Science of Mathematical Education and Position of Mathematics on it.

Abstract

Now a days it is insisted that the researchers of mathematical education research scientifically into it, and it is expected to build up the theory of mathematical education as a science or a discipline. But until now it has been left to be undetermined whether this discipline is belong to pedagogy or not, and how this discipline should be related to mathematics. We make researches in this paper into relation of mathematics with this discipline. At first, we consider some expected properties of this discipline as a science. These are as follows: (1) It is stemed from real problems yielded by the activities of teaching- learning process of mathematics, (2) It may be identified one of emirical sciences, and (3) satisfied that this discipline should have some scientific properties. We will state it as a metascience of the problems of teaching-learning process of mathematics. (4) It is possible to study as an interdiscipline between many subjects. Under the above properties of our theory of mathematical education, we can call it science of mathematical education. We consider the position of mathematics on this science in the next three aspect: (1) necessity of consideration of "mathematics about", (2) mathematics as educational content, especially in the context of the process of translation of mathematics into subject matters, for example, in the context of general framework in which mathematics comes to existence and develop itself which is made of the triples, situation-model-theory (= mathematics) introduced by A. Revuz, (3) usefulness of mathematical models, non-metric as well as metric. We list up some papers on the studies of mathematical education in each aspect for the purpose of explaining concrete content of each and showing satisfiability such that each aspect do not contradict itself.