One strategy I use is something I call momentum building. Let’s say it’s a Tuesday and either the class is done presenting or no one has signed up to present a problem. In either case, the focus could be on the next set of problems and having students leaving the class feeling they have a good start and can accomplish the work. To set this up, I focus on a problems, one-by-one, and use a variation of Think-Pair-Share.
First, I ask students to read the problem statement, and then think to themselves about it (Think). This initial part is to ensure they understand the statement of the problem.
Next, I asks students to think about how they might approach this problem. At this point I might give a leading hint, such as suggesting a proof by contradiction or drawing a diagram or picture that has some key piece without reducing the challenging. I think about this part as taking students to the trailhead and giving them a heads up about the terrain.
After this longer, more involved think phase, I ask students to work with their partner on their ideas (Pair). This is the “Pair” stage, and I often roam the class to listen in or check in with groups. This part might also go on for several minutes, depending on the nature of the material they are working on. Working on the proof of a Intermediate Value Theorem takes more thinking and discussion time compared to unpacking a basic definition. I adjust the time based on the context.
Once I have a sense that students have had a good chat, then it’s time to call on groups to make public their ideas and come up with a strategy or ask questions. (Share) I write the word “strategy” on the board, and preface the discussion that we don’t want solutions or answers shared out. We want only strategies or approaches. In this phase, I preselect groups I've checked in with, and I also ensure I am calling on different people over time. A typical opening is “[Name of Student] could you share what you discussed with your partner?” and move through groups until we have a decent outline of the problem. Alternative strategies are often suggested, and then students have a good sense for multiple ways to move forward on the problem. Students can also ask questions. Perhaps they have questions about a concept or definition or are wondering if a certain technique works.
This whole process can be repeated, and then students leave with momentum for several problems. This catches people up, uses the whole class as a resource (AKA hive mind), and still leaves vital individual tasks outside of class for students to complete problems and find their own proofs.
Another way to think about momentum building is that it is a strategy for reducing variance. It employs a team effort towards getting the whole class on the same page. Class discussion is vital in momentum building, because discussion makes public the strategies needed to solve a problem. All students have access to this information and time to ask questions about them.
A fine line between making the gaps too small and leaving excessively large gaps exists here. This is one of the instructor “dials” in IBL teaching, and how much to turn this dial is student dependent and time dependent. Towards the beginning of the term, an instructor may want to error on the side of smaller gaps to build class norms and broad engagement, and then increase the size of the gaps later in the term on some tasks. Too easy of course is not useful and too much frustration also something to be avoided. Additionally, having a range of problems from easier to harder can also keep students appropriately challenged for their specific development at that moment in time.
Momentum building can be a positive feedback loop, which can lead to a highly successful course. Authentic, repeated successes can lead to amazing things. If you find your students are not engaged at the level you want and some are straggling behind, consider using momentum building strategies to get your class on the same page.
