The Magic Circle

The Northern California and Nevada Section of the American Association of Physics Teachers held its Spring Conference at Lake Tahoe Community College Saturday, April 21. Beautiful campus; beautiful day.

In the back of the meeting room, officers had prepared a poster of "Mister Equipment" (Mystery Equipment). There were photos of strange-looking apparatus. New teachers often inherit apparatus whose purpose is not intuitively obvious. At meetings, there is a healthy mix of new teachers and veterans. The vets can often identify and describe the mystery apparatus. I hadn't seen the lonely poster until the end of the meeting, when an officer asked if any of the apparatus were—as yet—unclarified.

Even when I made a hasty scan of the assorted oddities, I passed an item at the top of the poster. It was titled "The Magic Circle." It wasn't really a piece of apparatus. It was a simple graphic image.

"That's mine!" I exclaimed. "The Magic Circle is my 'invention.'"

The Magic Circle is a kind of graphic mnemonic I designed in 1988 because Susie Klippi was just not getting graphical kinematics. She wanted to; she was trying. But it wasn't happening, and I wanted to help her. I did the best I could as a still very green one-year "veteran."

The context is the challenge of being able to translate between position and velocity graphs during uniform accelerated motion. The velocity graphs have diagonals, and the position graphs have curves. Physics learners have trouble with these things because it's really calculus that's going on here. The slope of the position graph indicates the value of the velocity graph, and all that jazz.

I spent too much time on kinematics back in those days, and gave it too much weight in the scheme of things. Still, it was my own "No Child Left Behind" that compelled my to design a mnemonic that would help struggling students get past this hurdle.

At the end of graphical kinematics units in subsequent years, I would reveal The Magic Circle. At that point, students had been slogging through the exercises, some with more joy than others. When I show the Magic Circle now, students' minds are ready for it, and a wave of happiness \ briefly sweeps through the classroom. But students soon complain: "Why didn't you show us this 'trick' in the first place?" Rather than engage them in the finer points of pedagogical philosophy, I simply tell them to add this to the growing list of ways I've managed to disappoint them.

I eventually prepared a manuscript for publication in The Physics Teacher, but it was rejected by then-editor, Cliff Schwartz. I still show the trick to my second-year AP students, where graphical kinematics still holds some importance. But they are less in need of the mnemonic. All in all, The Magic Circle © 1988 by Dean Baird has faded in significance for me.

But there it was on Saturday. I gave a quick, impromptu lesson in the oddly-configured meeting room. It was not my best presentation, and I don't think I sold The Magic Circle to any of the conferees still present at the end of the day.

Here's the unpublished manuscript if you're interested.

The Magic Circle: A Training Wheel for Graphical Kinematics