Conservation and executive function (EF) are important early childhood skills; however, knowledge about their relationship is scarce. Hence, in this study, this relationship is investigated, and a comparison is conducted between the Piagetian conservation and EF tasks to obtain the total hemoglobin (mMmm) for the left and right brain activity in the prefrontal cortex of children, using a functional near-infrared spectroscopy. As a case study, a survey was conducted in the home of a four-year-old child (boy) in Japan in 2020. His home was selected as the primary place of investigation owing to the spread of the coronavirus disease 2019 infection. The researcher was an expert in pedagogy and psychology. The following hypothesis could be formulated from the case studies analyzed herein: From the viewpoint of the brain activity in the prefrontal cortex, there may be a link between the conservation of quantity and EF. The preservation of quantity is closely related to mathematics education. This hypothesis can thus expand the scope of research and practice in the fields of psychology, education, and mathematics education. Furthermore, the results may help psychologists, psychiatrists, teachers, parents, and others involved in the development of children sublate the value of their concept of conservation and improve their support methods.