The bilingual math dilemma - Language switching costs in declarative and procedural arithmetic knowledge

Language Switching Costs (LSC), characterized by slower and more error-prone responses when the language of encoding and retrieval differ, provide insights into the language-dependency of knowledge representations. A growing body of experimental research has revealed LSC in declarative arithmetic knowledge such as arithmetic facts. However, it remains unclear whether these costs extend to procedural arithmetic knowledge. Furthermore, the long-term stability of LSC has not been investigated, studies on their relationship with individual differences in cognitive competencies have yielded inconsistent results, and the cognitive processes underlying LSC are not fully understood yet. To address these research gaps, we trained 122 bilingual participants over four days on artificial arithmetic facts (declarative knowledge) and a novel arithmetic procedure (procedural knowledge) in either their first (L1) or second language (L2). Participants were tested on the trained material in both languages at four time points: 1 day, 1 week, 1 month, and 3 months after training. In all test trials, participants were required to indicate potential translation processes into the trained language and into Arabic digits. Results revealed LSC in reaction times for both declarative and procedural knowledge, persisting up to 3 months post-training. These findings, together with the results from the translation self-reports, suggest that both declarative and procedural arithmetic knowledge are language-dependent, which only partly agrees with triple code models on arithmetic. No associations between LSC and individual differences in cognitive competencies were observed. These findings are of both theoretical and practical relevance for bilingual knowledge representations in arithmetic.