Okay, that’s obviously an exaggeration; I answer lots of questions every day. One time a student asked me “If I put on my sock inside out, does that mean everything in the universe except my foot is in my sock?” I mean… wow. The only thing I could say was “yes… yes it does.” This was in front of an entire seventh grade class with zero contextual setup. Career highlight right there.

While I do answer plenty of questions, I try not to, and here’s why. Often, people see the teacher as the gatekeeper of the arcane wizardry that is mathematics, and the students are our lucky pupils upon whom we bestow the proper incantations to invoke said magic. This is a myth. Math is not a secret to be revealed, but a landscape to be explored. Teachers are not gatekeepers; we’re tour guides. But because of the prevalence of this myth, these are the two most common questions I hear every day:

• How do I do it?
• Is this right?

These questions (which Peter Liljedahl calls “stop thinking questions” in his book, Building Thinking Classrooms) are students inadvertently buying into the myth that the teacher is the gatekeeper of what is right and true in Math. Answering these questions reinforces the myth, robbing students of opportunities for mathematical discovery and deep thinking.

So how do I respond to these questions? If a student is even bothering to ask, they clearly want to learn, so it is my task to help them. However, I do this not by answering the question, but by asking questions back. Ideally, these will either guide the student to the discovery on their own, or help them come up with a more specific and thoughtful question that I will answer. Here’s what that might look like in the case of a student trying to find the equation of a line given two coordinate points:

If the student asks “How do I do it?“

• Unlock prior knowledge:
  • What will a complete answer look like? What form will it take? How will you know if it’s done?
  • Do you think the slope will be positive or negative? How can you tell?
• Leverage tools and resources they have available:
  • Do you have notes on this type of problem?
  • Have you tried graphing it? What do you notice about the graph?
• Help the student reframe the question:
  • What have you tried so far?
  • Which part are you stuck on?

If the student asks “Is this right?“

• Build confidence:
  • What steps did you take to get that answer?
  • Were you unsure about any steps that you’d like me to look over?
• Help check their work
  • Have you tried plugging in a point?
  • Does the equation match the graph?

By helping students reframe these two questions, we are inviting them to join us as explorers and thinkers in the world of mathematics.