id: 06581530
dt: j
an: 2016c.00626
au: Braithwaite, David W.; Goldstone, Robert L.; van der Maas, Han L. J.;
Landy, David H.
ti: Non-formal mechanisms in mathematical cognitive development: the case of
arithmetic.
so: Cognition 149, 40-55 (2016); corrigendum ibid. 151, 131 (2016).
py: 2016
pu: Elsevier, Amsterdam
la: EN
cc: F32 F33 C32 C33
ut: mathematical cognitive development; concrete to abstract shift; arithmetic;
syntax; perception
ci:
li: doi:10.1016/j.cognition.2016.01.004
ab: Summary: The idea that cognitive development involves a shift towards
abstraction has a long history in psychology. One incarnation of this
idea holds that development in the domain of mathematics involves a
shift from non-formal mechanisms to formal rules and axioms. Contrary
to this view, the present study provides evidence that reliance on
non-formal mechanisms may actually increase with age. Participants ‒
Dutch primary school children ‒ evaluated three-term arithmetic
expressions in which violation of formally correct order of evaluation
led to errors, termed foil errors. Participants solved the problems as
part of their regular mathematics practice through an online study
platform, and data were collected from over 50,000 children
representing approximately 10\% of all primary schools in the
Netherlands, suggesting that the results have high external validity.
Foil errors were more common for problems in which formally
lower-priority sub-expressions were spaced close together, and also for
problems in which such sub-expressions were relatively easy to
calculate. We interpret these effects as resulting from reliance on two
non-formal mechanisms, perceptual grouping and opportunistic selection,
to determine order of evaluation. Critically, these effects reliably
increased with participants’ grade level, suggesting that these
mechanisms are not phased out but actually become more important over
development, even when they cause systematic violations of formal
rules. This conclusion presents a challenge for the shift towards
abstraction view as a description of cognitive development in
arithmetic. Implications of this result for educational practice are
discussed.
rv: