Recently, my colleague Tom and I decided that, since we were teaching in adjacent classrooms, it might be fun to combine our classes and co-teach a lesson. Tom and I have very different strengths, both as test-takers and teachers. I love algebra, and I’ll always seek out an algebraic solution to a problem (even when this might not be the most efficient method—my strength is also a weakness). Tom prefers non-algebraic methods, like drawing diagrams or picking numbers. And our strengths inform what we emphasize in class.
So, for our joint lesson, we chose a number of GRE problems that could be solved in more than one way, and then took turns demonstrating each method. First, we each used the method we preferred (algebra for me, picking numbers for Tom), and then we switched and demonstrated the method we were less comfortable with. Here’s one of the GRE problems we used: Read more
Here’s a hard problem that I used to teach in session 1 of our GRE course (my poor students! This was a rough intro to GRE math.)
If you’d like to, give yourself a minute or two to try this (but don’t bang your head against it for too long). If you’re thinking wow, I have no idea what’s going on here—well, it’s a good thing you’re reading this. And even if you do feel comfortable with this problem, it might be worth reading further to see how the techniques used to solve this are more broadly applicable in GRE Quant. Read more
I am an incredibly anxious person. Like all of us, I worry about the big things (work, money, relationships, illness), but I also descend into fear when confronted with absurdly small things (the weird look the Dunkin’ Donuts cashier gives me when I ask for six sugars, the ominous clicking sound my toaster makes—WILL IT BLOW UP AND KILL ME???). Learning to manage my many anxieties is one of my main challenges on a day-to-day basis.
So I relate, strongly, to the students I work with who struggle with GRE anxiety. This anxiety manifests in a few common ways: Read more
I recently did an exercise in one of my classes in which I asked each student to teach one or two problems to their classmates. I think some of my students suspected that I just wanted to make them better appreciate how hard teaching can be (like how my parents want me to have grandchildren so I can know how much they’ve suffered). But in truth, my hope was that this activity would help my students to study more effectively at home, and I was happy to discover that this turned out to be the case.
A lot of us, at times myself included, think of studying as a skill distinct from teaching. As I’ve seen with many students, though, the practices that make for a good teacher also make for the most effective student. The things that I think about as I prepare for a class are the same things that you should be thinking about at home when you sit down to work through a new math topic or GRE problem set. With this in mind, here are a few good teaching moves that you can apply to your studying. Read more