What makes it great?
My wife and I attend many musical events each year. One series we like is entitled, "What Makes It Great." These lecture/concerts are held in the Merkin Concert Hall of the Kaufman Music Center in Manhattan, New York City. Each of the four events is two-part. For the first hour or so Rob Kapilow, a wonderfully energetic musicologist, gives a lecture demonstration with fellow musicians, illustrating passages and variations on a musical piece or conductor’s works, e.g., Beethoven’s Appassionata Piano Sonata or the works of Harold Arlen. In the second portion of the presentation the musical group performs, either the entire piece under study or selections from the composer's repertoire.
Our next event in the What Makes It Great series is The Music of Duke Ellington – “If it ain’t got that swing it don’t mean a thing.” We are really looking forward to that event early in April, much more than to our income tax filing deadline!
Last night Rob and the wonderful musicians of the Harlem String Quartet took the audience deep into the nuances, the construction, and the beauty of Antonín Dvořák’s Piano Quintet in A Major. We went from soup to nuts, from opening bars to ending crescendo with attention to detail at every step, even singing along to remember the melodies and rhythms. We participated! We were shown what makes this music great, we experienced the sounds in snippets and in sweeping measures of intricacy and ecstasy. It was a wonderful evening and we were privileged to be informed, entertained, lifted, and surrounded by beautiful music.
On the drive home (about an hour to Cornwall NY from New York City) I got to thinking about what the phrase, “What makes it great,” means in the context of teaching mathematics, in particular for our project SIMIODE in which we encourage colleagues to use modeling in the teaching of differential equations – not exactly a lyrical phrase, but music to our ears in a different sense.
One of the things about modeling is that it is challenging, both technically and intellectually, as was the music we heard last night. In modeling you could come away with a sense of the “outing.” Indeed, you could come away humming the theme, at least understanding the theme. Most importantly, you had motor/mental memory of the event, of the experience and you knew of failure and success and you could sense when it was happening again in other contexts; in the case of modeling in differential equations, you could see it coming when confronted with a vague or unstructured situation like it again; and you did not panic this time. You kind of knew what to expect and you ratcheted up your game. It is not just another regurgitation of a technique, but rather it is an engagement with a process, a meeting the challenge moment. While it is at times painful, a racking of the brain sort of pain, it is oh so rewarding to go through the process and produce something, perhaps not the greatest or best (Is there such a thing as best?) model, and then examine it and question it even more, perhaps sharing with others for their scrutiny and reaction.
For those of us who use modeling in our teaching we are blessed when we see our students years later and the relate classroom experiences with specifics on certain modeling activities to us. They recall the struggle, the flashes of inspiration, and the momentary success sometimes followed by the dashing to bits of the theory, because they forgot the obvious case, they ignored gravity, or they failed to satisfy a physical or initial condition. The key is they remember what made it great, namely the tension, the energy employed, the conflict, the counter melodies, and the sense of accomplishment that they did it; they built the model.
The experiences I can share with students as they build models makes the moments in class (and out of class) great for me and I am forever grateful for the company of my students on the journey. These mutually shared experiences are what makes teaching great for me. Thank you students. Thank you Dvořák!