Tuesday, January 24, 2023

Lesson 4.1.4: Residuals and LSRL (Day 96)

WHODUNNIT?

First Verse:
Was Mrs. fixing snacks in kitchen?
Was Dr. hearing songs in atrium?
Professor's iPad by the pool now?
Did Miss kill the victim?

Second Verse:
A cougar's mauling was the method?
Or had a green snake's bit begun it?
Or object's falling was the weapon?
Just tell me whodunnit!

As I mentioned in one of my winter break posts, this week I'm bringing back two of my previously performed songs since they fit this week's Math III lessons. So I guess this means that I'll be blogging more about Math III than Math I this week.

For starters, yesterday was the Chapter 7 Quiz. And now I'm rearranging the later Chapter 7 lessons to make the order a bit more logical. Today I do the murder mystery based on Newton's Law of Cooling -- which explains today's "Whodunnit?" song. There are no examples of this in DeltaMath -- there's just a single question in Lesson 7.1.4 of the CPM text. Thus it fits on a day like today -- the quiz corrections take over most of the block, and then there should be time left for the murder mystery.

Tomorrow will be the other main topic of Lesson 7.1.4 -- compound interest. Originally I was going to do compound interest yesterday, but since I gave the quiz yesterday, I'll teach it tomorrow instead. (And before you ask, the rearrangement wasn't done just to make the lessons fit the songs.) On Friday we'll begin the two main laws of Trig -- and I have decided to do the Law of Cosines before Sines, even though Sines come first in the CPM text.

As for the "Whodunnit?" song, I first performed it in December 2019 (even though I didn't blog abut it until January 2020, during winter break), and so I wrote it my usual EDL for December, 12EDL. In order to make it a 14EDL song for January, let's change the last note to Degree 7, which is F#. As I explained on the blog three years ago, the tune originally ended on F# before I changed it, and now I change it back. It contains only verses, so it's another AA song. So it marks our third AA song since we switched to 14EDL.

Here's what it looks like in Mocha. It's exactly like the version from three years ago except it now contains F# as the last note (Line 160):

https://www.haplessgenius.com/mocha/

10 N=16
20 FOR V=1 TO 2
30 FOR X=1 TO 3
40 IF X=3 THEN Y=14 ELSE Y=9
50 FOR Z=1 TO Y
60 READ A,T
70 SOUND 261-N*A,T
80 NEXT Z
90 FOR R=1 TO 1400
100 NEXT R
110 RESTORE
120 NEXT X,V
130 DATA 8,2,10,6,8,2,11,6,8,2
140 DATA 8,6,7,2,11,6,12,2
150 DATA 9,6,8,2,6,6,9,2
160 DATA 7,32


As usual, don't forget to click on the Sound box before RUN-ning the program. If you wish to restore the original version, change Degree 7 in Line 160 to Degree 6.

It's written differently from our previous AA songs because it contains rests (Lines 90-100), which make the song sound more mysterious. The first three lines of each verse are identical, while the last line is different, as it now goes D-E-A-D-F#. (What word do those first four notes spell again?)

As the original was in 12EDL (which is like A minor), the riff for the first three lines is Am-E-Am. But with F# in the last line, I need a new chord. We might simply play Am over F# -- Am/F#, which is also an F# half-diminished chord (F#m7b5). In ordinary songs, we don't expect a half-dim chord to be a resolution, but in 14EDL, this is a 7:6:5:4 subharmonic chord, which might be more stable. Playing this chord in class today serves to make the song sound even more mysterious.

Today is Elevenday on the Eleven Calendar:

Resolution #11: We follow all protocols for COVID.

By now we've all completed our second post-winter break COVID tests, so now it's all about staying safe and being careful. Then this is my eleventh resolution in the classroom. On the blog a few years ago, I've declared that my own Elevenday resolution is to focus on my communication skills with my students and fellow teachers -- and that resolution is still in force.

In fifth period Math III today, I begin the quiz corrections, intending to play "Whodunnit?" halfway through the class and then starting the murder mystery in CPM. Unfortunately, there is way too much talking during the corrections.

On one hand, this is a carryover from the final exam, when I had to give out several zeroes. On the other, talking during the actual quiz was a non-issue yesterday. Going into today, I'm hoping that today would be more like yesterday and less like finals day last month, but my hopes are quickly dashed.

I don't know the exact number of talkers, but it's somewhere between six and ten. And this sets up a situation that almost always lead to arguments. No matter what I do, someone will say that it's unfair:

  • If I punish only one student, then I'm singling out a student, which is unfair.
  • If I punish several students, I'm unlikely to figure out the exact set of talkers. I'm likely either to punish an innocent student or fail to punish a guilty student, which is unfair.
  • If I punish everyone, that will contain innocent students, which it's unfair.
  • If I punish no one, everyone will talk through the quiz and the lessons. Then when it's time for the common department Chapter 7 Test, students will complain that they never learned the material, so their grades will drop, which is unfair.

After going back and forth among these options, I end up choosing the third -- today's quiz corrections no longer count, and so their original quiz scores remain.

The scenario where a significant number of students are talking is a fairly common one -- it happened all the time at the old charter school. It usually means that I allowed the students to get away with something early in the year (the Willis period), and so they figure that they can break rules all year.

In this case, back during the Chapter 1 Quiz corrections in August, one student probably asked me, "Is it OK for me to talk during corrections, since I'm already done (or already had 100%)?" I didn't want to say "no," because the student would think I was mean for not allowing finished students to talk. But as I now see, silence is the only way to go. By letting my students talk during quiz corrections, I convince them that it's OK to talk during the actual quiz, lessons, and ultimately the final.

And unfortunately, the talkers include two girls who were demoted from honors. They already learned Chapter 7 in their honors class, and both students scored 100% yesterday -- so naturally the others want to talk to them in order to get help on their own quizzes.

There's not much I can do once the class has reached this point. A significant number of students will talk during the upcoming Chapter 7 Test, and it will be difficult to punish them.

Keeping my eleventh resolution in mind there, perhaps communication is the key here. Before the test, I can inform the students that they are not to talk during the test. If a few students are talking, then those students will get zeroes. But if, say, five or more of them are talking, then rather than attempting to figure out who's in violation, I will immediately assign standards to the entire class. (In other words, they must close their Chromebooks and start writing standards.)

Yes, this is unfair -- but anything I can do at this point is unfair. It's not the same as giving the entire class a zero, although grades might drop because the standards would take time away from the test.

(By the way, the answer to the murder mystery in the CPM text is that the murder must have occurred around 3:15 PM -- and it was around 3:15 in class when we arrived at this conclusion.)

Just as it's important for me to communicate with students, I must also do so with other teachers. I admit that I don't really communicate with my fellow teachers today -- yes, it's Elevenday, but it's also Tuesday, and getting together is tough on Tuesdays. Yesterday was Monday -- a common day for department meetings. And so I talked with the other Math I teachers yesterday.

As it turned out, some teachers waited until this week to give the Math I Stats Project. Since I'm already finished with the project, I move on to Lesson 4.1.4, on residuals and LSRL (least squares regression lines -- in other words, lines of best fit). Technically, there is a Desmos activity for this lesson -- but the Desmos directs students to go to DeltaMath instead, and DeltaMath takes the entire period.

The built-in Stats calculator easily handles linear regressions. And some of the DeltaMath examples involve crime rates in a New York county -- crimes, as in murders, as in "Whodunnit?" Thus my song for today, originally intended for Math III, unwittingly fits the Math I lesson as well.

I'm also starting to have more problems with my freshmen not putting their Chromebooks away properly -- they leave them either on their own desks, or on an empty desk (so they all point to each other and say "That's not mine! You put it away!), or in the wrong slot in the cart.

So I talked to my neighbor teachers yesterday. Both of them are implementing a checkout system where students must surrender either an ID or something else of value (such as a phone), and the collateral isn't returned until the Chromebook is returned properly. I'm strongly considering doing the same in my own Math I classes, perhaps as early as Friday (the day of the quiz, so the Chromebooks are needed).

This is another example where a classroom structure can replace arguing. I care deeply about putting the Chromebooks in their proper slot, but our students obviously don't care. I could try to convince them that taking care of Chromebooks matters -- and since they won't easily be convinced, it would turn into an argument. Instead, the trick is to convert this into something the students do care about, like an ID (or a phone). Arguments are eliminated -- students who don't surrender the collateral will just fail the quiz, and those who don't put the Chromebooks back will lose the collateral.

This is my first post since the celebration of Chinese New Year -- the Year of the Rabbit. Sadly, there was a shooting in Monterey Park, a town here in Southern California with majority Chinese population, over the weekend.

But as usual, I like to discuss the calendrical significance. January 22nd seems a bit early for the big holiday -- and indeed, it's the earliest that it's occurred so far in my lifetime. It's possible for Chinese New Year to fall on January 21st. The last time it did so was 1966, and the next time will be 2061 (so it's possible that I can make it to that date -- I'd be eighty years old).

According to this link to the Archetypes Calendar (a calendar similar to the Chinese Calendar), it's possible for Chinese New Year to be as early as January 20th:

https://www.hermetic.ch/cal_stud/arch_cal/arch_cal.htm

But it hasn't happened in over a thousand years, since the year 497. Note the significance of that year -- it's just before the Gregorian exceptional year (no Leap Day) of 500, and nearly two centuries after the last exceptional year of 300. Thus the equinoxes and solstices occurred earlier in 496 than in almost any other year -- and so Chinese New Year 497 was about a month after that early winter solstice.

Anyway, I wish many condolences for the families of those whose lives were in Monterey Park.

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