Site swap notation

This last week with a focus this term on mathematical models and the mathematical universe began on Monday with the Nova special Mathematics Explains The Universe and then continued on Wednesday with a counterpoint to the mathematical universe. 


Although at 8:00 I opened with a video on the map of mathematics, by 11:00 I had stumbled into amore appropriate video, Why do people hate mathematics?

The video provided a better foundation for the introduction to the laboratory.

  • Is everything mathematical?
  • When we say this, what do we mean by "mathematical"?
  • What mathematical models are possible?
  • What does it mean to "understand" a system of mathematics?
  • Can an abstract math class teach math?
  • How does one teach mathematics?

I then did as I have done in the past. With nothing visible in the lab, this term hiding the box itself in a back cabinet, I taught site swap diagrams as an abstract pattern. And again students identified the pattern and correctly answered what the next element would be. They learned site swap mathematics as a completely abstract symbolic notation system. That provides the opening to note that from the perspective of the non-science major students in the course being able to answer site swap pattern questions is just as useful to them as being able to factor a quadratic equation. And equally useless. Both are useless skills with no application in their lives. Why teach either one?

And yet the whole course was built around mathematical models of the physical world: math can be useful, but only in specific fields. Math explains the physical world around us. 

When polled, only two students said they liked math and no student felt that they were good at math. Twelve to fourteen years of math classes have convinced the students that they cannot do math, will never be good in math, and the vast majority now dislike the subject. Way to go math teachers. Turning off generation after generation. Because little kids are excited when they learn counting and adding. Teachers make sure they burn that excitement out of them. And how could it be any different given the math stack that as taught? And, more importantly, tested. 

But ultimately this lab is about closing the term on a fun note. And so I show what the notation means and then pull out the juggling balls.

Athina Viola two ball one hand


Athina was quickly able to move to three balls, Jarret working with two

Serjet and Ashlen

Mersayes

Mersayes

Serjean and Ashlen, Sharla at the table

Jenna reassembles the Plush Crush from Scentco

Melina also moved quickly from two to three balls using the third ball swap in technique

Fiji working on putting a Plush Crush back together


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