1 research outputs found
Substitution and sameness: two components of a relational conception of the equals sign
A sophisticated and flexible understanding of the equals sign is important for arithmetic
competence and for learning further mathematics, particularly algebra. Research has
identified two common conceptions held by children: the equals sign as an operator, and the
equals sign as signalling the same value on both sides of the equation. We argue here that as
well as these two conceptions, the notion of substitution is also an important part of a
sophisticated understanding of mathematical equivalence. We provide evidence from a
cross-cultural study in which English and Chinese children were asked to rate the
âclevernessâ of operational, sameness and substitutive definitions of the equals sign. A
Principle Components Analysis revealed the substitutive items were distinct from the
sameness items. Furthermore, Chinese children rated the substitutive items as âvery cleverâ,
whereas the English children rated them as ânot so cleverâ, suggesting that the notion of
substitution develops differently across the two countries. Implications for developmental
models of childrenâs understanding of equivalence are discussed