Floral litmus solutions and site swap notation

 Laboratory thirteen 

As of 8:10 the room remained empty

Diosticka looks for color change for a known acid, lime fruit, and a known base, baking soda

Fanney and Rita Mae have moved on to testing unknown substances

Fanney

Fanney adds an unknown, Destiny records results

Leona compares the color change due to an acid to the original flower color

Joyner records data

Diosticka with floral litmus solution

Rita Mae makes notes

Fanney, Rita Mae, Diosticka and the table of unknowns

Rita Mae, Diosticka, Fanney, Destiny

Jayleen and Jeannette test their floral litmus solution for reaction to a known base

Cassandra, Eboni, and Trisane compare results for unknowns. Cassandra records results.

Chance, Wadel Likaksa Jr., and Wenry Dawson work on identifying unknowns

Jayleen with floral litmus solution

Jeannette with original color, acidic solution, and basic solution. 

Holidays this term prevented "laboratory 14" from happening. Thus site swap notation was the last laboratory. 

I began at 8:00 with only Joyner. This is the usual sequence of arrival in the class - Joyner, then Fanney and Destiny, followed by Leona and Diosticka. Rita Mae did not join today.

I began with Marcus du Sautoy's The Code from BBC Two on NetFlix. For reasons that escaped me, ChromeCast paused every ten minutes whether or not the phone was active. 

Then I proceeded with the board introduction to abstract site swap notation.

Again, I treated the above as an abstract system. This time I ran the swap into the top diagram. In the afternoon I went with an L-R sequence. Students again were able to predict the next L or R, the next color, even the color four sites down. I made no mention of the system. After I confirmed that they could predict the next color or site, I asked them, "But what does this mean? How would you ever use this in life?"

This term I went for factoring a factorable quadratic. I opted to keep the system unexplained and ungrounded in geometric representations of (x+1) by (x+1). I wanted the abstract uselessness of the equation on the right to remain completely detached from reality. The students provided the factors.  After I confirmed that they could factor the equation, I asked them, "But what does this mean? How would you ever use this in life?" 

None seemed to know. As one said, "We use it in mathematics class." A perfectly sealed system: teaching material only meaningful to the material being taught. I argued that both the left and right sides of the board were equally meaningless. Bear in mind the class is 100% non-physical science, non-engineering majors. 

Diosticka

I noted how the class had focused not on "even problems one through thirty" but on a single equation that arose FROM a physical system we had measured. The data generated the equation thanks to Desmos. 

Leona working on a three

Then I demonstrated the meaning to site swap notation mathematics using Koosh balls 

Leona

Math should be primarily taught in context, in a relevant situation. Any mathematics classes should explore mathematics from a less structured approach, more qualitative, philosophic. A mix of math, patterns, systems that behave mathematically. Let the math arise from the material, not be the material. Use Desmos and Photomath. 

Eboni, Trisane with Koosh balls, Cassandra

Jeanette, Jayleen

Working on a three

Chance, Wadel Likaksa Jr.

Trisane progressed to being able to keep three aloft in a site swap 3

Cassandra

The term ends on the most successful of my "online" courses, providing support for the idea that a class must meet at least once a week for the students to remain engaged.