Abstract
This research aims to investigate how to support the development of high school students’ covariational reasoning of sine and cosine functions. To achieve this goal, we conducted classroom design research where we experimented with a hypothetical learning trajectory aimed at fostering students’ continuous smooth covariational reasoning of sine and cosine functions. The Freddy’s actual learning trajectory confirms our general learning hypotheses, indicating that the visualization and manipulation of the simulation of a Ferris wheel’s movement in GeoGebra applets incorporating measuring instruments foster the development of covariational reasoning of sine and cosine functions. The results of this research are consistent with previous studies that have found that the use of interactive activities in dynamic digital environments, simulating a Ferris wheel, promotes the development of students’ covariational reasoning regarding sinusoidal functions at a smooth continuous level. Integrating covariational reasoning with hypothetical learning trajectories offers promising implications for educational practices which are discussed at the end.