WHAT TO DO WHEN YOU HIT A "CEILING" IN LEARNING MATH? Somebody asked me this question recently. I defer to the math education experts but as a Harvard student in a mathematical field I do know a little about learning math. 🧵
My experience with learning math is before you can progress to the next level, you need to develop mental models of the current material that allow you to think extremely quickly. The best teachers will give you the models, but you might have to find or invent them yourself.
Good representations are only half the story because you also need to practice them over and over again until they're automatic. I'm not a psychologist. So I don't know but maybe there are people who are naturally quick or can come up with their own models easily.
I don't think it matters how you get the right mental models as long as you use them. Once you have the these models, I've found that learning math calculations isn't any more complicated than learning dance moves.
The important thing is it's not enough to UNDERSTAND. You have to be FAST and you can get there through a combination of good mental models AND practice.
Math piles abstractions on top of abstractions. You have to know the early stuff to get the later stuff. So if you're not fast at the lower level material, the lack of speed piles up until you can barely move forward. Most people then feel like they've hit a "ceiling" with math.
I saw this when I was tutoring. Kids that needed a calculator to add "8+7" were usually in deep trouble because that meant "8x+7x" required them to pause and think, and then "8x+7(x+9y)" was an absolute chore, which means calculus was mission impossible for them!
My advice to anybody who feels like they hit a ceiling with math is to go backwards down the stack and work on your speed at the lower levels. You will find that this will free up a lot of mental energy to move forward with the higher level stuff.
The way the school system is structured, people often get pushed into new math classes when they aren't fully prepared. Even getting an A in the previous material doesn't mean you have built up the speed needed for the next level.
Often when people feel overwhelmed by the pace, math phobia can set in. Fear is the mind killer. It makes it harder to concentrate which makes the lack of speed even worse! This is why working on your speed is critical!
To summarize. My advice for people who hit a math "ceiling" is:
1. Go backwards to earlier stuff if you need to
2. Slow down until you get it
3. Focus on your speed once you understand!
Good luck! 🧵
1. Go backwards to earlier stuff if you need to
2. Slow down until you get it
3. Focus on your speed once you understand!
Good luck! 🧵
