Table of Contents
- Introduction
- Biden & Presidential Consistency
- COVID-93: What If?
- Guitar Music: An Alternative to EACGAE Tuning
- "Do-Re-Mi" on the 18EDL Guitar
- "Whenever You Multiply" Chords
- Eugenia Cheng Chapter 7: Dreams for the Future
- Gender Stats for My Class
- Racial Stats for My Class
- Conclusion
Introduction
I hope you enjoyed your Thanksgiving this year, even though the way that we celebrate holidays this year has changed. This is the first of two Thanksgiving break posts.
We enter the holiday season of what has clearly been a tough year for many. Indeed, some bloggers and tweeters often use the phrases "that's so 2020" or "because 2020" to imply that the current year is some sort of annus horribilis -- a Murphy's year in which anything that can go wrong, will go wrong.
The obvious reason for this being Murphy's year is the pandemic -- and many bad or strange things that happened this year are ultimately related to the disease. For example, as a former Bruin, I might say that the UCLA football team playing Cal last week on a Sunday, on short notice, at 9 AM local time, " was so 2020" (or "because 2020"). But the reason for the schedule change was ultimately the pandemic -- many players on UCLA's would-be opponents tested positive for the virus. So I could have easily have said "because of the coronavirus" without mentioning a year at all.
Though are a few bad events this year that aren't indirectly related the the pandemic. For example, hurricane season is always tough on those who live near the Atlantic -- and even an ordinary hurricane season during the pandemic would have caused trouble. But instead, it had to be one of those few seasons with so many hurricanes that we had to use a second alphabet to name them. Subtropical Storm Alpha, named for the first letter of the Greek alphabet, hit Western Europe in mid-September. The most recent storm was Hurricane Iota (the ninth Greek letter), a devastating Category-5 hurricane that hit Central America hard.
As a Californian, I wasn't affected by the hurricanes. But then again, we were hit hard by wildfires. Two of these wildfires -- Silverado and Blue Ridge -- occurred in Orange County, and at least one of my students had to evacuate because of a wildfire.
And on a personal note, three of my contacts on Facebook lost their fathers this year (actually four, since two of them are brothers). I, if you recall, lost an uncle this year. None of these deaths are known to be related to the coronavirus.
I'm still not sure though whether this was the worst year of my life. Indeed, 2017 was worse for me personally -- or to be more precise, professionally. It's well-documented here on the blog the problems I had with my teaching career that year.
Besides -- some good things did happen to me this year. Here in Southern California, we celebrated the championship seasons of the Lakers and Dodgers. And my professional career took a major step in the right direction for the first time since that aforementioned year 2017, as I picked up the long-term math position at an Orange County middle school.
That takes us to my main goal of today's post. As difficult as it is to be a teacher during this time, I'm sure that it's just as tough on the students. And so I wish to write about the challenges that my current students are having as they strive to continue their education -- in a way that I never dreamed of back when I was their age.
And I'll get to other topics today as well, including the last chapter of Eugenia Cheng's fourth book and some more details about music and the songs that I'm performing in class.
Biden & Presidential Consistency
Last Friday, the Associated Press called Georgia for former Vice President Joe Biden. This is the last state to be called, and it's enough to make Biden the President-Elect of the United States.
I try to avoid politics during the school year, which is why I waited until Thanksgiving to discuss the results of the election. (This post has the "Eugenia Cheng" label -- and I've noted before that posts with the Cheng label may be political.)
Indeed, it's now time for my traditional "Presidential Consistency" post. This goes back to a certain complaint about the Common Core -- our leaders come up with Common Core and other paradigms for public school students (No Child, Race, and so on), but then they send their own children to private schools that are independent of these mandates.
Presidential Consistency is a proposal that seeks to remedy this problem. Here's how it works -- the curriculum the Prez's own children use at whatever school they attend, that curriculum is automatically defined to be the Common Core. This way, the nation's children would receive the same quality curriculum that the leader's own children get.
Of course, there's one problem with the proposal this year -- Biden, as the oldest Prez ever elected (his 78th birthday was on the day he won Georgia), has no school-age children. Even the second-oldest, current President Trump, has a son Barron who just started his freshman year of high school. So what should we do about Presidential Consistency?
One solution is to consider his grandchildren instead. Here is a link to the Biden grandkids:
According to this link, Biden has two grandchildren now in high school -- Natalie and Robert. They are the children of the late Beau Biden, who died of brain cancer five years ago.
And so it's possible to come up with a Presidential Consistency based on their high school. But as these are the grandchildren and not the children, they aren't public figures, and so their school is unknown.
As the former VP is Catholic (the second Prez of that faith, after JFK), it isn't a stretch to assume that his grandchildren attend a Catholic school. So we might consider looking at some local religious schools and use this to guess what Presidential Consistency might look like. Indeed, just last week, one girl in one of my classes is applying to a Catholic school, and I was called upon to write a letter of recommendation for her.
I found out that at this school, Algebra I is followed by Algebra II, not Geometry. Therefore I was asked whether to recommend this student for Algebra I or II next year. Obviously I selected Algebra I since she's currently in my Math 8 class though I wasn't sure whether to choose Honors or not. She currently has a B in my class, but this school prefers mostly A's for Honors. The girl did receive an A on her Unit 3 Test (and this is the linear functions one, where many students struggled). And so I endorsed her for Honors -- perhaps that will increase her chances of getting into the school. There are placement tests to determine whether she'll be placed into Honors or regular Algebra I.
Not all Catholic schools go Algebra I-Algebra II-Geometry though -- back when I was a tutor five months ago, many of my students attended a Catholic school, but this school went in the traditional Algebra I-Geometry-Algebra II order. The reason for doing the Algebra I-Algebra II-Geometry is evident -- students forget Algebra I during their year of Geometry, so the hope is that if we teach Algebra II first, they'll still remember some of the Algebra I they learned and be more successful.
Returning to President-Elect Biden, since he was born in the year 1942, this makes him a member of the Silent Generation. This makes him the first Silent to be elected Prez -- all the leaders from JFK to GHWB are members of the Greatest Generation, depending on how it's defined. (Using the pattern I established on this blog, the Greatest Generation is 1910-1928, so LBJ, born in 1908, was on the cusp between the Greatest and pre-Greatest gens.)
There were four Baby Boomers (1946-1964) elected Prez -- Clinton, GWB, Obama, and Trump. Notice that of these four, three were born in 1946. But there is no Silent/Boomer cusp -- the Baby Boom definitely started in 1946, since World War II ended in 1945. This is why Biden truly will become the first Silent President.
Meanwhile, speaking of generations, some people wonder what the next generation after Generation Z ought to be called, since Z is the last letter of the alphabet. Well, once we exhausted the hurricane alphabet, the next storm was Alpha. And so some authors are beginning to refer to the next generation as Gen Alpha. Using the pattern I established on the blog, Gen Alpha will be 2018-2036 -- although the inventor of the name "Alpha" prefers defining a generation as 15 years, not 18:
To me, maybe we should come up with more descriptive names for generations besides Latin and Greek letters, although Alpha is suitable as a temporary name. By McCrindle's definition, most of Biden's grandchildren are fully Gen Z, although his oldest is a Millennial while his youngest is Gen Alpha.
An alternative to looking at the President's children is considering the Vice President instead. But President-Elect Kamala Harris has no biological children. Her husband Doug Emhoff has two children from a previous marriage -- both have graduated from high school. Both Harris and her husband were born in 1964, placing them on the Boomer/X cusp (also known as "Generation Jones").
COVID-93: What If?
It's difficult for me to understand what Gen Z is going through now with their education, since I'm not a member of Gen Z. I'm on the X/Millennial cusp ("Xennial"), and so I already completed my education years ago.
So I have an idea. I will ask the question, what if the pandemic had occurred decades ago, instead of right now? To answer this, I will imagine a different world in which the pandemic occurred back when I was the age of my current students -- a "What If?" scenario.
Right now, I'm teaching two different grade levels. My younger students started distance learning as sixth graders and are currently doing hybrid as seventh graders. My older students started distance learning as seventh graders and are currently doing hybrid as eighth graders.
And so for today's "What If?" I can place the pandemic during my own Grade 6-7 transition, or during my own Grade 7-8 transition. I decide against the former, because the idea is for this "What If" to simulate my current students' lives. My own Grade 6-7 transition had me moving from elementary to middle school, but my students attend a 6-8 middle school, and so the transitions aren't comparable. So I'll choose the Grade 7-8 transition, a same-school transition for me as well as my students.
This transition occurred for me in the year 1994. But recall that even though 2020 is Murphy's year -- the year of the pandemic -- the name of the disease is COVID-19. (The reason for this is that the disease was discovered in China in late 2019 and announced to the world on New Year's Eve.) Therefore if we wish to place the pandemic in 1994, the name of the disease needs to be COVID-93.
This "What If" takes place in a different universe from the real world. In the real world, the disease COVID-19 caused a pandemic in 2020, and in this alternate universe, the disease COVID-93 caused a pandemic in 1994.
For our COVID-93 "What If" the calendar will follow the real timeline for COVID-93. Therefore COVID-93 causes the schools to close around Pi Day 1994, just as COVID-19 really caused schools to close around Pi Day 2020.
For this "What If?" we will pay close attention to technology. In particular, we can't say that we would have switched to online learning in March 1994, because the Internet was still in its infancy in 1994 -- most students and teachers wouldn't have had access to it. For this "What If?" we need to imagine how schools would have handled a 1994 pandemic using only 1994 technology.
But some readers might wish for me to consider 1994 politics as well -- in particular, perhaps the California Governor in 1994 wouldn't have been as strict as Gavin Newsom, and so schools might have reopened on a different schedule in 1994 than under Newsom in 2020. But this is a tricky one -- yes, Pete Wilson was a Republican while Newsom is a Democrat. But notice that the US President at the time was Democrat Bill Clinton -- an argument can be made that states will reopen more quickly where the Governor is of the same party as the President (since the Prez seems to held more accountable for the economy, while the Governors are more accountable for saving lives). It also bears noting that 1994 was a gubernatorial election year, not a presidential election year.
The best thing for me to do is just ignore 1994 politics altogether. Our closing and reopening timetable for COVID-93 will simply match the COVID-19 timetable -- I won't try to figure out how leaders of different parties would have acted.
OK, so let's begin the "What If?" now. It'd interesting to see how 1994 would have been different if COVID-93 had happened. The big news that year was the OJ Simpson case -- would that incident had even occurred if everyone was under lockdown in June that year? And in sports, the major story was the major league baseball strike. If there had been a pandemic during that labor dispute, it's possible that baseball would have been cancelled completely. It's also possible that the owners and players -- knowing that everyone was hungry for sports during the pandemic -- would have worked harder to come up with an agreement and avoid the strike. The 1994 season would then look like the real 2020 pandemic season -- shorter, but with a World Series. Perhaps the Dodgers, who won the 2020 World Series, would also have won in 1994 (since they were in first place at the time of the strike). An intriguing possibility for a champion is the Montreal Expos (who were also in first place at the time).
But of course, our focus is on my education, not sports. Here's a list of the classes I was taking during the third quarter of seventh grade:
1. Science 7
2. Computers 7
3. P.E. 7
4. Algebra I
5. Core English 7
6. Core History 7
(Note: "Core" obviously doesn't mean Common Core -- it means that English and history were taught by a single teacher. I explained this in previous posts when I discussed the "Path Plan.")
Back in 1994, school still started after Labor Day, and so mid-March would have been about midway through the third quarter, not the start of the fourth quarter.
While my classes for Periods 3-6 were yearlong classes, first period science was only a semester class back then. (Our school changed it to yearlong the following year.) And the Computers class was only a quarter in length -- it was part of an exploratory wheel of electives. The last day before spring break was scheduled for April Fool's Day, which was also Good Friday -- upon returning from spring break, we would switch classes with the "Home Arts" (or Home Ec) teacher, and that would be the fourth quarter elective on the wheel.
Pi Day that year fell on a Monday, and so let's say that when COVID-93 hits, I wake up and find out that the schools have been shut down. This means that I never make it to the Home Ec classroom.
Since it's 1994, we don't have online learning yet. But we can still have distance learning. Here's my guess of what distance learning would have looked like -- each Monday (perhaps starting on Pi Day itself), we go to school to pick up independent learning packets. This might be set up as a drive-thru in order to minimize touching, but there are also ways for students to pick up packets on foot if the parents work and there's no one to drive during school hours. These packets contain information from all classes and are due the following Monday. For the rest of the week, students can set up appointments in order to meet with a teacher and get additional help.
Just as with the real COVID-19 pandemic, let's say that with COVID-93, no harm can be done to the students' grades -- third and fourth quarter grades can't be any lower than what they were at the time of the pandemic. This definitely would have benefitted me -- while my strongest quarter of seventh grade was the second, my third quarter still beat my fourth.
And this was most noticeable with my grades in the classes that aren't yearlong. In the original timeline (that is, the real world where the pandemic doesn't happen until 2020), my science grade was a B third quarter, but a C fourth quarter. (I've mentioned my science grades in past posts as well.) So under COVID-93, I would keep the B for both quarters.
The Computers class has nothing to the Internet, of course. This class was mostly about applications such as word processing and spreadsheets (the pre-Office versions of these apps). I'm actually not sure what this class would have looked like under COVID-93 -- a modern version of this class would simply have students submit their computer assignments via the Internet. The teacher can't really give us assignments because not everyone even had a computer at home. (I had a computer of course -- the one on which the Mocha emulator is based.) I wouldn't be surprised if the school would just handwave all elective classes away (and let me keep the A that I got, as opposed to the B in Home Ec that I earned in the original time) and focus on the academic solid classes.
Now let's move on to the start of eighth grade. During the real COVID-19 pandemic, schools in California are allowed to reopen based on the county's color-coded tier -- Orange County, which was briefly in the red tier (before returning to purple) opened its schools, while LA County, which was always purple, kept its schools closed.
The schools I attended as a young student were all in LA County. So I'd be justified in saying that --since it's likely that LA County students will have distance learning for the entire 2020-21 school year (as the county can never get off the purple list) -- my schools would have remained closed for the entire 1994-95 year under COVID-93. But then again, the goal of this "What If?" is to place myself in my eighth graders' shoes -- and having my school shut just because it's LA County isn't exactly walking a mile in their shoes. And so for this "What If?" I wish to say that LA County schools reopen at some point during the 1994-95 year, even if COVID-93 cases never drop low enough.
Of course, we could go the political route -- Newsom wasn't Governor in 1994, so his rules regarding when schools can reopen don't apply. But since I'm trying to avoid politics in this "What If?" I will instead take a technological route -- we can have schools in purple counties stay shut in 2020 because there's an alternative to opening them, namely online learning. But since that alternative wasn't available in 1994, it's likely that school reopening rules would have been more lenient. Parents are more likely to accept distance learning now (when it's online) than they would have in 1994 (when it's just a bunch of packets).
So for this "What If/" when exactly should my school reopen? Again, if the goal is to simulate my students' experience, then we should choose the first week in October, since my students returned to school on October 6th. But another theme of my "What If?" is what Homer Simpson calls crisitunity -- a pandemic is a crisis, but I seek to find opportunity in that crisis. During the real COVID-19 pandemic, my crisitunity is this long-term sub position -- had there been no pandemic, my regular teacher would still be teaching and I'd be stuck as a day-to-day sub.
There's one crisitunity I can get out of an eighth grade pandemic. The worst thing that I ever did as a student occurred on November 30th, 1994 -- due to a dare, I hit my P.E. teacher, and was ultimately suspended from school. (I've mentioned this incident to my students, especially if I'm subbing in an eighth grade class on the last day of November in any year.) It would be a crisitunity if the school didn't reopen until, say, December 1st. Then this incident never occurs, and I never get in trouble.
Then again, it's possible to assume that even if school reopened in September, I can avoid hitting the teacher and getting in trouble. I've often discussed tracking on the blog before -- it leads to the idea of keeping good students away from bad kids who might get them in trouble. As it turns out, at no point did this make a difference in my life than my eighth grade year.
At our school, seventh graders mostly take the same classes, except for math and possibly their elective wheel (say if they're taking a yearlong Band or Choir class). But eighth graders are placed into regular or Advanced classes. To get into Advanced, a student must earn B's or better in the seventh grade. (So this school isn't at strict as that Catholic school I mentioned earlier, where A grades are needed to get into Honors.)
In the original timeline, I was placed into Advanced English and History but not Advanced Science -- due, of course, to that fourth quarter C grade. But under COVID-93, the school closes before I get that C, and so my third quarter B grade counts for fourth quarter. And thus in this "What If?" I get into Advanced Science -- and so I never meet the bad students who would steer me wrong.
At this point you might be saying, hold on a minute! I was dared into hitting my P.E. teacher, so how would getting into Advanced Science help me avoid the kids who dared me? Here's how -- during P.E., I almost never interacted with these kids, except perhaps when playing a sport. But in science class, they were seated next to me. These guys would then recognize me in the locker room as we dressed for P.E. -- and that's when they dared me into hitting the teacher. And so if I hadn't been in their science class, they would have just ignored me in the locker room. And so we assume that I avoid the suspension, and make COVID-93 into a true crisitunity, no matter when school starts.
Well, here's my decision for when school should start -- the episode in which Homer Simpson actually uses the word crisitunity actually first aired in 1994 -- it was on Sunday, December 18th. So let's start my crisitunity right after Homer's. While Monday, December 19th, might be a possible reopen date, it's unlikely that a district would choose a first day that close to Christmas. (In the original timeline, the last day of school before winter break was Friday, December 23rd, but even then, I can't see a school wanting to open just one week before Christmas vacation.)
We returned to school on Monday, January 9th, 1995, and so that's the day I choose. Notice that many schools prefer opening at the semester -- since our school didn't start until after Labor Day, our second semester wasn't until the last day in January. But I'll keep January 9th for this "What If?" anyway. It's definitely after the November 30th incident, and so I do avoid my suspension.
When the school reopens at the start of 1995, it will be in a hybrid situation. Of course, "hybrid" here doesn't mean part in-person and part online. Here I assume that in order to keep class sizes small during the pandemic, students will still attend class only on certain days, just as under COVID-19 -- even though there is no online learning on the days that aren't in person.
I don't know what exactly hybrid will look like in this district during the real pandemic -- after all, it's in LA County, where schools are nowhere near reopening, and so it doesn't have to declare any sort of hybrid plan now at all. The district website does mention a distance learning schedule, and so it's possible to extrapolate that the hybrid schedule -- both during the real COVID-19 pandemic and our "What If?" COVID-93 pandemic -- will be similar or identical.
This schedule more resembles the one at my Orange County District #1 (where I haven't subbed since mid-September) than at Orange County District #2 (where I'm a long-term sub). For distance learning, only three classes meet each day -- odd periods Tuesday/Thursday, even periods Wednesday/Friday. (As usual, all classes meet on Mondays.) Each of the three classes is an hour long, and then this is followed by lunch and then an hour of tutorial to add up to the 240-minute state minimum.
And so for my COVID-93 hybrid, Cohort A is Tuesday (odd) and Wednesday (even), and then Cohort B is Thursday (odd) and Friday (even). To make it simple, let's assume that the cohorts are determined by last name, so those at the start of the alphabet attend Tuesday/Wednesday. As a Walker, I would be placed on the Thursday/Friday cohort.
Under COVID-19, Mondays are full distance learning. The same will be true for COVID-93, except here "distance" means pick up the packets to work on at home. The teachers discuss these packets during in-person learning Tuesday through Friday.
P.E. is a tricky issue. In the original timeline, I was dropped from the third period P.E. class of the teacher I hit (as a sort of cooling-off period) and so I had independent study P.E. instead. (For third period, I was placed in the library, and so I became a library aide.) My current school is doing something similar for P.E. for all students (not just those who get suspended from regular P.E. classes), and so students only attend Periods 1-5 on campus. But the schedule I posted here has six periods, and so I assume P.E. must be an on-campus class. (I wish I knew what Orange County District #1 does for P.E., as it will likely be similar here. But I took the long-term job in District #2 just before District #1 opened for hybrid.)
Still, I don't get suspended from school, since I never meet the students during science class who would have dared me (and some of them had last names that would place them on the other cohort anyway). In eighth grade, my first-semester schedule under COVID-93 would have been (including the Advanced Science class that I would have been placed in):
1. Advanced Science 8
3. P.E. 8
5. Advanced English 8
2. Advanced History 8
4. French I
6. Geometry
While seventh graders would now take a full year of science, Science 8 at our school was still only a semester long class, and so eighth graders got an extra semester of elective instead. That class was supposed to be Keyboarding (that is, typing). In the original timeline though, I never make it to the Keyboarding class -- after the suspension, the school simply keeps me as a library aide while P.E. is restored to my schedule. I'm not sure what would happened under COVID-93 -- I don't get suspended and so I never become a library aide, but Keyboarding requires many students to touch the same computers during the day. It's unlikely that students would have their own personal laptops in 1995.
I have one final thing to say about COVID-19 vs. COVID-93. This month, there has been promising news regarding a COVID-19 vaccine. It's now possible that a vaccine could be released to the general public by late June (as I considered the best-case scenario in an earlier post), thus allowing school to return to normal next school year.
But this doesn't mean that a COVID-93 vaccine would be available by late June 1995, or that my freshman year would necessarily be normal. Vaccine development, after all, is technology -- and it might have taken longer to create a vaccine in the mid-1990's than it does today. So even if my current eighth graders get to be ordinary freshmen next year, we don't know what would have happened in my day if a similar pandemic occurred when I was their age.
Guitar Music: An Alternative to EACGAE Tuning
So far when I've been performing songs in my classes, my guitar has been tuned to EACGAE. The real impetus for this tuning is the broken tuning knob on the D string. But then I also keep referring to a hypothetical guitar fretted to 18EDL (Arabic lute tuning?), and then I supported tuning such a guitar to EACGAE (with strings C and G white and all the other strings yellow, using Kite colors). But now, after I play a few songs, I'm wondering whether EACGAE is such a good tuning after all.
Once again, we must heed the difference between standard 12TET fretting and 18EDL fretting. For example, an A minor chord can be played as x00200 in 12TET. But in 18EDL, this doesn't work because the fretted A is white, while the open A is yellow. As these notes aren't in unison, the resulting chord will be dissonant. This is why Am7 (x00000) is playable in 18EDL, but not Am.
Indeed, I pointed out that G major is a key that goes with EACGAE in 18EDL, mainly because two chords that are friendly with G major -- C and D7 -- are easily playable:
C: xx0030
D7: xx2223
But one chord is missing here -- G major itself. Unfortunately, we can't take advantage of the open string G because the chord has no other open strings. Instead, we must play chords like G/D or G/B:
G/D: xx2023
G/B: x22023
When I need a G chord in class, I try to play G/D, but this is problematic. The broken D string -- which obviously isn't tuned to D -- isn't exactly tuned to Concert C either as it's a little sharp. For some reason, the C string doesn't sound too bad when I play the C chord shown above. But when I fret it to the original D to make G/D (or D7 for that matter), the resulting D is slightly sharp, so that my G chord tends toward a Gaug chord instead.
So what I ended up doing is playing a three-string G chord: xxx023. Not only does this avoid the broken D string, but it has G as the bass note. But this isn't a full G chord, as it lacks the fifth D.
If I'm going to claim that G major is the home key for our tuning, then we should be able to play a G chord, full stop. Our G/B, G/D, and three-string chords aren't really G chords.
To remedy this problem, I propose retuning one more string -- drop the low A string down to G, leading to the tuning EGCGAE. Then this leads to an easily playable G chord:
G: x02023
There are three strings with standard tuning (G and both E's), and three strings dropped a whole tone (A, D, and B strings). And using Kite colors, there are now three white strings (C and both G's) and three yellow strings (A and both E's).
The C and D7 chords don't use the new open G, and so they remain as listed above. The one chord that changes is Am7 -- if we fret A on the new string G, then the lower A is white while the higher A is yellow, and so they are no longer a perfect octave apart. (Technically speaking, playing all six strings open produces a just Am7 chord, but A is no longer the bass note. The chord would then be properly written as Am7/E, or even C6/E since C is closer to the bass than A.)
That we lose Am7 isn't insignificant, because Am7-D7-G is a common cadence in G major. Still, the most important chord in G major isn't Am7 -- it's G major. I'm willing to lose Am7 if it means making the G chord sound better.
I'm not sure what will happen to my actual guitar if I tune the A string down to G, since my guitar is still in my classroom while I'm home for Thanksgiving. While open G as a bass note should make the G chord sound better, the fretted D is still out of tune. I'm hoping that the bass G will drown out D enough so that its out-of-tune-ness is less noticeable.
I'm still considering what songs to play when I return to school next week. As the eighth graders begin their Benchmarks, I'll likely sing "Benchmark Tests" again, but that song is in C major, not G. The seventh graders might get a different song. It's possible that none of the songs I play next week will be in the key of G anyway, and so EACGAE vs. EGCGAE won't matter that much.
"Do-Re-Mi" on the 18EDL Guitar
On Election Day, I played the song "Vote" -- a parody of "Do-Re-Mi." That day, I blogged that I would revisit how to play an 18EDL version of "Do-Re-Mi" later on. Well, later on is now.
We begin with the easiest part -- naming the solfege syllables in 18EDL. I return to the Xenharmonic website for inspiration, even though this website is based on EDO scales, not the EDL's we want:
We ignore the 46EDO column in the chart there -- just look in the "Ratios" column for the ones we want, and then read across the chart to find the solfege syllable. Here's the resulting chart:
Degree Ratio Solfege
18 1/1 do
17 18/17 ra
16 9/8 re
15 6/5 me
14 9/7 mo
13 18/13 fi
12 3/2 sol
11 18/11 luh
10 9/5 te
9 2/1 do
Every scale begins with "do," and we can keep "re" for 9/8. But there is no "mi" because that's reserved for the 5/4 major third. Instead, it's "me" for the 6/5 minor 3rd and "mo" for the supermajor 3rd 9/7.
The link above distinguishes between the syllables "lu" and "luh." It uses "luh" for 18/11 and "lu" for similar intervals such as 13/8. But Kite's color for 18/11 is "lu," and I don't how to pronounce the extra "h" in "luh" to distinguish it from "lu," so I'll be tempted to sing it as "lu."
But of course, just coming up with syllables is nowhere near finishing a full "Do-Re-Mi" song. To finish the song, let's look at how we construct "Do-Re-Mi" in standard 12EDO.
For example, the first line goes "Do, a deer, a female deer." The first word of the song is "do," and the first note of the song is the tonic, "do." But for "a deer, a female deer," the song moves up to different notes besides "do." If we were to write the entire song in solfege, then (based on my "Do-Re-Mi" score that I have -- actually, it's more like a lead sheet or "fake book") we obtain the following tune:
Do-re-mi-do-mi-do-mi,
Re-mi-fa-fa-mi-re-fa,
Mi-fa-sol-mi-sol-mi-sol,
Fa-sol-la-la-sol-fa-la,
Sol-do-re-mi-fa-so-la,
La-re-mi-fi-sol-la-ti,
Ti-mi-fi-si-la-ti-do,
Ti-te-la-fa-ti-sol-do!
And also, our focus for an 18EDL guitar needs to be on the chords, not just the tune. My score lists chords for the various lines. My score, which is in the key of C major, lists C for the "do" line, G7 for the "re" line, C for the "mi" line, and G7 for the "fa" line. I actually think that F sounds better for the "fa" line -- and indeed, when I played "Vote" in class, I played an F chord here, not G7 (especially considering the problems I mentioned earlier with G chords on my guitar).
There is a quick trick to come up with chords for a song given only its tune. If a song is in the key of C major, then we play a C chord over the notes C, E, or G (that is, the notes of a C chord) in the tune. We then play an F chord over the remaining F chord notes (F or A), and G7 over the remaining notes of that chord (D or B). If we do this to the tune "Twinkle Twinkle Little Star," then we obtain the following sequence of chords: C-C-F-C-F-C-G7-C.
But here's the thing -- if the melody contains the note C and we add the notes E and G for harmony, then we're adding notes from the C major scale. Likewise, if we see the note D in the melody and add a G7 chord (G, B, F) in the harmony, then those three added notes come from the C major scale. Yet on our guitar, if it's fretted to 18EDL, then the entire 18EDL scale in the key of C is played on the C string, and the entire 18EDL scale in the key of G is played on either string tuned to G (if there are two such strings, assuming EGCGAE). However, the notes on the other strings (particularly the yellow notes) aren't found in 18EDL scale. Thus if we use those strings to play chords, then we're harmonizing an 18EDL melody by using notes not in the 18EDL -- as opposed to the major scale examples earlier.
Consider the key of G, and we wish to play a chord on G itself. We can start with a G in the bass. If we want to try a minor chord (since 18EDL contains a minor triad), we can play the higher G at the third fret to produce green Bb. But then at what fret do we play the A string? The first fret here doesn't give us green Bb -- instead, it gives us suyo A# (an interval 20/17 over the root G), and this note will clash with the green Bb.
Instead, we'll more likely to play the second fret, giving us yellow B, a 5/4 major third above G. Then instead of green Bb, we play both G's open -- and this is leading to the G major chord (x02023) that I listed earlier. But this chord uses the yellow B and not the red B that appears in the 18EDL scale. And so suddenly we're harmonizing 18EDL using a chord that doesn't appear in 18EDL.
If we think about it, the original reason for our interest in 18EDL and other EDL scales is the Mocha computer emulator -- and this emulator plays only melody, not harmony. Now you can see what I'm getting at -- we can program a melody in Mocha, run the code, and then while the music is playing, we get out our guitar and play chords as the harmony. While the guitar is fretted to 18EDL, the chords that we play aren't necessarily pure 18EDL chords, since we can play non-18EDL notes on other strings.
So what we should do now is associate each note of the 18EDL scale with a chord that we can play on our guitar. We've already found one for the root G -- the G major chord. It uses a yellow B (so we may call this a G-yellow or G-yo chord). This same chord can also be played under white D, since this note is part of both the G 18EDL scale and the G-yo chord. But we can't play G-yo under B, since the scale uses red B and the chord uses yellow B.
I'm still struggling to figure out the best chords to play here. The one thing about music based on exact ratios (just intonation) is that it sounds very good in one key, but transposing to another key is difficult as compared to our standard EDO scales. In fact, I had trouble coming up with chords that will work for both keys, G and C (since we can build an 18EDL scale on either the G or C strings). The only completely transposable chords are the major 6th/minor 7th chords. This is because the open strings EGCGAE (or even EACGAE) form such a chord, so all we have to do is use a single barre finger across all the strings to play any maj6/min7 chord. So we can include as many such chords as possible.
For the "do" line in C major, we simply play the top four strings open to make a C6 chord. (Of course, fretting the A string to produce white C is also possible, to form a C major chord.) For the "ra" and "re" lines, we fret the second and fourth strings as follows:
do: xx0000
ra: xx1010
re: xx2020
The chord for "ra," while still technically a sixth chord, sounds more like a C#dim7 chord. The chord for "re" can be either G6 or Em7. We can add the lower G to make it G6 and the lowest E string to make it Em7.
For "me" we use a barre at the third fret to produce Eb6. Then the rest of the chords follow the same pattern as earlier:
me: xx3333
mo: xx4343
fi: xx5353
sol: xx6666
lu: xx7676
te: xx8686
While some of these chords sound like maj6, min7, or dim7 chords, they get less accurate as we move down the fretboard. In fact, the chord listed for "te" here isn't a min7 chord, but more like a chord with both a major and minor 3rd (and hence is dissonant). Fortunately, the Eb6 chord for "me" can also be played under "te" (Bb) instead, just as the C chord can be played under "sol" (G).
The chords for "do," "ra," and "re" have simple equivalents in the key of G. But by the time we reach "mo," we get chords that are unplayable in the key of G (unless we can stretch our fretting hands).
"Whenever You Multiply" Chords
And these are the chords we would need to need to play "Whenever You Multiply" correctly. Since I used my COMPOSE program on the TI using 18EDL, this is truly a native 18EDL song -- which is why we should use the chords listed above to accompany it.
When I performed this song in class, I played it in the key of G, even though it would have fit my vocal range better if I had sung it in the key of C instead. So let me list the chords for the key of C here, since these are the chords that I listed above.
The first three lines of this song start with "me," and so the opening chord is Eb6 (which can also be interpreted as Cm7). The fourth line starts with "do" (C), and so it needs a C6 (or C major) chord.
The fifth line contains the notes "lu" and then "me." The chord listed for lu above should sound like a sort of dim7 chord, with a root note of lu A/lu Ab. Yes, we have our usual problem with naming Degree 11 notes here. In this context, I prefer lu Ab (that is, ilo 4th = A4) because the note fretted on the 6th string become luyo F -- a note both a major 6th above lu Ab and fairly close to wa F. The resulting chord is thus lu Ab-wa D-luyo F-yo B, which is approximately a dim7 chord. (In class, I ended up actually playing an F major chord -- that is, interpreting the lu note as A rather than Ab. Indeed, in the key of G, this ended up being a C chord -- the simple C chord that I already knew how to play.)
The sixth line contains the notes "ra" and "fi." The chord for "ra" is another dim7-like chord, but the chord for "fi" (which contains thu notes, thu F-gu Bb-thuyo D-wa G) might perhaps be closer to Gm7 than any dim7 chord. (While thuyo D is noticeably sharper than wa D -- here tho 6th = M6 -- it's still closer to D than any sort of Eb. But thu F approaches F#, and so the chord may approach Gm-M7.)
The seventh line contains the notes "te" and "me." As noted above, the single chord Eb6 can cover both of these notes. And the last line contains the notes "sol" and "do," both of which are covered by C6.
Of course, until I get an actual guitar fretted to 18EDL, I can't be sure what any of these chords will actually sound like.
Eugenia Cheng Chapter 7: Dreams for the Future
Because I'm busy with this long-term sub position, I've intentionally stretched out our side-along reading book -- one chapter each week or so -- so that we reach the last chapter on Thanksgiving. And since it's a holiday, I have time to give a full summary of the entire chapter -- the way that we usually do our side-along reading books.
As usual, Cheng writes about uncomfortable topics about gender, race, and politics, and so those who disagree with her views can skip this and all posts labeled "Eugenia Cheng."
Chapter 7 of Eugenia Cheng's x + y is called "Dreams for the Future." Here is how it begins:
"Here is my dream train design."
OK, so Cheng places a diagram here that I can't post. Let's skip to her description in the next sentence:
"Every train platform would use both sides of the train: one side for entering and the other side for leaving."
So hopefully you can visualize what this train looks like. The author proceeds:
"This particular example is mostly a fantasy, as it would be ludicrously expensive to rebuild all existing train stations and trains to this design, although situations with entrances and exits on opposite sides do exist on a small scale, such as on some light rail facilities at airports for transfer between terminals and on some elevators, often at underground train stations."
I've actually seen a tram set up like this before -- at the Getty Center, a museum here in LA. My first visit to the museum was during my senior year of high school -- the tram took me all the way up to the top of a hill, and I could see the college that I've been admitted to, UCLA, from that hill. If I recall, not only do passengers exit from the opposite side as the entrance, but the exit doors open first, so that people have a chance to vacate their seats before others try to sit down there.
As the title tells us, Cheng tells us her dreams for the future in this chapter. But even though this book is about gender, she warns us that it's not all about making men and women equal:
"So we were stuck making a false choice between various gendered ideas of how to change the status quo."
The author tells us how mathematicians dream up new ideas in our field:
"It's about dreaming up new concepts and new structures. Sometimes it's about dreaming up new concepts that generate new structures, like with imaginary numbers."
At this point Cheng includes another simple diagram. Arrows join "congressive individuals" and "congressive structures" to each other, showing how they can influence each other.
"One abstract example of this is the 'prisoner's dilemma,' which I (and many others) have written about elsewhere. It's a favorite thought experiment in philosophy and game theory showing that collaboration can produce better results than competition."
And in fact, I already discussed and blogged about Cheng's description of the prisoner's dilemma from her third book on logic. If you wish to find this old post on the blog, it's from September 2018, back during our side-along reading of that book. So I don't need to repeat it now.
"This might sound gendered, when the whole point of this book is to argue for an ungendered approach, but I think this is an ungendered approach to feminism."
The next section of the chapter is called "Congressive Math." Here the author seeks a new way for us to teach math in order to help girls be more successful:
"I think it's also what it introduced to children at the very beginning of school, when it's all about play and exploration with blocks and toys and other things they can touch and feel."
Since Cheng is a category theorist, it's understandable that she proposes category theory as a class that should be taught in high school.
But some people might criticize her approach to teaching math. So far, I've avoided using the following word when discussing her book, but you already know what word I use to describe those opposed to new ways of teaching math, so let's stop beating around the bush. The word is "traditionalists."
"Of course, this is often a criticism of the idea of getting more women into math -- some people believe that women really are worse at math and so to get more women into math we'd just have to lower the standards."
The author tells us that many women have shown their appreciation for her approach:
"To me this shows that ungendered terminology can both help us escape those divisive sweeping statements and help with the gender imbalances that currently exist."
The next section is called "Congressive Research." Here Cheng reminds us that research really does involve mathematicians working together:
"Some very heartening congressive aspects, at least in math, are the rise of global collaboration and the free sharing of both research and exposition, as we discussed in Chapter 5."
At this point the author quotes Alexander Danvers, a psychology researcher:
"He argues that the (ingressive) approach of trying to get 'eye-catching, wild' results does not do as much for cumulative scientific understanding, and that celebrating such high-risk work when it does go well skews scientific culture so that scientists spend more time on questions that are of interest only when the results are positive."
The problem with traditional journals is that they leave so many contributors out:
"It is related to the false dichotomy between research and teaching, in which people think breaking new ground is more important than making it possible for people to come with you."
The next section is called "Congressive Education." Here Cheng tells us how the current system encourages cheating:
"There are even online services where you can pay math PhD students in distant countries to do your homework for you. There are some more congressive systems of assessment by 'standards' or 'descriptors' rather than by grades, where instead of a single ranking there is a description of various important aspects of skill in certain areas, and the aim is to achieve proficiency in each one."
The idea of abolishing grades is interesting but controversial. Indeed, earlier in her book the author quotes Alfie Kohn, a well-known opponent of grades. Eliminating grades will be difficult -- consider what happened when there were no meaningful grades in spring 2020 due to the coronavirus. Many students did absolutely no work.
Here she tells us what she wishes to be taught in school:
"I also have a list of 'pet peeves' of human interaction that I sometimes wish were addressed in school: how to speak at a volume so that the people you're talking to can hear you and nobody else can (which includes learning both to project and also lower your voice), how to avoid hitting 'reply all' to a group email, how to be on time for appointments and meet deadlines, how to walk through a door and make sure you don't let it close on the person behind you."
The next section is called "Congressive Question Time." Here Cheng mentions race as well as gender, as far as asking questions is concerned:
"In case you're wondering if I'm suffering from confirmation bias: on one occasion, at the Auckland Writers' Festival Waituhi o Tamaki, people with questions queued up at a microphone, and after a few questions a white man shouted from the audience, 'Why are all the questions from white men?'"
Unfortunately, having the audience write down their questions doesn't solve the problem:
"It leaves the ingressive energy bouncing around the room. Eventually, I devised a way to run a congressive question time that neutralizes ingressive behavior without falling into the one-dimensional traps."
The author's solution is to have everyone have discussions with those around them, while she, the presenter, hears the discussions and shares what she hears. As a teacher, I give presentations in the classroom, and so this might be a way to get students talking in my classroom.
The next section is called "Congressive Workplace." Here Cheng tells us that we won't be able to eliminate competitiveness completely:
"Promotion might be necessary because people gradually take on more and more responsibility. One way to make it more congressive might be to make it more about sponsorship and mentorship than about putting yourself forward."
The author refers to two of her personal heroes in discussing how we can all play to our strengths:
"This is a way to get much more out of everyone, as we've seen in the case of Dame Stephanie Shirley, and yet in my institutional academic job allowing people to play to their strengths was seen as unfair. In Becoming, Michelle Obama writes of working to remedy the imbalance in her law firm, which predominantly hired people who were male and white."
In the next section, Cheng leaves the world of math and proceeds to another field -- "Music." Hey, I've already added the "music" label to this post, and so this is right up my alley:
"Whenever there is a move away from this in which everyone gets a prize, there is an ingressive backlash from people who think that the 'everyone gets a trophy' culture is ridiculous and doesn't breed excellence."
At this point the author invokes the name Alfie Kohn again -- in his No Contest, Kohn argues that competition is the opposite of what is needed to play music well. She proceeds to describe a more collaborative music organization that she herself founded:
"It's rather ingressive to care about wrong notes anyway; it is more congressive to care about the feelings we communicate and share with everyone in the room."
The next section is called "Congressive Discussions." Here Cheng suggests a better way for people to communicate with each other than simply arguing:
"Congressive discussions are instead a way to establish a connection between people as well as greater understanding."
The author tells us that politics is naturally confrontational, but other subjects need not be:
"If a scientist has made a breakthrough worthy of news, then the interviewer's aim is more obviously to get the scientist to explain it to everyone (although journalists who don't specialize in science do sometimes have a skeptical "What on earth is the point of this?" spin on more esoteric aspects of science)."
Thus arguments should no longer be about winning and losing:
"I have learned about congressive arguments from the most congressive person I know, my friend Gregory, with whom discussions are always about discovery and not about right and wrong."
The next section is called "Restorative Versus Punitive Justice." Here's how Cheng starts this key section, which is about a topic that's been in the news lately:
"Becoming Ms. Burton is an extraordinary and important memoir of an extraordinary woman, Susan Burton, and her journey to becoming a social activist rescuing women from a systematically racist criminal justice system in which she was herself trapped for years."
I won't post all the details of this story here on the blog. I do notice that Burton's story takes place in LA, and so I wouldn't be surprised if it's in a neighborhood not far from the old charter school. The author highlights the following:
"It is even senseless from a financial point of view -- she writes that taxpayers pay up to $60,000 per year to incarcerate a person, a sum comparable to tuition at an elite university."
Barton proposes "A New Way of Life," a system of restorative justice:
"This might seem like a naively utopian dream for the future, but congressive social structures have existed for a long time, just not in white capitalist societies."
This leads directly into Cheng's next section, "Native American Cultures." Perhaps this section is perfect for today, since it is Thanksgiving:
"In The Sacred Hoop, Native American writer Paula Gunn Allen writes about tribal social structures that were deliberately undermined by white colonial invaders."
As usual, our author uses her own terminology to summarize Allen's conclusions:
"I would extend this to say that in an ingressive society people are given power only if they use it in ingressive ways."
The next section is called "Congressive Democracy." Here Cheng compares the American system to the UK's parliamentary democracy:
"It is possible that this is why it is taking much longer to get a woman president of the United States than a woman prime minister of the United Kingdon or a woman chancellor of Germany."
Of course, since this was published, we elected our first woman Vice President in Kamala Harris. The author goes back to a 1980 debate when candidates GHWB and Reagan had a polite discussion about immigration from Mexico:
"This sort of polite, compassionate consensus seems unthinkable now, especially on that topic. A two-party system is another ingressive aspect, as is the first-past-the-post (FPTP) voting system (also called 'winner-take-all,' which makes it sound even more ingressive)."
Another possible voting system is called "ranked-choice voting":
"To avoid the logistical complication of everyone actually voting again, voters are allowed to rank all the candidates on their ballot in their order of preference, so that if their top choice is knocked out, their vote can then be redistributed to their next choice."
One state that has recently adopted ranked-choice voting is Maine, in reaction to the election of Governor Paul LePage without a clear majority:
"It seems LePage has called himself 'Donald Trump before Donald Trump became popular.' Indeed, apparently the more a Maine voter supports Trump, the less they support ranked-choice voting."
The whole idea is to stop rewarding adversarial politics:
"Again, it's a way we could create a congressive structure to nurture rather than force congressive behavior. This is another potential benefit of ranked voting systems: they encourage a less combative and partisan campaign because candidates need to appeal to their opponents' supporters in order to pick up second-choice votes."
The final section is called "Changing the Status Quo." Here Cheng expresses surprise that men aren't the ones more opposed to her ideas upon hearing them:
"However, I have encountered objections from women who have been very successful by learning to emulate ingressive behavior."
The author reminds us that yes, prejudice still exists and that we must address it:
"But the idea is to separate those out from the questions of character that we have been discussing throughout."
Continuing along this line:
"This is still an important part of dismantling explicit sexism, but it will not address indirect and structural bias in the system. I believe that the new dimensions of ingressive and congressive traits can help us overcome bias that can't be addressed on the dimension of gender alone."
The reason for adopting more congressive structures is evident:
"Thus we leave all of those opportunities to the ingressive people who base their self-esteem on nothing in particular and so might well be less skilled at the task in question, less willing to improve, and less willing to grow."
And it all starts with teachers of traditionally ingressive subjects -- math teachers, like me:
"Jessa Crispin reminds us that 'breaking away from the value system and goals of the dominant culture is always going to be a dramatic, and inconvenient, act.' We don't have to change the entire world at once, and we don't have to work on all scales at once."
For example, I can start by changing just one classroom -- my classroom:
"In fact, I feel that thinking this way has given me radical clarity about how to live my life, how to contribute to the world, and how to be a good feminist, working to change power structures while still recognizing the experiences of individuals and the range of other dimensions on which they experience advantage and disadvantage."
Cheng concludes her book with the following:
"I hope that we will choose congressivity and work together, congressively, to build a better future for everyone."
Gender Stats for My Class
And that's exactly what I wish to do -- build a better future for everyone in my classes. And since Cheng implores us to avoid both male/female and ingressive/congressive biases, I will begin by analyzing the number of males and females in my actual classes.
Here are the gender breakdowns for my classes:
Period 1 (Math 8): 18 boys, 13 girls
Period 2 (Math 7): 10 boys, 11 girls
Period 3 (Math 7): 9 boys, 18 girls
Period 4 (Math 8): 14 boys, 12 girls
Period 5 (Math Skills): 11 boys, 5 girls
The first thing we notice is that for the eighth grade classes, guys are in the majority, but for the seventh grade classes, girls are in the majority. I'm not quite sure why -- it's just how the chips fell.
If girls really struggle to learn math more than boys, then it means that my seventh grade classes will have more trouble learning this year. It means that I'd have to come up with more congressive approaches to teaching in order to make sure that these female majorities are truly learning.
But then again, Cheng tells us that girls are often afraid to ask questions in class. What I suspect here is that girls are afraid to ask questions when guys are in the majority. In all-female classes, or classes with many more girls than guys, the girls are more willing to ask questions. This is why some people propose having single-gender classes for all middle school students.
In fact, I think back to the old charter school, where the gender stats were reversed -- eighth grade girls and seventh grade boys were in the majority. I remember the eighth grade girls being very outspoken and competitive -- perhaps even more ingressive than the eighth grade guys.
So perhaps my biggest worry at my current school shouldn't be the seventh grade girls, since they're in the majority. My worry needs to be the eighth grade girls, as they are outnumbered by the guys. I must make sure that these girls are having opportunities to learn.
So far, all I've listed are the gender stats by period. But as we know, the hybrid plan divides the classes into Tuesday/Thursday and Wednesday/Friday cohorts, and some students in each class have also opted out of hybrid and are fully online.
Lately, there seem to be slightly more guys opting out of hybrid than girls. These guys are either officially changing their designation to online, or they unofficially do so simply by logging into Google Meet instead of going to class. This was most noticeable last Friday, when only one male student in each class actually attended class in person.
Let's look at Friday's cohorts in more detail. In second period, there are eight students, with only three of them boys. One of them is always online, and one of them is always in person. The third boy is often goes back and forth between online and in person -- he was online last Friday. Of the five girls, all attend in person, but one was absent on Friday.
In fourth period, there is an even split -- of the dozen students, six each are guys and girls. But last Friday, five of the guys attended online while only two girls did. The previous week, only two guys attended online (while a third was absent).
And in fifth period, there are eight students in Friday's cohort. Of these eight, five are guys, but only one ever attends this class in person, so he's always been alone as the only boy. Normally all three girls attend class in person, but one was absent on Friday.
If more guys attend class online, then this might help the girls out more. It's much easier to ask questions about the math in-person than online, so having more guys online clears the way for the girls in-person to ask more questions.
Of special note is the online Desmos activity, Polygraphs, that we played in class. This game has both congressive and ingressive components. For each round, students get a different partner, and the two partners must work together congressively to match their lines. Both partners either win that round or lose that round together. But then they each get a point for that round, which then allows their overall scores to be compared to determine an individual ingressive winner.
In the fourth period Thursday cohort, one guy and one girl refused to work together -- when they were partnered, they simply refused to ask any questions about each other's lines. Notice that in this case, the guy was in person and the girl was online.
Indeed, fourth period Thursday is a cohort with guys having the majority. Guys outnumber girls overall 8-6, including 5-4 in-person and 3-2 online. This class, along with the first period Tuesday and Wedneday, are the classes where I must make sure that guys don't take over and that my teaching doesn't become too ingressive.
Racial Stats for My Class
As we see above, Cheng mentions race a little in her most recent book (though not nearly as much as she did in her third book). And so I decided to investigate the racial breakdown of my classes. To do this, I check the students' reported race on Aeries, especially since some of the online students I've never seen, so I have no idea what they look like or what their race is.
Racial demographics matter mainly because of how SBAC scores are reported. Recall that my old charter school was predominantly black, but there were many Hispanic students in my seventh grade class -- and more importantly, none in my counterpart class at the sister charter school. Since the SBAC score report combined my school with the sister charter in giving a score, the Hispanic subscore was a useful proxy for "was taught by me personally, rather than at the sister charter." And if I had realized this at the time I was teaching there (rather than when the scores were reported, by which time I'd already left the school), perhaps I would've made a better effort in teaching that class.
Yes -- Cheng tells us that standardized tests are an ingressive way to evaluate students, and so in her ideal world, we wouldn't be judged by them so strongly. But we're not in Cheng's ideal world -- we're in the real world, where state test scores matter. Schools will look at my scores when deciding whether to hire me, so if I want teaching jobs in the future, I must make those scores as high as possible. And this includes the racial subgroup scores -- so if I wish to impress future employers, I should do a good job in teaching my most diverse class.
Finding my most diverse class is tricky: it might be second period Math 7. Among its twenty students, there are eleven whites, four Hispanics, one black, one Korean, and two "decline to state." But it's very close -- depending on what race the two decliners are, another period might be more diverse.
The least diverse class is easier to identify -- it is fourth period Math 8. Of its 27 students, there are 22 whites, two Hispanics, and one each of black, Asian, and Native American.
Interestingly enough, of all the black students in my classes, only one is fully black. The other students are all biracial white/black, including two who are triracial (white/black/Asian). And even the one guy who's listed as full African-American (in my Math Skills class) is in a mixed-race household -- I also have his sister in another class, and she's listed as mixed race Asian. Notice that for the SBAC, these students will be reported under the "two or more races" subcategory, not than African-American. This reflects the fact that this school is located in Orange County and not inner-city LA like my old charter.
Once again, the Hispanic subgroup will be the key. Overall, I have slightly more seventh graders in this group than eighth graders -- the lack of Latino/as in my fourth period is nearly made up for by the number of them in first period.
And so I conclude that the best way to raise my subgroup scores is to teach Math 7 effectively. This is in addition to teaching Math 8 effectively to help the girls out. Math 8 has already had its toughest unit before Thanksgiving, but now Math 7 will get its tough unit on algebraic expressions. According to Aeries, there aren't many language learners here -- the only students who might struggle with English are two Chinese sisters, and they seem to understand enough of what I'm saying to learn their lessons.
Of course, it goes without saying that I should be teaching all my students as effectively as possible, regardless of what their race and gender are.
Conclusion
Eugenia Cheng has an appendix at the end of her book. It's about three different ways that we can respond to criticism, such as:
"Typical woman!"
Ingressive: Typical man!
Passive: [Silence]
Congressive: That was hurtful.
And looking at her other examples, I see a similarity between Cheng's ingressive/passive/congressive trichotomy and Lee Canter's hostile/nonassertive/assertive, which in turn I've compared to JK Rowling's teachers Snape/Flitwick/McGonagall. In each case, we as teachers are directed to follow the middle path, to either McGonagall, assertive, or congressive.
I'm not quite sure how Cheng made up her coined words "ingressive" and "congressive." I doubt that she just chose random numbers between 1 and 26 and said "9, so that's I, 14, that's N, 7, that's G," and so on until she reached "ingressive," then chose 3 for C, 15 for O, and then put "co-" with the last part of "ingressive" to make "congressive." (Indeed, when I was double-check my old post on Cheng and the prisoner's dilemma, I also reread her rhetorical question about why C-A-T means "cat.")
The word "ingressive" is, in fact, a real word. But it only has a specialized meaning with linguistic sounds and has nothing to do with Cheng's definition. She likely just modified the word "aggressive," since ingressive people do tend to be aggressive. "Congressive" has no definition before Cheng, although the first eight letters do spell "Congress."
Moreover, the prefixes "in-" and "con-" are also used in the names of two different types of pedagogy -- "instructive" and "constructive." Instructive education is traditionalist, and we've already seen Cheng deride traditionalism as ingressive. And constructivists do often have their students work together in groups -- and working together is congressive.
And so I enjoyed reading Cheng's fourth book x + y -- and fortunately, we don't have to wait very long for her to release her fifth book. In fact, her Molly and the Mathematical Mysteries has already been released in the UK, but we Americans will have to wait until late March to get it. It appears that this is a children's book, so the target demographic is closer to my students' age than mine. Still, Cheng is an author I know and like, and so I'll probably make it our next side-along reading book when it comes. As for now, I might post about x + y at least once more, as I learn to apply what I learned to my teaching.
We know that by American standards, Cheng is considered left of center. And so I like to link to someone right of center in this post -- Darren Miller, of Right on the Left Coast:
There are two schools of thought when it comes to calling on students in class. One says to choose students randomly, perhaps by drawing popsicle sticks with their names on them out of a bucket. The other says to choose only those students who volunteer, as calling on a student who doesn't know the answer can be stressful to that student.
You can probably guess which method I choose. Go ahead, guess!
If you guessed the first method, you're right!
Well, I have my calculator choose names at random, and so I agree with Miller here. I wonder whether this method would be considered ingressive or congressive, though. Of course, if girls are the ones who are too afraid to volunteer, then random choosing should help them learn the material and participate more in class.
I will make one more Thanksgiving post this week.
