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

When Two plus Two Does Not Equal Four: Event-Related Potential Responses to Semantically Incongruous Arithmetic Word Problems Kristie J. Fisher (kjfisher@uw.edu) University of Washington, Department of Psychology, Box 351525 Seattle, WA 98105 USA Miriam Bassok (mbassok@uw.edu) University of Washington, Department of Psychology, Box 351525 Seattle, WA 98105 USA Lee Osterhout (losterho@uw.edu) University of Washington, Department of Psychology, Box 351525 Seattle, WA 98105 USA 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. Keywords: ERP; analogy; mathematical cognition; N400 effect; P600 effect Introduction A common task facing the cognitive system is conceptual integration of individual items into a meaningful whole. For example, language comprehension requires conceptual integration of consecutive words into meaningful sentences. Similarly, comprehension of arithmetic problems requires conceptual integration of numbers and arithmetic operators into correct mathematical expressions. In this paper, we explore the conceptual integration of simple arithmetic word problems, which are unique in that they require conceptual integration of language and of mathematics. Conceptual Integration & ERPs The process of conceptual integration, and the conditions under which it can be disrupted, have been investigated in a variety of domains using event-related potential (ERP) methodology, which measures the electrical brain activity elicited by a particular stimulus. Work in this area has shown that two key aspects of conceptual integration, meaning and structure, are indexed by two distinct and highly reliable ERP components—the N400 and P600 components, respectively. The N400 component is negative-going and peaks around 400ms after presentation of the stimulus. This component is highly sensitive to contextual semantic meaning. The magnitude of this component is larger for semantically incongruous compared to congruous items—a difference known as the N400 effect. The N400 effect was first documented in sentence processing. For example, the italicized word in the sentence, “The cat will bake the food” will elicit an N400 effect relative to, “The cat will eat the food” (Kutas & Hillyard, 1980). Subsequent work has shown that the N400 effect is elicited in response to conceptual incongruities in other domains. For example, incorrect answers to simple symbolic (e.g., “4 x 4 = 21”) and verbal (e.g., “Twelve plus three equals sixteen.” ) arithmetic problems elicit an N400 effect (e.g., Niedeggen & Rosler, 1999; Fisher, Bassok, & Osterhout, 2009). Thus, the N400 effect is generally accepted to be a domain-general index of semantic congruence. The P600 component is positive and peaks at around 600ms after stimulus presentation. A P600 effect is elicited by violations of syntax within a sentence (e.g., “The cat will eating the food I leave on the porch.”; Osterhout & Holcomb, 1992; Osterhout & Mobley, 1995) and by violations of structure, such as a wrong note played in a harmonic scale (Patel et al., 1998). Such violations of syntax or structure lead to larger P600 amplitudes, relative to control conditions (i.e., the P600 effect). Furthermore, Osterhout and Mobley (1995) found that when there is any kind of violation within a sentence, syntactical or semantic, an N400 effect is also elicited by the ending word of the sentence, even though that word is perfectly correct. This last-item N400 effect is likely the result of the experimental paradigm typically used in