Site swap notation

The last physical science laboratory of the term seeks to bring home the meaninglessness of the manner in which mathematics in taught in schools at present. 

I start off my outlining the "math stack" from counting through arithmetic, algebra, and on up through calculus and beyond. I note that there are other fields of mathematics that do not make it into the stack, and yet they are no more useless to the average liberal arts major than knowing how to factor a quadratic equation. Because factoring quadratics is not a useful life skill. There are far fewer people on the planet getting paid to factor quadratic equations as a living than there are people who are paid to play video games for a living (check out the Asian competitive video game playing scene). 

Then I lay out the patterns seen on the board and ask the students to predict the next letter, colored circle, arrow, or number in the sequence. Today all of the students were successful in answering my questions. I even ran a 42 site swap into the top equation and showed how that changed the order of the colored circles. I then suggested to the class that they could take and pass a quiz on the sequences, I could assess their learning of the patterns, and then I could report to my administration that the students had mastered site swap mathematics. And everyone would be happy. Without anyone understanding anything about the system, what it is useful for, or whether they would ever need to use the system again in life. And that is exactly what we do in algebra class. Teach an abstract system of making marks on pieces of paper, quiz the students on making the right abstract marks, and then the students never need to make those marks again until their future child comes home from high school needing help on their algebra one homework. 

Sure, there are professions that do math, but none do "thirty problems, even numbers only" That is an Italian mathematicians competitive gambling game. No one who actually uses mathematics does so in the fashion in which mathematics is taught in schools. The way mathematics is taught in the schools is akin to teaching the fine art oil painting by having the students paint a white picket fence. There is no relationship there. Little wonder most students are happen to have completed their mathematics requirement and never see another equation again.

I teach one equation a week, an equation that arises from data gathered in class, an equation that models an actual concrete, physical system. One equation. Real data. Real meaning. 

With that introduction, I then proceed to produce the concrete, tangibles of site swap mathematics. Juggling. I demonstrated a 3, a 51, and the 42 swap.

Jessie May tackled juggling with the Plush Crush balls from Scentco

Jessie May knows the 3 start

She was shocked when the Plush Crush ball burst apart on hitting the floor. I did omit mentioning this possibility. There is a nice video on how to reassemble the ball.

Jessie May

Jessie May

Renay

Renay

Renay juggling a 3

Richard working on a 3

Renay

Renay

Darla Rose 

Renay with the board in the background

Adelina getting ready to try to throw a 3

Left board at 10:30

I quizzed the students prior to showing them the juggling gear and all answered each question I asked correctly. Learning outcome achieved. Any yet the students have no comprehension of the meaningfulness, if any, of the system I have taught them. It is an abstract system without any basis in lived experience. Like algebra. I think you can teach algebra, but in some vastly different way. Something less like "do problems one to thirty even numbers only." Perhaps more akin to one equation a week - the approach in physical science. Maybe one a day. Based in something concrete, physical, if possible. And include looking at symmetry, beauty, design, art. Think Desmos art. 

At 11:00 I started blank slate. I asked the class what is the first thing taught to the youngest students in math class and built from there. 

Bethlyanne with the Plush Crush balls.

The Plush Crush balls would come apart and Saya would put the ball back together. 

Leipolanda watches Blossom juggle.

I have redeveloped my teaching of juggling. I now suggest three paths to learning. Although I demonstrate a 3, I suggest to those who play softball that they try to learn a 51 first. When I was living in Africa I taught myself a 51. The idea of both hands throwing simply did not dawn on me, and I had no jugglers to watch at that time. I would only stumble into 3 accidentally when my Ghanaian roommate began dropping avocados down to me from the tree. The avocados were coming down too fast to catch each and set them down. So I began popping some back up into the air, which bought me enough time until the next set came down. The existence of 3 suddenly revealed itself to me there under the avocado tree. 

Rose Anne and Bethlyanne

Saya

Saya learned on an alternate path to juggling. She could perform "dapadap" - the juggling of two balls in one hand. I now teach what I think of as "dapadap third ball injection." Once a right hand dapadap is up and stable, toss a third ball held in the left hand into the dapadap while catching the falling ball back into that left hand. Continue to dapadap, occasionally switching in the ball in the left hand for an airborn ball. Eventually inject ball three continously. 

Blossom with a well controlled 3

Leipolanda tries a 3

Bethlyanne works on reassembling the Plush Crush ball