Can young students operate on unknowns? (English)

van denHeuvel-Panhuizen, Marja, Proceedings of the 25th conference of the international Group for the Psychology of Mathematics Education. Vol. 1. , (ISBN 90-74684-16-5). 130-140 (2001).

Algebra instruction has traditionally been delayed until adolescence because of mistaken assumptions about the nature of arithmetic and about young students’ capabilities. Arithmetic is algebraic to the extent that it provides opportunities for making and expressing generalizations. We provide examples of nine-year-old children using algebraic notation to represent a problem of additive relations. They not only operate on unknowns; they can understand the unknown to stand for all of the possible values that an entity can take on. When they do so, they are reasoning about variables.