You Need to Know When to Stop

Friday was one of those days when I was happy to put a big X through the date on the calendar. No disasters, just a steady stream of annoyances and minor frustrations, all of which I played some active role in creating.

In my second geometry class, I made the mistake of sending a student to the board despite the fact he missed class the day before and was not completely up to speed on the material. He is a very bright student who consistently earns the top score in the class, so I suppose I have a tendency to assume that he understands whatever is going on. We were using the Triangle Side Inequality Theorem to write an inequality describing the possible values of one side given the lengths of the other two. The student got the basic information correct, but got lost when I tried to generate discussion about why the “or equals to” was not necessary in his answer and why “3 < x < 10″ might be a better way to write the answer than “10 > x > 3″. Not sure what the exact combination of lack of understanding by the student, poor wording of questions by me, and general tiredness was that made a top student unable to answer simple questions, but things went south somewhat quickly. I should have remembered the student had been out the day before, apologized to him for putting him on the spot about material he’d missed, and asked someone else to take over at the board. Naturally, I didn’t think of that until a hour later.

After school, one of my AP Calculus students came by to practice related rates problems. He did quite well with basic problems — things like “Find dx/dt for this relation given values for dy/dt and x” or “Find the rate of change of volume of a cube given the rate of change of side length”. When he came in he told me as much, and said that his difficulty lay in writing appropriate equations to represent a word problem. He worked on a number of these and had me check his work at various points. With one exception, every single mistake he made was in material covered in 9th grade (known as “Integrated Algebra” here in New York). Some of these, like forgetting to square the coefficient of a term in parentheses, were minor enough that I could write them off to end-of-the-week exhaustion. Others, like drawing a complete blank when faced with a situation that called for simple right-triangle trigonometry, made me worry about what a disservice we might be doing to students by ramming them through a state curriculum that touches lightly on many, many topics without going into depth on many.

Later on, I thought more about the AP Calc student’s struggles and realized that I had made a similar error as I did earlier in the day. At some point, I should have told him that maybe he needs to step away from math for the time being, as due to some combination of being tired and being frustrated, he was making too many easy mistakes that would only lead to him being more frustrated with the class.

Knowing when to walk away from a difficult problem in order to come back to it feeling refreshed and thinking more clearly is a useful and important skill to learn, and it’s one I need to remember to teach when necessary.