What CA Means to Me
Selim
Mathematics Teacher
Cambridge, MA
Describe a time a CA student has inspired you.
In our Precalculus: Analysis course we study conic sections, whose origins go back to the ancient Greek mathematician Apollonius of Perga. The objects of inquiry (circles, ellipses, hyperbolas, and parabolas) are potentially quite abstract, and I recall being puzzled by them in high school myself.
In 2004, Max Brooke '07, then a freshman in my Geometry class, expressed an interest in creating a dynamic model of the solar system for his yearly project, using the visualization software Geometer's Sketchpad. It dawned on me that this could bring to life the conic sections, which naturally exist within the solar system: planets move around the sun in elliptical orbits, moons circle the planets, interstellar comets follow hyperbolic and parabolic paths. When Max created a stunning mini model and showed me the feasibility of the task, I decided to make this a term project for my upperclassmen in the Analysis course.
How did that work out?
In 2007, Carly Anderson ’08 and group of pioneering students used a 3D interface in Geometer's Sketchpad to create a stunning, dynamic 3D solar system with tiltable axes of rotations. This work was so significant that at a National Council of Teachers of Mathematics meeting, the creator of Geometer's Sketchpad demonstrated Carly's work to a large crowd of stunned math teachers. CA students’ innovation, coupled with the flexibility of CA’s curricula, allows such amazing progression of works.
Why do you find hands-on projects an important component of teaching math?
I strongly believe that time-limited tests, for the most part, can never hope to emulate real-life situations or invoke a state of mind that can solve truly important and challenging problems that matter. Well-conceived, hands-on projects can represent real-world challenges more thoroughly, and thus encourage ingenuity, creativity, and collaboration.
Some of your students’ math projects incorporate art. How is this interdisciplinary approach helpful in your teaching?
I am a great believer that one should always investigate a new field by building bridges from areas of strength. When a student who is already interested and strong in, say, the arts, approaches geometry from this area of strength—by studying the works of masters who merged the two fields, such as Escher or Vasarely, for example—he or she will find it easier to relate to, enjoy, and grow in mathematics.
What prompted you to start the Mathematical Puzzle and Research Society—and what’s behind your fascination with the Rubik’s Cube?
The Mathematical Puzzle and Research Society is based on my deep belief that hands-on, recreational logic puzzles are the best ways to awaken mathematical curiosity and talent. Among puzzles, the Rubik’s Cube is absolute royalty! I have been fascinated with it since it came out in the 1980s. Over the years it became an obsession of sorts as I tried and failed to master it. When I was teaching in Turkey, where I grew up, I located a Rubik’s master in Istanbul and taught my students his techniques, but at that point I did not fully understand them.
When did you finally master the Rubik’s Cube?
Here at CA, during a bout with the flu, I decided to visit my old heartache, the Rubik’s Cube, with an incredible resolve to master its secrets. After days of deep reflection and experimentation, the mist started to lift and for the first time I was able to comprehend how to solve the last face of the Cube. I discovered a simple principle I call “palindromic dualism,” which basically involves fixing a piece, securing it by putting another piece (its dual) in its place, and reversing the exact steps taken to undo all the damage done by the initial fix. I was able to solve the entire last face with this single idea. Needless to say, I was in intellectual heaven.
Why did you start the Rubik’s Olympiad?
The Rubik’s campaign I launched at CA last year was a result of my desire to share with others the knowledge that gave me great bliss over the years. I started the Rubik’s Olympiad because I knew we had some true masters and speed demons at CA.
