I learned more math working here at Wells Academics in my senior year of college than I learned in my years earning a Mathematics degree at UCSD.

Why?

Because there is no better test of how well you understand something than having to teach it to someone else.

I remember when I started here at Wells Academics, Jared asked me what levels of math I was comfortable with. “All levels” of course! I was a math major! Geometry, trigonometry, algebra, calculus. That’s kid’s stuff.

Then I sat down and worked with my first student. I realized very quickly that “I got an A when I was tested on this” is very different from, “I’m able to answer questions an intelligent high school student might ask” and “I’m able to communicate ideas effectively to a student who is confused.”

This memory has influenced the way that I hire instructors. But more importantly it has influenced the way I teach. I can sense very clearly when I am teaching something that is on the edge of my expertise as opposed to something that I am rock solid on. It’s given me an “early warning” that this is something that I need to put some time to reach a higher level of mastery on.

It also influences my expectations for our students. When my students claim that they understand a concept, I ask them to teach it to me. It becomes very quickly apparent to what degree the student has mastered the concept. Much more so than just having the student work through a problem (which they may have just memorized their way through). Not being able to explain something is a sign that the student will not be able to use that concept in a way that they didn't expect or hadn't practiced. It's a reason students go into tests feeling confident, but don't get the grades they expect.

Too many students learn very rigid styles of thinking in their classes at school. As long as they can mechanically work through a problem, it doesn’t matter if they understand the underlying principles. I’ve yet to meet the student who, coming in for a session the day before a test on logarithms, can satisfactorily answer the question, “What is a logarithm?” Most students seem surprised to be even asked the question in the first place.

How students can use this idea in their test prep

When you are working through a problem that you feel that you’re just barely on the edge of understanding, start from the beginning and explain, out loud, how you would teach this concept to another student. Don’t just say the steps you took. Imagine you are teaching this problem to a brand new student. What are the important concepts to understand? Why did you do each step in the process?

It’s important that this is out loud: it’s easy to gloss over something if you are only thinking it through in your mind.

Listen carefully to your explanation. There will be parts which, to you, sound crystal clear. There will also be parts in which you search for the right way to explain. Lot’s of hemming and hawing. Don’t let yourself off with “I get it...I just can’t explain it”. Being able to explain something is a demonstration of a high level of mastery. Your inability to do so is an opportunity: you found a gap in your understanding! Dig in to this (or make a note to ask your instructor about it during your session.)

Another great way to put this to use? Create study groups.

How parents can help

Ask your son or daughter to explain some concepts to you that they are learning about in their test prep (or even in school). If they are currently working with us, look at their most recent session reports to get some ideas of what they’ve been covering in sessions and homework. Even if it’s a topic that you personally are not confident with, just be an interested listener.

Ask questions. Try to understand what they are explaining to you. You’ll be able to hear when your son or daughter is confident and explaining clearly versus uncertain and hesitating.

Want to discuss an SAT/ACT test prep program that teaches your kids to think, rather than to memorize and regurgitate? Contact us, email help@wellsacademics.com or call 858.551.2650 today. I’d love to talk with you about how we can help.
-Vince