Mathematical models and hula hoops

In the summer session the day starts off with Mathematics Explains The Universe. The laboratory carries twin goals. One is to show that any physical system can have an underlying mathematical model. The system does not have to be something serious and "scientific." The second goal is to reinforce that as a teacher you have to engage in lifelong learning, be willing to learn new skills, and be willing to take some ego risks in the classroom. Be willing to accept that failure is an option in any particular lesson, and to not take oneself too seriously. 

When a hooping vice president arrived at the college and explained that different hoop diameters were preferred for various hooping move types, I realized that there might be math under the hooping. Which meant learning to hoop. And engaging in an activity unusual for a 63 year old male math and science professor. 

This term some strong hooping capabilities and a willingness of the students to engage in hooping led to being able to capture some video of the laboratory. 

The session began with the background left behind on the board from the morning session. 

Benalyne and Piruno practice hooping

There is a wide enough variety of hoop diameters to get some solid data

A-Ann hooped a 74 cm hoop that was too small for me to handle, Fancylynn timing

L-Jane measuring a diameter, Joanalynn recording data

Marmayon timing A-Ann, Fancylynn recording data

Ivan and Cordny

Ivan and Cordny would get a constant period for every hoop at around 0.5 seconds per rotation. Their slope was statistically zero: no relationship between diameter and period. While all of the other groups obtained a positive linear relationship (larger hoops having a longer rotation period), the point of the course is that science is what is measured in the laboratory. What we can experimentally show to be true or not. That three groups obtained a relationship suggests a possible emergent truth to the linear model. There would still need to be an explanation for the data obtained by Ivan and Cordny and perhaps closer attention to hooping technique might be the key. The three groups use a circular hip movement, one that I myself learned from female students almost a year ago. From what I saw, Ivan and Cordny used an approach more akin to the one I had previously used of rocking back and forth to pulse the hoop, which doesn't work well and requires more motion and energy. That said, the data is the data, and this experiment provides a good opportunity to bring that concept home. Science is what can be measured, determined to be most probably true. Science is not a matter of opinion or belief. It is a system of physical world truths. As Neil deGrasse Tyson has noted, science is not something you get to choose to not believe in. 

Joanalynn measures a diameter while L-Jane records the data

A-Ann, Marmayon, and Fancylynn crunch their data

There is nothing more precious that an instructor can obtain than the time, attention, and focus of their students. All of the students were fully engaged in analyzing their data, trying to understand how the hoops are behaving. They are scientists and are doing what any particle physicist would be doing at CERN: crunching their data and trying to understand what the data is telling them in terms of the mathematics being obeyed. 

The course emphasizes the usefulness of cell phone apps. The Dutch schools have just banned cell phones in their schools. All schools. Congratulations on desperately trying to cling to the twentieth century. My students will outcompete and outperform those Dutch students. My students have learned that a cell phone is a productivity tool, a scientific analysis tool. 

And I would argue that my students are discovering that inquiry is fun. Science as inquiry is fun.

Utilizing Desmos' ability to plot two y values against common x values from a single table. 

Some wrap up notes on the board.