How do we measure what students understand about arithmetic operations that is not tied to knowledge of specific numbers or facts? Other psychology researchers have shown that children and adults are sensitive to a variety of arithmetic principles. In math ed, scholars have documented students’ depth of understanding, flexibility, and comfort with arithmetic and algebraic operations. We sought to develop tasks that would help us characterize operation concepts, such as grouping concepts for multiplicative operations. This project has gone in many directions. Here are some of our findings:
Sidney, P.G., & Alibali, M.W. (2013). Children’s and adults’ models of whole number division: Consistency or variability?. In M. V. Martinez, & A. C. Superfine (Eds.) Proceedings of the 35th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Chicago, IL: University of Illinois at Chicago.
Sidney, P.G. & Alibali, M.W. (2013, April). Developing operation sense: Children’s and adults’ arithmetic with countable and uncountable amounts. Poster presented at the biennial meeting of the Society for Research in Child Development, Seattle, WA.