Today I subbed in a high school special ed Chemistry class. This is in my first OC district. With two of the classes being co-teaching and the other having an aide, there's no need for "A Day in the Life."
(No, I won't compare the science in this class to science at the old charter school, since this is a high school class. Note that a chemistry unit appeared in eighth grade pre-NGSS science and seventh grade under the Preferred Integrated Model of NGSS.)
And the one class I actually teach is extremely small. There are 17 students enrolled in the class, but only four of them are Cohort B -- and all four of them have opted out of hybrid! The only reason there's any student in this class is that one girl in Cohort A has an arrangement to attend school everyday. (I've seen this happen with another girl in special ed at my long-term school.) She also has a one-on-one aide, and so this period has three adults for only one in-person student.
As for the two co-teaching classes, one doesn't have any students show up for in-person class, and so the resident teacher just sends me back to my room. (This class has only two students listed for in-person Cohort B anyway, so it's possible that both are absent or just late.) The other co-teaching class ends up being my largest today, with seven in-person students.
Returning to the one class that I teach myself, today's assignment is on Google Slides. It's listed as Slideshow #10 for second semester, and the first slide contains a "Do Now" Warm-Up. This suggests that this teacher assigned a slideshow with a Warm-Up each day that the class meets.
At the old charter school, I assigned Warm-Ups all the time. (My predecessor, like today's teacher, referred to Warm-Ups as "Do Now" -- and some of my students there continued to call them "Do Now" due to force of habit.) But during my long-term, I didn't assign Warm-Ups -- I wasn't sure how to do Warm-Ups during the pandemic era, and besides, the regular teacher apparently didn't have them.
But the two questions asked in today's "Do Now" are rather interesting:
1. How are you feeling about the Periodic Table? Do you feel like you understand it a little?
2. How are you doing? Anything now at home or at school you would like to share with me (this is private)?
Many teachers on either Blogger or Twitter have pointed out that personal relationships have declined during the pandemic for obvious reasons. They believe that it's their duty to maintain such relationships by asking questions like the one above, with key words like "feeling, "share," and "private."
I, of course, never gave my long-term students any Warm-Up at all, much less one where this sort of question is asked. I admit that I was never good at asking students this sort of "feelings" question, whether before or during the pandemic.
Today I sing "Palindrome Song" for the last time during Palindrome Week. While there will be two palindromic dates of the form mm-dd-yy coming up (12-11-21 and 12-22-21), neither of those falls on a school day. December 11th will be a Saturday, and December 22nd is too close to Christmas (except in New York, where schools are open until the 23rd). And so the next Palindrome Week at school will be in February 2022.
Meanwhile, as January 2021 comes to an end, I realize that no, I haven't thought much about the New Year's/Decade's Resolutions at all. It's Fiveday on the Eleven Calendar, so today's resolution is:
5. We treat people who are great at math as heroes.
But of course, it's Chemistry class, so I can't discuss any math heroes. Of course, chemists are heroes as well, especially the chemists who are working on coronavirus vaccines. Then again, I have only one girl in my in-person class and she finishes her assignment quickly, so she doesn't need extra motivation. (I don't know how hard the at-home students are working, or whether they need motivation.)
The original version of the fifth resolution was about 1955 and how students nowadays need to pay less attention to phones and more attention to class, as they did back in 1955. In sixth period I do notice a few students playing on phones, but that's the co-teaching class. If the resident teacher has nothing to say about phone use in that class, then neither do I.
So obviously, even with the new versions of the resolutions, it's still difficult to enforce these the way I did this time last year, before the pandemic. Perhaps the "one word" challenge that Shelli posted on her blog -- and my own eighth graders did the first week of the year -- makes more sense these days.
But if I replace my New Decade's Resolutions with a "one word," what word should I choose? I told my students about Shelli's "joy." but I don't wish to copy her word.
Each year, in addition to the Rapoport Calendar, I buy a Page-a-Day Word Calendar. The first word on the calendar this year was divulge. But while I do wish to reveal more information about myself as a way to enhance communication, the word has a more negative connotation -- as in divulging things that should remain secret. So it wouldn't do as a word of the year.
The second word on my calendar is homage. And not only is that a much better word, it already fits my fifth resolution. "We treat people who are great at math as heroes" becomes "We pay homage to people who are great at math" -- and chemistry, and any other field that contributes to making the world a much better place than it was last year.
And so it's settled -- my "one word" for 2021 is homage. Of course, I'll continue to follow resolutions that are easy to maintain during the pandemic, especially the seventh resolution on singing in class.
Oh, and speaking of music, today I subbed at the same school where I was from March 11th-13th -- the last three days before the schools closed. In fact, I arrived on campus expecting to be in the very same English classroom as those three fateful days, until I was sent to Chemistry instead. It's the room that had all those guitars -- and yes, the room where I lost my old songbook. Chances are that the book has been long since thrown away, but there would have been no harm in looking for it when I returned -- and even if the book is gone, I could have still played "Palindrome Song" on those guitars. (There's a possibility that I might return to that room soon after all, but I won't discuss it on the blog until then.)
Today is the day I promised that I'd discuss guitar music on the blog -- and I admit that yes, part of the reason I chose today was that the guitar room had been on my schedule all week. (Otherwise I might have posted music on Monday and then finished Arthur Benjamin on Tuesday-Friday.) I'll still write something about guitar music anyway, but it will be some time before I perform any guitar music.
Anyway, my guitar has been fixed, and I now have standard tuning (EADGBE) again. Back before my tuner was fixed, I was using EACGAE and EGCGAE tuning and suggested that these are potential tunings for an instrument fretted to 18EDL (as in the Arabic lute). But that was mainly because my D string was stuck on C, not necessarily because these are the best tunings.
I played around with several possible tunings on paper. Suppose we were to ask, what tuning, with Arabic fretting, produces the most just major and relative minor chords? For this, let's try to play as many chords related to the key of C major (C, F, G) as possible, and with true bass notes on the lower strings (so that we're playing F, not F/A). The Kite color of all strings will be either white (wa) or yellow (yo), as I suggested when I came up with earlier tunings.
Then the best tuning I was able to come up with GADACF (with D and A's yo, all others wa). To find this tuning, I started with the bass notes -- on the lowest three strings, the notes wa G, yo A, yo B, wa C, yo D, yo E, and wa F are all playable. Then I tune the higher strings in order to make a six-string G chord be playable (a possible G7 chord here is 023220).
But I'm through with alternate tunings. I finally have standard tuning on my guitar again, and I'm not getting Arabic fretting at any time soon. So from now on, I'm only looking at standard tuning.
Then again, I'm still using Mocha and EDL scales to generate my songs. And so here's a question -- given standard tuning EADGBE, how should we color the strings (wa and yo) in order to maximize the number of just major and related chords?
Well, that's easy. For starters, we'll color the G and D wa, and the B and E's yo. This produces a playable major third (wa G-yo B) and well as two playable major sixths (wa G-yo E and wa D-yo B, which can both be inverted to minor thirds).
That leaves only the A string. There are several reasons why yo A is preferable to wa A. First of all, there is no playable 18EDL scale starting on wa A in Mocha, while there are such playable scales based on wa D and wa G. And second, fingering yo A at the second fret produces yo B, and this note can be used to make a six-string G major chord (320003).
From this point, it's easy to find some other chords that are playable on the guitar. Since we're using standard EADGBE tuning, it remains only to check whether the commonly fingered chords contain notes that are colored correctly. Most importantly, notes that are an octave or perfect fifth (or fourth) apart must have the same color, or the chord will be a wolf chord (dissonant).
It's easy to check that D major (xx0232) will be colored correctly. But the usual C, A, and E chords all contain both a wa E on the D string and the open yo E string, so these aren't playable.
As for minor chords, we can add bass notes to the G and D major chords to produce an Em7 (020003) and a Bm7 (x20232) chord. There's reason that minor sevenths are playable but not pure minors -- it's possible to finger a yo string at the third fret to produce a wa note, but we can't finger a wa string to produce a yo note. Thus adding the seventh to a minor chord gives us an extra wa note for us to play on the wa strings.
OK, so our playable chords are G, D, Em7, and Bm7. It's worth continuing to investigate other chords that are playable, including those fingered at the first fret (su) or fourth fret (red/ru).
Here are all the notes that are playable at the first nine frets:
(Note: here ilo 4th = A4 and tho 6th = M6. This allows luyo and thuyo to be slightly above wa.)
Written as octave-reduced intervals (using G = 1/1, since G major was our first chord), we get:
Here's what all of this means for now. If I write a song in 18EDL and play chords on the guitar, then I should be playing only chords that fit a potential Arabic fretting (even though I'm playing it on my standardly fretted guitar). Thus I can play G, D, Em7, Bm7 but not C, A, E, and so on. Thus it's worth exploring more playable chords to go with these songs. (Again, this only applies to my original songs that I declare to be in an EDL scale -- established tunes, songs from Square One TV, and so on, can be played using whatever chords they need).
By the way, any note that doesn't contain "yo" in its color is playable in Mocha. This includes the full 18EDL scales playable on the G and D strings. The scale starting on D is fully in my vocal range -- the open D is sung below middle C while the D at the ninth fret is just above middle C. But the scale starting on G exceeds my range -- the G above middle C is difficult for me to reach. Therefore if I use the 18EDL scale in the future, I'm likely to use the one based on D. (This also explains what I mean when I say a string is tuned to wa D -- it means that it matches the wa D note in Mocha.)
Today is the review for Monday's Chapter 9 Test. In many ways this is a light chapter. While the modern Third Edition includes surface area in Chapter 9 (Lessons 9-9 and 9-10), my old Second Edition stops after Lesson 9-8. Then again, students who have trouble visualizing three dimensions will struggle on tomorrow's test.
By the way, this test lands on a Monday. Some teachers may question the wisdom of scheduling a test on a Monday, right after students forget over the weekend what they reviewed on Friday. In the pandemic era, a Monday test is equitable -- all students are online on Mondays, so we know that all of them are taking it at home rather than having some take it at school and some at home.
If we compare this to other teachers, notice that the science teacher at yesterday's school gave the test yesterday and today. So the students in the Tuesday/Wednesday cohort take it at home while those on the Thursday/Friday cohort take it at school. She has no way of preventing the students at home from using notes, and so she allows this to be an open-note test for the in-person kids as well.
Well, at least our students won't have any Euclid on their test. Let's return to his next proposition:
Yesterday we construct the perpendicular from a point not on the plane, and now we construct the perpendicular from a point on the plane. This construction uses yesterday's as a subroutine.
This construction is even sillier than last Friday's to perform inside a classroom. This time, we have a point A on the floor and we wish to find a point directly above it. First, we label point B on the ceiling and use yesterday's construction to find a point C directly below it. Then we construct the line through A that is parallel to BC. This last construction is the usual plane construction -- but Euclid performs this construction in the plane containing A, B, and C. This plane is neither the floor nor the ceiling, but an invisible vertical plane that isn't even necessarily parallel to a wall. There is no reasonable way to perform this construction in the classroom.
And so there's no way that our students can physically perform this construction. There will be nothing like this on tomorrow's test, even though ironically, it would be easier to answer test questions about this construction than physically perform it.
Notice that the U of Chicago text doesn't actually provide the construction for drawing a parallel to a line through a point not on the line (which is a simple plane construction). The only way implied in the text to perform this construction is to make two perpendicular constructions (which we did in yesterday's post).
Many texts that teach the construction of parallel lines use copying an angle (as in corresponding or alternate interior angles). Lesson 7-10 of the Third Edition is on constructions, and duplication of an angle is given, but still no parallel lines. (I also see some DGS "constructions" mentioned there -- I wonder whether this is similar to Euclid the Game, as alluded to in last Friday's post.)
If you must, here is a modernization of the proof of Proposition 12:
Given: the segments and angles in the above construction.
Prove: AD perp. Plane P
Proof:
Statements Reasons
1. bla, bla, bla 1. Given
2. AD perp. Plane P 2. Perpendicular to Parallels (spatial, last week's Prop 8)
The proof is trivial since both BC perp. Plane P and AD | | BC are true by the way Euclid constructs these lines -- in other words, they are part of "Given." If (and that's a big if) we were to prove this in the classroom, it would be more instructive to show Euclid's proof of both yesterday's and especially today's propositions directly, than to attempt to convert the proofs to two columns.
Anyway, here is the Review for Chapter 9 Test.
