Thinking about nothing: Development of concepts of zero

Abstract

Two studies are reported investigating children's conceptions of the number zero. The first, with 31/2–61/2‐year‐olds, charts preschoolers' understanding that zero is a number among other numbers with its own unique value, namely nothing. Children's achievement of this understanding occurred in three phases. At each phase understanding of zero lagged behind comparable understanding of other small numbers. The second study, with 51/2–10‐year‐olds, investigated children's developing conception of simple algebraic rules, such as a + 0 = a. Results showed that even the younger children had some understanding of several algebraic rules. The older children had acquired more such knowledge, but at all ages algebraic understanding was advanced for rules pertaining to zero, in comparison to those pertaining to other small numbers. These results suggest that zero plays a special role in children's increasingly algebraic knowledge of number. We conclude that since zero is difficult to conceive of and use originally (Expt 1) children develop special rules for its use, and that this provides a first step towards their formulation of more general algebraic rules (Expt 2) and towards an expanded conception of number and mathematics.