Brain-mechanistic responses to varying difficulty levels of approximate solutions to arithmetic problems

Approximate strategies are crucial in daily human life. The studies on the "difficulty effect" seen in approximate complex arithmetic have long been neglected. Here, we aimed to explore the brain mechanisms related to this difficulty effect in the case of complex addition, using event-related potential-based methods. Following previous path-finding studies, we used the inequality paradigm and different split sizes to induce the use of two approximate strategies for different difficulty levels. By comparing dependent variables from the medium- and large-split conditions, we anticipated being able to dissociate the effects of task difficulty based on approximate strategy in electrical components. In the fronto-central region, early P2 (150-250 ms) and an N400-like wave (250-700 ms) were significantly different between different difficulty levels. Differences in P2 correlated with the difficulty of separation of the approximate strategy from the early physical stimulus discrimination process, which is dominant before 200 ms, and differences in the putative N400 correlated with different difficulties of approximate strategy execution. Moreover, this difference may be linked to speech processing. In addition, differences were found in the fronto-central region, which may reflect the regulatory role of this part of the cortex in approximate strategy execution when solving complex arithmetic problems.