Site swap notation

The last physical science laboratory of the term seeks to bring home the meaninglessness of the manner in which mathematics above arithmetic is 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. 

This is done entirely in the abstract without any reference as whether the above has any meaning or use. I do not explain what LR mean, this morning I merely mumbled something about Linear Regressions. At 11:00 I started with RL and mumbled about this being ReaL numbers.

At 8:00 I had finished the introduction of site swap notation as an abstract number system when a student arrived late. I asked another student if she would teach the late arrival site swap notation, which she did. 

Throughout the impromptu lesson the student teacher checked to see that the late arrival understood what she was teaching. As seen above the student had no questions. During the session the student responded to specific questions correctly. The student teacher did a phenomenal job of presenting material that she had only just learned. All abstract and devoid of any meaning. I can say that she has mastered the notation and manipulations and is able to teach that to others. 

Jasmine

The twist is that I make the same claim for most of algebra. Learning to factor equations of the x²+bx+c or ax²+bx+c is, I argue, as equally meaningless as learning site swap notation. A closed system in which we test students and they master material that has no meaning to them and will not be used by them again. And while the course is a general education physical science course for non-majors, essentially all college students are required to take algebra.

Myena

The argument I am making is subtle: I am not arguing that algebra is useless or that there is no benefit to learning algebra even though you will never use it. Obviously algebra is enormously useful. So is anatomy and physiology, accounting, and computer programming. That they are useful doesn't mean everyone needs to take microbiology, crop management, and macroeconomic theory. But the current approach of working problems one to thirty, even numbers only, is meaningless and useless. 

Myena

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 happy to have completed their mathematics requirement and never see another equation again.

Sanjay

In physical science 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. Using technology such as Desmos to handle the work of fitting an equation to the data. 

Tommy

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. Math in context. Perhaps this does not help, but it provides a context. Some faculty ask why physical science doesn't have a math prerequisite. I turn that around: all math classes should have a prerequisite such as physical science in which the use of the mathematics is encountered. Give the students a reason to learn the math. Math should be encountered in context first, then tackled in the abstract. And then tools such as Desmos or Photomath should be encouraged and used. 

Jocela and Kiora

I wrap up this laboratory by passing out balls and having students attempt to juggle and try 3, 51, a 42 swap if they are able to. I also show them some techniques for learning to juggle and provide feedback on their learning. I can point out when they have slipped into a 51 launch rather than a 3.