Understanding the Quadrilateral Concept of Junior High School Students Based on APOS Theory in Terms of Differences in Cognitive Styles

摘要

This study was designed to describe the understanding of quadrilateral concepts in junior high school students based on the APOS theory (Action, Process, Objects, and Schemes). The research used qualitative approach to explain the understanding of two junior high school students who had equal mathematical abilities and each had field-dependent (FD) and field-independent (FI) cognitive style with descriptive explanations. Quadrilateral task and interviews guidelines were used to explore student's quadrilateral concept. The results of this study indicated that for the action stage, both could solve understanding problems related to quadrilateral concept. For the process stage, the FI subject explained the process or the calculation coherently in every step taken in problem with understanding the characteristic of shapes to define quadrilateral concept, meanwhile the FD subject explained the process with interpreting quadrilateral concepts and calculating all steps to find the shapes area in problem verbally. In the object stage, both could compare two or more shapes in quadrilateral problem and prove steps to find areal of shapes correctly in problem. For the scheme stage, FI subject could infer the relationship between shape's properties in quadrilateral to explain quadrilateral concepts and make conclusions. In the other hand, the FD subject did not have abilities in schema stage like FI subject performed.