After the AP Calculus Exam, I gave my students a project for the remainder of the year. We discussed the parametric functions for a cycloid, the traced path of a point on a rolling circle. The students' task was to create a modified cycloid by having a circle roll along a path of their choosing. The students used Desmos to animate their graph and Screencast-O-Matic to record their animation. The assignment was as much an assignment on parametric functions as it is an assignment on baby programming on Desmos. Below are their creations.
Desmos is a fantastic graphing calculator, but it has some limitations when graphing physical situations, because it is not designed as a physics simulator. As the student was perfecting the epicycloid circle-in-a-circle graph, the inner circle was not rotating fast enough, so that it was "slipping" as it moved along the outer circle. This was a very difficult error to catch in a graphing calculator. Perhaps this is an accepted limitation of the medium.
On Friday, not fully knowing fully what their roles would be, math club took the bold step of electing our first Math Club Co-Presidents. Of eight students present at the meeting, six expressed an interest in being president. After the votes were counted (two votes apiece) it was nice to see that everyone who ran had received at least one vote from someone other than themselves. We selected our two co-presidents, juniors Sam and Kathy, with four votes each. I was glad to see that the students selected one boy and one girl and one international student (Sam) and one American-born student (Kathy). This is fairly representative of our group as a whole.
This election was remarkable for a number of reasons. I've worried that students come to math club just to humor me. The fact that six students have a desire to lead our club gives me confidence that students actually enjoy the club I've set up. For a while, I've wanted to make our meetings more student-run and student-directed. Having specific leaders – who volunteered for that role – to turn to lets me shift a lot of the responsibility for that onto them. As his first official duty, I had Sam lead the review of the day's math problems. He did a great job of facilitating a discussion of students' answers and directing questions. Later, Kathy proposed the idea of having students give small presentations on a topic of their own choosing. She already has an idea about something called Russian Peasant Math that she'll present this fall. Math club is starting to feel like an activity the students enjoy and are choosing for themselves.
Some colleagues and I recently enrolled in Coursera's free Teaching Character and Creating Positive Classrooms online course. The course is taught by KIPP's Dave Levin and supplemented by insight from numerous education and psychology experts. This is the first of my four week-by-week synopses.
Week 1: Students have aspirations but often have trouble following through to achieve their goals. Teachers can help students by engaging them in intentional dialogue about setting and reaching goals. The dialogue would help students articulate the specific goal and any potential obstacles to achieving that goal. For each obstacle, students should make a specific plan of how to overcome it. At the end of the dialogue, students may say something like,
"I would like to achieve ... goal. Along the way, I may face ... obstacles. I know that I may get sidetracked from my goal. When ... obstacle arises, I will do ... to overcome the obstacle."
My Classroom: I see this as being especially helpful with my CP freshman students. Perhaps I could include a 10 minute individual writing exercise where students go through the thought process above. Exams are around the corner and they could use some motivation to study...
I started this blog to share my transformation from math nerd to math nerd who loves to share math with young people. I teach high school in Philadelphia, Pennsylvania. Your comments are always welcome.