id: 05729520
dt: j
an: 2010d.00324
au: Jones, Ian
ti: A diagrammatic view of the equals sign: arithmetical equivalence as a
means, not an end.
so: Res. Math. Educ. 10, No. 2, 151-165 (2008).
py: 2008
pu: Taylor \& Francis (Routledge), Abingdon, Oxfordshire; British Society for
Research into Learning Mathematics (BSRLM)
la: EN
cc: E42 E43 C32 C33 F32 F33 H32 H33
ut: equals sign; arithmetic; diagrammatic activity; algebraic thinking
ci:
li: doi:10.1080/14794800802233688
ab: 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 computer-based
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.
rv: