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Abstract:
Until recently, it has been assumed that adults solve
single-digit multiplication problems using a single, efficient
solution procedure; that is, adults retrieve the answers from a
network of stored "facts". Recent research suggests that adults
report using a variety of "procedures" to solve simple single-digit
addition, subtraction, and multiplication problems. However, these
self-reports have not yet been supported by independent analysis of
performance to verify their veridicality. Hence, the goal of this
research was to provide converging evidence (behavioral and
electrophysiological data) with respect to the veridicality of
self-reported nonretrieval strategy use. Participants solved the
multiplication problems defined by the combination of all
single-digit (0-9) operands. On each trial, participants were told:
(1) to solve the multiplication problem as quickly and accurately
as possible, and (2) to describe how they solved the problem. Event
related potentials (ERPs) were recorded from a high-density
(128-channel) sensor net. Reaction times (RTs), error patterns, and
ERPs revealed fundamental differences between retrieval and some
nonretrieval strategies (e.g., rules versus fact retrieval).
However, other subsets of self-reports were indistinguishable
suggesting important modifications of theories of arithmetic. An
alternative theory of the cognitive and neural bases of
multiplication will be discussed. More generally, we have
demonstrated the importance of using multiple sources of evidence,
including electrophysiological, to elucidate theories of
cognition.
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