When designing mathematical educational tasks, a designer tries to anticipate how students will react. Students, however, may look at a task in a way that differs much from how teachers or instructional designers look at it. In relation to this, one speaks of the difference between the actor’s and the observer’s point of view. In this article, we elaborate on this distinction, outlining a theoretical and empirical perspective on the differences between these two points of view. To do so, we use the data from a small scale teaching experiment with a geometry applet that we had designed.