On School

XLV

2024.05.05

I was just at my brother’s graduation (congrats, Zeke!), and ended up thinking a lot about school.

Reflections on the interplay and differences between memorization and understanding below.

Why School?

Why even go to school? It’s a serious question, and I can think of a few answers.

I’m actually a proponent of school, and a proponent of going to a “good enough” school. When I say “good enough,” all I mean is a place with a sufficiently high density of talented and interesting people so that you can position yourself in subsets of the university where it’s relatively trivial to meet them.

As a specific example of one of those places, my friend Bobby, who is now going to Liberia to serve in the Peace Corp and whose blog you should check out here, started a group at U of M called Power Hour, which is still going on today. If you were to attend an event hosted by Power Hour, you would be bumping into a lot of people who had some sort of lesson or wisdom to share about starting a business or otherwise building something cool, which is terrifically important to cut the learning curve. While I cannot compare this talent density to what I would have gotten at a more selective university, I truly have no regrets in that regard.

Now, outside of meeting people, you’d think you’d go to a university to learn. In the past, based on many of the classes I took, I thought this was not true.

After all, until I started taking upper level math classes, I did not spend much time attending lecture, and, when I had to, I wasn’t spending much time paying attention.

Regardless, though, I think attending university gave me a good chance to experiment with learning something as quickly as possible, but for somewhat of a counter intuitive reason.

As much as I’d like to say “I didn’t care about getting grades,” to some extent, I did. And, really, there are two paths I am aware of to getting good grades in school, and, as always, one seems much harder than the other but is actually much more fruitful in the long run.

Memorization Problem

One of my go to principles is Goodhart’s Law, a formulation of which is:

Translating this to University: originally, someone probably observed that students who understood the material of a course performed better on a final test than students who did not understand the material of a course.

Okay, easy enough. If you do better on a test if you understand what we’re testing, let’s just test you!

The problem is, as we go on over time and continue to standardize and effectively commoditize tests, the statistical regularity of someone’s understanding of the material being highly correlated with test materials certainly collapses. Tests fail to become a good measure of whether or not you understand something. Why?

More specifically than Goodhart’s Law, here are some ideas; here, expensiveness is gauged in cost in focused hours of labor:

1) It is comparatively expensive for a teacher to make completely new tests every year when they could simply change variables in their old tests

2) It is cheaper for the teacher to give past tests and their answers as study guides than it is to make study materials to help you truly “learn”

3) Students perceive that there is an easier way to score well than to understand the material.

Number 3 is maybe most important. If there is a seemingly easier way to score well on tests than understanding, students will find it. Overtime, test scores will be less correlated with understanding the material, and more correlated with the seemingly easier way to score well on tests: memorization.

Memorization vs Learning

To clarify, when I say memorization, I mean just practicing flashcards or studying old tests in the hopes of seeing every “type” of problem and memorizing what formula to apply to it. In school, we would call this “plug and chug”: you memorize problem formats and map them to the solution.

Teachers, in part, enable this when they give out similar tests every semester and use past tests and their answers as study guides.

On the other end of it, you have what we’ll call learning or understanding. This is actually fundamentally understanding why something works the way it does. Maybe we could even consider this thinking in “Axioms,” having a fundamental set of rules from which you can make new rules or challenge old rules and update your own belief. Here’s an old post of mine that makes a similar, more fleshed out distinction between knowledge and understanding as I am now between memorizing and understanding.

Memorization and learning are different in a lot of ways, but here’s an absolutely critical one:

Learning is exponential. Memorization becomes linear.

We’ll dig back into that after an example.

Spreadsheets 101

As an example, we’ll take a specific class I took in Ross; we’ll just call it Spreadsheets 101—real class, fake name.

Now, the thing about Spreadsheets 101 is that it was effectively an intro statistics class in which you had to execute all of the operations in a spreadsheet. The class was not very complicated, but was considered a “challenge class” in Ross… that was the colloquial name given to any class with objective grading.

Going into the class, I personally had a rudimentary and conceptual understanding of normal distributions and power laws from reading Taleb’s non technical books; I think at that point I had read The Black Swan, Antifragile, and possibly Fooled by Randomness. Additionally, I understood from trading that options were priced based on a typically lognormal distribution and could translate Implied Volatility into expected movement.

So, I had my practitioner’s understanding, but had taken no formal courses on the stats or spreadsheets and had never heard of these poisson distributions or the P Value of a correlation. However, I was able to learn it pretty quick, but not because I was spending hours studying or doing homework—I actually wanted to understand the material as quickly as possible, as I knew this would truly be the least expensive thing to do in the long term.

The course work and tests followed the format of presenting a business problem that implied the use of some sort of statistical method which you would have to identify and then do a computation with, probably in excel.

Now, the way NOT to learn this that I saw many of my classmates doing: poring over practice quizzes and past exams in an attempt to memorize the question pattern that mapped to an excel function. They were building up a series of if-else statements, a collection of rules memorized to navigate through solving the problems. If I see these words, I use this excel function.

On the other hand, what I did and I’m sure anyone else who was trying to learn did, was focus on understanding the actual concepts as quickly as possible. I did not want to memorize excel functions—in the long term, that’s useless. As a matter of fact, I spent 0 time memorizing excel functions, because I could write them down on a note card. Besides, the function names are designed to be relatively intuitive, anyways.

I wanted to understand the core concepts we were actually being taught, and since, in this class, there weren’t many, it didn’t take much time at all.

There were far fewer fundamental concepts than there were ways that the teacher could ask about them on the test.

While it might be harder at first to learn one fundamental principle than it is to memorize three rules, it is certainly easier to learn three related fundamental principles than it is to memorize 20 question formats and their answers.

If you actually understand what you are being taught, you don’t need to memorize the questions, and you don’t need to worry about “trick questions” in which Mrs. Teacher switches up the pattern to catch the memorizers. Not that one trick question is a credible threat to memorizers; remember, it is often expensive for the teacher to have much more than one trick question. And, even if she does, and she starts failing the memorizers, then she’s the bad guy for “testing on material not covered in class,” or, in other words, creating a question that was not easy to solve via memorization.

Learning is Key

So why memorize? Because at the start, it’s probably easier. Remember, school is a a finite game played over a small time scale where there aren’t necessarily outsized returns for getting a 99% instead of a 93%, so why even bother trying to get a 99%?

Well, the problem is that the real game you’re playing is life long, and the returns of learning are actually non linear, while the returns of memorization become linear.

Sure, as you work on the meta skill of memorization, you get better at memorizing; at some point, the relationship decays into a line, though. Even if you memorize everything you are told, unless you’re learning and making connections, you are limited by how many things you are told.

From my own experience, even in the context of school, learning and understanding accrued a lot of benefit over memorization, and I expect it to continue to do so over time. Read this recent Paul Graham essay for further rationale as to why.

Even if, in the start, it is harder, I am firm believer that learning trumps memorization. That being said, the interplay between the two warrants more discussion. Perhaps we’ll examine it next week.

Thank you to all of my professors who actually encouraged us to understand the material.

If your classes encourage memorization, they are doing you a disservice, exceptions probably being when memorization is absolutely critical to your job function. If you are memorizing something you could understand, you are doing yourself a disservice.

Accept the difficulty of learning now; it will make learning later less challenging.

Live Deeply,