Be less helpful: Effective Questioning in Math Class

You finish your lesson and your class of 35 students busily gets to work (or so is the dream). Regardless, students are practicing, and Emily's hand goes up. You walk over to her desk and she utters the infamous words you love to here:

"I don't get it."

Whether Emily's "question" is the exact phrase above or some similar form of an ambiguous misunderstanding, it leaves math educators in very dangerous territory. We can take one of two routes:

1. Answer this question only.
2. Help answer this question and potentially many after it.

The second option is really the point of practicing math, right? ...To problem solve and effectively reason through a question so that learning takes place. I think this is where we would all like to be be when we walk over to answer Emily's "question". Due to large class sizes and impatience, though, often the first routes is taken. Observe:

Imagine Emily's Math 10 question was determining a leg of a right triangle using the Pythagorean theorem and you decide the best way to answer her question was the following way:

Emily: "I don't get it."
Teacher: "This is a tricky question. You have to use Pythagoras...like this..."
(*and you finish the question for her, effectively modelling how to answer it*)

Despite the proud moment of demonstrating that YOU know how to determine the leg of a right triangle, you have actually just stolen a great deal of learning from Emily. How could you have used the opportunity to help build her problem solving skills to answer a similar question in the future. (We don't want to keep coming back, right?)

"I don't get it!" implies what? Does she have everything correct but hasn't square-rooted the result? Is she using cosine? Is she incorrectly squaring the legs? Does she even understand the question? This is your opportunity to be less helpful...Start by being unbelievably (painfully) vague. Try something like:

"What don't you get?"
"Do you understand the question?"
"Tell me what you DO know"
"Have you seen a question like this before?"
"Tell me more..."

Only after we have discovered where Emily is struggling can we begin to even start helping. Again, don't give her the answer. Lead her on the journey with ever-more-specific questions. A conversation could look like this:

Emily:    "I don't get it."
(immediately you see that she plugged a leg into the hypotenuse location)
Teacher: "What don't you get?"
Emily:    "I am not getting the right answer."
Teacher: "Can you explain what you've tried?"
Emily:    "I drew a triangle and subbed the sides into Pythagoras. The answer isn't the same as the back of the textbook."
Teacher:  "I'm glad you checked. What do you know about using Pythagorean Theorem?"
Emily:     "You plug the sides into c^2 =a^2 + b^2 for any right triangle."
Teacher:  "Great. What does the a, b, & c represent?"
Emily:     "Sides."
Teacher:  "yes..." (wait...forever if need be)
Emily:     "well, c has to be the hypotenuse and a & b have to be the legs."
Teacher:  "Are you sure?"
Emily (eyes go wide): "I know what I did!"

Emily is less likely to make that mistake again if she is the one that walked through the problem.

If students are continually subjected to a lack of help (careful with that implication), they are going to be better able to reason through what they know and what the might not. As educators, our goal is NOT to answer individual questions, but rather to give students the skills to make them capable of reasoning through their problems and if anything else, at least they won't start their questioning with "I don't get it."

Be less helpful. Determine what they DO know. Answer questions with questions. Ask for more. Get it?