Chapter 6: What's Normal? Continued (Days 40-41)

Today in Stats, we cover the next six pages in Chapter 6. The students continue to learn about Normal distributions, including the 68-95-99.7 rule for estimating how many data values lie within one, two, or three standard deviations of the mean.

The text also shows how to determine how much data lies between any two z-scores by use of a function on our TI calculators. But here's the problem -- I have a TI-83, and the text appears to be based on TI-83 (although it's labeled simply as TI). But the class set of calculators are TI-84 -- and the normalpdf and normalcdf functions are more powerful on the TI-84. Whereas the TI-83 assumes that the mean (mu) is zero and the standard deviation (sigma) is one, the TI-84 allows us to enter our own values of mu and sigma as parameters. And this catches me off-guard. The students zip through my prepared material quickly, since they don't need to perform the extra step of standardizing the data into z-scores. At least this gives me extra time to work with the special ed student. He doesn't have any TI calculator (or even a smartphone) at home, and so he needs to work on his assignment in class.

But this raises another common issue -- more powerful calculators can often do in seconds exactly what we are teaching our students to do. We have calculators that can differentiate and integrate symbolically, so should we still teach our students Calculus? Back before I was student teaching, I observed an Algebra II teacher showing her students how to graph circles on the calculator by solving the equation for Y1 and Y2 (for the plus/minus sign that appears in the solution) and graphing both parts separately. I pointed out that the TI-83 has a CIRCLE function that graphs circles more accurately, until she reminded me that that would completely miss the point of the lesson. The students are supposed to be learning how to solve equations for y.

And so I wonder, are the students supposed to be practicing how to find z-scores -- and thus am I, by having the students enter mu and sigma, taking that away from them? It's tricky -- unlike avoiding symbolic differentiators or the CIRCLE function, they must use the normalcdf function. And the normalcdf function just happens to ask them for mu and sigma.

Meanwhile in Calculus class, I begin with a Warm-Up. Yesterday's Section 3.1 was on polynomial and exponential functions, and so today's Warm-Up is on differentiating y = r^3/3 -- also known as the Bart Simpson derivative, from the episode "Bart the Genius." In fact, I show them the clip from the episode, and tell them that when I was young and in high school, one student called out "hardy-har-har" when the teacher was showing us a formula from BC (1/2 integral r^2 dtheta, nor dr, but it's close enough).

Today we move on to Lesson 3.2, on the product and quotient rule. But here's the problem -- that one girl finally finishes her test (she earns a 93), and several other students retake it. This forces me to rush the lesson -- and products and quotients aren't something you'd like to rush. Thus I'm strongly considering simply posting some notes to Google Classroom very soon. Since one of the two assignments I give today consists of odd-numbered problems, I might show the students step-by-step how to do the evens, so that they at least have a fighting chance of figuring out how to find these derivatives.

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