Advanced-Level Students’ Understanding of Exponential Equations:

Abstract

This paper reports on a study which explored high school students’ conceptual understanding of the techniques of exponential functions. Thirty-one advanced-level students participated in the study. The study used APOS (Action-Process-Object-Schema) theory, a constructivist theory framework, to investigate participants’ conceptual understanding of exponential functions. Activity sheets constructed with tasks based on exponential equations were administered to the participants. The written responses were used to identify participants’ mental constructions of these concepts. Furthermore, interviews were carried out to clarify participants’ written responses. The written responses and interview discussions pointed out that participants exhibited procedural tendencies in exponential functions. Most of the participants could not solve exponential equations, especially the radioactive‑decay functions. In addition, many participants did not have appropriate mental constructions at the process, object and schema levels, since most of them could not coordinate processes and encapsulate them into an object. This paper raises some important implications for mathematics education and further provides applications of genetic decomposition design and modification.