The Critical Mistake Every Teacher Makes

Any time I try to teach something—usually math—I am always tempted to make one fatal error. I want to explain the answer before I ask the question. This is a terrible idea. I have to stop myself every time.

I don't know why this tendency exists, but I'm not the only one who feels it. This mistake is most common in math class. Every teacher wants to begin by presenting a formula and then give examples of how to use it. This is completely backwards. Don't give students the answer before presenting the problem!

You would never begin a murder mystery with the sentence "Marianne is the killer." Who? Why do I care? Am I really going to read the rest of this? Even if the reader continues, they're bored right from the outset.

We begin every math class by spoiling the fun, then wonder why nobody is interested.

Without the context of a meaningful problem, simple math feels complicated. Until a student has felt the pain of not having the answer to a burning question, the answer means nothing and will be quickly forgotten. (The teacher, who already knows the context, will not notice that anything is wrong.) Once you understand the problem, you're 80% of the way to understanding the solution.

Aim to teach like this:

  1. Give some examples of the type of problem at hand. They should be a variety of different-looking circumstances which all require the same new mathematical tool.
  2. Ask students to attempt the problems and identify exactly where their existing toolkit falls short.
  3. Provide enough of a hint that students can fill in the missing steps themselves.

When you begin with the problem, students demand to know the answer and are often able to figure it out for themselves. It's easy to do this backwards, but there is incredible value in getting it right. Cultivate the skill of beginning with the question, not the answer. Your students will thank you.