複素数学習における数の承認に関するメタルールの変容過程

抄録

　　The purpose of this study is to clarify how metarules for the endorsement of numbers change in development of numerical discourse from real numbers to complex numbers. Commognitive theory is chosen as a theoretical framework in this study. To achieve this purpose, the data was collected in two lessons in which two second grade high school students participated. It was analyzed through four interrelated characteristics (keywords, visual mediators, endorsed narratives, and routines). As a result, three metarules and commognitive conflicts were identified: MR1; Endorsing objects, which can be realized in real models, as numbers, MR2; Endorsing objects, which can be expressed on a number line, as numbers, MR3; Endorsing objects, which can be expressed on a complex plane, as numbers, CC1; A conflict between real numbers and complex numbers, CC2; A conflict relating metadiscourse for discourse for defining numbers, CC3; A conflict between real numbers and ordered pairs.

　　The contributions and an implication of this study are as follows: (i) identified three metarules for endorsement of numbers and their changing processes, (ii) indicated that one of the opportunities for the change of metarules is to introduce new visual mediators, (iii) indicated the importance of interactive consideration of the duality of complex numbers (algebraic-geometric).