The Art of Questioning in Mathematics

Help students work together to make sense of mathematics

	"What do others thing about what __________ said?"
	"Do you agree? Disagree? Why or why not?"
	"Does anyone have the same answer but a different way to explain it?"
	"Would you ask the rest of the class that question?"
	"Do you understand what they are saying?"
	"Can you convince the rest of us that that makes sense?"

Help students to rely more on themselves to determine whether something is mathematically correct

	"Why do you thing that?"
	"Why is that true?"
	"How did you reach that conclusion?"
	"Does that make sense?"
	"Can you make a model and show that?"

Help students to learn to reason mathematically

	"Does that always work? Why or why not?"
	"Is that true for all cases? Explain?"
	"Can you think of a counter example?"
	"How could you prove that?"
	"What assumptions are you making?"

Help students learn to conjecture, invent, and solve problems

	"What would happen if ________? What if not?"
	"Do you see a pattern? Explain?"
	"What are some possibilities here?"
	"Can you predict the next one? What about the last one?"
	"How did you think about the problem?"
	"What decision do you think he/she should make?"
	"What is alike and what is different about your method of solution and his/hers?"

Help students to connect mathematics, its ideas, and its applications

	"How does this relate to _______?"
	"What ideas that we have learned before were useful in solving this problem?"
	"Have we ever solved a problem like this one before?"
	"What uses of mathematics did you find in the newspaper last night?"
	"Can you give me an example of ________?"