When students get tripped up on math problems, they make one of two mistakes:
1) They either forget what to do
2) They don’t know what to do
For this video, we’re going to address mistake number two, not knowing what to do.
To solve this problem, I’ll introduce another mental model for math.
To demonstrate, I want you to picture a pyramid.
The base is wide with lots of stones.
As you move up, the pyramid gets more narrow
Now, ask yourself, what would happen if you started taking blocks out of the bottom level?
The pyramid would start falling apart.
Take away a few blocks at the bottom, and the entire pyramid crumbles.
IN life, and math, your grades and your success work just like the pyramid structure.
At the bottom of the pyramid are the fundamentals, the basic classes, and the required knowledge
Necessary to move up to the next level.
Each level higher requires more skills below it.
Without them, your math career comes to a screeching halt.
Consider this equation:
x + 4 = 10
Without knowing about variables, constants, operations, and equations, you can’t solve this problem because You don’t know what you’re looking at.
And even worse, if you can’t solve this problem, you can’t go on to other subjects like calculus.
This is why textbooks list prerequisites for each class. Prerequisites are the lower levels of the pyramid.
Without them, you have no foundation to build on.
If you skip fundamentals and jump straight to the advanced stuff at the top, your fundamentals are weak. Weak blocks eventually crumble, leveling the entire pyramid.
So when you start any new math class, figure out the required classes needed to understand the class.
And even if you took the required classes, skim through the information again before starting your current class.
Building and mastering fundamentals doesn’t sound exciting. But it will take you farther and faster in math than any other skill.
Case in point:
I used to know a student who got consistent A’s in math. He wasn’t a genius. He wasn’t even clever.
But every year, he’d go through the prerequisites needed as a refresher over the summer before his new class started. He’d spend 1-2 weeks refreshing his memory from prior courses. Then he’d go back through his old notes.
By doing this, he strengthened his pyramid foundation.
But he didn’t stop there…
After looking through the prerequisites, he’d skim through the current class and learn the fundamentals.
He started learning lessons AHEAD of time. He’d have his questions for the teacher or tutor ready in advance.
So when classes started, he had a list of what he knew and what he didn’t know.
He leaped miles ahead of Ahead of everybody else because he had the fundamentals built.
Think of it as running a race where you get a 30 second head start. It’s UNBEATABLE.
You see, part of leveling up your grades comes from mastering fundamentals.
Each fundamental creates another Block in the pyramid.
Stack up enough blocks, and you’ll climb higher than you ever thought possible.
So the next time you take a class, you do two things:
1) you go back over the prerequisites for the class
2) you start studying the current class EARLY, ahead of everybody. Write down your questions so you can ask
Them in advance
Do this, and you’ll never miss a problem because you were “in the dark”
