id: 06690693
dt: j
an:
au: Kibbe, Melissa M.; Feigenson, Lisa
ti: A dissociation between small and large numbers in young children’s
ability to “solve for $x$” in non-symbolic math problems.
so: Cognition 160, 82-90 (2017).
py: 2017
pu: Elsevier, Amsterdam
la: EN
cc: H31 F31 F21
ut: approximate number system; objects; number; numerical cognition;
mathematical cognition; cognitive development
ci:
li: doi:10.1016/j.cognition.2016.12.006
ab: Summary: Solving for an unknown addend in problems like $5+x=17$ is
challenging for children. Yet, previous work found that even before
formal math education, young children, aged 4- to 6-years, succeeded
when problems were presented using non-symbolic collections of objects
rather than symbolic digits. This reveals that the Approximate Number
System (ANS) can support pre-algebraic intuitions. Here, we asked
whether children also could intuitively “solve for $x$” when
problems contained arrays of four or fewer objects that encouraged
representations of individual objects instead of ANS representations.
In Experiment 1, we first confirmed that children could solve for an
unknown addend with larger quantities, using the ANS. Next, in
Experiment 2a, we presented addend-unknown problems containing arrays
of four or fewer objects (e.g., $1+x=3$). This time, despite the
identical task conditions, children were unable to solve for the
unknown addend. In Experiment 2b, we replicated this failure with a new
sample of children. Finally, in Experiment 3, we confirmed that
children’s failures in Experiments 2a and b were not due to lack of
motivation to compute with small arrays, or to the discriminability of
the quantities used: children succeeded at solving for an unknown {\it
sum} with arrays containing four or fewer objects. Together, these
results suggest that children’s ability to intuitively solve for an
unknown addend may be limited to problems that can be represented using
the ANS.
rv: