
05729520
j
2010d.00324
Jones, Ian
A diagrammatic view of the equals sign: arithmetical equivalence as a means, not an end.
Res. Math. Educ. 10, No. 2, 151165 (2008).
2008
Taylor \& Francis (Routledge), Abingdon, Oxfordshire; British Society for Research into Learning Mathematics (BSRLM)
EN
E42
E43
C32
C33
F32
F33
H32
H33
equals sign
arithmetic
diagrammatic activity
algebraic thinking
doi:10.1080/14794800802233688
Summary: It is recommended in the mathematics education literature that pupils be presented with equality statements that can be assessed for numerical balance by attending to notational structure rather than computation. I describe an alternative, diagrammatic approach in which pupils do not assess statements but instead use them to make substitutions of notation. I report on two trials of a computerbased task conducted with pairs of pupils and highlight two findings. First, the pupils found it useful to articulate the distinct substitutive effects of commutative (`swap', `switch') and partitional (`split', `separate') statements when working on the task. Secondly, the pupils did not notice that some of the statements presented were in fact false, which suggests their substituting activities were independent of numerical equivalence conceptions. This demonstrates that making substitutions offers task designers a mathematical utility for equality statements that is distinct from, but complementary to, assessing numerical balance.