Children’s Coordination of Linguistic and Numeric Units in Mathematical Argumentative Writing

Mathematical argumentation and proof has long been identified with algebraization. Much literature discusses the relationship between the two, but with little specificity on how particular semiotic features in argumentation relate to coordination in early algebra. Further, there is a particular lack of research on this topic in the elementary/primary years of schooling. The present study examines how children’s unit coordination in early algebra (particularly the concepts of equivalence and multiplicative reasoning) co-occurs with their coordination of grammatical information units. Coordination of information units was examined through reference use via the semiotic tool of detailing. Results suggest that second and third grade students who coordinate reference chains to support a mathematical claim in their argumentative writing tend to have higher multiplicative reasoning and conception of equivalence scores on several tasks. However, features of certain tasks may influence whether and how such unit coordination interacts with reference use.