This paper introduces a view of educational process as a 3-layer system comprising human brain, personality psychology, and classroom pedagogy. It aims to present a classroom as a place where educational neuroscience and educational psychology meet to result in effective pedagogy. The paper demonstrates the advantages of such approach for mathematics education. Among them are understanding of mathematical anxiety as a defensive reaction of the brain on operating memory overflow, finding gifted and talented students objectively, assertion of possible limitations on the educational goals given unfavorable conditions, restricted time of information perception, limited liability of teachers and instructors for the success of their students, and opportunities for better outcomes when group learning, peer leadership, or cross-discipline teaching and learning are implemented. As examples of applications, a technology - based teaching technique MARTA and Virtual/Augmented Reality are discussed.