Chapter 8: What's My Line? Continued (Day 62)

Today is the first day of school since the end of Daylight Saving Time this year, with the clocks set back one hour. On the old blog, I would write biannual posts about Daylight Saving Time and whether it would be better to have Year-Round DST instead. But now that I've become a full-time teacher, I have less time to write about other issues like DST and need to focus on what's going on in the classroom.

(Actually, I do have something to say about the clock in my classroom -- it has never worked, always taking more than 60 minutes to tick off one hour. Thus it showed the wrong time both before and after the DST clock change. I've asked for someone to fix my clock but to no avail.)

I will write briefly about the clock change -- three years ago, Proposition 7 passed, allowing for California to implement Year-Round DST. But it can't happen until Congress allows for it -- and unless there's something about Year-Round DST in that big infrastructure bill that passed, Year-Round DST is still forbidden. (I can argue that clocks and timekeeping should count as infrastructure.)

OK, so let's get back to math. Once again, even though this is a Stats blog, my focus is still currently on my Calculus class. This is because, as promised, the math department chair (that is, my partner teacher) observed my Calc class to determine what's right and what's wrong with my teaching. The lesson is Section 3.9 of the text, on linear approximations and differentials.

Going into this class, I notice that the lesson contains four examples. I knew that chances are I wouldn't get through all four examples -- especially now that I want to make sure that the students are truly understanding the lesson. The goal is to intersperse each example from the text with an example of my own, so that I can ask the students to try each problem on their own.

I even came up with four different possible assignments from the text based on how many examples we get through. If we complete all four examples, then the HW can be #1-21 odd. If we only get through the first example, then I can only assign #1 and #3, as even #5 is already tied to the second example. I'm really hoping that we reach the second example so that I can assign more than two problems.

Well, here's what really happens today -- I cover the first example. It's a verbal (that is, a wordy) example, based on the temperature of a cooking turkey, just in time for Thanksgiving. (According to AP, we must focus on all four ways to represent a function -- verbally, numerically, graphically, and algebraically.) I call on one girl at random to answer a similar question about pressure and altitude.

Then I reach the second example with about 11-12 minutes left -- too much time to go straight to the Exit Pass, but not enough time to cover the example, ask a similar question, and do the Exit Pass. And so I really just do the second example -- and I can't be sure that my students fully understand it.. I briefly mention a story from when I was a young Calculus student -- someone challenged me to find sqrt(901), and it's easy to use linearization to come up with the very accurate answer 30 + 1/60. But I'm determined to get to the Exit Pass and give more than two HW problems.

After having observed my class, my partner teacher points out that yes, I really should have given more than one opportunity for the students to show what they know. I explain that my intent is to show them the second example until I realize that we're running out of time. So then she suggests ways for me to be more efficient with my time.

For starters, she tells me that I can use more guided notes, where much of the information is already printed out on paper. Originally from the start of the year, I was considering using guided notes, but I didn't know how to print notes from my Google Slides lessons. After she shows me how to do so, she points out that guided notes are especially important during word problems, so that the students aren't spending so much time copying paragraphs. (Notice that Section 3.9 is more verbal than most sections.)

My partner teacher informs me that the students are sitting too far from the front board. I've noticed this earlier, and so I decided to use the side board for my Calculus class. Instead, she suggests that I move the students closer to the front, and instead use the side board for announcements (special bell schedules, upcoming tests, and so on).

There are ways for me to get more participation from the students. One way is to have the students discuss how to solve problems with a partner. In a class like Calculus, one thing I can do is show some of the more complex examples already completed, and then have the students ask their partners why I perform a certain step at a certain time.

My partner teacher and I make plans for tomorrow's class. The goal is to finish the remaining two examples from this lesson, and then begin preparing for the next week's test.

Don't worry -- I will finally mention Stats in this post. Interestingly enough, both Stats and Calculus classes are working on linear approximations. But there are key differences. In Stats, lines of best fit are based on all the data points. If the data don't fit on a line, the resulting linear approximation will not be very accurate. In Calculus, linear approximations are more local, and depend mainly on the behavior of the function near the center of the approximation. Thus it doesn't matter what the actual shape of the function is -- near a different point, we just choose make another linearization.

I hope that I can continue to improve teaching Calculus so that my students will be well-prepared for next week's test -- and ultimately for the AP exam. And of course, I want to develop better teaching habits that will spread to my Stats classes as well.