Find the center and radius of a circle. If you remember the Pythagorean Theorem, you’re almost there. Circles and right triangles go hand-in-hand when you’re graphing circles. Ultimately, grpaphing circles involves just a few transformations, starting from the standard equation of a circle.
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I thought I would watch my first pencast on a topic that I was pretty sure I already understood with the hope that I could focus on critiquing the format, look, etc along with making the evaluations asked for. So I chose the "Find the Center and Radius of a Circle" pencast.
First of all, I have never seen anything like a pencast. I love it! The situation is very much like sitting in a classroom without the possibility of the teacher standing in front of what he/she is writing so the students cannot see it (not that you Doc does this, but it has been a problem for me before.) As a viewer, you can see what is being written and hear the explanation at the same time, feeding both visual and audible senses. I would definitely think that this combination allows for easier learning of the material.
Second, my pencast was automatically set up to see the faint outline of all the writing before it was "written." Since I had an idea of what was going to be said beforehand it was interesting to be able to see a preview the direction the pencast was going, however during the video I often found myself looking ahead and missing some of the spoken teaching because my attention was drawn away. It was not until I was mostly through the pencast that I realized it was an option that you could change. My recommendation here would be to leave the option to change, but default to default to beginning with a blank screen rather than the faint outline.
As far as the pencast, itself, the clarity was great and I had never thought/learned about the Pythagorean theorem in that manner (at least not that I can remember), so it was interesting to find myself actually learning from a pencast that I thought would be very much beneath my level of mathematical education.
Overall, the setup of the site and the idea development in this pencast was very well done.
Thank you!
The whole presentation was simple and straightforward, which made it easy to watch. The connections made between the equation of a circle and the standard definition of a circle and even the pythagorean theorem was interesting and easily seen. One thing that was not mentioned that might be an additional insight would be how similar the standard definition is to the distance equation. Basically this is the same as pythagorean theorem but it explains why there are negative signs within the squares. It seems a little obvious, but I had never directly thought that about how the radius is a constant in the equation because any point around the circle is equidistant from the center.