG. By focusing on building a wider understanding of the system, I’ve been able to generalize to new situations and build novel solutions. For me, this deeper understanding is also more durable: when I can slot information into my DAG, it sticks with me near-permanently.

While it’d be nice to neatly wrap up this post with a suggestion on how to incentivize this teaching style, I honestly don’t know how. Pedagogy reforms like Common Core have largely been a disaster - this style of instruction requires a deep understanding of the material and the teaching ability to execute on this understanding. Even if we had a fleet of teachers all of whom were capable of teaching like this, they aren’t incentivized to. The benefits of this way of thinking play out over years, so you can’t reward this behavior on a per-teacher basis. It would never show up on a standardized test.

It may be that we need new interactive styles of instruction to unlock this, but these beliefs would need to be embedded into those systems. All I know is that when I’m teaching, I’ll continue to encourage my students to think about the wider picture. I hope that you will too.