Questions to Ask

· Helping students work together to make sense of mathematics

“What do others think about what Mary said?”

“Do you agree? Disagree?” “Why?”

“Does anyone have the same answer but a different way to explain it?”

“Would you ask the rest of the class that question?”

“Can you convince the rest of us that that makes sense?”

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

“Why do you think that?”

“Why is that true?”

“How did you read that conclusion?”

“Does that make sense? Why?”

“Can you make a model to show that?”

· Helping students learn to reason mathematically

“Does that always work?”

“Is that true for all cases?”
”Can you think of a counterexample?”

“How could you prove that?”

“What assumptions are you making?”

· Helping students learn to conjecture, invent, and solve problems

“What would happen if . . .? What if not?”

“Do you see a pattern?”

“What are some possibilities here?”

“Can you predict the next one? The last one?”

“How did you think about the problem?”

“What decision do you think he should make?”

“What is alike and what is different about your method of solution and hers/his?”

· Helping 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?”

“Can you give me an example of . . .?”