抄録
The purpose of this paper is to consider the learning of the complex number from a viewpoint of the reconstruction of the concept. In this study (I), I examined how to introduce a complex number constructively from the real number. This method is on the basis of a finitely generated from real number field. But there are some problems in this method about the use of the operation. To get over this problem, I proposed adopting the reconstruction of concept in learning of the complex number. The development of the complex number is put in order as follows. The first stage; The grade thought the concept of the complex number in the range of the real number (The middle time of the 16th century〜17th century) The second stage; The grade which a complex number is used as formally (About the end of the 17th century〜18th century) The third stage; The grade when the general ideas of the complex number are put in order and which the number system establish (About the end of the 18th century〜19th century) The beginning of "the third stage" contributes greatly in the development of the complex number concepts. A complex number could be reconsidered from the level of the high concept level due to what Gauss thought the complex number in two-dimensions. And the number system in modern mathematics was established after this. As for school mathematics as well, it considers that it is necessary to reconsider a complex number from the high concept level. And, Ishitani (1961) is insisting that it is important to compare an incidence system with a logical system of numbers. As for learning of the complex number as well, It is important that an incidence system is compared with the logical system and unified. Based on such a thing, I examined a method that reconsider a complex number in the school mathematics from the high general idea level.
