Teachers’ abilities to make sense of variable parts reasoning

ABSTRACT

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.

KEYWORDS:

• Multiplicative reasoning
• fixed number of variable sized parts
• proportional reasoning
• ratios

Acknowledgments

The work reported here was supported by the National Science Foundation under grants DRL-1621290 and DRL-1054170. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. The authors wish to thank all the members of the research team for their assistance with the analysis for this paper.

Additional information

Notes on contributors

Chandra Hawley Orrill

Chandra Hawley Orrill is a Professor of Mathematics Education in the Department of STEM Education & Teacher Development at UMass Dartmouth. Her research focuses on how teachers understand the mathematics they teach, particularly proportions and fractions, and how to support the development of that knowledge.

John E. Millett

John Millett is a Ph.D. student in the Department of STEM Education & Teacher Development at UMass Dartmouth. His research interest is focused on how students understand mathematics.