Stuff I Always Say

Here are a few things I say over and over again to my students, with good reason, I think:

Make it make sense! When you learn something, don't just learn it by rote; think about it deeply until it makes sense to you. That way you'll remember it better and will be able to know when to use it and when not to use it.
Where am I? Where am I going? This is a reminder to be mindful doing math. Try to avoid the "What am I supposed to do?" mentality. Instead, take stock of where you are and where you need to be and use all your wits, your whole brain, to get there. Often it's not so much about remembering as about figuring it out, but that only works if you relentlessly demand that the math you learn makes sense.
Plug in what you know; solve for what you don't! Often a solution is hiding in plain sight and you can find it by this method. A classic case is that of finding a slope-intercept equation given two points. What you know are the two points, so plug them in to the formula for slope. Then you know the slope, so plug in one of the points and the slope into y = mx + b, and solve for what you don't know, b. You could figure that out even if you didn't remember the technique.
Say what you mean! I learned this from one of my most influential mentors/professors, John Dyer-Bennet of Carleton College, along with this next one:
Draw a picture! Sometimes a picture can really help guide intuition.
If you want it right, write! Mental math is a wonderful thing, but if you are the least bit confused or unsure of what to do next, start writing. Even if you don't know what to write. Don't skip steps unless you are sure you know what you are doing.
Whatever you practice during homework is what you'll do on the test. If you skip steps, rush through calculations, make mistakes, and don't check your work, that's what you'll do on the test.

Jon Dreyer • Math tutor • Computer Science tutor
781-696-2614 • 81 Baker Ave, Lexington MA 02421-6228 • email