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…

In this paper, we focus on the design of assessments of mathematics teachers' knowledge by emphasising the importance of identifying the purpose for the assessment, defining the specific construct to be measured, and considering the affordances of particular psychometric models on the development of assessments as well as how they are able to…

In this study we explored to what extent middle school teachers were able to appropriately identify proportional situations when presented with various mathematical structures and if there were relationships between attributes of the teachers and their ability to identify proportional situations. Interestingly, there were no strong relationships…

We report the development of a multiple-choice instrument that measures the mathematical knowledge needed for teaching arithmetic with fractions, decimals, and proportions. In particular, the instrument emphasizes the knowledge needed to reason about such arithmetic when numbers are embedded in problem situations. We administered our instrument to…