To show the derivative of sinx based on simple geometry

We always face the struggle as year 10 Maths teachers in trying engage pupils in deep learning of the derivative of sinx. If we try to show the derivative of sinx by first principles, we'll need to invoke L'hospital's rule for sinx/x which can be shown via the squeeze theorem of sector area between 2 triangles. Unfortunately, pupils may not have the prior knowledge for this to make meaningful connections. I've thus attempted to show the derivative of sinx from another perspective based on simple geometry via the following videos.

After going through the process of creating the videos to show and explain the derivative of sinx, I realized how powerful a learning process this can be if students were to go through similar process in collaboratively explicating the gaps of reasoning in the Maths Java applets. In a way, by representing the thinking behind the creation of these Java applets, students will be thinking more deeply to make meaning of new concepts to be learnt based on

1. the understanding that derivative of a continuous function at any point x is the gradient of the tangent line at that point x which is given by the gradient of the secant line very near the point x
2. their prior knowledge of simple geometry

The process of students creating these mathematical reasoning videos (should have some drafts) can also be leveraged on to provide ongoing and immediate feedback to help bridge their understanding and refine teachers' instruction.















Here's another similar learning design idea.