# When Two Plus Two Does Not Equal Four: Event-Related Potential Responses to Semantically Incongrous Arithmetic Word Problems

- Kristie Fisher,
*University of Washington*
- Miriam Bassok,
*University of Washington*
- Lee Osterhout,
*University of Washington*

## Abstract

Extensive research measuring event-related brain potentials (ERPs)
shows that semantic incongruity is indexed by the N400 effect and
syntactic/structural incongruity is indexed by the P600 effect. We used these
indices to examine how people coordinate their semantic and arithmetic knowledge
when they read simple addition and division word problem sentences (e.g.,
“Twelve roses plus three daisies equals fifteen”). Prior work in
problem solving has shown that word-problem solutions are modulated by analogical
alignment of semantic and arithmetic relations, such that people avoid or commit
errors on misaligned problems (e.g., Aligned: “Twelve roses plus three
daisies equals fifteen”; Misaligned: “Twelve cookies plus three jars
equals fifteen”). Here, we found that such analogical alignments modulate
the comprehension of word-problem sentences. Specifically, we found that
analogically Misaligned semantic relations elicited a P600 effect. Furthermore,
an N400 effect was elicited by the last number word of Misaligned problem
sentences, even when it was a mathematically correct answer. These results show
that analogical alignment between semantic and arithmetic relations can be
indexed with the P600 effect and provide a foundation for future ERP work on
analogical reasoning.

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