Framing a robust understanding of proportional reasoning for teachers

Proportional reasoning is foundational in school mathematics. Despite the importance of proportional reasoning, little has been written about the knowledge needed for teachers to teach proportional reasoning relative to its importance. In this paper, we present an initial definition for a robust understanding of proportional reasoning for teaching based on synthesizing past scholarship in conjunction with an empirical study of the knowledge resources practicing teachers use to make sense of proportional reasoning tasks. As a result of this effort, we present here an initial framing of operationalized knowledge resources based upon our definition for a robust understanding that could be used as an analytic tool. We also describe how such a framework of knowledge resources is useful in the context of teacher education, and we provide an example of how the framework was used to analyze the knowledge resources a teacher employed to make sense of a proportional reasoning task. We end by discussing possible implications our framework has for designing teacher education experiences and further research that is needed.