An event-related potential study of number format and the problem-size effect in arithmetic
Danielle S. Dickson1, Bianca O. Obinyan1, Nicole Y. Y. Wicha1; 1University of Texas at San Antonio
Arithmetic problems differ in difficulty, with 9x7 posing more of a challenge than 3x2. Adults are slower at solving and recognizing the solutions to problems with larger solutions, a phenomenon which has been named the problem-size effect. Number format (“nine” vs “9”) also influences arithmetic processing efficiency, with faster RTs for problems presented using Arabic digit numerals. It has been difficult to trace the cognitive source(s) of these effects with behavioral data alone, leading to multiple similarly plausible theoretical explanations. Here, we measured ERPs at the solutions to multiplication problems that varied in both problem size and number format (2x2 design). Two operands were presented as either spoken number words or as sequential Arabic numerals. Adults verified the correctness of the Arabic numeral solution – whose size was used to classify the problem as large (>25) or small. Consistent with prior results, correct solutions elicited a more positive response than incorrect solutions. This effect was driven by a P300 to correct solutions, as well as by a co-occurring N400 effect when number words were the operands. Problem size manifested largely on the incorrect solutions, with a larger late positivity (LPC) for small problems than large. This LPC was more prominent when the operands were digits than number words. There was also a substantial main effect of operand format, with its own characteristic timing and scalp distribution. Our findings suggest that both problem size and number format independently influence arithmetic answer recognition at differing timescales and at different levels of cognition.
Topic Area: THINKING: Problem solving