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What is 120 plus 12?

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"What is 120 plus 12?" I asked the student. The student and I were measuring the circumference of a hoop that exceeded the length of the 120 inch tape measure. The student had chosen to measure the circumference and to use inches. The tape measure was 12 inches short of the circumference, the student was holding the tape measure showing that the gap remaining was 12 inches. The student looked up from the measurement in hand and said nothing. I waited.  Students in a prior term timing the period of a hoop. The period of a hoop is linearly related to the diameter. "Just add the 12 to the 120, what is 12 more than 120?" The student looked at me blankly. I waited. After twenty seconds, the student asked, "I can use my cell phone calculator?" The student pulled out their cell phone and obtained 132.  "You couldn't do that calculation in your head?" I asked. The student indicated that they could not.  ❖ "Plummeting math scores prompted lawmake...

From Doom to Ready Player One: Simulated universes

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This term ended on simulation theory. As the week had been heavy with videos, and this was the last class day of summer session, ending on a playlist felt depressing. In the usual last minute cobbling together of a new angle on topic, videos were pulled together in the hour ahead of class. The session opened with Doom Alpha Versions . These versions were developed in 1992 and 1993. The video was paused in places to point out the pixelated characters and the extensive use of square grids. Then the third segment of 10 Games that take realism too far , Officer Down, was shown. The realism is startling.  This was followed up by RPGs with the most romance options . This is moving beyond point and shoot and into human relations. Or relations with elves, dwarves, or perhaps Sméagol.  Then, circling, back to 1982, Tron was used to demonstrate the evolution of graphics. The video was paused at a light cycle to point out the very basic shapes being used: spheres, segments of spher...

Site swap notation

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SC 130 Physical Science has centered on performing experiments with physical systems that obey mathematical relationships. Mathematics has been at the core and center of the course. The board from yesterday was still up which shifted the focus from whether mathematics should be taught abstractly or in a specific contexts to a focus on what does it mean to be mathematically literate in a mathematical universe? During the term the students repeatedly demonstrated a complete loss of algebraic knowledge, although all had completed either MS 100 College Algebra and some had completed MS 101 Algebra and Trigonometry. Given this, how can a student prove that they "know" mathematics? What does "mathematical literacy mean?" What does it mean to "understand" mathematics? To be able to do mathematics? How can or should student demonstrate mathematical knowledge in this age of AI? Where copy and paste results in solutions? How shoul...

Forcing an xy scattergraph for short columns in Google Sheets

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In a data exploration involving hoop rotation period versus diameter Google Sheets does not always produce the desired scatter graph. The issue appears to small sample size or short columns.  Spreadsheet Selecting a scatter chart for this data results in the following chart for some students:   Note the monotonic spacing on the x-axis. Google Sheets has defaulted to a form of line graph with monotonic spacing on the horizontal axis. To reunite the paired data, select Use column A as label under edit chart on a laptop or desktop computer.  Note that this option is not accessible from the Google Sheets mobile app. Of note is that while working inside the Google Sheet chart module in the mobile app the chart appears to configure as expected. Once one exits the chart module, the columns split into two data sets. There is no known easy fix on mobile. The repair essentially requires getting onto a laptop or desktop.  There are hackarounds. One is to manually type the data ...

Hoop rotation exploration

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This summer term the hoop rotation laboratory was made less specific, less prescriptive of what had to be measured. In the past the laboratory was guided by the following directions and questions: In this laboratory you explored the relationship between a hula hoop diameter in centimeters and the natural rotation period for the hula hoop in seconds.  What is the nature of the mathematical relationship between the hoop diameter and hoop period? Is the relationship linear or nonlinear? What is the equation that relates hoop diameter to the hoop period? Do hoops with larger diameters have longer periods? This summer the intent was to leave the decisions on what to measure to the students. The concept was to make the laboratory more of a practical test of the students' ability to explore an unknown system. To remove some of the scaffolding and framework. This summer the directions were: If the universe is mathematical, then every physical system is obeying mathematical equa...