Science education and art education are regarded as the basis of the modern school education. The relation between science education and art education, however, has never, so far, been taken into full consideration. The reason for this fact is that we cannot express clearly in words the quality of the aim and end of art education. The most essential aim of school education is the impartment of both knowledge and joys of artistic creation. In this treatise the writer, first of all, divides the pupil's attitude towards objects into 'the attitude of scientific cognition' and 'the attitude of artistic cognition'. Subsequently, the writer sets forth his views as to what has been taught through science education in connection with the matter of cognition, and refers to the necessity of art education investigated from entirely different viewpoints. And the writer, taking concrete examples, shows how rational cognition is being formed through the present education of mathematics, and points out that the above-mentioned cognition has the quality positively opposed to the modern ideas of art.