How Can You Succeed at Learning Higher Math as an Adult?

Math’s rules are like training wheels on a bike.

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Answer by Dmitriy Genzel, computer science Ph.D.:

Usually the problem that people like you have is that they got lost at some point in their education. Usually it isn’t at the level of the last class you completed, but somewhere earlier. We all use our intuition to do math. You can learn the rules, but if you don’t understand what they are for and why they are the way they are, you are limiting what you can learn. The rules are like training wheels on a bike, and as you get to the next level, your instructor assumes you know how to bike, and then you crash.

So you really need to go back and see if you understand why, say, ab+c = abac. And as you go through the curriculum, at some point you are going to start just saying, “I don’t get this completely, but I sort of understand. I can still do the problems. I can keep going.” At that point you need to go back; this is where things broke for you. As a kid, you just went ahead and your math building got a hole inside and unraveled. Some holes are harmless, but many aren’t, and you are probably not in a position to know which are which.

One thing that is very helpful to realize is that math has to be the way it is. Almost nothing you learn is “just because,” but it is the only way it can possibly be. If you understand why, you have half the battle won, and you won’t make half the mistakes that other people make, and you’ll never forget a concept, just like you don’t forget that objects fall down and not up.

Tutors can help you get through the place where you got stuck, but it should be you driving it. Sometimes tutors just help you pass tests; they teach you the rules but not understanding. Sometimes they don’t understand themselves. You need to figure out what is the first topic that you don’t completely get and get the tutor help you really get it, and then you can go forward.

My kids are doing algebra now, and I recommend Art of Problem Solving Algebra. This book, if you use it as it tells you to, won’t let you get away with learning rules without understanding. I do not recommend Khan Academy as a primary source, since it’s based around the idea that you want to learn how to use math more than about understanding why math is the way it is. You can get away with the former, even through many college courses, but the latter really makes it possible for you to go as far as you choose.

How can I succeed at learning higher math as an adult when I was bad at it in school? originally appeared on Quora. More questions on Quora: