The cognitive process of extended trans students in understanding the real number system

Abstract

There were seven levels of student schema development in learning real analysis. Extended trans was the highest cognitive level. The purpose of this study was to describe the cognitive process of students in understanding the real number system. This was the initial part of development research. We want to know the highest initial ability students have about real number systems. The subjects of this study were 12 students of Real Analysis at the Bachelor of Mathematics Education Program. Students were interviewed based on assignments. Data were analyzed using fixed comparison techniques. The results of this study were that students can build linkages between actions, processes, objects, and other schemes (performing retrieval of the previous schema) by using and selecting procedures or operations in real number systems. He was able to apply the concept of the properties of bounded set to problem solving so that a mature scheme was formed. The scheme can be used to solve related problems. Also, can build new structures based on mature schemes that they already have. The conclusion of this study was that students can interiorize, encapsulate and thematize schemes that mature into a deductive structure.