The purpose of this study was to investigate how teachers understand one specific aspect of proportional reasoning. We were interested in understanding the extent to which practicing teachers were able to make sense of reasoning that involved the fixed number of variable-sized parts perspective. We used two items, drawn from a larger dataset, that encouraged teachers to reason about proportional situations using a variable parts perspective. We analyzed teachers’ responses to these items using the knowledge in pieces perspective to identify fine-grained understandings teachers were applying to the situations. Our findings suggest that reasoning about variable-sized parts is not something all of these teachers did. Further, we found certain proportional structures that seemed to support teachers who were able to reason from this perspective.
Orrill, C. H. & Millett, J. E. (2020). Teachers’ abilities to make sense of variable parts reasoning. Mathematical Thinking and Learning.