Mine is probably one of the more sparsely-decorated classrooms at Dana Hall School. I will throw a poster or two up from time to time, but as I learn more about teaching and learning, the messages I want to send my students tend to shift, and the posters come down. But there is one wall decoration in my room that I don’t see coming down anytime soon: the handmade banner stretched above the whiteboard at the front of my room:
I admit, it’s fun to see students, in the first few days of classes, notice it, furrow their brows a bit, and silently mouth possible interpretations. Eventually—and this usually happens by at most the third week of classes—a brave student will raise her hand and ask, “Mr. Enlow… Sorry this is kind of off-topic, but… What does that sign mean?”
Right into my trap.
Invariably, before I can say anything, another student will pipe up, proud of having figured it out on her own: “It means, ‘What Do You Do When You Don’t Know What To Do?’” (At which point I wonder whether we will eventually be able to communicate with each other entirely using acronyms and context.)
This scene takes place in all of my classes, from Geometry to Advanced Topics, but in the ensuing conversation with the students, my message is always the same: “Yes, the mathematics you will learn this year is important. But even more important is that, by the time the year is over, you have developed some ways to answer this question.” And this message is consistent throughout the Math Department as well.
What do students do when they don’t know how to solve a problem? For too many, the default is to give up or ask for help. Now, of those two options, asking for help is certainly preferred. (We make it clear that there is absolutely no shame in asking for help!) But what we hope to reveal to students is that there are things that they can try themselves in order to try to make some inroads: examine all the information they’ve been given, and see what they can deduce from it; make a simpler version of the problem, and try to solve that; draw a picture or diagram; think about what information you would need in order to solve the problem; even sleep on it, and come back to it the next day with a fresh pair of eyes!
Not all such strategies are practical for things like testing environments, of course. But mathematical problem-solving in general does not easily lend itself to time constraints. More importantly, the more that we can reveal to students the internal resources they have at their disposal, the better job we will have done teaching them that they are capable of much more than they think they are.
Relatively few of our students will actually go on to become mathematicians, but we can help them all become more persistent problem-solvers. And that will be of service to them no matter what their futures hold.