An APOS analysis of preservice mathematics teachers’ understanding of limits of trigonometric functions

This paper reports on an APOS analysis of first year undergraduate pre-service mathematics student teachers’ understanding of the Sine Limit Identity(SLI), , and its application in computing limits of trigonometric functions. It was a case study of sixty-eight pre-service mathematics teachers. The student teachers explored various ways of computing . They also learnt how to apply the SLI in evaluating limits of other trigonometric functions. In order to determine the participants’ level of understanding, the researchers analysed the participants’ responses to given test items, against a constructed genetic decomposition. The results of the study revealed that although more than half of the students could evaluate the sine limit, three quarters of them made some procedural, conceptual and extrapolation errors when applying the SLI in computing limits of related trigonometric functions. Based on the findings, the researchers recommended inclusion of visual computer applications like Geogebra as teaching tools for teaching limits of trigonometric functions. Such applications allow students to visualise relationships among variables. The researchers also recommended further research on teaching strategies that aim at improving the teaching of limits of trigonometric functions.