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We present a discussion from an introductory, calculus-based physics course, which took place late in the semester. Throughout the course, lectures had been interactive and “responsive” (Author, in press) to student thinking. In a lecture late in the semester, students had just handed in a homework assignment that included the following problem (from Close, Gomez & Heron, 2013).
5) A block and a cylinder, each of mass M, are on a level, frictionless surface. There’s a string tied to the center of the front of the block, and another string wound many times around the cylinder. Each string exerts the same force. The cylinder has radius R and height 2R; the block has sides 2R.
a) If they both start from rest, which one gets to the finish line first?
b) Find the angular acceleration of the cylinder.
The instructor (the Nth author) polled students for their answers to part a, saying he wanted to discuss this problem “very briefly.” Most had the block winning; several students argued the problem was the same as an earlier one that had the block sliding and the cylinder rolling. One student dramatically challenged their reasoning, argued that in this case “there is no friction” so by Newton’s 2nd Law the two must tie. But, he added, he “wasn’t really happy” with that conclusion.
Students argued the question for 20 minutes, drawing on Newton’s Laws, comparisons to prior problems, energy principles, kinesthetic experience, as well as several at-home experiments. Under pressure for time, the instructor explained that the two tie, at odds with several students’ findings from experiments they had thought to conduct for themselves. They persisted in asking questions about it, and the discussion continued for an additional 10 minutes.
We consider this an episode of students’ engagement in scientific inquiry (c.f. Engle and Conant, 2002) in that the students were looking for and assessing connections among ideas and evidence, from theoretical work in the course, their own kinesthetic intuitions as well as experimentation, as well as for their displays of emotional investment in their reasoning, including to press the professor for further discussion. In these ways, the students showed aims, values and expectations associated with science (Authors, 2011).
This episode is one of nine we have analyzed, of students’ engagement in science. Here, our analysis points to several aspects of this moment that contributed to the emergence and sustaining of the discussion, including the following:
● Students had spent time on the question before class, so as a class they arrived with multiple threads of reasoning, including several involving prior questions.
● The question activates rich kinesthetic experiences, including compelling intuition for an answer in conflict with a theoretical argument.
● By this time late in the semester, students had come to expect their ideas and questions to become the focus of attention, and the instructor expected and valued their contributions.
● Several students were stable and assertive in their sense-making.
We close with discussion of patterns across the nine cases.