This recent comment^{1} regarding students who are afraid of being wrong, reminded me of a resource I recently shared at a PD session for math teachers. These questions are a good starting point for creating classroom discussions in a math class (*although I think they could easily be adapted to other disciplines*): Developing Mathematical Thinking with Effective Questions.^{2}. Questions are broken down into subsets. I’ve included the questions for promoting problem solving and for encouraging conjecturing:

To promote problem solving, ask…

• What do you need to find out?

• What information do you have?

• What strategies are you going to use?

• Will you do it mentally? With pencil and paper? Using a number line?

• Will a calculator help?

• What tools will you need?

• What do you think the answer or result will be?

• What do you need to find out?

• What information do you have?

• What strategies are you going to use?

• Will you do it mentally? With pencil and paper? Using a number line?

• Will a calculator help?

• What tools will you need?

• What do you think the answer or result will be?

To encourage conjecturing, ask…

• What would happen if…? What if not?

• Do you see a pattern? Can you explain the pattern?

• What are some possibilities here?

• Can you predict the next one? What about the last one?

• What decision do you think he/she should make?

The other categories are:

To help when students get stuck, ask…

To make connections among ideas and applications, ask…

To encourage reflection, ask…

To help students build confidence and rely on their own understanding, ask…

To help students learn to reason mathematically, ask…

To check student progress, ask…

To help students collectively make sense of mathematics, ask…

This list is not exhaustive. There are other good questions. Of course, good questions need to be followed by appropriate wait time. Answering our own questions just lets the students off the hook. We might was well explicitly tell them, “*Don’t worry,* *I’ll think for you.*“

Asking the right question(s) or responding to student’s statements in the moment requires practice. I wish this had been something that I could have gotten better at *before* I started teaching. I’m lucky that I spent quite a bit of time as an assistant in the classrooms of some amazing teachers, from whom I learned a lot. But doing is not the same as watching. I’m still working on refining this to make it flow right.

^{1}This comment from Mr. Teachus arose from a comment I made on this post of Dan’s about his issue with mathematics textbooks (*If you followed that train of thought, good for you*).

^{2}From PBS TeacherLine. The vast majority of the other questions are good too. But what with copyright and all, I didn’t think I could post them all. (*Seriously, do we need to copyright questions to ask in a math class?*)

Lots of those in the first group are different ways of asking George Polya’s two biggies: “what are the givens?” and “what are we trying to find? (or prove?)”. (He has more, but if I remember right, they are all ways to make progress toward those two.)

I’m interested in what in your observations of other teachers was particularly valuable, and what insights more specifically you have had since then?

I can’t remember who taught me to use this powerful question, but it has given me more insight into student thinking in so many areas: “How do you know?” When kids give answers to questions, we don’t necessarily know the context–they sometimes arrive at correct answers through faulty thinking.

Thanks for the link to the PBS doc, Jackie. I have shared it with others.