Clip 13/15: Modeling with Polynomials Post-Lesson Debrief - Part 1

Amy Burke and Deidre Grevious debrief the lesson; Amy observes that the students were engaged with the mathematics — not only with the physical construction of the model, but also with building their own arguments from initial conjectures, revising their thinking, and developing more concrete thinking in a second conjecture. She notes that when students transitioned into using Desmos, some students — as she had anticipated — were unclear about which element was the independent variable and which was the dependent variable. She also saw a lot of conversation about scale and effective means to visualize the data.  

Amy comments that, with prompting from her to change the domain and the range (sometimes by encouraging pairs to share their approaches with each other), students were able to change course when needed. She praises the work and reasoning of the student who identified errors in the class data; he noted that not only was the number wrong, but that it didn’t make sense, making reference to his grid paper to support his argument. Amy conjectures that this reality would have come up in table work with the graphs, when students would have recognized that as an outlier.  

Deidre said she saw two groups compare their data, wondering whether or not the incorrect data could be true, and stating, “What made it wrong?” Amy comments that one table was working through “What do the x intercepts really mean” in this task, which brings up “real mathematical questions.” Deidre asks how Amy pushed their mathematical thinking; Amy says she was trying to have students restate their thinking, and why it didn’t make sense, though she notes that she may not have been successful in that regard. That group had graphed the data with the quadratic, found a negative intercept, and concluded that it didn’t make sense. Amy shares that the students did not quite attain conceptual clarity, or, as Deidre put it, “they weren’t sure about the reality versus the model.” Amy comments that she thought about this in sequencing students’ share-out at the end of the lesson, but there may have been missed opportunities due to the timing.  

Lastly, Amy and Deidre discuss the affordances of the technology in the lesson, whether students needed to enter the data themselves, for example. Amy says that the students seeing their own data was valuable.