Inspired by this post, I wanted to share a little bit about how I introduce circles. When I pose the questions that follow, I usually use PollEverywhere to survey the entire class at the same time. I find this encourages table discussion. Keep in mind, when I show the students these equations, students HAVE seen the Pythagorean theorem, but other than that, this is the first time they have seen anything resembling the equation for a circle. The answer is not at all immediately clear and many students take a "guess and check" approach to finding the solution
About me and my school
When I started teaching AP Computer Science A in 2015, it was easy to approach a subject that was new to me in a way unlike how I had been teaching mathematics. Initially, I allowed students to retake their exams simply because I knew I lacked the experience to write fair exams on my own first try. I kept the policy because it seemed almost natural, the course itself seemed conducive to a policy that allowed students to resubmit code until it worked. At that time, I could not see how the same policy could carry over to my math classroom and a discipline that is notorious as a harsh exam environment. Finally, in 2017, having grown frustrated with feeling that I was perpetuating a culture that rewarded exam performance over learning, (mind the distinction: it’s one thing to take an exam for the sake of one’s learning, I take issue when students perceive they are learning for the sake of their exams) I decided I could try what I was doing in C.S.
A project that is successful in that regard must embody at least three principles:
- It must require student choice. More is better.
- It must resemble a real life application.
- It must be an end in itself. To superimpose exam questions on the project content is to dilute the meaning of the project itself and redirect the students' attention back to the very falsehood we meant to avoid in the first place: an exam is the ultimate end and indicator of success.
This year, I've come up with the "Geometric Dwelling" project.
Over the years I've made dozens upon dozens of geometry diagrams. Most were made for one-time-use. Eventually, I got the bright idea to simply post them online to optimize the utility of each one. All of these diagrams are free to use or revise without restriction.