Site swap mathematics

The morning dawned cool and wet.

As I have done of late, I prepositioned the juggling balls in the classroom.

Summer term wrapped up on site swap mathematics. As in the spring I shifted to a preview of the final to tie together the mathematical models encountered on the journey this summer. This doubles as a final preview - without my saying so - and provides a segue to introducing a mathematical model that the students have not yet encountered. 

Then I launch into site swap patterns starting with 3. After the students can make correct predictions for 3, I introduce 51. Finally I show that colors can be switched, swapped, between adjacent blanks, sites, for 42. Students are able to demonstrate mastery of site swap mathematics and everyone goes home believing they learned something. And yet they have learned nothing. At least nothing more than they did when they learned to FOIL quadratic equation factors. At this point I have not mentioned juggling nor any reference to what site swap mathematics means. 

I even asked the students, "When will you ever use site swap mathematics?" That's a rhetorical question.

The students will not see or use either site swap or FOIL after they leave college. 

If you want to anger a mathematics instructor ask them, "When will I ever use this stuff?" Some may have some rehearsed answer that they trot out, but in reality no student in a general education non-major physical science class is ever going to use quadratic mathematics again in life beyond college.

Then I show the class what the notation means, counting off landings of a red ball in a three ball set consisting of a red, green, and blue ball. After a demonstration of 3, 51, and 42, I invite the students to attempt site swap 3. 


Berny tries to start a three


Etwet working towards a three as well



LaPrincia has a site swap 3 well in hand.

Sru, learning three

The site swap laboratory ends the labs on a high note, a part of the peak-end design of the course. End on something fun, leave them laughing so to speak.

LaPrincia, a site swap 3 well under control


Comments

Post a Comment

Popular posts from this blog

Plotting polar coordinates in Desmos and a vector addition demonstrator

Image
In an earlier post I noted that Desmos did not directly plot polar coordinates. Not only was I incorrect, but Desmos responded to my blog to correct me! Although I had at some point seen that one could define a function f(x)=3x+5 and then have Desmos calculate f(6), I had not absorbed how this might be used to plot polar coordinates. The above works beautifully . Realizing that I could effectively program Desmos, I applied this thinking to demonstrating how to add two vectors when given the magnitudes m and the direction angles theta. The graph calculates the i and j components for the two vectors and then adds the vectors, graphically displaying the result while also providing information on the magnitude and direction of the vector sum. m1 and theta1 are the magnitude and direction angle for one of the two vectors, m2 and theta2 are the magnitude and direction for the other vector. All four are dynamically interactive and can be changed. The diagram purports to illustra
Read more

Setting up a boxplot chart in Google Sheets with multiple boxplots on a single chart

Image
The  Google Statistics  add-on for Google Sheets can display multiple boxplots in a single chart. The key is the layout of the data. One column should be the variable by which the data is to be grouped, the other column should be the data to be box plotted. Set up the Statistics add-on with the data to be plotted as the variable, and the grouping column as the "by" variable. In this image I had deselected all but the boxplot option, the result was the appearance of the Moment, Standard errors, and Confidence intervals options. The default is apparently a 95% confidence interval for the mean. The result is multiple boxplots on a single chart with a common scale. The new tab that is created also quotes 95% confidence intervals for the mean. Note that as of 2018 the Google Statistics add-on cannot be found by search in the add-ons. In addition, as of May 2018 the add-on no longer verifies, possibly due to the add-on not having been updated since August 2017. One may ha
Read more

Traditional food dishes of Micronesia

Image
Clara, Jennette, and Joanie presented ground hard taro cooked in an umw, effectively a hot rock oven. Pohnpeian: rotama. Pingelapese: sero. Mwoakillese: rodma. Mortlockese: Amahd. Kosrae: rodoma. After cooking in an umw the rotama is pounded with the petiole of a palm frond. Rotama is made from hard or swamp taro, known as mwahng on Pohnpei, mweian on Pingalap, pula in Mortlockese, and pahsruhk on Kosrae. In traditional times on the outer islands the women had primary responsibility for tending the taro while the men handled fishing and climbing tasks. Joesen and Noeleen presented fermented breadfruit from the outer islands of Yap such as Woleai and Eauripik. The raw ingredients were actually brought in from Yap, Noeleen prepared the maare.  The leaf wrap is ti leaf - Cordyline fruticosa. Pauleen, Barnson, Trisha, Verginia, Con-ray, and Maylanda from Kitti, Pohnpei brought in mahi umw, koahpnoair koakihr, and uht sukusuk. Above is breadfruit umw, mahi umw, one o
Read more