The essence of a matter is gradually treated as an independent subject unrelated with the nature, then points, lines and planes become harmonious and balanced to be an abstract painting that emphasizes the purity. Such canvas consisting of points, lines and planes, the most fundamental elements of abstract painting, and the spirit of a painter emphasize the inner world of men. Kandinsky, Mondrian and Malevich also started from the natural form, went through the process of simplification and transformation, and then completely escaped from the object to actualize a geometrical and expressional abstract painting merely with points, lines, planes and colors. It is not easy for children to understand the aesthetical values and expressional form of such abstract painting. They are accustomed to the idealogical and objective way of expression to depict matters similarly. Therefore arts teachers should make lots of efforts and prepare various opportunities to inspire children with the comprehension of abstract painting and the desire of expression and to represent and appreciate it. Especially children, who showed the interest in and desire for arts in their early days, should be upgraded with their function to draw an object similarly as they grow. If the children, who are short of the ability of representational painting and bored with skill-oriented arts education, are taught about aesthetical principle with a plan of teaching abstract painting through points, lines and planes and guided about the abstract painting with various materials and techniques, they might escape from the stress of representing realistic matters, and understand and get access to the abstract painting more easily with unlimited imagination, creative colors and thoughts that come from students themselves\' visual impression and free variation of things. The purpose of this study is to present a general plan of abstract expression for points, lines and planes that children can make access to the expression of abstract painting naturally. It is also to reach the goal of modern arts education by letting them understand the abstract painting and by fostering their aesthetical emotion and creativity. Hopefully this study might help children to understand points, lines and planes that are the fundamental in abstract painting and the essence of it, raise their capacity of expression and appreciation, cause creative interest rather than functional representation of things, higher aesthetical sense and creativity and understand the modern style of arts.