One of the common struggles for instructors is engaging a larger portion of students. A typical scenario instructors find themselves in is that a small group of students do the bulk of the talking. The Usual Suspects, The Fab Five, The Fantastic Four... they chime all the time. There's another, larger group that sits quietly. What we really want is for the quieter students to talk more and the Fab Five to listen more and pick their spots. Instead of a polarized class of talkers and nontalkers, we would like to push the poles towards the center, where everyone is engaged. How can we accomplish this?
Enter the
engaing more students framework:
 Pairs or small group discussions to get people talking
 Instructor visits
 Not asking for volunteers
 Calling on groups to "Share what you discussed."
Let's say a student or group just presented or shared an idea or solution to the whole class. Instead of asking the class for questions right away, the instructor can prompt students to
discuss what was just shared in
pairs or small groups. They should be instructed to come up with at least one comment, question, or (substantive) compliment.
Groups can be assigned to be the initial commenters. I sometimes ask two groups to start the class discussion portion of the presentation. I let them know ahead of time so they are primed and ready (and not cold called), and I rotate these duties around the class to spread opportunities around the class evenly.
Next, while groups are discussing, I make
instructor visits to listen in and check in. If there are 10 groups in a class, I plan on visiting 24 per presentations, and remember where I left off. In the next round I pick up where I left off. The purpose of visiting is to check in to see how students are thinking so I get a sense for where people are at. I can also help groups sharpen their questions or comments, and get groups used to talking about the topic so that it is easier for them to chime in. I also make it a point to talk to the quieter students in my classes in a friendly way, usually 11. "Hey Pat, what did your group talk about?..."
After a short period of time, it's time for a whole class discussion. One of the main things to
avoid is asking, "
Are there any questions?" Instead, I have a plan to
call on the preselected groups or ask specific groups to comment, where I spread the opportunities evenly over time. An easy way to do this is to have a seating chart or diagram of the groups and go through the list in order and then repeat. Another simple organizational strategy is to call on the groups who you visited first, and then open the discussion to anyone else.
A key idea here is that you are not asking people to optin, by asking for volunteers. Optins allow students to do nothing to optout. Passive students can stay passive to optout, by not responding to "Are there any questions?" That is, it takes zero effort for students to do the thing you don't want them to do. Instead by using this framework, all students are prepared to say something. Calling on students in a way that is not stressful and spreads the work evenly ensures equal opportunity for students to participate. Small group discussions also encourages students to engage every round. (Hence, creating an environment that supports learner agency.)
One of the positive effects of this framework is that the quieter students engage more and the "Fab Five" are not dominating class discussions. All students can be engaged, and this offers a greater sense of the class working as a team to learn together. Class discussions are more useful, and more questions can be asked and addressed.
Flexible Framework: The example above can be adjusted in many ways. I'll just mention a couple ideas, and let readers take it from there. Instead of a student presentation, the instructor could present a problem or ask students to work on an example or review what has just been presented. The framework can then be used at that point. It's also worth pointing out that the framework can also be used by instructors who primarily lecture, and and can be a launching point for instructors to start the journey towards active, studentcentered instruction.
Details: some important details include using quality math tasks, avoiding instructor questions like "Are there any questions?", using good, professional technique when doing instructor visits, student buyin, and setting up a class culture where students feel comfortable discussing and sharing their ideas.
Contrast: Let's look at the optin model, where we ask, "Are there any questions?" In this case, students can passively optout by doing nothing, and we get the common split where only a small group of students talks and the rest sit back.
The final takeaway is that something useful and doable can be done in essentially any setting to get more students or even all students involved in class daily. All instructors need is to start with the engaging more students framework and find ways that work for them to implement some form of it.
\humor

Engage! 