Site swap notation

I chose this term to follow the path laid down in the summer term - to put up a correctly labelled 3 site swap and then ask if the students understood the diagram. I did not fully explain the diagram.

Then I demonstrated a 3, laid out a 51 and demonstrated that, and wrapped with a 342 swap diagram to show that the equations made testable predictions. This was then tied to two themes:

  • Math in the abstract is not comprehensible for many learners. Math is comprehensible when there is a concrete framework on which to hang the abstract ideas and concepts. At least especially so for early learners. 
  • Math makes predictions that can be tested, shows us possibilities. And the advanced math of cosmology may not make sense to most of us, but the math provides the means for discovering new physics and new understandings of the universe.  Just as site swap can make predictions that can be verified, so too the complex mathematics underneath general relativity and quantum mechanics.
Johsper, Yostrick

Very high throws from Trevalouva

Trevalouva, one ball too high to see

Melsina and Sunet

Phillip Phillip and Mayleen




Phillip. John on the left.

Mayleen Araisang, Austin




3 with 342 swap midstream
 I setup the site swap laboratory without obfuscation other than not spelling out the R and L abbreviations. Labeling was straightforward and direct. The balls were hidden. I used the usual approach of completing the site diagram for a 33333... site swap. Then I asked students if they understood, including individual call outs. Many responded by nodding their heads in agreement. I would then double check with a re-ask of the question - so you do understand this? A couple students were brave enough to venture that they were either confused or not sure they understood. I then suggested that no one actually understood what I had written, and this was all right. What was on the board could not possible make meaningful sense.

I used this as a science methods teachable moment to address the teacher education program students. Students, at least here, will often respond to "Do you understand?" with "Yes" regardless of whether they understand or not. Asking specific questions of specific students may be a useful alternative elsewhere to probe for actual understanding, but here that would risk embarrassing the student. Education in the home here does not involve checks for understanding but rather the expectation of see and then flawlessly reproduce a specific skill. Demonstrate and then faithfully copy.

I then showed what the diagram meant using a red, green, and blue ball. 

After I juggled 3 I laid out 51 as a theoretical possibility, and then I juggled that. Predicted possible and confirmed. Finally I  returned to the 3 diagram to show the 342 swap. This too I confirmed. I mentioned a 441 as being predicted to work and tested by others, but that I could not myself execute the 441. I told the students that the math in videos we were seeing was also beyond me, but that I could accept the results in the same way I accept that a 441 exists.

The following are  set of shots to try to capture Sunet multiplexing four balls

Three up

Two aloft, two on multi

Three high

Pair aloft

We wrapped with the class attempting to juggle a 3 or 51 pattern. What might surprise a visitor to the class is that many of the students learn to juggle from the get go there in class, with little more instruction than the demonstration. Over the years I have come to understand that the students watch and then, for the most part, faithfully replicate my action. Some students do bring precursor skills, but some simply learn from scratch. And rather than the usual one ball, two ball, three ball recommended learning sequence, some simply start from three and mimic my motions successfully. The first attempt might be a flash (a single three throw set), but by period end they have gone beyond the flash.


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