as a class to help us all make sense of this idea. Occasionally, the presenter and the audience all needed to think more deeply about a particular important concept, idea, or technique. In such situations, we sometimes decided to stop the presentation and send the students into small groups to make sense of a particular important question. We want to highlight this choice as another important teacher tool in an inquiry classroom: Depending on the situation, we can locate responsibility for sense-making somewhere along the continuum between just the presenter, all the way to the whole class, and make choices in the classroom accordingly. Because this approach of giving questions back to the class is so natural in our other IBL classes, it was only during reflections at the end of the semester that we realized that this was a component we hadn't typically seen in other presentation-focused inquiry classes. It's wonderful to identify another "control knob" to adapt the learning environment to the goals, needs, and flow of student inquiry.
Focus Questions for Learning, for Presenting, for ...
We also noticed that some of our Focus Questions did not make for good presentations: "Explain in your own words how you make sense of this proof" often prompted deep thinking but did not make for interesting, engaging, or accessible presentations because students would just read several dense pages of their writing. At the other end of the spectrum, we realized that computation-focused exercises from the book often needed a more explicit prompt for students to reflect on, and explain the bigger point of this exercise. Reflecting more deeply we realized that the Focus Questions serve several purposes: on the one hand, to engage students in activities to deepen and challenge their thinking during the reading; on the other hand, to present some coherent of mathematics to the whole class. We are using this lens to review our Focus Questions critically in preparation for teaching this class again, hopefully in another year or two.
Work in Progress: Differentiation
One aspect of running a presentation focused class that we have not quite figured out yet is how to differentiate the class well enough so that all students are working at their learning edge. We have a good sense of how to do this is inquiry based classes where the focus is on group work and whole class discussions. In her blog "Inquiry is Differentiation" Chrissi summarizes some of the structures in a group setting that allow for wide differentiation of pace, tools, scaffolding, encouragement, extension questions, etc.
When our focus was on presentations, it seemed that the whole class is for much of the time focused simultaneously on one particular presentation by one particular presenter. While all students are expected to have prepared the material themselves, it is our observation that there will be variation in the depth, tools, representations, and other dimensions of their preparation. Some students seemed overwhelmed or lost in some presentations (busily copying down the presenter's notes). For others the material in some presentations was so clear that they looked like they could recite the argument along with the presenter. What could we do in this presentation focused format to provide both groups with more learning opportunities at their learning edge?