Block and Cylinder – Reflections

Why is this science?

Over the course of this discussion, we see students working toward a coherent, mechanistic understanding of what would happen. They are looking for and assessing connections among ideas including the theoretical principles of Newton’s Second Law and conservation of energy, solutions to several prior problems, as well as their own kinesthetic experience.

Thus they are noting and working to reconcile contradictions between these lines of reasoning, such as between their sense that the block would be easier to pull (so it should go faster) and the argument that the same force on the same mass should mean the same acceleration. The evidence of engagement came in the students’ displays of interest, including their pressing the instructor for further discussion.

What contributed?

We see several aspects of the moment playing a role.

Students’ variety of knowledge and experience related to the question
The students have many ways of thinking about the question available, including

  • earlier problems they had solved, including one about a race between a block sliding (without friction) and a cylinder rolling, and another about a rock sliding across the ice to hit a stick and make it spin;
  • kinesthetic experience and intuition about pulling on something that unwinds, such as a ball of yarn, which comes off easily;
  • informal experiments with cans and other objects; and
  • physical principles including both conservation of energy and F = ma.

Their emergent sense of a problem
When Michael speaks up to challenge the idea that this question is like the earlier one about a block sliding and a cylinder rolling, he takes a disputative tone —  “No it isn’t!” — and there’s an audible response from the class. He then presents the reasoning that with no friction, the total force acting on each object is the same, and they have the same mass, and F=ma implies they have the same acceleration. At the same time, he takes a stance of questioning, saying not only that the question “gave us a lot of trouble” in his discussion section but also that he still “wasn’t really happy with it.”

Both his F = ma argument and his stance of uncertainty seem consequential for the discussion. The class as a whole works not only to settle on an answer but to make sense of it, including responding to new arguments as they arise.

Students’ expectations of what happens in lecture
The students seemed to expect this kind of thing should happen in lecture. That is, there were a number of students who felt it was appropriate to raise questions or offer ideas, without explicit invitation from the instructor and even at times over his moves to end discussion. By this point in the semester, the students had a great deal of experience of lectures taking up their ideas and questions.

The instructor’s guidance
While the instructor speaks of needed to move on, he also shows appreciation for what is taking place, and he facilitates it, mainly in calling on students to speak, choosing when to have them speak with each other and vote in clicker polls, and often revoicing and trying to clarify their arguments. He also prompts students to respond to the reasoning they think is flawed, and in one moment discourages a reference to angular momentum, an idea the class had not yet discussed.

All together, with so many lines of reasoning available and students expecting and working to make sense of the situation, they keep finding new aspects of the question to consider. Thus as students introduce new arguments, other students wish to respond, pushing the conversation forward.