A students’ ability to construct and transform units undergirds large swaths of their mathematics, especially as it relates to whole number operations, fractions, and early algebraic reasoning. In this talk, I introduce unit transformation graphs (UTGs) as an approach to modeling students’ mathematics and provide examples from a study of students enrolled in a mathematics for elementary school teachers course. UTGs are graphs in the mathematical sense, with vertices representing constructed units and directed edges representing unit transformations, such as iterations or partitions of a unit. These graphs illustrate students’ mathematics by specifying the mental actions they use to construct and transform units when solving tasks, such as fraction composition tasks. They also demonstrate the power of constructing two- and three-level, at higher stages of units coordination. The talk will conclude with suggestions for using UTGs for teaching and research, including research on teaching and teaching about research.
Professor of Mathematics Education
Department of Mathematics