Originally posted August 30th, 2010 when I was working with another Cooperating Teacher (CT) at another high school in another district.
Having spent over 25 years in high-tech, I am definitely an advocate for technology, as long as it provides some advantage, efficiency, or other benefit. My experience with it this past Sunday while creating a lesson for my Math Analysis (Trigonometry and aspects of Pre-calculus) classes was anything but positive. It was encumbering, painful (literally, more on that someday), and exasperating. My wish to project math coolness in .pptx format was more a Faustian bargain with my ego than anything. After over four hours, yes, you read that right, four hours, making slides in Gatesware, I found myself wondering why I even started in the first place! The following four were the most complex graphically of the entire set.
While I had a few decent slides to show my students, the depth of my labor would neither be known nor cared for, and the “bang for the buck” factor was less than 1.0 so it was grossly inefficient. I could have accomplished the same lesson plan using transparencies in one hour, maybe two with start-up inefficiencies, but nowhere near the laborious labyrinth I found myself trapped within all day Sunday. “Never again!” friends and countrymen will I struggle under the yoke of Billware, or Steveware for that matter, trying to make the simple easy to understand and instead the simple becomes complex not only in form but in result…ugh!
So, it might be a few days before I put a slide together on my computer…and I’ve broken out my transparency pens for good measure. If I only would have heeded my inner adult and not the sirens’ song of my “I can do that!” ego. Who said you get wiser as you get older??
So while I sit here, tarnished and a bit shaken, my students learned (or more precisely were shown) what they needed to know, mostly, about angles in “Standard Position” and about “Coterminal Angles.” My CT felt my slides might have confused a few students which I accept as a possible outcome, even though I did strive to make it as understandable as possible.
Worse yet, my “Group Activity” problem (see below) bombed with my CT. She felt it was way too challenging for her students since it required them to think about the problem in ways they were not taught before. While I agree it forced them to use their thinking cap, and put their heads together stretching their minds a bit, I felt it was a doable problem and an interesting one at that, from my “neophyte teacher” perspective that is.
I am very open to my CT’s concern that the difficulty of the problem could freak the students out since it required them to think and collaborate about a topic with which they were unfamiliar, or uncomfortable with. At the same time, I was stunned when my CT said that the students likely did not learn that the measure of a central angle formed by two radii that intercept an arc on a circle, or sphere, is equal to the arc length, whether defined in degree or radian measure.
The school is pretty high-powered, API score-wise so I thought this topic surely was covered; it was included in the charter HS for disadvantaged youth at which I volunteered last year. My CT also said she was not sure if it was in the CA math standards for geometry so that might be the reason it was not covered. My quick check of the Geometry standards shows the following standards, where one could argue this concept should be covered, but I am nowhere near as familiar with the standards as my CT.
8.0 Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures.
9.0 Students compute the volumes and surface areas of prisms, pyramids, cylinders, cones, and spheres; and students commit to memory the formulas for prisms, pyramids, and cylinders.
11.0 Students determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and solids.
I’ve included my problem below for posterity sake (or until I drop it from this post.) I have not figured out how to format in this editor so it might not look that great.
Assume the Earth is a sphere with a radius of 6374 km: