**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 . . .?”