Representation updating outweighs rule switching in fraction equivalence: Evidence from ERPs and multiscale entropy

Executive function is a fundamental mechanism of human cognition, yet its specific roles in mathematical processing remain relatively underdeveloped. The study investigated behavioral and neural dynamics involved in evaluating fraction equivalence, aiming to disentangle cognitive costs associated with rule switching and representation updating, which are core to executive function. Thirty adults participated in a novel two-stage fraction-equivalence task involving both symbolic and figural representations. Contrary to findings typically reported in classical task-switching paradigms, behavioral results showed better performance in switch conditions than in non-switch conditions. Notably, participants demonstrated the poorest performance in the non-switch condition involving solely figural representations. ERP results indicated that switch conditions generally elicited larger N2 and P3 amplitudes, suggesting efficient engagement of cognitive control processes during representation transformation. When controlling for the representation presented in the first stage, a rule-switching effect emerged only when the first-stage representation was symbolic, but not when it was figural. This pattern suggests that updating processes associated with figural representations may influence the cognitive mechanisms underlying rule switching. Further analysis revealed that the Symbol-to-Symbol (SS) condition elicited significantly larger N2 and P3 amplitudes than the Figure-to-Figure (FF) condition, indicating that figural representations may provide less effective cognitive support for representation updating and lead to poorer behavioral performance. Multiscale entropy (mMSE) analysis further confirmed greater neural complexity in the FF condition, suggesting increased cognitive demands during processing. Overall, these findings indicate that when domain-general rule-switching mechanisms are applied to mathematical content, the underlying cognitive processes may undergo reweighting, highlighting the interaction between executive control and mathematical representations.