Bilingual problem size effect: an ERP study of multiplication verification and production in two languages

The problem size effect (PSE) is defined by better performance solving small problems (e.g., 2x4) than large problems (e.g., 8x9). For monolinguals, the PSE is larger when problems are presented in unfamiliar formats (e.g., written words), reflecting increased processing difficulty. Bilinguals are typically faster and more accurate at retrieving multiplication facts in the language of learning (LA+) than in their other language (LA-). We hypothesized that the less familiar arithmetic language (i.e., LA-) would elicit larger PSEs than LA+. Here, fluent Spanish-English bilingual adults verified spoken multiplication problems presented in LA+ and LA- while event-related potentials (ERPs) were recorded (Experiment 1A). To further promote language differences, we increased task difficulty by presenting problems at a faster pace (Experiment 1B) and requiring bilinguals to verbally produce solutions (Experiment 2). Language differences in performance were only observed for Experiment 2, where solutions were produced more slowly in LA- than LA+. In the ERPs, a PSE was driven by larger P300s for small than large solutions. A language effect was only observed under time pressure where LA- elicited a PSE at the 2^nd operand. Additionally, the PSE was smaller for LA- at the solution. This suggests that categorizing multiplication facts is more effortful in LA-. In sum, very subtle language differences arise in fluent bilinguals when problems are more difficult, such as larger problems presented under time pressure in a weaker language. Critically, the effect of LA+ is at the level of response production and not access to the facts from memory.