Quiet, low-energy classes are the ones that make me the most nervous as a teacher. As a long-time IBL instructor I have become accustomed to loud, boisterous classes, where students are engaged, communicate, work together, and ask questions to me and to each other.

At the start of the term some of my classes have a quiet or passive personality. Students may not have had an IBL class yet, and hence are likely to expect to sit, take notes, and generally not interact with others during class time. A potential problem with quiet students is that they give you little to no information about what they are thinking (and not thinking). Student thinking is critical in day-to-day IBL teaching. An IBL instructor doesn't know exactly the lesson plan for tomorrow, until today's class is over. Using what is known about what students are doing well and what they need to work on, is bread and butter in IBL teaching.

*What can an instructor do to liven things up, when students are (initially) reticent?*

There are several options. My main goal is to reset classroom norms so that students understand that making their ideas and questions known to others is the default. Reseting norms can be accomplished via tasks that require students to engage verbally. My most preferred setup is to use

*pairs*. When you are talking to one person, it's awfully difficult to hide in the conversation. In contrast, within a group of 4 students, one or two students could sit back and let the others talk. Hence, I like pairs (while simultaneously admitting that personal preference is a part of the decision). I also use other sizes, but pairs are the default, especially for quiet classes.

In a full IBL course, pairs can do a range of activities, from working on problems, reviewing a presented solution, getting started on a new problem set,... Asking students to share what they did in pairs is a safe, easy way to open discussions. The stress of having to be right isn't a factor, and students are more likely to offer thoughts, questions, or ideas that can generate a productive discussion.

Making a

*pairs seating chart*and ensuring all pairs are called on regularly ensures that all students are regularly involved. In a full IBL course, the requirements to present and comment are built into the course. Getting quieter students to offer comments, can be done via the pairs structure. For example, ask students to review and discuss a solution or proof in pairs (after a proof is presented) will generate more and better comments and questions. I normally phrase the task as, "Please review the proof and come up with 2 questions or comments." Then I call on pairs rather than ask for volunteers, and spread the work around to ensure all pairs get called on regularly.

In "hybrid" IBL courses, where the course has a larger percentage of instructor talk time, then the implementation of pairs becomes more specific. What I'm envisioning in this situation is an instructor just getting started with IBL, or an instructor in a situation where significant IBL time is not feasible. In this case, the instructor may be using some Think-Pair-Share or group work as components to their teaching. Here are some examples:

- Let pairs discuss a concept or strategy: "In pairs, discuss for a minute a strategy you might use for this problem." Listen in on a few conversations, and choose one or two to share to the whole class.
- Check for understanding even when building skills: "Please work in pairs to apply the techniques discussed to the following cases." As you walk around, you can ask students how they are doing with the exercise.
- Pause for moment to let students try something on their own first. This could be the next step of a problem or proof. Or it could be that you ask students to justify a statement or review what just happened. After the pause, ask students to check in with
*one*neighbor. As students talk, you can visit a few pairs and ask a pair to chime in. (Be sure to visit different people each time you do this to spread the work around.)

The above are just examples. An infinite variety of ways to get students to talk more exist, and the main point I want to get across is the

*framework*. Use clear, specific mathematical tasks and pairs to get students to think and then talk. Once they start talking, they can open up.