In my last post, I shared that it was only through personal experience that I truly understood the important role that confidence plays in developing one’s problem-solving abilities. Understanding it is one thing; actually helping our students build their own confidence is quite another.

The most common symptom of low math confidence is giving up too soon when presented with an unfamiliar-looking problem. “This problem looks hard. I don’t even really understand what it’s asking. I couldn’t possibly get the right answer, so why should I even try? I will only get further confirmation of what I already know: I don’t understand math, and I never will.” (I’m exaggerating, but not by much.) How do you begin to chip away at that attitude? Talk is cheap; these students need to see for themselves that they can do more than they think they can.

I’ve taught geometry to freshmen and sophomores for a number of years now, and the two things that most often prevent my students from building their problem-solving confidence are time pressure and “assessment threat” (the fear of receiving a permanent bad grade). By removing (or at least greatly alleviating) both of these, we can at least start to turn down the volume on the loop of self-defeating tape playing in our students’ heads. Just this year I came up with an idea of how to do so.

The first step was getting students to buy into my idea. Right now, for better or worse, their currency is “points,” so that is where we’re starting—with weekly extra-credit opportunities.

Every Monday, Wednesday, and Friday morning, from 10:00 to 10:30, my school has what we call “conference period,” essentially a free period for all students during which all upper school teachers are available in their classrooms for help. Every Wednesday, during conference period, interested geometry students can go to the auditorium, where they are given a single problem based on recent class material. The problem is always “nonstandard” in that it does not resemble problems we have worked on in class or for homework. Students may work on the problem for the entire half hour if they like. If they want their work to be considered, they turn it in; if not, they don’t. A correct answer gives them a small amount of extra credit. (See the sample extra-credit question in the figure.)

Most students who attempt these problems come to me immediately afterward to talk about them. I find that they are much more interested in doing “post-game analysis” on these problems than on problems they got wrong on, say, a test. In their minds, questions they were asked on a test were ones they should have known how to do but did not. This failure is not something they like to dwell on. But because I present the extra-credit questions as being challenging up front, any shame the students might have felt about not knowing how to do the problem is greatly diminished. When the problem is one that everyone struggled with, students are much more comfortable admitting to being unsure about how to approach it.

Often, the students who have successfully solved an extra-credit problem have not been the ones I would have expected to do so, and this observation has been one of my favorite things about this experiment. It has given students who tend to struggle on timed assessments—because of time pressure or assessment threat—an opportunity to show me (and themselves) that they really do understand what we’ve been learning in class and how to apply it. My hope is that we can start to undo some damage, build some confidence, and develop some problem solvers.

Matt Enlow, matt.enlow@danahall.org, preaches the gospel of mathematics at Dana Hall School in Wellesley, Massachusetts. He is a regular contributor of (mostly) original math problems to Brilliant.org and tweets (mostly) mathematical musings at @CmonMattTHINK.