Site swap mathematics

What does it mean to understand a mathematical concept?
What constitutes mathematical literacy, knowing mathematics?
How can a student demonstrate that they possess quantitative reasoning skills?
What do we mean when we say that we have learned mathematics? Taught mathematics?
How should math be taught? As an abstract set of concepts? Taught in isolation, in a math class?
Or should math be taught only in context, in non-math classes? 
What constitutes mathematics versus "not mathematics" for a school curriculum? What math should be taught and why?
And why is the universe such there are mathematical patterns that describe the universe?


In this laboratory a system of abstract notation is taught without context. Just as symbols on a board. The notation is site swap notation mapped out linearly. Students usually quickly discern the pattern and are able to determine what should appear in subsequent sites. Once the class demonstrates mastery, then the illusion of understanding is taken away. Absent context, the mathematics has no meaning. The mathematics is no more useful than the quadratic formula - neither site swap nor the quadratic formula are ever again used by the non-major students in physical science. 

KC

Both sections followed the progression of teaching site swap without context.

Vandasia and Tayshaun engaged in an ever increasing distance ball exchange

Then the context is introduced: site swap mathematics is the mathematics of juggling. Useless? Of what use will factoring a quadratic ever be to non-majors in a general education science course? They are more likely to entertain children with their juggling skills than to ever solve a quadratic equation in their life. That there is a mathematical system underneath is a core theme to the course: the physical universe is mathematical. 

LizzyAnn working on dapadap


Leann practicing with two balls

Bennie works on reassembling the shatter ball

Tommylee proved adept at reassembling the shatter balls

Finolla and Lashanna


Lanve, could already dapadap, moved to juggling three balls on the first try by using the dapadap ball insertion approach. 

End of session board


Jay-brion


Kealoha


Kyle, two balls



Elvanie, dapadap


Lousaintra practicing with two balls



Lousaintra practicing with two balls


Meramy working on moving from a two ball dapadap to a three ball juggle


Elvanie watching Lousaintra attempt a two ball dapadap


Elvanie working on a three ball juggle


A playlist on simulation theory led off with the improvement in computer graphic technologies as exemplified by the Tron series on Friday. Simulation theory wrapped up the week. 

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