I am starting the school year in precalculus having students develop both their collaboration skills and their ability to model real world scenarios with mathematics. It is the beginning of the school year and many learners are still a little uncomfortable with each other and with their confidence in math class. I wanted to have a productive class discussion, and to make students feel safe to engage in dialogue around the content. I decided to create a discussion that appeared natural as a gateway to get some of the less confident learners engaged in the content.

At the start of class I presented a scenario to optimize by modeling with mathematics. Learners worked in randomly assigned small groups to develop an optimal solution and then, in the last 20 minutes of class, each group was to present their solution and reasoning. I wanted the learners in the audience to ask challenging questions to learn more about the groups thinking after each presentation.

Here is what I did:

While listening to learners work on a task in small groups, I circulated, listened, and wrote questions for each group on separate index cards. I was also thinking about how to sequence their presentations based on their approaches as described in the book, 5 Practices for Orchestrating Productive Math Discussions.

When each group was setting up to present, I would discretely hand the questions written on index cards to a less confident learners. After the group presented their thinking, I would ask, “Does anyone have any questions for this group?”

The learners would look around nervously in an awkward silence while I glared uncomfortably at a learner with an index card. Eventually, uncomfortable with the silence, the learner would ask the question on their card. Then, the presenting group would respond, which led to genuine student questions, thinking and further discussion.

By the last groups presentation, many of the learners seemed comfortable to ask questions and engage in thoughtful whole class discussion!