irly straightforward to collect this information every week before our class. Given that we had realized that interesting gaps and mistakes were actually desirable for our presentations, we slightly modified the rubric as indicated here:
Indicate the degree of your progress on each problem using the following scale:
4 - I am ready to present a solution to this problem, including interesting gaps and possible mistakes. (We don't expect perfect presentations.)
3 - I've made a solid start on this problem and am willing to share my progress.
2 - I have ideas about how to solve the problem, but I'm struggling to consolidate them.
1 - I understand what the problem is asking and could explain it in my own words
0 - I do not understand the problem or I haven't looked at the problem
Using Corrin's suggestions, we downloaded the data into a spreadsheet and then color coded the numerical data. The image shows a color-coded grid for each of the 12 Focus Questions, going across from left to right. Each line corresponds to one student name (not shown here). In the picture you can see the a quick visual overview of where the class is at. We can see who is struggling or under prepared and which problems were particularly challenging. We could use this information to decide what to focus on in class and to choose who to call to the board to present what problem. This image suggests, for instance, that there is no need to present questions 2, 11, or 12--albeit for different reasons. Based on just this data which questions would you be curious about for an engaging presentation that could advance most students' learning in this class?
Where we initially wanted to use the Presentation Rubric to encourage students to put effort into being well-prepared for class, we are using this Preparation Rubric to communicate the importance of student effort in a better way.
Presentations and Giving Questions back to the Class
When questions arose around the presenter's work (or around the bigger mathematical picture), we typically collaborated 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.
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