Site swap notation wraps up physical science term

Laboratory fifteen in physical science has the intent of wrapping up the term, expanding the students conception of what constitutes a mathematical model of a physical system, and having some fun. Daniel Kahneman in Thinking, Fast and Slow noted that the remembering mind rates experiences using a peak-end rule. We remember the best moment and the final moments of an experience when we reflect back on that experience. Although I had not known this particular fact when I designed laboratory 15 five years ago, I had always shared George M. Cohan's belief that one should "always leave them laughing when you say goodbye. I want the students to have positive affective domain responses to science, and ensuring the end experience is fun has an impact on those perceptions.

In the past I framed laboratory fifteen as a exposure to an alternative mathematical model that exists outside of the traditional mathematics "stack" of arithmetic, algebra, geometry, trigonometry, calculus, differential equations, and on up into advanced mathematics courses. I put the stack on the board and then introduced site swap notation.

Summer 2015 I opted to start by simply putting an abstract notation on the board and speaking about the notation purely abstractly. I chose to do this again fall 2015. I make no reference to juggling or balls. The diagram above gives one a flavour of the language I use. The schedule this fall took out laboratory 14, so 13 preceded 15 directly. Thus I had just been talking about the spin of electrons in orbitals. So I led with that, suggesting that three electrons could occupy two spins states only if one was kicked up. Well this led to a system that so closely mimicked juggling, that at one point I said "ball" instead of "electron." The system was not so abstract and was much more comprehensible than I originally intended. Still, a presentation is like that, sometimes running down a slightly different channel than one might have originally intended. These are not rehearsed presentations, there is no teleprompter.

This led very naturally into showing the patterns via juggling.

After the lecture I invited the students to try to master a 3. Some tackled the 51. A few attempted a 342, Heroleen and Trinia were able to juggle from the get go.



Rebecca Martin




Trinia and Nancy attempting to pass a three ball cascade from one person to the other

Non-participation in this lab is so rare that when it occurred this term I chose to capture it. I also, for the first time, chose to count participation as the lab report. Non-participation was not a zero, just a blank. 

Karmerihna demonstrates skill with three

Bee Heartly trying to get three under control



Darlene, high initial throw

Cynthia improves

Darleen, Cynthia


Bee Heartly drops one

Liana and Samantha



Andy prepares himself

Darlene showing control of the balls

Karmerihna displays her quickly developing skills

Bee Heartly, much improved control



Bee Heartly works on a 51 pattern

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