Exploring the limits of trigonometric functions: results and reflections from a pilot study

Abstract

In this paper, we report a pilot study on engaging a group of undergraduate students to explore the limits of sin(x)/x and tan(x)/x as x approaches to 0, with the use of non-graphic scientific calculators. By comparing the results in the pretest and the post-test, we found that the students had improvements in the tested items, which involved the basic concepts of limits, but had room for further improvement in those that required them to explain their answers. An analysis of the students’ performances in the tests by using the APOS (i.e. action-process-object-schema) theory framework is reported. Reflections and suggestions on how to teach the topic more effectively are provided.

Keywords:

• limits of trigonometric functions
• exploratory approach
• APOS theory

Acknowledgements

This paper was supported by the HKIEd's Teaching Development Grants. We are very grateful to the referees for providing valuable comments and suggestions for revision of the original version of this paper.