Site swap notation

What does it mean to understand a mathematical concept? What constitutes knowing mathematics? How can one demonstrate the ability to engage in quantitative reasoning? What do we mean when we say we are teaching and learning math? How should math be taught? How should math be tested? Should math be taught in isolation, in a math class? Should math be taught in context, in non-math classes? 

In this laboratory a system of abstract notation is taught without context. Just as symbols on a board. The notation is site swap notation mapped out linearly. Students usually quickly discern the pattern and are able to determine what should appear in subsequent sites. Once the class demonstrates mastery, then the illusion of understanding is taken away. Absent context, the mathematics has no meaning. The mathematics is no more useful than the quadratic formula - neither site swap nor the quadratic formula are ever again used by the non-major students in physical science. 


Both sections followed the progression of teaching site swap without context.

Valerina three ball juggle

Then the context is introduced 

Angeline two ball juggle, Arleen watching 

Angeline watching, Arleen site swapping three

Valerina

Susan

Aimee two ball dapadap

Josh site swap three

Aiko, a seated site swap three

Sonya dapadap with two balls. Site swap 40 perhaps.

Cathleen practicing towards site swap three 

Tayshaun three on late catches 

Marvin

Ensalyn

Gaynor, John

Ensalyn and Kimberly
 
Not everyone in this generation has given up reading fiction via print on paper

Comments

Post a Comment

Popular posts from this blog

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, o...
Read more

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