The purpose of this research was to analyze differences in brain region activation and changes in functional connectivity using functional near-infrared spectroscopy (fNIRS) to determine whether a spatial program improves children’s mental arithmetic performance. The subjects of the study were second graders in elementary school, and a spatial program consisting of mental rotation, spatial visualization, and spatial orientation was provided. Mental arithmetic was presented in two types: numerical calculation and missing-term, with addition and subtraction. The results of the study are as follows. First, the mental arithmetic mean increased after the spatial program intervention, but increased significantly only in the missing-term task of subtraction. This shows that the spatial program has limitations in transferring to the child’s numerical ability. Second, after the spatial program intervention, the brain activation areas in the DLPFC and OFC significantly decreased for addition, and the activation difference in the DLPFC and FPC was observed for subtraction. Third, in the pre-test, the functional connectivity of the brain was significantly higher between the DLPFC and FPC. In the post-test, the functional connectivity of the right hemisphere increased, and significant connectivity between channels was higher within the DLPFC region. This means that the spatial program can increase the functional connectivity of the brain and increase the complexity of neurons.