The other night my 10-year old son came to me for help with a word problem involving volume. It was late at night and I was tired. I could’ve given him a hint about how to solve it, or even worse, solve it for him. Instead, I ended up spending half an hour with him as we then expanded upon his newly constructed knowledge. It was worth it!

I wanted to make sure that my son understood the problem he was trying to solve, so I asked him to explain what he was trying to do and why. Realizing he didn’t understand the problem, I encouraged him to read it again and explain the different components as he progressed. Once he understood the problem, he immediately saw what he needed to do to solve it.

When I started teaching almost two decades ago, someone mentioned how knowing when to help a student during problem-solving was “an art that requires much experience.” He was concerned that giving a hint at the wrong time could destroy those important “aha” moments. He was right about the latter; my experience, however, informs me that there are simple signs we can use to know when to give a hint. It’s more (pedagogical) common sense than art.

Let us put this in the context of the 3-stage problem-solving cycle.

The first assistance students should receive, if any, should be directed at helping them understand the problem. Experience tells me this is often the missing (and ignored) link, even when students seem engaged scribbling and doodling.

Once we have verified that a student understands the problem, avoid giving hints about how to solve it until the student is on the verge of frustration (or already frustrated). Offer a hint that doesn’t give away the problem and observe how the student reacts. At this stage, we should evaluate whether the student is ready for this particular challenge. If not, we need to decide whether to change the problem altogether or offer problems that will address the prerequisite knowledge and skills.

In a nutshell, give a hint only after it is clear that a student understands the problem and is stuck. A hint given at the wrong time, either too soon or too late, can ruin the creative process, not only for the student, but for everyone in the room.

About the author: You may contact Hector Rosario at hr111@caa.columbia.edu.