I have spent many years of my elementary teaching career building a community of learners who approach math with eagerness. I’ve learned that students need to be mentally engaged in a challenging and worthwhile mathematical task that emphasizes the conceptual aspects of the mathematical topic and promotes the formation of mathematical connections if they are to learn skills with meaning and be able to use those skills to solve problems.

It is not so critical whether students “discover” everything for themselves but it is critical that students are allowed to do some genuine mathematical work on their own. If teachers do all the work and students are left only to copy and imitate and practice what the teacher has done, they are less likely to make sense of the material, remember it later, transfer it to new situations, or do well on standardized tests.

The most important thing with respect to student learning is the nature of the learning task students engage in. Students need to be encouraged to think and persist with respect to the mathematical task, and the teacher should refrain from stepping in too early to provide students with answers or tell them exactly what steps they should use. Rather, the teacher can support students by asking them questions that guide them toward mathematical learning. This can be effectively done in a range of instructional settings from the most student-centered to the most teacher-centered.

Reform-minded teachers pose problems and encourage students to think deeply about possible solutions. They promote making connections to other ideas within mathematics and other disciplines. They ask students to furnish proof or explanations for their work. They use different representations of mathematical ideas to foster students’ greater understanding. These teachers ask students to explain the mathematics.

I have found that math games are an engaging and mathematically challenging task that can effectively offer students the opportunity to be engaged and talking with one another, and where they are encouraged to question and think about the mathematics and mathematical relationships. Have you ever used a ditto or workbook page that could make that claim?

Of course, it is not enough to teach students the game and let them play it. It is the teacher’s responsibility to move from group to group, listen to the conversations, and ask probing questions. My most-used question is, “Can you convince your partner and me that you are correct?” After hearing the question several times, the students usually begin to ask the question of their partners without my prompting.

Other questions that are well worth asking are:

• What card do you need?

• Which cards would not be helpful?

• Prove to me that a ____ is what you need.

• Why do you think that?

• How did you know to try that strategy?

• How do you know you have an answer?

• Will this work with every number? Every similar situation?

• When will this strategy not work? Can you give a counterexample?

• Who has a different strategy?

• How is your answer like or different from another student’s?

• Can you repeat your classmate’s ideas in your own words?

• Do you agree or disagree with your classmate’s idea? Why?

Too often the teacher or the partner is willing to give the other player the answer, thus making it possible for that player to do no thinking whatsoever. The teacher’s or partner’s questions to that player should be:

• What can you do to help yourself? Use your fingers to count? Count the dots on the dice or cards? Use manipulatives to figure it out? Draw a picture? Start with something you already know?

**The power of questioning is in the answering. As teachers, we not only need to ask good questions to get good answers but need to ask good questions to promote the thinking required to give good answers.**