I got a 70 on my 8th grade math final and it’s stuck with me ever since.
Partly because it was ingrained in me from a very young age that my grades were incredibly important (frankly, what mattered most).
But more because I learned that simply reading through a math book isn’t the way to learn — it feels good and productive but the reality is far from it.
Integrating Knowledge (Not Just Regurgitating)
In their work on human learning and memory, McDaniel, Roediger, and Brown divide learning into two types: mechanical and elaborative. Mechanical is rote reproduction. You read a textbook chapter for a second time. You look over your notes. Elaborative involves incorporating it into your lattice of knowledge (this can take many forms). It can mean trying to recall it without looking at your notes, relating new pieces of knowledge to old pieces of knowledge, or asking deeper, follow-up questions about the material.
The rule of thumb: mechanical is a waste of your time and elaborative actually leads to results.
Of course, this isn’t always true. If you’re re-reading the textbook to understand a certain dynamic, that can be really helpful (although, it would do you so much good to simply try to explain what’s going on before reading about it again even if your explanation is far off from the truth). But it’s mostly true.
The Challenge: AP Calculus
It was my 12th grade math AP test that led me to my strongest conclusion on learning: to create is to understand.
I didn’t have to do good on my senior year tests. I was already in college. My real motivation was to learn math for the sake of it. I thought it was cool, I wanted to study a CS, so I thought that it would be both fun and useful enough to dedicate hours to.
This time, though, I didn’t use my 8th grade strategy. Instead, I refused to do anything unless I was building from the ground up.
The Solution: Creativity!
While others studied by memorizing the product and quotient rules, I studied by deriving them. I wasn’t satisfied by simply plugging numbers in. I wanted something deeper.
This is hard. Both because it expands your mind beyond its current limits and because the school system doesn’t reward this type of thinking.
To succeed in school, you want to get good at consuming and regurgitating. Understanding what’s under the hood isn’t really necessary. But to succeed in applying the lessons you learn in school beyond the confines of school? You need to build from the ground up.
Creativity is the strongest signal of understanding. Brandon Sanderson speaks on why this is the case in a podcast with Ali Abdaal. Sanderson describes the difference between a cook, who cannot create, and a chef, who can create.
A cook follows directions. They look at the recipe, put the ingredients together, and usually get a good meal out of it. But they can’t create. They don’t know why their meal tastes good. If it were to taste a little off, they wouldn’t know what to fix.
A chef is beyond directions. They are intimately aware of why food tastes the way it does and how different foods combine to form novel flavors. If one of their recipes goes wrong, they’ll have a sense for why. They understand food and, so, can create with it.
If you want to know if you can truly understand something, create.
Creativity also serves as the greatest tool for learning. It’s not just a test of understanding; it builds understanding. When you set out to create, you have a hypothesis. You think x will interact with y to create z. If it does, you can bet that you know your stuff. But if it doesn’t, you can examine exactly why it didn’t go to plan. You have a creative hypothesis that can be tested, broken apart, and analyzed.
In broad daylight, you see what you don’t understand. Then you can fix it. Create again and test again.
I wish I could go back to my 8th grade self and tell him that he should stop flipping through pages and start putting pen to paper, but I’m kind of glad I can’t. You see, I didn’t realize it, but I actually had a creative hypothesis for that final test. I thought that to study math was to read over formulas. If I felt good about it, I got it.
I tested that hypothesis, and it failed. I realized I didn’t understand studying, and I did research. You create all the time, and I suggest you do it more intentionally. Because learning from our creativity’s triumphs and mistakes — that’s the way to true learning.