My Visit (Days 67-68)

Today is the day of my visit to the main high school, to see an experienced Calculus teacher at work. I will describe the details of this visit in "A Day in the Life" format. But first, let me explain the bell schedule at this school. Like my own school, this flagship school has a block schedule, but the two schedules are completely different.

A few years ago, I wrote about how block schedules work at different schools. A traditional six-period day (like regular Mondays at my home school) have classes of a little less than a hour each. We can naively combine two periods at a time into blocks, but the resulting classes would be about two hours long. Hardly any block schedule school actually does this -- instead, almost every block schedule school does something to shorten the classes somewhat. My home school, for example has an extra period (Advisory, a sort of zero period), while other schools have a seventh period. Other districts have two-hour blocks, but devote the last 20 minutes or so to "embedded support" where only D and F students need to stay.

The flagship school does something else -- instead of three blocks per day, there are four blocks, so that each one is about an hour and a half in length. Then three block days contain a dozen periods, so that each of the six classes meets twice during the three block days. This means that there are two all-classes days (Mondays and Fridays) instead of just one.

Wednesdays are one of the block days at this school. The periods that meet today are 1, 3, 4, 6. Since the Calculus teacher doesn't have a first period class, he asks me to come near the end of first period.

9:00 -- I arrive at the flagship high school and meet the experienced teacher. Yes, he's experienced -- way more than I am. He's been teaching for over 20 years (and is now the department chair at this school) -- indeed, that's long enough that he could have been my Calculus teacher back when I was a young high school student. During nutrition, he tells me what to expect in his classes today.

9:40 -- Third period arrives. This is the Calculus BC class.

Even though the lead teacher knows that I have only AB, he wants me to see his BC anyway. The BC class has reached Section 5.6 of the Calculus text, on integration by parts.

The BC class begins with a quiz. It contains four questions -- two integrals, a derivative, and the last one is a related rates problem. The derivative problem is d/dx [xe^ln(x^3)]. But notice that the function we're differentiating simplifies to x(x^3) or x^4 -- so the derivative is just 4x^3. I glanced at a few students' quizzes -- and not one of them realizes that the function simplifies to x^4.

After the quiz, the main lesson proceeds as usual. I wish to spend more time blogging about the lead teacher's fourth period class, so I'll cut off my description of the third period class here.

11:10 -- Third period leaves and fourth period arrives. This is a Calculus AB class -- and I want to write about this class in full detail.

Whereas the BC class takes a quiz today, AB already took a weekly quiz and are getting the results. The quiz is worth 21 points, and the lead teacher laments that the scores were low. Too many students had single-digit scores out of 21.

11:30 -- The lead teacher now goes over the homework. But, as he explains, he does homework completely differently from how I do it.

First of all, the homework is on Section 3.2, the Product Rule. Apparently, the teacher assigned something like #1-50 all. (And we thought that the #1-19 all that I assigned my own class for this lesson was too many!) He asks the students which problems they want him to go over -- and he goes over them a few at a time. It takes him several days to explain all the problems -- thus he doesn't expect them to complete fifty questions in one night. Instead, the assignment is due the next day after the explains the last problem.

12:00 -- The lead teacher goes to the main lesson. The lesson today is Section 3.4, the Chain Rule -- that's right, since it takes so long to go over homework, the lessons are well ahead of the HW.

The Chain Rule lesson is itself spread over several days. Today the teacher covers the General Power Rule (that is, the derivative of u(x)^n) and the General Exponential Rule (the derivative of a^x).

And I can see his teaching philosophy throughout the lesson. First of all, he derives (and calls on a few students to help him derive) the two rules that we use today. He reminds the students that back in Lesson 3.1, he proved that the derivative of e^x is itself. The class used the limit definition of derivative to show that the derivative of f(x) = a^x is f '(x) = a^x f '(0), and then they used Desmos to discover that f '(0) < 1 for a = 2 and f '(0) > 1 for a = 3, so the value of a such that f '(0) = 1 is between 2 and 3 (and, after some trial and error, approximately 2.7, or exactly e). Today he rewrites a^x = e^(x ln a) to show that its derivative is a^x ln a -- that is, the f  '(0) from earlier is exactly ln a.

Then he gives several examples. Apparently, many of these examples aren't from the text, since he has examples numbered 14, 15, 16 (and the text rarely goes past Example 10). For each example, he allows the students time to work out the examples -- and reminds them that as long as it's not a quiz, they can discuss with each other.

12:30 -- The final task is a group activity -- the lead teacher tells me that he's done this several times before with the BC class, but this is the first time in AB. The groups are assigned a row of derivatives for them to find. Each group works on the A problem together. Once they reach the correct answer, one group member works on each of B, C, D. The B-students can move around discuss their solutions with the B-members of other groups, and likewise with B and C. Then they return to their original groups and discuss how they arrived at their answers. (This is often called a "jigsaw" activity.)

12:45 -- Fourth period leaves for lunch.

I request that the department chair introduce me to another teacher -- the general Stats teacher. The main reason I wish to meet him is because of what my own principal told me yesterday.

And here's the shocker -- the general Statistics class that I've been teaching since August is, in fact, a one-semester course! The second semester is Trigonometry.

The Stats text contains 21 chapters, and I just completed Chapter 8. This is right around where I want to be, if this had been a one-year course. (Notice that 8/21 * 180 is right around 68, so it makes sense to complete Chapter 8 on Day 68.) But now that I know it's a semester course, completing only Chapter 8 by the end of the semester is too slow.

The Stats teacher at the flagship school tells me that ordinarily, his goal is to reach Part 4 on probability (consisting of Chapters 13-16). But this year, he'll only reach Part 3 on gathering data (Chapters 10-12), since he must fill in gaps in the students' knowledge due to the pandemic.

Indeed, his plans for the second semester Trig course are similar. The Trig text contains seven chapters, and he usually starts Chapter 6 in an ordinary year, but this year we'll be lucky to start Chapter 5.

By the way, notice that only general Stats is one semester -- Ethnostats is a full year. I don't ask to meet with the Ethnostats teacher since this is also his first year teaching the course. My goal today is to meet with experienced teachers -- mission accomplished.

1:15 -- I arrive back at my home school.

There are a few minutes left for lunch. The other teachers are all in the lounge, eating a special box lunch from Chili's -- partly for Thanksgiving, partly because it's our secretary's last day at the school, so we want to throw her a party. I already paid for my Chili's meal, and so my lunch is already in the lounge waiting for me. I eat the meal as fifth period begins -- my classes are already being covered for the day (by other teachers -- as expected, my sub was pulled to cover elementary school).

But of course, today's visit leaves me much to think about. First of all, visiting another school today reminds me of back at the old charter school, when I also went to our sister charter in November. Then again, it was for a completely different reason -- my car happened to break down in the same city as the sister charter, so I couldn't drive to my home school, and my counterpart teacher at the sister charter was also out sick. So it made sense for me to cover for her.

And I'll continue to process what I learn today as I plan for my classes moving forward.