This is the first report of the study carried out during the last 4 years. The objective of this research is to clarify the acquiring process of the number concept in children by the "method of experimental education." Here, its problems, principles and methods are discussed. In the orthodox study of the developments of the children's number concept, the central problem seems to be the discovery of the hierarchy of the developmental stages of this concept, as are typical in Piaget's or Werner's researches. In their theories, we think it is assumed implicitly that the acquisition of number concept is initiated by internal factors such as maturation or readiness. There is no doubt that Piaget's study is one of the most brilliant works in this field. Internal factors, however, should de the most important determinant and the role of learning should have little significance, if the establishment of the order of developmental stages is the most important point concerning the number concept or mathematical education. But we think that in acquiring the number concept the symbolic mediation process is sine qua non, which has cultural origin. So, the external factors, learning, experience or education should have equal importance. Does the term "maturation" mean after all the sudden appearance of new behavior pattern? It is extremely difficult to tell whether such behavior pattern is caused by maturation or by experience. Using the traditional method of simple observation of the developmental phenomena, it might not be possible to determine the significance or the role of maturation in causal relations. This methodological reflexion leads us to the point that the method of exprimental control of the developmental processes has to be applied in order to get basic solution of the role of maturation or experience. Such method has already been used by Gesell and Luria successfully. We try to extend the same type of method into a more general methodology and give a name of "the method of experimental education." It has analogical significance with the method of experimental embryology in biology. That is to say, the method of experimental education applies some operations on the apparently natural process of the number development, and tries to find out, by the consequent responses, what causal factors are working on it.