Actually, I should say it's my second visit to this classroom. This school has a block schedule, and January 24th was an even block day, while today is an odd block day. Thus none of the students today recognize me from two and a half weeks ago.
All of this regular teacher's even classes are freshmen. Today she has one freshman English, her conference period, and one senior English. During the conference period I must cover another class -- also senior English, and this class also has an aide. Since this is a high school non-math class and one class has an aide, I won't do "A Day in the Life" today.
The regular teacher has her two English classes doing the same assignment despite their being different grade levels -- an article on opioid abuse. Students must highlight, complete Cornell notes, and then answer some reflection questions. The aide has her seniors do something different -- since they are currently reading Jon Krakauer's Into the Wild, they have two writing assignments related to this book. The half-page Warm-Up is on whether parents should choose their children's occupations, while the two-page Journal entry is on whether they hold unfounded beliefs.
Today is Sevenday on the Eleven Calendar:
Resolution #7: We sing to help us learn math.
Of course, this isn't a math class, so learning math isn't relevant. I do have a music incentive, since today is a palindrome, I sing Square One TV's "Palindrome Song."
Yes, today is 02-11-20. It's one of three palindromic dates this month -- next week it will be 02-22-20, and last week we included all four digits of the year, 02-02-2020. But of those three palindromes, today is the only one that's not on the weekend.
(Arguably, there was also another Palindrome "Week" this month, from 02-1-20 to 02-9-20. But including a zero on the month without a zero on the day is a bit too contrived.)
The freshman class today is definitely an improvement from the last class on January 24th. This time, I sing "Palindrome Song" each time four more students finish the Cornell notes as opposed to waiting until the end of the period. This keeps the incentive relevant and discourages the students from playing around (with adult objects, as they did on the 24th).
In the senior class with an aide I don't sing, since she basically runs the class. In that class, there's also a student who receives a traffic ticket for DUI from one of the campus security officers. He leaves the ticket on the floor at the end of class -- after having written the F-word on it.
If you recall from January 24th, there was an argument about the last 20 minutes of class, "embedded support" time. Today, the aide tells the students that those who fail to complete the two-pager must stay during embedded time instead of take an early lunch. Of the fourteen students, only two stay, and so the aide plans on giving the other dozen students a detention.
I correct this issues in my solo senior class. Instead of reading the names of the students who get to leave early (off of their papers), I check-off the ones who turn in it and write the names of the students who must stay. This works -- once they see who must stay for embedded, most of them rush to finish the Cornell notes, and no one must stay more than one minute (nor do I have to assign anyone a detention).
Today I also begin my Valentine's Day pencil incentive. The first four students in each of the three classes gets a pencil. (This is one reason why the music incentive today is based on fours -- the students get a verse as soon as the pencils run out.)
Unfortunately, the seniors in the solo class aren't motivated by either the pencils or the music -- only the embedded time threat gets them working. I often include candy with my holiday incentives, and so I wonder whether some of them would have worked harder for the candy. But I didn't pick up today's job until this morning -- I already had the pencils, but not the candy. I would have purchased some Valentine's candy during the conference period, except I don't get a free period today.
There are a few other things I wish to mention in today's post. First of all, the California Science Test scores were finally released last week -- it was on e Day, but since we were distracted with the e Day songs in that post, I waited until today to discuss them:
https://edsource.org/2020/california-science-test-results-2019/623501
Let's look at my old charter school students. These were the kids I had in sixth grade the year I was there, and they took the science test last year as eighth graders:
https://edsource.org/2020/california-science-test-results-2019/623501
The scores are not good for my old charter. Nearly 70 students took the test in the two testing grades (fifth and eighth), and only four students (two in each grade) scored a 3 or 4. This is a much lower rate than the state as a whole, or even the surrounding LAUSD district.
I have more to say about the scores, especially when we separate them by race -- recall that I use race as a proxy for campus (our campus vs. our sister campus). However, I try to avoid mentioning race outside of traditionalists' posts -- and there's already a traditionalists' post scheduled for tomorrow. So I'll wait until then to complete my analysis of the science test scores.
Instead, let me write about something else -- our Queen has spoken:
http://fawnnguyen.com/meet-me-here/
He jiggles the locked door handle, eager to come in. I stand and extend my hand to shake his and introduce myself. His teacher had warned me of his puppy eyes and that he liked to talk. After some chitchat, I ask him as I write on a piece of paper, “You go to the store and there’s a sign that says three apples for two dollars. Say you want to get six apples, how much would that cost?” I slide the pen and paper toward him.
Recall that Fawn Nguyen is a coach now, not a teacher. So this is clearly a student whom she's assigned to coach. He's working on a proportional reasoning problem:
He does not know what I mean. I refer to the paper and explain that the problem has three pieces of information, “You told me that you added the three and six. Is there something else in the problem that you did not use?” He admits that he did not use the $2.00.
They end up solving the problem using manipulatives:
He chooses three markers carefully, picking his favorite colors apparently. I ask him for payment, and he hands me two $1 notes. Pointing to the paper still in front of him, I say, “Remember the original problem. Tell me about the problem again.” He looks at the paper and the markers and money notes in front of him, “I need three more apples.”
At the end of her story, Nguyen writes:
Before meeting him, his teacher had shared that last year when he was in sixth grade, he’d met his goal of “multiplying multi-digit numbers.” I didn’t really know what this meant. I had no context and did not have the student in front of me. So I asked if I could meet him.
Oh, so I assume he's a seventh grader now. I think it's interesting how Nguyen begins not by asking him about math, but about his favorite type of apple (in this apple problem). Again, just click on the Nguyen link if you wish to solve the problem in full.
I'm still reflecting on the Starbird Calculus lectures that we just finished. And in fact, I think back to when I was first learning about Calculus -- not in Calc class, but when I was watching the TV show Homework Hotline (mentioned in my November 19th post) and Calc problems were called in.
When I first learned about the sine and cosine functions, for some reason I always believed that they were just complicated polynomial functions. Certainly I was aware that polynomial functions had only finitely many zeros while sine and cosine have infinitely many, but I assumed that restricted to the interval 0 to 360 degrees it was a polynomial. (And yes, I knew about non-polynomial functions such as 2^x, but to my young mind, 2^x made sense as it's just exponents, hence just multiplication, while surely this weird "sine" and "cosine" can be written in terms of multiplication and addition.)
I actually tried to find a polynomial for "sine" that passes through (0, 0), (30, 1/2), and so on, but to no avail. On another show (not necessarily Homework Hotline), there was a brief mention of polynomial approximations to the trig functions (like x, x - x^3 + 6, and so on), but the polynomials that appeared on the screen went too quickly for me.
It was actually Homework Hotline that ended my misconception about sine and cosine. A student had called in a problem about the derivatives of sine and cosine. The teacher on the show then replied that the derivative of sin x is cos x and the derivative of cos x is -sin x (Starbird Lecture 7). I knew that the derivative of any polynomial is another polynomial of lesser degree, and so the second derivative of sin x couldn't be -sin x unless sin x isn't a polynomial at all.
And thus this cleared my misconception. Whenever I read a story such as that of Nguyen's seventh grader, I must remember that at that age (or slightly older), I often had misconceptions as well -- his was that everything is addition and mine was that everything is a polynomial. They might be at two different levels of math, but in the end they are both misconceptions about the mathematical world.
In Lecture 7, Starbird shows the easy way to find derivatives of polynomials. I still remember how in Calc AB, our teacher showed us derivatives using the limit definition, and assigned homework that night before showing us the power rule the next day. That night, one girl asked her older brother to help her with the HW, and of course he showed her the power rule. She was so delighted that she ended up bragging to all the other students -- and the teacher -- that she knew a much easier way to do all the HW problems!
One more memorable day in Calc BC is all due to a Simpsons episode. We were learning how to find the area under a function in polar coordinates (r as a function of theta). The formula is:
(1/2) integral _0 ^2pi r^2 dtheta
You might figure out where this formula comes from if you remember that the area of a sector of magnitude theta is (1/2) theta r^2. (This formula is not in the U of Chicago text.) So we can divide out polar curve into tiny sectors of radius r(theta) and magnitude delta-theta -- the area of that sector must be (1/2) delta-theta r(theta)^2. Then we do as Starbird does so often in his lectures -- add up all of these tiny sectors by taking an integral.
Anyway, as soon as the teacher showed us this formula, one guy says "R D R R!" and several others laugh, including me. The teacher replies, "No, it's r^2 dtheta, not r^2 dr." I, of course, knew that this student was making a reference to the first season Simpsons episode "Bart the Genius," where a teacher shows Bart a Calculus question whose answer was r^2 dr, or R D R R. (I wish I could claim that I was the student who made the R D R R joke that day, but no, it was someone else.)
By the way, here's a clip of the R D R R scene:
When I first watched this episode, I was only in the third grade (a year younger than Bart). At that time I hadn't seen any Homework Hotline Calculus questions, so I was just as stumped about the answer R D R R as Bart was.
Lesson 10-9 of the U of Chicago text is called "The Surface Area of a Sphere." In the modern Third Edition of the text, the surface area of a sphere appears in Lesson 10-7.
This is what little I wrote last year about today's activity:
- From the U of Chicago text: calculate the surface area of the earth. Then compare the area of the United States and other countries to that of the entire earth.
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