An APOS analysis of student’s understanding of quadratic function graph

Abstract

Abstract The purpose of this study is to describe students’ understanding of the graph of quadratic functions. In this study, APOS theory (Action, Process, Object and Schema) used as a theoretical framework. The subjects of this study were two students at a college of education, one male and one female who had equal mathematics abilities. Data collection techniques were written tests and semi-structured interviews. The data generated were analyzed through the stages of data reduction, data presentation and conclusion. The results showed that at action of male subjects drawing graphs directly in the Cartesian plane and uses the general form of quadratic functions while female subject makes a table of points to make graphs and used the general form. At process, male subject enters several numbers to the equation then connects the points but female determines the intersection points with the coordinate axis, looks for other points, looks at the direction of the graph then draws the graph. At object, male subjects make a graph by shifting the top of the other graph, while female determine the function formula by adding constants from the original graph. In this study the two subjects were not yet at the stage of the scheme.