Site swap mathematics

Site swap mathematics is a chance to expand the concept of what constitutes a mathematical model. Site swap mathematics is not something taught in the usual stack of mathematics, as if there is only one path and that path is from addition to calculus. While one might argue that site swap mathematics has no useful application, neither do quadratic equations for the elementary school pre-teacher program majors or for my agriculture and natural resources program majors. Neither are going to have to factor a quadratic equation to get through their working day. Site swap is no more useless than most of the other math they have been exposed to after eighth grade. 


The board starts off as seen above. Without any further background I ask the students what letter comes next (filled in above already) or what color comes next. The use of red, green, and blue is intentional as this may bring up memories of the primary colors of light, acting as a distractor.



Continuing to work purely abstractly I cover the number of hops until a color repeats. I also note that the color and letter combinations also repeat in the same number of alternate hops. That can be seen in the above diagram. Above can be a seen a three site hop above the colors for red to red, below is a three site red-R to red-R. I do not explain what R and L mean, and to date no student has ever asked.


After questioning students and asking them to make predictions, I explain that they could now pass a quiz or test on this material, I could document the learning, put my assessment in the assessment system, and everyone would be happy that learning had been measured and documented. And yet nothing is understood. I then make the jump to algebra, which can be seen above. Noting that this is exactly how mathematics education works. A completely abstract system taught abstractly that leaves students confused, disliking mathematics, and possessing no useful information. Students finish mathematics courses with no clue as to what use the math will be in their life - which is probably none for most of my students. They are not in fields where they will ever see a quadratic equation let alone have to solve one. Well, not until their children are in an algebra class. A multi-hundred year scam. 

Yet math has meaning. I show them the geometric (algebra blocks) meaning to x² + 8x + 15. I ask them about how to factor and students almost invariably cite the FOIL system of first, outer, inner, last. I note that this works only for (x+a)(x+b). None of the students have any clue that it breaks down for (x+a+b)(a+c+d). This term I introduced the breadfruit distribution system from brother who have breadfruit to brothers who do not have. This system works no matter how many terms are present. 

After much berating of the field of mathematics education, I show the students what the diagrams mean. Site swap mathematics is useless, but that feature of math hasn't stopped math teachers from inflicting math on generations of students. Curiously enough little preschool children love math and counting. School and teachers destroy this inherent curiosity and love by the time most students graduate high school. 

After the demonstration of site swaps, I ran a video on three ball site swaps I found that well covered them. I then covered the three ways to learn to juggle. The one ball, two balls, three balls progression is the first way. The second is for students who know how to juggle two ball in one hand, a local playtime activity called dapadap. The third is the visual motor motion memorization 


Ian works with two balls


Memichin, Stella, and Alathea


Siniann


Rindy

Mia, Pevirleen, Memichin, Stella


Alathea and Renae


Rindy, Emleen, Wayne, Siniann

Site swap makes mathematics fun again


Pevirleen practicing with two



Ruth, Darian, Aryoleen




Ivy, Alyssa


Alyssa


Leriangelica and Ivy


Malachi and Deshawn


Lonie "Ney"

Leriangelica, Deshawn, Ivy


Ivy



Later that evening




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