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

Yanhui Xiang,Yiqi Jiang,Qihan Wu,Lei Mo,Xiaomei Chao

doi:10.1038/srep24194

Abstract

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.

Highlights

Of the difficulty of executing approximate strategies
Dehaene et al found that the regions activated by approximate arithmetic were mostly located in the visuo-spatial areas of the brain, such as bilateral parietal regions or the posterior occipital lobes, whereas brain regions activated by exact arithmetic were more consistent with language-specific areas, such as the left frontal lobes[11]
Among studies using simple arithmetic problems, many have demonstrated that participants usually obtain the answer directly by fact retrieval from memory, and that cognitive processing is automatic[18,19]

Summary

Introduction

Left frontal lobe-damaged patients showed poor exact arithmetic abilities, but demonstrated no impairment in executing approximate arithmetic[14,15] These studies prove that approximate strategy and exact strategy processing use distinct brain pathways. Stanescu et al used simple arithmetic as problem material, and problem size as the variable determining difficulty, and identified differences in cognitive processing and location, depending on whether participants used exact or approximate strategies[17]. Participants tended to adopt exact arithmetic strategies to solve small-split problems and approximate arithmetic strategies to solve large-split problems Behavioral evidence, such as task performance characteristics, including speed− accuracy tradeoff, shows that low speed and a high error rate characterize exact arithmetic processing, whereas high speed and a low error rate characterize approximate arithmetic processing. The contrast between the small and medium split can be used to verify the conclusion of El Yagoubi et al for the case of Chinese participants[9,10], while the contrast between the medium and large split can be used to explore difficulty effects in approximate problem solving

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