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.

Google Earth Postings

It's the first time I've tried to geo-tag Milford Sound in Google Earth. Open the Milford Sound.kmz file under Google Earth Postings menu (you need Google Earth application which is another of Google great freeware).

This approach offers potential to be applied in project based learning for Environmental Science, History and Social Studies, Ecology, English Language and English Literature. See example here. The information and media representations in the geo-tag sort of get connected in a meaningful way to the actual 3D visualization of the actual location in Google Earth. In this way, the situatedness of the learning at the various locations during the learning trail or overseas learning journey can be preserved.

I would imagine that if there are more people geo-tagging Google Earth locations meaningfully, then we can be surfing a 3D geo-web. Other than searching for locations, maybe we should be able to search for geo-spatial content as well? Or maybe web 2.0 kind of 3D geo-web applications?

VoiceThread

VoiceThread is a platform for pupils to discuss and comment on slides. Comment and discussion threads can be in the form of voice, text and doodling. These threads are directed at the specific slide of discussion, not achievable by other asynchronous discussion platforms. You can get a free account and try commenting on my slides on derivative of sin(x) here.

Learning Strategies Blogging

Reading the learning strategies carnival post by Steve caused me to think about how by consciously blogging about their learning process and strategies in problem/project based learning, pupils can develop the meta-cognitive skills to self-regulate and self-direct their learning.