Mathematical Conversations

Whole Class Discussion: Show of Hands

This semester we are video taping our IBL classes and as I am watching the videos I am reflecting (again) on all the pieces necessary for a productive whole class discussion. My goal for a discussion is to make the “Big Mathematical Ideas” visible by having students construct connections between different solution strategies or attempts.

Dr. Volker Ecke working with students

As I walk around listening to the student groups grappling with making sense of the mathematics on their own, how can I encourage and support their efforts without just giving them "the answers"? How to engage them in mathematical conversations that will make their thinking visible?

While you lecture you might not see any student mistakes but one of the eye-opening experiences of inquiry-based learning is the huge amount of mistakes you observe.

I have seen in the classroom how students’ conceptual understanding grows out of getting lost, feeling confused and making mistakes. Yet at the end, I still tend to “tell” students to not make mistakes anymore or at least not to repeat mistakes. How? By assessing their learning with presentations, tests, written homework, and final exams using rubrics that give the highest score to the work that has no mistakes... So how can I avoid sending mixed messages and create better rubrics and assessments?

Prof. Christine von Renesse in a mathematical conversation with a student

The following video clip was filmed in a Calculus 2 class for math majors. While transcribing the video I noticed that my story of what happened in my interaction with Loghan was different from the actual exchange that you see in the video.