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Yule Blog Prompt #13: My Favorite Lesson of 2020...or One That Totally Flopped
This is an interesting one. My favorite lesson isn't an individual lesson at all -- in fact, it's something I did throughout the year, before and during the pandemic, and at different schools.
A few years ago, I came up with the idea of singing songs in the classroom. It was intended as a "brain break" of sorts, except that it's more like a "music break." Here's how it worked -- about halfway during the class period, I would start singing a song about math. Many of these songs came from Square One TV, an old math show that aired during the late 1980's and early 1990's. Some of these are parodies of common songs with the lyrics changed to math. And a few of them are original creations of my own.
When my long-term assignment began, I brought a guitar to leave in the classroom. Now music break is a regular feature of my class. I especially enjoy performing on hybrid days -- the 100-minute blocks can be tough on middle school students, and so a music break can be helpful. I usually chose one song to perform that week, since each class sees me only one hybrid block day per week.
Let me list the weekly songs that I've performed so far:
"Ghost of a Chance" and "Vote" were chosen only because of the calendar -- those songs fit Halloween and Election Day respectively. "Whenever You Multiply" and "Solve It" are my first original songs during this long-term -- these songs describe multiplying/dividing signed numbers (for Math 7) and solving linear equations (for both Math 7 and Math 8). Then I returned to Square One TV with the song about the trick for multiplying by nine.
The purpose of all these songs isn't just to give students a break on block days -- it's to jog their memories when working on math problems. Thus when we're solving equations, I start singing "Solve It" to remind them which step is next. The next step might require them to multiply or divide both sides by a negative number, so then I immediately switch to "Whenever You Multiply." And if the number they must multiply both sides by is nine and the student struggles to remember the 9's times tables, it's time for me to switch to "Nine Nine Nine." So I might sing three songs to solve one problem!
The other part of today's prompt is a lesson "that totally flopped." Well, I can name one entire unit that totally flopped -- Math 8 Unit 3, on linear functions and slope. And part of the reason that it flopped is that I failed to sing an appropriate song during that unit.
I taught Unit 3 during the weeks of October 19th-November 6th. As you can see, one of the songs I performed that week was "Less Than Zero," which was for the benefit of my seventh graders. And the other two songs matched the calendar, not the content. At the time, if you had asked me to perform a slope song, I'd have told you that I didn't have a slope song to sing.
But here's the thing. When I was doing research for this Yule Blog Challenge -- that is, going back to blog posts from early this year to find three good things or decide what my favorite lesson from 2020 is, I rediscovered an original slope song that I had written!
The post was dated March 6th. It was the last day of a three-day assignment in a Math 8 class. While I did sing songs when subbing, I rarely wrote original songs for day-to-day subbing (since after all, I wouldn't know what math topic to write a song about). But since this was a multi-day assignment -- and the eighth graders were about to take their second trimester finals, I decided to write a song about one topic on that final, which was slope.
I wrote the song in my notebook. A week later, I took out my notebook to perform some Pi Day songs (even though it was an English class, it was Pi Day Eve and the regular teacher had several guitars in his classroom). I was almost home that day when I realized that I'd left the notebook in the classroom -- and you know what happened next. The pandemic struck, the schools closed, and I'd never return to that room again. (Even when the schools reopened, I didn't even try to retrieve the notebook -- I assumed that six months later, the book would have been thrown away by then.)
Over the summer, I created a new notebook of songs, using lyrics that I'd recorded on the blog. But by then, I'd completely forgotten the slope song. (If it had been a song that I'd performed several times, I would have remembered it, but I'd written it and sung it only once before the pandemic.)
And so by the time I reached the slope unit during my long-term in October, I didn't have a slope song in my notebook to sing. What's sad about this is that in my March 6th post, I wrote that it was just a short song, and that I would extend it the next time I taught slope. Well, that exact situation occurred just 7-8 months later, but I didn't perform the song at all, much less extend it. If I'd sung it, the eighth graders might have remembered slope better, and perhaps earned higher scores on the Unit 3 Test.
Thus singing marks my favorite lesson of 2020, and failure to sing marks my biggest flop. (Note: In my last post, I mentioned the Quizizz lesson during Unit 3 as one of the three good things of 2020. But on second thought, Quizizz was enjoyable, but it didn't raise Unit 3 scores that much. Since I need to count Unit 3 as my biggest flop rather than as a good thing, I went back and edited Tuesday's post.)
Music: Guitar Chords for My December Songs
I've added the "music" label to this post. Here on the blog, I usually discuss the actual chords that I play for my classroom songs, but I haven't done so since Thanksgiving. And so let's catch up with the songs that I performed this month.
Once again, I point out that tuning knob on my D string is broken -- it has been stuck at C. I've also tuned my B string down to A, so my guitar is currently tuned to EACGAE. Over Thanksgiving, I wrote that I was considering tuning the low A string down to G as well, which would give us EGCGAE. An extra string tuned to G would be helpful when playing songs in the key of G major.
But of all the songs I played in December, none were in the key of G. Therefore I kept the A string tuned to A. So all the chords listed below are still for the EACGAE tuning.
Let's start with "Nine Nine Nine." I played this song in the key of C major, using the following chords:
As soon as I finish that last week of the long-term, I plan on removing the guitar from the classroom -- and taking it directly to a Guitar Center to replace the D tuning knob. Then I'll finally return to the standard tuning, EADGBE. By the way, I've been devoting so many of these music posts to something called EDL scales -- an alternate way to fret (as opposed to tune) the guitar. It ultimately goes back to an old computer program, Mocha, that can be used to generate music.
I don't want to tie up this post with yet another discussion of EDL scales -- this post is also labeled "Calendar," and I want it to be my final Calendar Reform post for the holiday season (while I have all year to get back to EDL scales). I do wish to discuss what EDL scales mean for the guitar once I return to standard EADGBE tuning. (While nonstandard tuning and nonstandard fretting aren't necessarily related, I kept tying the two in past posts.)
All that's relevant now is that I've been using both 12EDL and 18EDL scales to create songs -- and while I said that I'd be using 18EDL moving forward, the slope song that I rediscovered was originally composed in 12EDL.
Completing the Slope Song
Here is the slope song that I just rediscovered from my March 6th post. I'll repost everything that I wrote back on March 6th -- the Mocha code that plays the song, an explanation of the 12EDL scale, and the lyrics.
https://www.haplessgenius.com/mocha/
10 N=8
20 FOR X=1 TO 35
30 READ A,T
40 SOUND 261-N*A,T
50 NEXT X
60 DATA 10,4,12,2,8,2,9,4,11,1
70 DATA 12,2,11,1,7,2,8,2,11,4
80 DATA 9,6,10,2,7,2,6,1,7,1
90 DATA 6,4,7,4,7,4,9,16,8,4
100 DATA 12,4,7,4,8,4,8,2,8,2
110 DATA 12,2,9,2,10,6,9,2,6,4
120 DATA 6,4,6,4,8,3,7,1,6,16
As usual, click on Sound before you RUN the program. Here are the scale and the notes used:
12EDL scale:
Degree Note
12 white A
11 lavender B (or Bb)
10 green C
9 white D
8 white E
7 red F#
6 white A
C-A-E-D-B-A-B-F#-E-B-D-C-F#-A'-F#-A'-F#-F#-D-E-A-F#-E-E-E-A-D-C-D-A'-A'-A'-E-F#-A'
Notice the notes "D-E-A-F#" in the middle of the song. This is actually part of the "Whodunnit" song that the pseudorandom generator produced. I decided to keep it anyway, since I'd changed these notes back in "Whodunnit" -- back then I changed low A to high A, but here I keep low A. Also, I keep F# here, but back then I changed F# to D (so that the notes D-E-A-D would appear in the middle of that murder mystery song).
Now let's add some lyrics. I just take the final hints that aide has already written on the board (plus my calculator comments for the sixth resolution) and then make it into song lyrics:
The Slope Song
Delta-y over delta-x,
Rise over run and,
y equals mx plus b.
Calculator,
Use it if you need, but,
Try in head just for me.
y minus y all over,
x minus x, and,
Keep, change, change, yes you see.
Calculator,
Use it if you need, but,
Try in head just for me.
Notice that more teachers are starting to use "delta" when teaching slope. Once again, as a young student I once tried to impress my Algebra I teacher by using delta in my homework, and now suddenly teachers are using delta for real. Meanwhile, "keep, change, change" is a mnemonic used to remember how to subtract integers (keep the first number, change the subtraction to addition, and finally change the sign of the second number). Since the slope formula requires subtraction in the numerator and denominator, "keep, change, change" is relevant here.
Of course, this is a fairly short song that I wrote in one night. If this were a full song to perform on the day that slope is actually taught (as opposed to just being reviewed and tested), a slope song should probably explain it all better. So the delta expression and "rise over run" equal the slope, while y = mx + b is the slope-intercept form, not just the slope. And of course, "y minus y" is really short for y_2 - y_1, which we'd really need to explain better. Perhaps one of these days I'll expand this into a full song that can be used to teach slope.
And that takes us back to the present. Well, "one of these days" means today. (Actually, "one of these days" should have occurred in October or November.)
My promise was not that I'd add more verses -- we can keep the two verses that are there. What I need to do is add extra lines to explain what it all means. So here is the completed song:
Delta-y over delta-x,
Rise over run and,
Use it if you need, but,
Try in head just for me.
y minus y all over,
x minus x, and,
Calculator,
Use it if you need, but,
Try in head just for me.
Karl Palmen's Weekend Rest Calendar
Let's continue this year's Calendar Reform posts with a new calendar I found on Calendar Wiki. The creator of this calendar is Karl Palmen -- a prolific calendar inventor.
https://calendars.wikia.org/wiki/Weekend_Rest_Calendar
The Weekend Rest Calendar is inspired by a tear-off calendar that normally displays one day per page but puts both weekend days on the same page. Such a calendar has 'dates' that consist of either one weekday or a whole weekend. Then we can have 12 months each of 26 'dates', except the last month, which has 27 'dates' in a common year and 28 'dates' in a leap year. Then leap years need occur only once every 15 or 16 years, because a common year starting on Saturday has 53 weekends and so 366 days.
OK, so on this calendar, six "dates" cover seven sunrises/sunsets. One date covers both Saturday and Sunday, since Palmen's tear-off calendar combines weekends on the same page.
Whenever I see a new calendar, I always try comparing it to previous Calendar Reforms. There actually exists another calendar where six days cover seven sunrises/sunsets -- the 28-Hour Day. There used to be a website for the 28-Hour Day, but it no longer exists. There is now an XKCD comic on the 28-Hour Day, but I don't link to it because it mentions an inappropriate joke. You can just find it on Google.
While neither XKCD nor the old 28-Hour website mentions a calendar to go with it, the Weekend Rest Calendar fits well with he 28-Hour Day. In both cases six "dates" cover seven days -- the difference is that Palmen has five 24- and one 48-hour "date," while XKCD has six 28-hour dates.
But forget the 28-Hour Day. There's something else I find interesting about the Weekend Rest Calendar, and that's the Leap Day rule:
The calendar uses the simplest accurate such cycle, which is the 62-year cycle with 4 leap years (17+17+17+11)
The numbers 11, 17, and 62 should look familiar. There's another calendar that has uses 11-, 17-, and 62-year cycles -- the Andrew Usher Calendar that I posted back on Leap Day (February 29th).
While I enjoy my Eleven Calendar, I know that in reality, it will never be adopted by the public. It's unlikely that any week other than seven days will be used, since the religious connection to the 7-day week is so strong (even though I've found ways to place religious holidays on my calendar).
I believe that the only Calendar Reform that has a chance of being adopted is the Usher Calendar. This calendar has two parts -- an invisible Leap Week and an visible Leap Day Calendar. The big change is that the Leap Day cycle is modified so that it fits the Leap Weeks -- and the cycles used in this calendar are 11, 17, and 62 years.
In fact, I wonder whether it's possible to align the Usher and Palmen Calendars. We might notice that Palmen's Leap Days (December 28ths) occur in years that start on Wednesday. In the Usher calendar, 366-day years starting on Wednesday have a special property -- such years have both a Leap Day (February 29th) and a Leap Week (Week 1 -- normal weeks are numbered 2-53). And so I referred to such years as Double Leap Years. (Years starting on Thursday always contain Leap Week, but the dates are wrong if they were to contain a Leap Day as well. In fact, Usher created his Leap Day rule for the express purpose of avoid having any year starting on Thursday contain a Leap Day.)
And so it would be nice if we could align the calendars so that Usher's Double Leap Years are the same as Palmen's December 28th years. But there is one problem -- Palmen's "Rata Die" epoch:
and the Rata Die epoch of Monday 1 January 1 CE in the Proleptic Gregorian calendar.
OK, so the year 1 in Palmer's Calendar starts on a Monday. Since every cycle is 62 years long, this means that the years 63, 125, 187,..., 1923, 1985, 2047,..., all start on Monday. Now let's check the dates on the Gregorian Calendar:
January 1st, 1985, was a Tuesday.
January 1st, 2047, will be a Tuesday.
January 1st, 2109, will be a Tuesday.
January 1st, 2171, will be a Tuesday.
and every 62nd year after that, up to the year 2419, falls on a Tuesday. The last time one of Palmer's cycles started on a Monday was 1923.
There's a reason for this. The Gregorian and 62-Year Calendars differ by about one day every 1771 years, and so every date after the year 1771 figures to be one day off. The only reason this makes any difference is that I want the transition to the Usher Calendar to be a smooth transition -- switching calendars in a year when both calendars match. But most of the time, the Gregorian and Palmer Calendars are one day off (and so would Usher, if we were to make Usher and Palmer match.).
In particular, the Double Leap Years I mentioned in my February 29th post are exactly one year before the Palmer December 28th years. That's because the "years beginning on Wednesday" are one year off.
It's possible to make the transition in Gregorian February 29th years starting on Monday. These years often match because January 1st falls after the Palmen 366-Day year (starting on Saturday) yet before the Gregorian February 29th. The next such year is 2024 -- after that it's 2052.
Notice that if we end up aligning Usher Double Leap Years to Palmen's December 28th years, then yes, these years will match, but not necessarily other years. On the Usher Calendar, 366-Day years can start on any day except Thursday, but Palmer long years start only on Wednesday and Saturday. But in the long run, the two calendars are equivalent.
I'm actually upset that I didn't come up with this idea before Palmen did. Indeed, the fact that no Palmen year can start on a Sunday reminds me of the fact that the Rose Parade and Rose Bowl game can never occur on Sunday. In such years, the parade and game occur on Monday, January 2nd. (But on the Palmen Calendar, dates span the entire weekend, and so January 1st would be both Saturday and Sunday in such years. So just have the parade and game on Saturday.)
Meanwhile, I was also fascinated with the Jewish Calendar. It turns out that the Jewish New Year can never fall on Sunday. In particular, neither Rosh Hashanah nor Yom Kippur can fall on the day before or the day after the Jewish Sabbath. To avoid this, the second and third months of the year can have either 29 or 30 days -- whichever results in Rosh Hashanah falling on a legal day. (Since Hanukkah falls near the end of the third month, it means that the date of the eighth night can differ by one day.)
So the equivalent in our calendar would be for every Saturday, January 1st to be followed by February 29th, so that the next January 1st is on a Monday. That is, we fiddle with the Leap Day so that the Rose Parade and Rose Bowl can always fall on January 1st, yet never on Sunday. (Notice that on this version of the calendar, since January 1st can never be Sunday, then January 2nd can never be Monday, and January 3rd can never be Tuesday, and likewise every date has one day it can never fall on.) It only remains when the extra Leap Days must occur, since only doing them in years starting on Saturday means that Leap Day is only once every six years, which isn't enough.
And this is essentially want the Palmen Weekend Rest Calendar does -- except, of course, weekends share a single date. And Palmen figured out how often the additional Leap Days need to occur -- namely four times every 62 years.
It might be interesting to have a version of the Usher Calendar with Leap Days only in years starting on Saturday or Wednesday, matching the Palmen Calendar (but with dates numbered normally, not with combined weekends). Leap Weeks occur either in years starting on Thursday, or Double Leap Years starting on Wednesday. This works, though it's no longer the calendar described by Andrew Usher. I point out that this simpler leap rule might be easier to motivate. -- I already used football to motivate the Usher Calendar in my February 29th post, so we can use football again (the Rose Bowl) to motivate the new leap rule. (Notice that unlike the other Usher holidays, New Year's Day really has to be January 1st and can't be fixed to a day of the week. But we can at least make New Year's Day avoid Sunday.)
Then again, while the Usher Calendar is the only Calendar Reform that could actually happen, I've always put more thought into my Eleven Calendar. But is the Eleven Calendar really my invention?
theAbysmal Eleven Calendar
I've read about theAbysmal Calendar a few years ago -- officially, this calendar began on December 21st, 2012 (the Mayan "end of the world") with the year zero.
While the main version of theAbysmal Calendar is a 13-month calendar, the author has posted several versions of his calendar. And it's come to my attention that there's even an 11-month version:
https://calendars.wikia.org/wiki/TheAbysmal_Calendar
https://decolonizingtime.wordpress.com/time-lab/theabysmal-2/363-day-calendars/
This particular calendar is a recent discovery, and to my knowledge, is the first with 11 months of 33 days.
And now I'm wondering, what the...? I've always thought that my Eleven Calendar was original, and now this guy claims that his calendar is the first 11-month calendar? (I use masculine pronouns here since, face it, most Calendar Reformers are male. I do acknowledge the Primavera Calendar, named for its female creator. And of course Wendy Krieger helped me with my Eleven Calendar as well.)
I announced my calendar on January 1st, 2016. The blog entries at theAbysmal are undated (how ironic for a calendar blog), so I can't be sure when his Eleven Calendar was created. I did check the edit history at Calendar Wiki and noticed that the edit mentioning an 11-month calendar was made just earlier this month. So it's likely that theAbysmal 11-month calendar is less than a year old.
I admit that theAbysmal Calendar was one of my inspirations. But at the time Wendy and I were working on the Eleven Calendar, there was no 11-month Calendar at theAbysmal website. Hence I was able to claim my Eleven Calendar as original.
Unlike most versions of theAbysmal Calendar that start at the winter solstice, his 11-month Calendar starts on the summer solstice, June 22nd:
The 363-day Calendar begins on June 22 (21), on or about the Northern Solstice.
He states that the two blank days are September 7th and April 5th, in addition to Leap Day, which occurs at the end of the year on June 21st. In the simplest version, theAbysmal Leap Day occurs four months after Gregorian Leap Day (and so the blank day moves up to April 4th in such years). The author hasn't developed a full Leap Day rule for any of his calendars, though he states that he's considering a 128-year cycle.
The following link shows a full version of his 11-month (and other) calendars:
https://decolonizingtime.wordpress.com/time-lab/symmetry-of-the-year/calendar-building-iv/
This author likes to begin counting with zero, and so the months are numbered 0-10, and the dates within each month are numbered 0-32. He refers to the 11 months of the year as "elevonths" (as in 11 months, of course) and the three 11-week thirds of the year as "terms" (so the sports seasons that I described in previous posts are actually terms).
I could align my Eleven Calendar with theAbysmal 11-month calendar, just as we aligned the Usher and Palmen Weekend Rest Calendars. But then I'd be conceding that theAbysmal is the originator of the Eleven Calendar, even though my calendar predates his by over four years.
Here's what I'm going to do. In my December 27th post, I mentioned a version of the Eleven Calendar that starts in the summer, on July 1st -- and that was weeks after theAbysmal edited Calendar Wiki to announce his 11-month calendar. Therefore, I acknowledge theAbysmal as the creator of the 11-month calendar that begins in summer, and align the holidays I mentioned in that post to his calendar. (I edited that post as well, to remove mention of anything that contradicts theAbysmal Elevonth Calendar.)
Note that theAbysmal doesn't state what the days or months are named, so here I go. The months will be named from July-May, so that each month overlaps the Gregorian month of the same name. The months will be numbered 0-10, as stated by theAbysmal. The days of the week will be named Zeroday up to Tenday, again in accordance with theAbysmal's numbering conventions.
And theAbysmal emphasizes the symmetry inherent in his calendar. It's possible to set up a six-day school week as detailed in previous posts, but do it symmetrically. Twoday-Fourday are school days, with Fiveday as the midweek day off. Sixday-Eightday are school days, and then the weekend lasts from Nineday to Oneday.
The Christian Sabbath can be Oneday since the Bible states that the first day of the week is the holiest for Christians. (Yes, the week starts on Zeroday, but the Bible mentions 1, not 0.) Then Zeroday becomes the Jewish Sabbath and Tenday the Muslim Sabbath. (I was considering making Nineday -- the penultimate day of the week -- be the Muslim Sabbath, but I also want Muslims to have a day of preparation for the Sabbath on Nineday.)
The two blank days, September 7th and April 5th (or 4th), can be Assumption and Easter, and vacation weeks can be set near those weeks. As for Christmas, the winter solstice is the middle day of the year, and so in the name of symmetry, we can place Christmas on that day, and take the entire week off for winter break. But notice that these three vacation weeks don't divide the year equally into three equal terms as defined by theAbysmal. I'll leave it open for now whether it's better to divide the year equally or around the religious holidays.
Holidays can be placed on the same day of the month each year, as previously stated. But the Fourth of July (which now means day 4 of month 0) is now a Fourday, which is a school day. But the date corresponding to Gregorian July 4th is now (00/12), a Oneday, so Americans might choose to place all holidays on the 12th of the month. Note that theAbysmal is Canadian, and so he might wish to place holidays on the 9th of the month, corresponding to Gregorian July 1st, Canada Day. (Then 01/09 would be the new Civic Day, 02/09 the new Labor Day, and so on.)
Notice that 03/00 corresponds to September 30th, and 03/32 is November 1st. Thus October 1st-31st line up in both calendars (except that October is now month 3 -- here I make no attempt to match up the Latin month names). Pi Day 03/14 becomes October 14th, which falls on Threeday, a school day.
One more thing about this calendar is that since it starts in the summer, students can advance to the next grade at the start of month 0 and leave it at the end of month 10. In fact, the months 0-10 can then be used for school pacing, particularly for a curriculum like APEX. Month 0 can be used for introductory activities, and then Unit 1 is taught in month 1, Unit 2 in month 2, and so on. If Christmas is on the winter solstice and winter break is the middle week of month 5, then the APEX Unit 5 (which is a semester final) can be given the first week of month 5. After winter break, the third week of month 5 another introductory week to get back into the flow of things, and then Unit 6 starts in month 6, leading up to the Unit 10 final in month 10. (This all presumes that we use winter break to divide the year into semesters, rather into the trimesters/terms mentioned by theAbysmal.)
All that's left is the year numbering. We know that theAbysmal uses 0 to name the year that started on December 21st, 2012, but he doesn't name the years in his Elevonth Calendar. I think it's better to let year 0 start on June 22nd, 2012, so that both this and the other Abysmal Calendars can use the same rules for Leap Days.
Once we acknowlege that theAbysmal created the Elevonth Calendar that starts in summer, then I remain the originator of the Eleven Calendar that starts in March.
Links to Other Challenge Participants
Today I link to Anne Agostinelli -- again, she doesn't actually mention Yule Blog, but she's linked to right there on Shelli's blog, so that's close enough:
http://53degreeshift.blogspot.com/2020/12/we-are-not-martyrs-we-are-not-trees.html
She mentions teaching both middle school and fifth grade:
Now, finally, I have come full circle back to the school where I began my career. My then-AP is now our principal and the vibe is back to the magic that prioritized kids and their families back in the good old days. I learned so much from my pit stops along the way, and I needed them to grow within and beyond my career, but I'm so happy to be "home" where I will finish my career.
And she has her own opinion of what's missing from teaching in 2020:
We are in a strange time in education, and too many districts are showing how little they value us by ignoring the global pandemic that is raging around us. Classroom teachers are omitted from the narrative, while we are the ones doing the actual work of nurturing youth through this challenging time.
Conclusion
Well, this concludes my last post for 2020. My final task this year will be to tear up the paper New Year's glasses that I wore twelve months ago, as a symbolic end of this annus horribilis. May we all have a much better year in 2021.
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