Silence need not indicate ignorance

The students in one of my statistics classes didn't understand something very well, primarily because they weren't interested in thinking about how to solve it. They wanted me to tell them how to solve it, so that even when I asked them to explain why they voted for one thing, they sat sullenly and refused to participate. (This is a stark contrast with the other class, where the students fall over each other to answer questions; I'm not sure why.) So, I gave 10 extra credit points on the next test to the one student who risked getting it wrong by explaining her vote. She struggles in the class, so she appreciated it a great deal.

At the end of that class, and at the beginning of the next, I explained something to the students. The following is a not-very-verbatim retelling.

When I was a college student, I would get frustrated when I didn't know how to solve a homework problem right away. In fact, I thought the teacher, or the book, had done something wrong. There should be an example of everything, so that I could see how to do it, and imitate the procedure in the homework.

As I get older, I see how mistaken I was. It's true that there is a place in education for memorization, but that's in grade school, when our little minds cannot reason very well, but memorize things easily, like the multiplication table and basic facts about addition and subtraction.

As we get older, however, memorization becomes more difficult, whereas faculties of reasoning develop. Thus, it is the responsibility of the teacher to challenge his students with problems whose solution they haven't seen, but which the teacher knows the students could solve if they only thought about it a little.

Our culture works very hard to tell you the opposite. If you watch television, people always seem to have ready replies. The answer matters more than the reasoning behind it. If a politician, or an "expert", doesn't have an immediate reply to a question, then we tend to think he's stupid, or has lost the debate; we score a point to the person who asked the question he couldn't answer.

In short, we interpret silence as ignorance.

As a mathematician, however, when I ask another mathematician a question, and she doesn't reply right away, I don't take that as a sign of ignorance; quite the contrary! I take it as a sign that she is thinking. In other words, silence is a sign of intelligence, not ignorance. Some problems require thought, and the answers don't come readily.

My Ph.D. research would be an example. I worked six years on my Ph.D. thesis. Four of those years I spent solving the main problem. [Here a student asked if I meant that it took me four years to solve one problem.] That's right: it took me four years to solve one math problem. It was a problem that no one had ever solved before, and it was a difficult problem. If it took me four years to solve it, that is hardly a sign of ignorance.

Remember that when you get stuck on a problem. Sometimes we don't know what to do, and we have to find our way. That doesn't necessarily mean that we're ignorant. If you don't know how to solve the problem, think about it. The time you spend learning to solve that problem is in all likelihood more important than any facts you will learn in this class. Most of you will never use these statistics in your jobs after graduation; instead you will use the skills you developed to solve that problem you didn't know how to do right away.