Study Math by Speaking It

Learning mathematics is like learning a language. There are three golden rules:

  1. 1) Spend a little time every workday. You cannot learn Russian the day before your Russian exam by reading the dictionary. You will do much better by putting aside an hour a day to work on your homework than by leaving it for the night before. One tip: count your time in hours, not completed homework problems. Relax and enjoy your date with math: explore ideas and don't rush.

  2. 2) Practice! To learn Russian, you need to speak it. Similarly, you need to learn mathematics by doing practice problems. If you are reading the textbook and it looks like nonsense, choose a simple example and try to work through it yourself. You will learn much more than the textbook could ever tell you. And, just like with a language, practicing with friends and mentors is even better.

  3. 3) Make mistakes! (Do it now so you don't have to do it on the final exam.) To learn to speak Russian, you have to dive in and try! And when you first start speaking, you won't get a single tense right. If you are paralysed by the need to do a problem correctly the first time, you will never solve it. You must try things and see why they do or do not work. Every mathematician and non-mathematician does this. My job description as a mathematician is something like this: "Bangs head against wall for extended periods and writes down many wrong things. Eventually writes down something correct once every month or so." So don't be afraid: I spend more of my day making mistakes than you do. I know what it's like.
  4. Here are some ways to practice making mistakes:

    • try something you don't think will work and see if it does
    • write in pen and cross out errors gently -- you may find out your previous work wasn't as useless as you first thought
    • try to do a problem more than one way and see if you get the same answer

And finally...

Remember, no one understands everything the first time. Learning math means going over things in lecture, then at home, then with the textbook, then with your homework, then in section, then in office hours, then in review sessions...

Afraid of mathematics? Even mathematicians can have math anxiety. If you want to talk about this, feel free to come by.

Don't hesitate to come to me.