Students' Mathematical Understanding in Solving Mathematics Problems from Theory Perspective of Schemp's Understanding

Abstract

This study aims to describe students' mathematical understanding in solving mathematical problems from the perspective of Skemp's theory of understanding which consists of instrumental understanding and relational understanding. This type of research is descriptive qualitative in which students' mathematical understanding in solving exponential problems is described based on the results of mathematical understanding tests and interviews. This research was conducted in class X SMA Darul Faqih Indonesia and the research subjects were taken from students with high, medium, and low mathematical abilities, each of which was represented by two subjects from each category.The results of this study indicate that students with high mathematical abilities are able to find mathematical relationships, apply them, and explain the reasons, which include relational understanding. Students with moderate mathematical ability are able to apply memorized procedures in finding solutions to problems but are unable to explain the reasons, which include instrumental understanding. Meanwhile, students with low mathematical ability have low mathematical understanding because they are unable to meet the indicators of relational understanding and instrumental understanding. This study recommends that students with low mathematics abilities are trained to apply mathematical theory to increase their understanding into instrumental understanding while students with moderate mathematical abilities are trained to find mathematical theory to increase their understanding into relational understanding.