Encouraging Mathematical Reasoning in the Classroom

In this standards-based assessment world in which we educators find ourselves, little thought is given to the development of mathematical reasoning skills. Instead, the focus has become test performance. No longer do we ask students to think. This lack of thinking skills has caused a lessening of enthusiasm in teachers’ and students’ attitudes – about school in general and mathematics specifically.

I think there needs to be a shift in the school culture toward promoting engagement through inquiry-based learning opportunities. I do not think any teacher needs convincing on this point.

One of the best ways to ensure active student engagement in math is the use of games. Good games for the classroom are engaging, fun, and create opportunities for students to explore concepts and develop mathematical reasoning.

Playing a math game is the first step on the road to mathematical reasoning. Teachers need to create opportunities for students to explore mathematical ideas by planning questions that prompt students to reflect on their reasoning during and after the playing of a game. When we carefully consider the questions we ask and plan an appropriate level of competition, students will focus on the mathematics and not just the game.

While the students are playing the game, the teacher’s job is to move from group to group listening to their conversations. Ask probing questions, such as:
• 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 other player is willing to give his/her partner the answer, thus making it possible for that player to do no thinking whatsoever. Not good! Your (and the 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.