Introduction
Today is the second day of Kwanzaa, a holiday celebrated by African-Americans. Technically, Hanukkah and Kwanzaa overlapped this year, but only in the daytime hours (as Jewish days start at sunset) -- thus the last Hanukkah candle was lit one night before the first Kwanzaa candle.
This also marks my first Calendar Reform post of the season. It's my tradition to write each year between Christmas and New Year's about various calendar-related topics. Although most Calendar Reforms are pure fantasy, the issue that I wish to discuss today involves the very real calendar at my current school.
Yule Blog Prompt #9: A Tool or Strategy from 2022 That I Will Continue to Use in the Future
Last year when I responded to this prompt, I wrote about interactive notebooks. In my Ethnostats classes, I had a notebook of sorts, but I didn't let the students take them home. At the time, I was worried about whether touching and passing out notebooks during a pandemic was a good idea -- and I knew that many students would refuse to bring the notebooks to school each day.
This year, I decided to start the interactive notebooks anyway. I did so after seeing the lone other math teacher at my school (my partner teacher), and some of my fellow Math I teachers are using them too.
So how are notebooks going so far this year? Well, just as I predicted, there are many students who don't bother to bring notebooks to school regularly. And the worst class by far is sixth period Math I.
Indeed, I did the Chapter 3 Notebook Check on the day of the final exam. Since it takes me so long to grade the notebooks, I decided to simplify the last check before grades are due. Each notebook would be scored as full credit, half credit, or no credit. In order to receive full credit, no more than five pages should be missing or incomplete. This sped up the grading -- as soon as I counted the sixth missing page, I marked it as half credit.
The total number of students who received full credit for their notebooks in sixth period is -- one. The other Math I totals were disappointing as well, but none so as much as sixth.
In this class, there are at least two intentional non-learners -- guys who have no intention of doing any work in my class whatsoever. So nothing I can do with notebooks will make them work. But there are also kids who seldom (as opposed to never) bring their notebooks. Since the Warm-Ups and Exit Passes are in the notebooks, they refuse to do any work during the first few and last few minutes of class -- and I suspect this contributes to the general misbehavior of this class throughout the period.
I don't know whether the other Math III teachers are using notebooks, but since I'm using them in Math I, it was an easy decision to do so in Math III as well. One thing about the Math III grade weighting is that homework and classwork are each worth 20% of the grade (as opposed to Math I, where homework and classwork together total 25%) -- and most of my classwork component is the notebook. Thus a student who never turns in a notebook must be perfect on everything else to get an 80% in the class -- the highest realistic grade such a student will get is 79%, a C+. Fortunately, my Math III students are better than Math I as far as turning in notebooks is concerned.
As for technology in the classroom, I regularly use DeltaMath for homework and assessments and Desmos for some of the lessons. One of the other Math III teachers had created a single Desmos for all of Chapter 3 (on solving equations and inequalities). Thus I counted Desmos as a classwork grade (a boon to those few students who never turn in notebooks).
Dividing the School Year into Quinters
Page 1 of the notebook was a table of contents for the entire year. I assigned it the second full week of school, which was in mid-to-late August, since the first day of school was on the tenth. The last page of the first semester was Page 67, which was a review page for the final exam. I assigned it during finals week, namely the week of December 12th-16th.
And this leads to my next topic -- the calendar, specifically the school calendar. We know that school must start in early-to-mid August in order to end the first semester before winter break -- a calendar that I've often referred to as the Early Start Calendar. But many teachers are tired of having to return to school so early in August. And so the union took a survey of teachers to decide upon a new calendar for next year.
As it turns out, the winning proposal is to start school a mere one week later. We were told that we couldn't shorten the first semester (which was 85 days this year), since 85 is less than half of 180. But we could start school one week later, since we could then have the semester end one week later -- if the calendar is approved, the last day of the semester will be December 22nd, 2023.
My worry about all of this is attendance on finals days. Recall that the Math I teachers decided to give their finals on the 13th and 14th because they feared low attendance on the 16th (Las Posadas). While that ended up not being much of a factor this year, the 22nd is not the 16th. Many parents might not send the students to school on the 22nd, or for the last few days leading up to the 22nd.
I've pointed out that in some locations such as New York City, there is regularly school on December 22nd, and even the 23rd (including this year). But NYC starts school after Labor Day, and so first semester finals (or "Regents," as they're called there) aren't until January. I don't know what attendance was like in NYC on Festivus this year, but that doesn't matter. My worry is what will happen at a school that schedules final exams on the 22nd and 23rd.
As it turns out, some Orange County districts this year -- including the one where I used to sub from 2018-20 -- had finals on the 23rd this year. My other OC district regularly ends the semester on a Thursday rather than Friday, so the last final in that district was the 22nd. This is mainly a problem in years when Christmas falls on a Sunday -- last year, when the holiday was on a Saturday, the last day of school was either Thursday the 16th or Friday the 17th.
In school districts with a two-week break, in years when Christmas is on a Sunday, the last day of school before the break is Friday the 16th. But school can't resume on Monday, January 2nd, because that is a legal federal holiday, New Year's Day Observed. So instead, they open on Tuesday the third -- and then there would be only 179 school days in the year unless that day is made up at some point. So having school until December 23rd (and resuming on Monday the 9th) avoids that problem -- the school year is a clean 180 days with no need to make any other changes.
No matter what, we must choose between starting the first semester in early August and ending it with final exams just days before Christmas. We can't start school later -- say after Labor Day -- because we can't fit half the school year, 90 days, between Labor Day and Christmas. But we might be able to fit about two-fifths of the year between September and December.
Six years ago on the blog, I introduced the concept of quinters -- dividing the school year into five terms instead of four quarters. Then two of these quinters fit comfortably between the Labor Day and Christmas holidays. The first semester would consist of the first two quinters, and then Quinters 3-4 make up the second semester (approximately January-April).
The fifth quinter (May-June) would be for other activities -- AP exams, SBAC or state tests, field trips, and other enrichment activities or projects. Indeed, a few MTBoS teachers have written about the concept of a "Winterm" right after winter break:
https://ispeakmath.org/2017/01/08/student-blogging-class-2017/
My fifth quinter would be similar, except it would last most of May and June (as opposed to a single week or two of Winterm). Students who fail classes can repeat them during the fifth quinter (if not during summer school). It would remove the need to have eight period days (as we've seen some local schools implements in recent years).
Let's see what a possible Quinter Calendar might look like. Let's consider the worst-case scenario -- when Labor Day is on September 7th, the latest possible date -- and see whether we can squeeze in 72 days between Labor Day and Christmas.
This will follow the old calendar that I followed as a young student -- back when school in November lasted until Thanksgiving Eve, and there were just two weeks of winter break. In particular, it closely follows my calendar for senior year (a year when Labor Day fell on September 7th):
So we notice that there are 70 days before winter break In some years there might be an extra week before Christmas, bringing us to 75. Our goal is to have 72 days in the first two quinters -- and 72 lies right between 70 and 75.
There is one problem with this calendar, though. This post might be labeled "Kwanzaa Post," but the African-American holiday that matters to us the most is the newest federal holiday, Juneteenth. On this calendar, Juneteenth would fall on June 19th, a Saturday -- so the observed federal holiday would be on Friday the 18th instead.
But on this schedule, the school is open on that holiday (that clearly wasn't a federal holiday in my senior year.) Sure, it's just for the teachers and not the kids, but still, you have teachers having to work on a federal holiday. There are a few ways to avoid this -- just have the last day of school be June 17th with no extra teacher check-out day, or eliminate Lincoln's Birthday (which is not a federal holiday) so that the last day for students is on June 16th, with teacher check-out on the 17th.
This problem only occurs in years when Labor Day is on September 7th. In all other years, Day 180 and the teacher check-out day both occur before the federal holiday. (It's just unlucky that the latest possible Labor Day, September 7th, corresponds to the earliest possible Juneteenth, June 18th.)
We can check to see when the other quinters will end. Day 36 is on Wednesday, October 28th, Day 108 is Monday, March 1st, and Day 144 is Tuesday, April 27th. Since this is based on a late Labor Day, these represent the latest the quinters can began and end. So for example, the first quinter would end on the Wednesday on or before October 28th (that is, the fourth Wednesday in October).
OK, so this is one way to implement a Quinter Calendar. If you want to have the entire week off for Thanksgiving or three weeks for Christmas, then you must either start the year before Labor Day or end it after Juneteenth.
By the way, even before the federal holiday Juneteenth was created, the "do not pass" date at the end of the year would be the summer solstice, around June 21st. There usually isn't a significant difference between the 19th and the 21st, so we might as well take the federal holiday to be the "do not pass" date (though the example calendar above is the one where 19th vs. 21st is significant).
Calendar Reform and Quinters
Since I'm promoting a Quinter Calendar, I ought to apply quinters to the various reform calendars that I've posted on the blog. But we shouldn't blindly apply quinters just for the sake of doing so. The original reason to apply quinters (rather than quarters or trimesters) is because they fir the holidays in our calendar better. If a reform calendar has differently-spaced holidays, then applying quinters to it might be counterproductive.
For example, consider the following calendar created by James Colligan. This calendar divides the year into 13 months of 28 days each, plus a possible Leap Week called "Pax." Although Colligan didn't name his calendar, it's usually called the "Pax Calendar," named for its Leap Week:
https://calendars.fandom.com/wiki/Pax_Calendar
The extra month is called "Columbus" and is placed between November and December.
Now let's try to implement a school year on this calendar. We can assume that Labor Day is the first Monday in September (which works out to be September 2nd) and that Christmas is on December 25th (which works out to be Wednesday).
It's obvious that the existence of the extra month Columbus means that we can squeeze more days between Labor Day and Christmas. Indeed, we can easily place 85 days -- the same as the calendar in my current district -- between those two holidays.
My district began on a Wednesday, with teacher days Monday and Tuesday. Starting from Labor Day, the teacher days are Tuesday and Wednesday, so the first day for kids is Thursday, September 5th. The other non-student days are a teacher day on the first Monday in October (the 2nd), Veteran's Day (November 11th, a Wednesday) and Thanksgiving week (the last week of November), with the semester ending on Friday, December 20th.
So we've magically solved the problem by inserting an extra month. There's no need for quinters on this calendar, since our current semester fits between Labor Day and Christmas. While it works, the time between Thanksgiving and Christmas might drag on. Since we've placed the holidays in the same months as the Gregorian Calendar, the new month Columbus has no holidays, and so the holiday stretch would feel more like a Big March. (Perhaps we should place a federal holiday in the new month -- the most logical would be the holiday of the same name, Columbus Day. Then again, my district doesn't close for Columbus Day, so it would make no difference.)
But we must think back to why so many teachers object to starting school in August at all. If it's because a month named "August" should be a vacation month, then this Pax Calendar solves it. But some people might not want to work in August because of the temperature. All the Pax Calendar really does is rename the dates -- it doesn't change the weather on that day.
We should check to see what date on the Gregorian Calendar corresponds to Pax September 5th. As it's a Leap Week Calendar, the dates don't correspond exactly. But according to the link above, the Pax year 2023 doesn't began on the same day as the Gregorian year (despite both beginning on a Sunday) -- instead, Pax year 2023 begins on Gregorian December 25th. Then Pax December 20th works out to be nine days earlier -- Gregorian December 16th.
So the last day of the semester is the same actual day in both calendars. And since both calendars have the same number of holidays in the first semester, it follows that they begin at the same time. Thus Pax September 5th is the same as our actual first day of school, Gregorian August 10th (actually the 11th, since the Pax school year starts on Thursday, not Wednesday, after we moved Labor Day). In other words, Pax September has the same weather as Gregorian August -- that is, it's equally hot. If the goal is to avoid having school on the hottest days of the year, we have failed.
Of course, we can create our own Pax year such that September lines up with Gregorian September. It would then, as a result of the extra month Columbus, push Christmas back to Gregorian January. This is the only real way to include a full semester after the current Labor Day -- delay Christmas. If we wish to keep Christmas where it is, then we must go to quinters.
Quinters: Other 7-Day Calendars
One of my favorite calendars to promote on the blog is the Usher Calendar. Like the Pax Calendar, the Usher Calendar is a Leap Week Calendar. But this Leap Week Calendar is invisible -- instead, it redefines holidays and Leap Days (that is, February 29th) to fit the invisible Leap Week Calendar.
This calendar was first posted to Usenet over a decade ago by its creator, Andrew Usher. So it's not posted on the Calendar Wiki website, though the following calendar is quite similar:
https://calendars.fandom.com/wiki/North_American_Weekday_Holiday_Act
For example, Presidents' Day is the same on both this NAWHA Calendar and the Usher Calendar -- it lies in the February 16th-22nd range. It matches the Gregorian Prez Day unless it's February 15th, when the new calendars switch it to the 22nd.
Anyway, since the Usher Calendar resembles the Gregorian Calendar, applying quinters to Usher is similar to doing so to the Gregorian. In fact, we can mostly use the same calendar as above, except with Presidents' Day on February 22nd.
Usher created his calendar before Juneteenth became a federal holiday. As I've stated above, I like the idea of placing Juneteenth on a Saturday between the 13th and 19th (so that the holiday actually falls on a June --teenth), but observe the federal holiday on the following Monday, not the previous Friday. (It works out to be the third Monday in June, exactly three weeks after Memorial Day.) Then the last day for teachers can indeed be June 18th as listed above, since the federal holiday would be the 21st.
Oh, and there's one more thing to fix -- the date of Christmas. On his calendar, Usher defined Christmas to be the Sunday between December 21st and 27th. Notice that this would mean that there would always be school on Christmas Adam -- and this could be late as December 25th. Of course, in years when this happens, Christmas itself wouldn't be until the 27th, but still, it seems wrong to have school open (with final exams, no less) on a day that's been a holiday for so long.
And indeed, winter break is still only two weeks, with only Thanksgiving and Black Friday off in late November as well. It's possible to start school in August to accommodate both of these breaks, but how early should we go?
Recall that in the invisible Leap Week Calendar, Usher numbered the weeks from 1-53. In his calendar, Labor Day is Week 4, so the two weeks before Labor Day are Weeks 2-3. Week 1 is Leap Week, which runs from Sunday-Saturday, August 16th-22nd -- in years without Leap Week, the weeks are numbered from 2-53 (strange, yes, but that's how Usher numbered them).
Usher intended the school year to be fully contained within Weeks 2-53. Thus this is the earliest the school year should begin -- two weeks before Labor Day. When Labor Day is on its earliest possible date (September 1st), the school year begins on August 18th.
So we can extend winter break by moving the last week before Christmas up to Week 3 (and this solves the Christmas Adam problem right away). And the three days Monday-Wednesday of Thanksgiving week can be moved up to Wednesday-Friday of Week 2, with teacher days Monday and Tuesday.
Notice that there's still a teacher day on the day after Labor Day. We can keep it on this day (thus giving the kids a four-day weekend) or switch it to a different day (perhaps a Monday in early October, matching my current district).
I was hoping to make the quinters exact -- 72 days before winter break, 108 days after. But as it turns out, it's difficult to squeeze in 108 days between Epiphany (the 12th day after Usher Christmas -- a Friday in the January 2nd-8th range) and Juneteenth (the third Monday in June).
This stretch contains 23 weeks. Assuming one of these weeks is spring break, that leaves us 22 weeks -- in other words, 110 weekdays. So there are just two days to spare -- but we already know we need to place at least three federal holidays -- MLK Day, Presidents' Day, and Memorial Day. And that's not to mention other days we might wish to place -- Lincoln's Birthday, Good Friday/Easter Monday (depending on when spring break is), and so on.
Of course, you might wonder, why are we bound between Epiphany and Juneteenth anyway? (After all, there's been school on January 6th before, and Juneteenth is new.) The answer is that this calendar is meant to be perpetual (and perhaps implemented on the Gregorian Calendar someday, even without switching to Usher). Starting school before Epiphany in some years would mean starting before January 1st, and ending school after Juneteenth in some years would mean ending after the summer solstice. (I assume that even Usher can't change New Year's Day -- it must be when December becomes January -- and likewise he can't control the solstice.) So Epiphany and Juneteenth are Usher dates that stand as proxies for New Year's Day and summer solstice.
It's possible to have 108 days if we have a bare minimum of holidays -- MLK Day, Memorial Day, and Ski Week (including Presidents' Day) instead of spring break. But this isn't desirable -- the Big March would extend all the way to the end of May with no days off.
Instead, the quinters are only approximately equal. There are 75 school days before Christmas and 105 days afterward. This is the best that can be done on the Usher Calendar (and perhaps on the Gregorian Calendar as well).
Before we move on, note that there exist calendars that preserve the seven-day week, yet move all the holidays around. The most extreme example is the Fixed Festivity Week Calendar:
https://calendars.fandom.com/wiki/Fixed_Festivity_Week_Calendar
All the holidays are squeezed into four weeks of the year -- one holiday week near each solstice and equinox on the calendar. Then, as the link above points out:
Employees do not get paid holidays in any other week.
(In particular, New Year's Eve or "Sylvester" is the Sunday of holiday week, but January 1st, a Monday, isn't a holiday at all.)
Each season contains 12 weeks containing 60 weekdays. Notice now that it becomes very easy to set up a school calendar. Instead of quinters, this calendar naturally suits trimesters corresponding to the seasons of fall, winter, and spring. The winter and spring holiday weeks become winter and spring break, dividing the year into trimesters that total 180 days.
And summer break would be longer. It's a Leap Week Calendar so the correspondence isn't exact, but if it's set up so that the summer holiday week always contains the summer solstice, then the fall holiday week would end up taking the fall equinox. Then kids could have a true summer break, spanning the entire season of summer, from solstice to equinox,
But then all three trimesters would become three Big Marches. (It would be just like having no holiday between Ski Week and Memorial Day in the Usher Calendar above, except times three.) Once again, I'm not quite sure whether this is desirable.
Quinters: 6-Day Calendars
Before we attempt to apply quinters to calendars with six days per week rather than seven, we must remind ourselves that we shouldn't apply quinters at all unless they naturally fit the calendar.
Of all the possible six-day calendars, the Sexagesimal Calendar is best suited for quinters:
https://calendars.fandom.com/wiki/Sexagesimal_calendar
http://www.sexagesimal.org/en_propos.php
The year is divided into six "sixths" of 60 days each. The first sixth, "Frigee," starts on the day of the winter solstice -- as a result, the fourth sixth, "Granee," starts on the summer solstice. Then Granee could become a summer break, with the other five sixths becoming the five quinters of the school year.
Indeed, instead of starting after Labor Day, the school year starts after "Liber Day." The extra five days of the year become holidays placed between the sixths. The calendar author most likely chose Liber for the August holiday because Liber is the god of books -- as in school books for the first day of school.
Each sixth contains 10 weeks of six days, with four weekdays each. Since each quinter requires only 180/5 = 36 days, there are nine weeks of school and one week of holidays.
These holiday weeks can follow the adventitious days already listed. For example, the author already lists Bacchanal day as subsuming "lover's day" (Valentine's Day) and "last day of Carnival" (Mardi Gras), so these can be expanded to a full week similar to the Fixed Festivity Week Calendar.
Like Fixed Festivity Week the holidays become concentrated into one week, but instead of having to endure twelve five-day weeks before getting a break, we only have to endure nine four-day weeks. And of course, four-day weeks fit odd/even block schedules better than five-day weeks.
There are other calendars similar to the Sexagesimal Calendar. Double Rainbow is the closest:
https://calendars.fandom.com/wiki/Double_Rainbow_Calendar
But its seasons don't line up with holidays as well as Sexagesimal -- for example, Violet season corresponds to December-January, so Christmas would be right in the middle of the season. And neither Yellow nor Orange lines up with the desired summer break.
The Primavera Calendar is essentially the Sexagesimal Calendar, except with each sixth divided into two months of conventional length:
https://calendars.fandom.com/wiki/Primavera_Calendar
And the Raenbo Calendar is nearly identical to Primavera, except that the names of the months and days look like their Gregorian counterparts, and the dates are written in dozenal/base 12. (The link to the Raenbo Calendar no longer exists.)
Conclusion
As Calendar Reform week continues, we'll look more at how to implement quinters in calendars with longer weeks.
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