Students' obstacles in understanding the properties of the closed sets in terms of the APOS theory

Abstract

An understanding of the concepts and principles of open sets can be done through activities in the form of mathematical actions, processes, objects organized in a scheme. This was the operationalization of the APOS theory (Action, Processes, Objects, and Schema). The purpose of this study was to describe students' mistakes in understanding the properties of open sets in terms of the APOS Theory. This research was part of development research. It was the stage need assessment stage. We want to determine the characteristics of students to determine the right learning model. The subject of this study were 15 students of mathematics education at the University of Bengkulu. Students were selected based on the tasks that they do in learning Real Analysis. Data was collected from paper and pencil results and task-based interview results. Data were analyzed qualitatively using fixed comparison techniques. The results of this study were that students can only coordinate two or more sets, and the difficulty of proving a set theorem closes. One such theorem was "F was a subset of R, F closed sets if and only if F contains all the cluster points". He can only take actions separately from the characteristics of the set given. The conclusion of this study was the difficulty of students in understanding the properties of the closed sets was the inability of students to carry out interiorization from actions to processes. Also, it was not able to encapsulate processes into objects. He was unable to reach the scheme of the properties of closed sets.