Most people will tell you they aren’t great at math.
When people say that, they’re generally referring to more complex ideas like trigonometry or calculus. I was certainly one of those students that struggled with those subjects in high school. Yet… I wasn’t always terrible at math. In fact, I was pretty good. In 3rd grade, the teacher would time how long it would take to complete 100 very basic addition or multiplication problems, and I got my time down to a cool 90 seconds.
Likewise, I’m sure you’ve also mastered the basic stuff. You know 2+2=4, and I’m sure you probably would have no problem multiplying two double-digit numbers together. So the question is… where did things go wrong? Why is it that so many people struggle with math, starting roughly long division?
The answer is pretty simple, actually. Think back to when you first started learning addition. How did your grade school teacher teach you how to add two single-digit numbers together? They most likely made it concrete. Two apples plus two apples equals four apples. Four crayons plus another three crayons equals seven crayons. It’s easy for anybody to visualize that kind of thing. This addition thing is pretty easy when I can literally objectify what I’m trying to do. 2+2 may not mean much, but when it means collecting as many Pokemon cards as I can get, then suddenly I’m a math genius.
There’s a great bit in the TV show The Office where the accountant Kevin struggles to do any math at all, but when you start relating things to literal pies — be they apple pies, cherry pies, or banana creme pies — then he becomes a math genius, able to multiply large numbers in his head without a calculator or even pen & paper.
With this in mind, you can probably understand pretty quickly why most people get lost in the math world around 7th grade: we lose any meaningful tie to the numbers. It just becomes rote memorization of formulas, and the further you get down the complexity track, the more difficult the rote memorization becomes. Eventually, most people give up and write advanced math off as something only nerds can do. Which, truthfully speaking, I do feel like some people who are good at math feel like they have this innate ability that sets them apart from the non-mathy people, which I don’t agree with at all. (Hold on to that thought — we’ll get back to it.)
Of course, I’m only using math as a practical example, but I’d contend this applies to any subject. I like to visualize this general concept as a set of nodes interconnected by lines that represent relationships, like the one below:
To sum up this entire post in one sentence, memory is the meaningful association between concepts / ideas / people / stuff. If there is no meaningful association made, then rote memorization falls apart pretty quickly.
Let’s revisit our math predicament. Starting off on our math journey, we pick up addition pretty easily because of how we can meaningfully associate it to physical objects like apples or crayons or Pokemon cards. But as we progress through the journey and fail to make a meaningful association to something like sine waves, we fail to apply those concepts later down the road, forever giving up on the dream to become the next Stephen Hawking.
If you think I’m off my rocker with this, this is actually how “memory champions” win memory competitions. Do you really think people are arbitrarily able to memorize full packs of playing cards? No, they derive meaningful associations by crafting something like a silly story that makes sense of the arbitrary order. Just check out this TED talk if you want further proof:
Considering how our brains create memories around concepts, it’s just a short skip and a jump to applying this to learning. I mentioned earlier that I, like many others, struggled with more complex math ideas toward the end of my time in high school. There’s no doubt in my mind that this was because I failed to create meaningful associations and tried to brute force memorize mathematical concept, which of course failed.
Now in my adult life, I’m going back and learning these complex mathematical ideas, and it’s coming to me quite naturally. Heck, I’d even say it’s pretty fun. You might be wondering, “Have you gone mad? How can anybody have fun with math??” And the answer is simple:
I’ve found a meaningful association in the realm of machine learning.
After all, machine learning is really nothing more than fancy math enacted on datasets. Predictive modeling has helped me to understand why calculus is so relevant to learn. Couple this with the fact that folks like Ben Orlin, Steven Strogatz, and Grant Sanderson (aka 3Blue1Brown) have come out with excellent resources, and I’ve finally cracked the code to learning math without beating my head against the wall. (Those familiar with Ben Orlin’s work will recognize that I’ve sort of emulated what he does with the drawings in this post. My hand drawn artistry is probably just as bad as his!)
This process has been extremely transformative for my learning journey as a whole. People ask me all the time how I’m able to hash out certification after certification, and the answer truly is this simple. Rote memorization doesn’t work; you have to make meaningful associations to the concepts you’re learning. In other words, start with why before learning the how. There, I just saved you how ever much Simon Sinek’s titular book costs.
I hope this makes your learning journey a much smoother one. You might find that, like me, you genuinely become fascinated by whatever you’re learning. Subjects like math sort of get a bad wrap, but I truly feel like anybody can learn it and potentially find joy in the learning.
Let’s wrap up here. Catch you all in the next post!