A combined application of APOS and OSA to explore undergraduate students’ understanding of polar coordinates

ABSTRACT

The aim of this study is to analyse undergraduate students’ understanding of polar coordinates based on two theories, Action, Process, Object and Schema (APOS) and Onto-Semiotic Approach (OSA). These two theories complement each other and each of them separately has been used in many research to explore students’ performance of mathematical concepts. However, the combined use of APOS and OSA in educational research in mathematics is scarce. Seven tasks of polar coordinates were designed to characterize the schema development of thirty-four undergraduate students in terms of intra, inter and trans. Results showed that most of the students had difficulties in doing the practical tasks and developing the mental constructions needed to solve polar coordinates’ tasks, particularly those mental constructions that have to be made to sketch polar curves and to plot the point $\left(r,\theta \right)$ in the plane where $r$ and $\theta$ were negative. Also, a lack of trigonometric knowledge caused the students to be unsuccessful in solving polar coordinate tasks. The complementary use of APOS and OSA helped us to have a better insight regarding students’ understanding of the concept of polar coordinates.

KEYWORDS:

• Polar coordinates
• APOS theory
• OSA theory
• schema development
• students’ understanding

ORCID

Vahid Borji http://orcid.org/0000-0002-3020-3648