My research covers two main areas: children’s mathematical representations and early algebra.

You can see my CV here.

My research on children’s mathematical representations investigates children’s early learning of mathematical notations including written numbers, graphs, tables, algebraic notation, representations for space, data, and measurement, and idiosyncratic notations. It builds from the assumption that conventional knowledge is built on prior understandings. From this assumption, it follows that children’s ideas about mathematical notations could be constitutive of their later conventional understandings. One of the central tasks of the investigation is to document how children initially represent numerical and mathematical understandings and how and why their expressive repertoire changes over time.

Early Algebra covers many topics in mathematics, including the four operations, but it does so in novel ways. Consider the operation of addition. By second grade most students are being taught to add 3 to another number. They have probably not been asked to consider expressions such as “n + 3″, where n might refer to any number. In using expressions to describe relations among numbers and quantities, young learners go beyond computational fluency and begin to develop the ability to make mathematical generalizations using algebraic notation. Early algebra does not aim to increase the amount of mathematics students must learn. Rather, it is about teaching time-honored topics of early mathematics in deeper, more challenging ways. Our position is that children who become familiar with algebraic content and practices from an early age and in meaningful contexts will do better in mathematics, regardless of the criteria used.