As a Mathematics major now studying code, I’ve learned that there are efficient ways to learn and the less efficient ways. The difference is relational understanding vs instrumental understanding.

In essence, relational understanding is “knowing how and why” as opposed to instrumental understanding which would be described as “rules without reason”. To understand the differences, think way back to the elementary school days when you had to learn the multiplication table. You might have memorized everything from 1x1 to 12x12 and were able to recite any multiple in between. However, to know why 3 times 4 was 12 you had to know that it meant to add 3 to itself 4 times. Knowing the latter provided you with much more powerful tools than just knowing the multiplication tables. By knowing what multiplication actually was, you were able to do far more than just 12x12 but 13x13 or 42x3. Just finding those answers was a tedious task.

To really know how to code, you must have a relational understanding of what code actually is. Don’t worry so much about syntax. Syntax is always documented. And as long as you know what you need, you can find the syntax in the docs. If you’re still having trouble after reading the docs, you can go to other resources like Stack Overflow. However, if you don’t even know what you’re searching for, you’re gonna have a bad time.

gonna have a bad time.jpg

Instead, when reading code, learning code, or writing code, think about how the code works.

As an example, let’s look at something that every rails programmer has used. The has_many relationship. It’s a necessity in back end development, but not everyone knows how it works. We all know that in order to have one model relate to many objects in another model, we need a has many relationship, such as a team that has many players. This is pretty much known fact, and common knowledge. What more do we have to do but put one line of code in the Team Model?

has many :players

But what if a player can be on many teams? Or, let’s get a little crazy, a player has many teammates? Holy cow. Hold your horses. Things just got super complicated. A simple has_many relationship won’t work here. We’re going to need a many to many through for the player to also have many teams and then a many to many self for a player to have many teammates. Where I see many coders having trouble is right here. They always try to memorize the syntax instead of relying on logic. Even worse, some might not even know what sort of relationships are needed because they were too worried about memorizing syntax that they forgot to learn about the overarching concepts!

What I’m saying here is to just know what you need at any given point of your program. You can always, ALWAYS, find syntax documented everywhere online. But let’s take this analogy one step farther. Learn the mechanics of a simple has many relationship and you’ll pretty much understand how every has many relationship works. Better yet, you’ll be able to write out each relationship as well!

So what’s the difference between relational understanding and instrumental understanding? In my true and honest opinion, instrumental understanding isn’t actually understanding at all. Instrumental understanding relies heavily on memorization and when things come down to the nitty-gritty, pure memorization will fall apart. Instead, strive for relational understanding. Know the inner workings of whatever you’re learning, whether it is something simple such as multiplication or something that we as a human race might never understand like quantum physics. Saying “I memorized the formula” is never enough.

So what if I can’t achieve relational understanding?

I had this problem so many times in my analysis courses that I was worried I would fail. And at these times, I at least tried to get the instrumental understanding down in hopes that later I will actually realize what is going on. Eventually, I had some “Ohhh” moments and certain things started to make sense. In the same way, if things seem impossible to understand, don’t surrender. Know that later on as you grow as a programmer, you might have to connect some dots in order to really understand what is going on. But in the end, you’ll come out as a much stronger coder.