The role of models for transferring understanding
by Rob Schoen (posted 5/20/11)

I have a mirascope on my desk in my office. Based on the interactions I see between office visitors and the mirascope, it is the single most intriguing object in my office (and yes, this does check my ego). I put it on my desk because of a conversation I overheard one day while sitting in a coffee shop. There were two male university students next to me, and they were highly intrigued by a question that one of them had posed. He asked "Why does our brain confulse left and right when we see a reflection in a mirror, but we don't get confused with the up and down direction in the reflections?" These two people generated several possible explanations (I suppose I might call them hypotheses), and all of their reasons were based on incoherent bits of knowledge about psychology and neuroscience rather than notions about optics or even a passing reference to a physical model. They eventually encountered their reflections in the spoons on their table, dared to ask each other how their reflection could be upside down, and thus they were completely baffled (ending the conversation with a shrug and apparent feeling of helplessness). I had a laptop with GeoGebra on my table. I was dying to introduce them to a model that might help them tie these incoherent ideas together, but I chose to finish my work so that I could return home to play with my one year old daughter. If I had known of this article, I would have shown it to the two university students and let them disentangle their ideas. Lingguo Bu has very elegantly taken these ideas to the next level with a beautiful GeoGebra-based model of the basic optics involved in the mirascope, showing a complex integration of basic ideas that result in a fascinating phenomenon. Does the author or my fellow readers know of other GeoGebra models of basic ideas and related ideas that may be even more complex? I would love to put them together into a coherent unit related to optics and geometry.