Arithmetic problem-solving whose components mainly involve the calculation, planning and reasoning, is an important mathematical skill. To date, the neural mechanism underlying arithmetic problem-solving remains unclear. In this study, a scheme that combined a novel 24 points game paradigm, conditional Granger causality analysis, and near-infrared spectroscopy (fNIRS) neuroimaging technique was developed to examine the differences in brain activation and effective connectivity between the calculation, planning, and reasoning. We discovered that the performance of planning was correlated with the activation in frontal cortex, whereas the performance of reasoning showed the relationship with the activation in parietal cortex. In addition, we also discovered that the directional effective connectivity between the anterior frontal and posterior parietal cortex was more closely related to planning rather than reasoning. It is expected that this work will pave a new avenue for an improved understanding of the neural underpinnings underlying arithmetic problem-solving, which also provides a novel indicator to evaluate the efficacy of mathematical education.