tandfonline.com – Lifting the understanding of trigonometric limits from procedural towards conceptual

The purpose of this paper is to follow the reasoning of high school students when asked to explain the standard trigonometric limit $\underset{\theta \to 0}{lim}\frac{\sin \theta }{\theta }=1$. An observational study was conducted in four different phases in order to investigate if visualization, by means of an interactive technology environment (Geogebra), can contribute in lifting high school students’ understanding from a mere procedural understanding to a combination of conceptual and procedural understanding. The obtained results confirm that the students were able to show a conceptual understanding only after using the digital interactive tool. Through comparing, exploring and self-explaining combined with the use of the interactive tool, the students managed to link different concepts together. The students were able to see and interpret the reason making the angle $\theta$ and $\sin \theta$ relate under certain conditions, thus leading to the standard trigonometric limit $\underset{\theta \to 0}{lim}\frac{\sin \theta }{\theta }=1$.