Facilitating greater student collaboration as a community of learners working towards the correct answer.
Based on my own reflection and the feedback I received about my number talks, I still need to work on moving away from having private conversations with individual students when they explain their strategies. When I have a private conversation with a student, we both turn our backs on the rest of the class, excluding and disengaging them as they can neither hear nor see what we are discussing. I want to work on how I can include more collaboration between my students, creating spaces where all my students can participate and engage in discussions about the problem and the different strategies they can use to solve it.
Thinking about this area of weakness, the first actionable step I could take is to be more intentional with my “turn and talks” that allow my students more opportunities to discuss the problem amongst themselves and for me to check their understanding. While an important pedagogical strategy, my students are often off-task during these “turn and talks,” rendering them meaningless. As seen in the video, they often simply shouted the answer to each other without explaining their thinking during these “turn and talks.” One way I could remedy this is to model my expectations for a “turn and talk” with my CM before I ask my students to talk with their partners. Another way I could facilitate greater student collaboration is by not having my students come up to the board, which inevitably leads to these private conversations. To prevent my students from coming up to the board, I could create another norm or I could do my number talks on the carpet. As I did in my third number talk, by doing it on the carpet, I created a more intimate environment where my students were closer and could hear each other. In such an environment, it was much easier to forge and foster more collaboration among my students.
Utilizing more “conceptual presses” with my students.
Based on the feedback I received on my second number talk, I also struggled with “conceptually pressing” my students so they could further unpack a strategy and delve deeply into exploring and understanding its mathematics. As per the number talk rubric, such “conceptual presses” can include asking my students to unpack a strategy, explain why a strategy works or challenge a strategy and offer a counterexample.
One actionable step I can take to improve in this area is to be more intentional in planning my number talks. For instance, when planning my number talks, I should reflect on where I can deliberately use these strategies to “conceptually press” my students and check their understanding. In particular, when anticipating my students’ thinking, I should also consider which strategies I would like to unpack or press more on given my ultimate goal for the number talk. For instance, if a student utilizes the central strategy of a number talk, I may plan to take more time in unpacking this strategy further by “conceptually pressing” this student. Thus, I can highlight the strategy for the rest of the class and check whether this student fully and deeply understands the strategy and why it works.
Highlighting key mathematical ideas.
In line with “conceptually pressing,” my students, the final place where I need to improve is in being more intentional and explicit in highlighting the key mathematical ideas for a given number talk. During all three number talks, I filmed this semester, I have attempted to highlight some of my students’ thinking. For example, during the second number talk, when Nico employed the central strategy of using the relationships between the problems to help him solve them, I uplifted and stayed with his thinking longer than others. I asked if any other students could explain Nico’s strategy in their own words. However, my students could not do so because I had not done a good job consistently and explicitly highlighting key mathematical ideas prior to this moment.
Thinking about this area of growth, one way I could improve is to begin the number talk with an “I can” statement that unpacks the central idea I want my students to take away from the number talk. Further, throughout the number talk, I must work on more consistently returning to this main mathematical idea by highlighting those strategies that show this idea and intentionally and explicitly including more students in conversation around them. Finally, the last actionable step I could take to highlight key mathematical ideas is to summarize the goal of the number talk at the end and again center those students’ strategies that align with this goal.
