
06622171
j
2016e.00168
Mart\'{\i}nezPlanell, Rafael
Cruz Delgado, Angel
The unit circle approach to the construction of the sine and cosine functions and their inverses: an application of APOS theory.
J. Math. Behav. 43, 111133 (2016).
2016
Elsevier, New York, NY
EN
C30
G60
APOS
trigonometry
unit circle
inverse trigonometric functions
genetic decomposition
doi:10.1016/j.jmathb.2016.06.002
Summary: We use ActionProcessObjectSchema (APOS) Theory to analyze the mental constructions made by students in developing a unit circle approach to the sine, cosine, and their corresponding inverse trigonometric functions. Student understanding of the inverse trigonometric functions has not received much attention in the mathematics education research literature. We conjectured a small number of mental constructions, (genetic decomposition) which seem to play a key role in student understanding of these functions. To test and refine the conjecture we held semistructured interviews with eleven students who had just completed a traditional college trigonometry course. A detailed analysis of the interviews shows that the conjecture is useful in describing student behavior in problem solving situations. Results suggest that students having a process conception of the conjectured mental constructions can perform better in problem solving activities. We report on some observed student mental constructions which were unexpected and can help improve our genetic decomposition.