Last Post of the Old Decade

Table of Contents

1. Introduction
2. Pappas Question of the Day
3. Definition of Decade
4. A Mild Implementation of the Eleven Calendar
5. A Radical Implementation of the Eleven Calendar
6. A Compromise That Respects Sabbaths
7. One Last Compromise
8. Loose Ends with the Eleven Calendar
9. Conclusion

Introduction

This is my second of three winter break posts. It's also my final post of the calendar year 2019 -- thus making it the last post of the calendar decade of the 2010's.

There has been much discussion this month regarding the end of the decade. In addition to "Year in Review" news stories, there have also been "Decade in Review" stories. Even though today's post is mainly about the Eleven Calendar, I'll also be retrospective about the past ten years of my own life.

Pappas Question of the Day

Today on her Mathematics Calendar 2019, Theoni Pappas writes:

What is the perimeter of this square?

(Here is the given info from the diagram: the diagonal is sqrt(91.125).)

Well, since the diagonal divides a square into two 45-45-90 triangles with that same diagonal as the hypotenuse, the leg of the triangle -- the side of the square -- is sqrt(91.125)/sqrt(2), which we can simplify as sqrt(45.5625) = 6.75. The square's sides add up to four times this, or 27. Therefore the desired perimeter is 27 -- and of course, today's date is the 27th.

Last week, we studied perimeter in Lesson 8-1 of the U of Chicago text. But 45-45-90 triangles -- used to get from diagonal length to side length -- don't appear until Chapter 14. (It's possible to get the side length using only the Pythagorean Theorem, studied later in Chapter 8.)

At some point we probably used a calculator to find a square root. It's possible to avoid a calculator if we cleverly eliminate the decimal under the square root. If s is the desired side length, then:

s sqrt(2) = sqrt(91.125)
s sqrt(2)sqrt(2) = sqrt(91.125)sqrt(2)
2s = sqrt(182.25)
2s sqrt(4) = sqrt(182.25)sqrt(4)
4s = sqrt(729)

Notice that 4s is the desired perimeter. Some teachers have their students memorize their perfect squares up to 30^2, and so we might even get sqrt(729) = 27 without a calculator. Otherwise, we might guess sqrt(729) = 27 and find 27^2 to verify it.

Once again, there is no 2020 Pappas calendar. This is my final post of the year, and thus it's my last mention of a Pappas problem on the blog. It's not her last Geometry problem, though -- next week she asks how many edges a dodecahedron has (given it has 20 vertices and 12 faces). We can use Euler's formula to find that it has 20 + 12 - 2 or 30 edges -- and the date of that problem is the thirtieth.

Her final problem on New Year's Eve isn't Geometry, but probability (which might be taught in a California Geometry class anyway). She asks for the probability of choosing two successive red marbles from a bag with six red, 21 blue, and four green marbles. Since there are 31 total marbles, the desired probability is 6/31 * 5/30 = 1/31 -- and the date of that problem is the 31st.

That wraps up the Theoni Pappas calendar for this year. I've enjoyed reading her calendar and answering questions on the calendar all year -- as well as during all eight years during the decade when she published her calendar. The only years this decade when she didn't have a calendar were 2013 (the year before I started this blog) and 2017.

And we already know that the new decade will begin without a 2020 calendar. Once again, I just hope that 2019 won't turn out to be the final Pappas calendar.

Definition of Decade

Twenty years ago, there was much discussion about whether 1999 or 2000 was the last year of the century and millennium. The nonexistence of the year 0 means that the twentieth century and second millennium didn't end until 2000, with the 21st century and third millennium starting in 2001.

But this seems to clash with our definition of decades. Indeed, the QNTM website, which critiques all versions of Calendar Reform, includes the following item on its list:

https://qntm.org/calendar

by that logic, 2000 was the final year of the Nineties

In other words, if 2000 was the final year of the twentieth century and third millennium, why shouldn't we consider it to be the last year of the 1990's.

The answer is that there's a difference between the "nth unit" (millennium, century, decade) and the unit (millennium, century, decade) of the x's. For example, the century of the 1900's was 1900-1999 -- the years with 1900 in their names. But the 20th century was 1901-2000. Thus the 1900's and the 20th century shared 99 out of 100 years.

Following this pattern, the millennium of the 1000's spanned 1000-1999, but the second millennium was years 1001-2000. They share 999 out of 1000 years.

And by the same pattern, the decade of the 1990's spanned 1990-1999, but the two hundredth decade was years 1991-2000. They share nine out of ten years.

The point here is that no one ever uses the phrase "200th decade." The only names given to the decade are 1990's or just '90's. Both of these names imply the digit 9 in the tens place, and so 1999 was the last year of that decade.

Both "1900's" and "20th century" are commonly used to refer to a century. I suspect that "20th century" is much more common, hence the insistence that the century didn't end until 2000. In particular, Google reveals 866 million results for 20th century and only 14 million for 1900's -- and the first result refers to the decade of the 1900's (that is, 1900-1909). Likewise, 2000's is most likely to refer to a decade, not a century or millennium.

In fact, the millennium doesn't appear to have a commonly used name at all. Neither "millennium of the 2000's" nor "third millennium" is often used. The insistence that "the millennium" didn't end until 2000 is likely in analogy with centuries (not decades), since a millennium is closer in length to a century than a decade.

The QNTM author makes his opinion clear with another item in the list:

there needs to be a year 0 and negative year numbers

With a year 0, the century and millennium ended in 1999. This eliminates the problem with "the decade" ending in 1999, one year before "the century" and "the millennium" ending. Instead, they would all end in 1999.

Here's a link where this issue is discussed:

https://www.npr.org/2019/12/27/791546842/people-cant-even-agree-on-when-the-decade-ends

Since I labeled this post "Last Post of the Old Decade," I'm taking the "Team Zero" side. I agree that the 203rd decade doesn't start until 2021, but we don't use "nth decade" to name decades. The decade that starts next week is the 2020's, or just the '20's.

This leads to one more related question -- on this blog, I've defined the "Millennial Generation" as consisting of those individuals who were born in the old millennium and graduated high school in the new millennium. If 2000 was the last year of the old millennium, does this make someone born in that year a Millennial? For that matter, is someone born in 1982 and graduated in 2000 a member of the Millennial Generation?

Actually, generation boundaries (or cusps) are much fuzzier than this. Not only is it uncertain whether a 2000 baby is a Millennial, but going a year or two either way (1998, 1999, 2001, 2002) keeps us in the gray area. Likewise, 1980-1984 is a cusp regarding the start of the generation. The in-between birth years of 1985-1997 are nearly always included in the Millennial Generation.

I myself was born in 1980, which is a part of the generational cusp. Lately, I've been hearing a new term, "X-ennial," to refer to the cusp between Generation X and the Millennial Generation. Similarly, the 1998-2002 cusp might be called "Z-ennial." This suggests that the Millennial Generation itself should be "Generation Y" -- a former name for this generation before the millennium caught on.

The Z-ennials were born just as we X-ennials were graduating high school. This suggests that we are currently on the cusp of a new generation after Gen Z (that is, something like 2016-2020). Of course, it remains to be seen what the next named generation after Z will be.

A Mild Implementation of the Eleven Calendar

At this point I will attempt to give a full implementation of the Eleven Calendar. So far, we know that this calendar contains 11 days per week, three weeks per month, and 11 months per year. But I have yet to give the days or months any names.

(Of course, this only adds up to 363 days. It's possible to add two or three blank days per year, or a Leap Week every five years or so. But this is beyond the scope of today's post. Here I'm only concerned with what the main part of the calendar, with its 363 days, looks like.)

There are several ways to implement the Eleven Calendar. One way is a mild approach -- keep as much of the Gregorian Calendar as possible. This includes some of its day and month names, as well as some holidays. More ambitious approaches destroy familiar aspects of our calendar.

Let's start with the mild approach. We can characterize this approach as requiring as few boxes checked on the QNTM list as possible. Every version of the Eleven Calendar needs the following box to be checked:

(x) every civilisation in the world is settled on a seven-day week

since there are obviously eleven days per week, not seven.

In our mild approach, we could keep the seven old day names and add four new names. But instead, let's divide our 11-day week into two part-weeks -- one with five and one with six days. This allows us to reuse our old day names and maintain some familiarity. We can also refer to previous Calendar Reforms that have five- or six-day weeks, such as:

Five-Day Examples:
https://calendars.wikia.org/wiki/Long_Summer_Modified_Gregorian_Calendar
https://calendars.wikia.org/wiki/Luni-solar_Modified_Gregorian_Calendar

Six-Day Examples:
https://calendars.wikia.org/wiki/60-Week_Calendar
https://calendars.wikia.org/wiki/6-Day_Week_Solar_Calendar_with_common_Muslim/Christian_weekend

Notice that the last calendar listed here keeps the Muslim (Friday) and Christian (Sunday) sabbaths (as its name implies), but drops the Jewish sabbath (Saturday). Instead, I take the suggestion that other Calendar Reformers make -- drop the most unpopular day of the week, Monday (which isn't the sabbath of any religion).

For the five-day part of the week, we drop Monday and Tuesday. Thus every 11-day week contains one Tuesday and two each of the days from Wednesday-Sunday.

Note that it might be preferable to drop Tuesday and keep Monday in order to avoid having two days starting with T -- so that TF can unambiguously mean "every Thursday and Friday," not "every Tuesday and Friday." Here I drop Monday instead only because "everyone hates Mondays."

Let's look at the months next. There are 12 Gregorian months and we need only 11, so the easiest thing to do is drop a month. Which month should we drop?

Some Calendar Reformers state that their least favorite month is February, and so this is the month they'd wish to drop in an 11-month calendar. Why is February hated so much? Well for one thing, most Calendar Reformers live in North America or Europe, where February is winter -- this isn't so terrible in California, but further north, Februaries are freezing. But for Australians and other in the south, February means summer.

Also, most Calendar Reformers are male. February means Valentine's Day -- a holiday when women are the main recipients of gifts and men are the main givers. So Valentine's Day is a holiday that many men can't afford. But in Japan and some other Asian countries, men are the main recipients of Valentine's Day gifts. Women receive gifts a month later, on White Day (same as Pi Day). And singles receive gifts two months later, on Black Day.

So I don't necessarily wish to skip February just because Western men hate Valentine's Day, ignoring the Asian men and Australian outdoor lovers who enjoy it. Of course, skipping any month of the year has its advantages and disadvantages. As teachers, for example, we might prefer to skip March in order to eliminate the Big March.

I don't wish to commit to which month to skip in this post. Instead, I will blog two possible calendars, each with its own skipped month. I randomly select January as the month to skip in the first version and October in the second version.

In the no-January version of the calendar, February is the first month of the year, and every month needs to be renumbered. I suggest starting with February as zero rather than one. This allows September-December to be numbered as months 7-10, in line with their Latin names. On the other hand, in the no-October version, let's keep January as month 1 with no month 0. Without October, there's no hope of matching the Latin names anyway, and keeping January as 1 allows Months 1-9 to match the Gregorian calendar.

Notice that New Year's Day in the new calendar doesn't necessarily have to match January 1st in the old calendar. Indeed, if we were to insist that the Eleven Calendar start on the same day as the Gregorian Calendar, then in the no-January version, 31 of February's 33 days would correspond to old January, with only the last two days corresponding to old February.

It's often desirable to make as many days as possible land in the same month on both calendars. For example, in the International Fixed Calendar (with 13 months), New Year's Day is the same, and the new month (Sol) is placed as far away New Year's Day as possible -- between June and July. Then all of new January and new December land in the corresponding old months, as do most of new February and new November. New March and new October have slightly fewer days in the old months of the same name, and progressively less until only about half of new June and new July land in old June and old July. The other halves of old June and old July are part of new Sol. This scheme allows the maximum overlap between old and new months of the same name.

For an 11-month calendar, we do the opposite. Instead of adding new Sol to take half of old June's and old July's days, the dropped month's days should be given half to the month before and half to the month after. Thus in the no-January version, new February should start near old January 16th. This also allows the month directly opposite the skipped month -- in this case July -- to be nearly aligned with the old month (depending on how the blank days are assigned). Then July 1st would be the same as the Gregorian Calendar, as would the Fourth of July, Independence Day.

In the no-October version, new November should start around old October 16th. Depending on how blank days are set up, April Fool's Day should be aligned with the Gregorian date. Also, notice that new January 1st, New Year's Day, now lies near the winter solstice. (In the no-January version, we can instead place April 1st near the spring equinox.) Some Calendar Reformers like starting months or years near solstices and equinoxes. To me, this is only desirable if the number of months is a multiple of four. In calendars with an odd number of months (like 11 or 13), at most one month can start at a solstice or equinox anyway, so why even bother?

We now wish to place holidays on the calendar. It's easiest to allow most holidays to remain in their previously-defined months, keeping their old definitions if possible. This means that holidays in the skipped months would no longer exist.

Well, we can't make New Year's Day disappear, since new years would still exist. In the no-January version, New Year's Day would now be February 1st.

In the Gregorian Calendar, most holidays are always on a Monday. In our new calendar, it might be easiest just to place those holidays on a Tuesday (assuming the no-Monday version), since every eleven-day week contains only one Tuesday anyway. This can include New Year's Day -- thus each week and month should begin on a Tuesday. The three Tuesdays in a 33-day month are the 1st, 12th, and 23rd, so these are when we should place most holidays.

Here's what the US Federal Holidays would look like on the new calendar:

New Year's Day: January 1st (February 1st in no-January version)
MLK Day: January 12th or 23rd (disappears in no-January version)
President's Day: February 12th or 23rd. Note that the 12th is an actual president's birthday (Lincoln), but the official name of President's Day is "Washington's Birthday," not Lincoln's. The 23rd is closer to Washington's actual birthday on the 22nd.
Memorial Day: May 23rd
Independence Day: July 4th is a Friday in the new calendar, so let's keep it there.
Labor Day: September 1st
Columbus Day: October 12th (disappears in no-October version). This is the actual day that the explorer and his ships landed in the New World.
Veteran's Day: November 12th
Thanksgiving Day: This is a tricky one. If we keep the definition "fourth Thursday in November," then this would be November 19th. We might prefer the next Thursday, the 25th, to be Thanksgiving instead since this is within Gregorian Thanksgiving range.

If we keep Thanksgiving on the 19th, then not only is Black Friday on the 20th a no-work day, but so would Wednesday the 18th, as this is the day after Sunday the 17th  (in order to avoid having a week with a lone workday). This is one of the weeks that doesn't have a Tuesday. On the other hand, with Thanksgiving on the 25th, there can theoretically be both work and school on Tuesday the 23rd and Wednesday the 24th. But many schools already close the day before Turkey Day, and once we take Wednesday off, then we must also take Tuesday off to avoid a lone workday.

It's also possible just to change Thanksgiving to Tuesday the 23rd and drop the need to have Turkey Day on Thursday. (But this would ruin Black Friday sales the day after Thanksgiving.)

If we keep Christmas on December 25th, then this is also a Thursday. Many of the arguments about Thanksgiving on November 25th also apply to Xmas on December 25th. Since there is never school on Christmas Eve, there can't be any school on Christmas Adam either (to avoid a lone day). It's also likely that more offices will take Friday off for Boxing Day, to avoid a lone day.

Let's now try to make a 180-day school year out of this. Notice that every 11-day week contains exactly seven school days. We might consider having 27 weeks of school -- since 27 * 7 = 189, this allows nine extra days for holidays (including the Tuesday holidays mentioned above).

Since the whole year has 11 * 3 = 33 weeks, this leaves six weeks for vacations (including winter, spring, and summer breaks). We might wish to take a week off for the Thanksgiving, winter, and spring breaks. Notice that winter break only needs to be one week long (the whole week of Christmas plus New Year's Day, return on the 2nd). And Thanksgiving only a half-week (recall that a week consists of 11-days, so taking Wednesday-Friday November 23rd-25th is only a half-week). We might choose to add an extra half-week to winter break (Tuesday-Friday the 2nd-5th).

Regarding spring break -- I haven't defined an Easter yet. If we choose to keep the lunar definition, notice that in the no-January version, April 1st is the spring equinox. Thus Easter would be always in April in this version. (Possible Sundays are 6th, 11th, 17th, 22nd, 28th, and 33rd.) In the no-October version, April is aligned with the Gregorian Calendar, and so Easter in March is possible (with about the same frequency as a Gregorian March Easter.)

This leaves three full weeks for the summer break -- that is, one full month. Let's keep July as the month with no school. That completes our mild implementation of the Eleven Calendar, except for a few loose ends.

(For example, in the no-October version, can there be a Halloween? This holiday is popular enough for us to keep. We might argue that Halloween really means "All Hallows' Eve" or the day before All Saint's Day, which remains as November 1st. Thus Halloween is Sunday, September 33rd.)

This implementation keeps the Eleven Calendar as close to the Gregorian as possible. It's good for those who want to make fewer changes, but it suffers some of the same problems. Thanksgiving, Christmas, and other holidays still exist, so we still have problems with airline travel, the need to take extra days off to accommodate travel, and so on.

A Radical Implementation of the Eleven Calendar

The most radical version of the calendar eliminates holidays completely. The days are simply numbered 1-11, as are the months.

I like the version of the workweek that I mentioned in yesterday's post -- three workdays, a midweek day off, three more workdays, and a four-day weekend. But which days are off days, and which ones aren't, can be different for each person.

With six workdays per week, we need 30 weeks of school, so there's only three weeks off. We combine this to a single month off -- and for each student and worker, the month off is the one containing that person's birthday. (For example, my birthday is late in the year, so assuming that the first month lines up with the Gregorian Calendar, my birthday would be in Month 11. Thus I would get Month 11 off.)

Now here's what the workweek looks like -- the midweek day off matches the number of the month that is taken off. (So I would get Day 11 off.) This completely determines the rest of the week. (For me, I'd work Days 8-10 and 1-3, leaving Days 4-7 as my four-day weekend.)

This version solves some of the problems with the Gregorian calendar. Because different people have different holidays, there's no holiday period when demand exceeds supply at the airports, so airlines can't jack up the prices. The same is true for amusement parks, with their blackout dates close to major holidays. At schools, it also solves the redshirt problem -- every student starts kindergarten the first full month after he or she turns five, and is scheduled to graduate high school during the last month before he or she turns eighteen.

But of course, there are lots of problems with this calendar. Indeed, previous nations such as the French (ten-day week) and Soviets (five-day week) tried something similar to this, where holidays and weekends are replaced with workers on different "shifts" like this. One problem faced was that the new systems didn't respect religious sabbaths.

Another problem was that family members might end up on different shifts. In some cases, this might be desirable (for example, if a father and mother are on different shifts, then there's more likely to be someone home to take care of the children). But it also means that the family members can't be together when they want to (for example, to go on vacation). Actually, the Eleven Calendar is designed to minimize this problem -- everyone has a four-day weekend and no one ever works more than three consecutive days, so every pair of individuals is guaranteed a common day off. But still, the vacation months will be different for people born in different months.

It's possible to reduce some of this by using last names as the basis for determining off-days. (This isn't easy with the Eleven Calendar, but I once saw a calendar with 14 months of 26 days each, with the days lettered A-Z. The letters can be used to determine the off-days.) Then people with the same last name (that is, family members) get the same days off.

But then again, this isn't my favorite version of the Eleven Calendar week anyway. I like the week layout (3 on, 1 off, 3 on, 4 off), but there are better ways to implement it.

A Compromise That Respects Sabbaths

Let's begin by trying to respect religious sabbaths. These are Friday for Muslims, Saturday for Jews, and Sunday for Christians. (Only the Abrahamic religions have anything resembling a weekly sabbath, so I'm not intentionally leaving out non-Abrahamic religions here.)

Just as important as the sabbath are the days of preparation for the sabbaths. This is especially important in traditions where the day starts at sunset rather than midnight -- for example, a Jew who works 9-5 Monday-Friday will often have the sabbath begin before work ends on Friday, especially in the winter when sunset is so early.

So the period Thursday-Sunday includes sabbaths for all three Abrahamic religions along with their preparation days. My ideal 11-day week contains a four-day weekend anyway, so we might as well let those four days be Thursday-Sunday to accommodate the religions.

As for the other seven days, we'll just number them as Days 1-7. Then Day 4 becomes the midweek day off. Schools are thus open Days 1-3, closed Day 4, open Days 5-7, and closed Thursday-Sunday.

Once again, there are six days per school week, so we need 30 school weeks with only three potential vacation weeks. But this time, we won't have a single month of no school. Instead, we'll divide the vacation into three separate weeks -- one each for winter, spring, and summer breaks

If we assume that the winter break is near Gregorian Christmas, and if we wish to space the three holiday weeks equally around the year, then spring break is in late April (Gregorian -- that is, a bit later than Easter, approaching International Labor Day) and the summer break is in late August (Gregorian, approaching American Labor Day).

With four-day weekends every week, the hope is that this will reduce the need to take extra days off during the year. But this doesn't avoid the airline/amusement park problem -- the holiday weeks are well-defined, allowing businesses to jack up prices around those holidays. We might trying adding some flexibility -- for example, if we define Easter as the Sunday near (Gregorian) April 25th, then schools may choose to take the week before or the week after Easter off. The same is true for Christmas (if defined to be on a weekend, especially if New Year's is no longer defined to be a week after Christmas). But that just means that businesses can raise prices for two weeks. And of course, the four-day weekends are also set up perfectly for price gouging.



One Last Compromise

Is it possible to compromise one final way so that sabbaths are respected, yet there are different shifts available in order to beat businesses and get lower ticket prices for airlines and amusement parks?

Suppose within each country, we designate only one day to be the sabbath. Christian nations (including the US) might choose Sunday, Israel might select Saturday, and Muslim nations might choose Friday. (To keep the rest of this post simple, assume that the US chooses Sunday.)

Now instead of considering all 11 shifts (as given under the "Radical Implementation" above), we only look at those with Sunday as an off-day. There are five such shifts, whose weekends are:

Thursday-Sunday
Friday-Day 1
Saturday-Day 2
Sunday-Day 3
Days 4-7 (with Sunday as the midweek day off)

Now we assign students and workers to these five shifts. Some might be more desirable than others -- for example, those for whom a preparation day is important might choose one of the shifts with Saturday included in the weekend. Religious minorities might choose shifts with Friday off (as either a preparation day for Jews or the sabbath itself for Muslims). Still others might prefer Day 1 off.

This instantly beats amusement park blackout plans. Parks can't blackout everyday -- even if they blackout seven days (Sunday and the three days before and after Sunday -- that is, every possible four-day weekend including Sunday), then everyone's midweek days off are white. (The exception is the shift that chooses Sunday as the midweek day off -- but then their entire four-day weekend ends up white.)

Airlines and other travel-related businesses are trickier to beat -- trips last multiple days, and as long as there are holidays, there will be price gouging near those holidays. There are four-day weekends and so less need to wait until a holiday to travel, but airlines can still raise prices on the days surrounding Sunday.

One simple version of the Eleven Calendar simply starts the new year on Gregorian March 1st and places the blank days at the end of the year -- February 27th, 28th, and possibly the 29th. If we simply named each month after the Gregorian month in which it begins, then February (the month which many Western men hate) is dropped, and September-December are months 7-10 to fit their Latin number names. (The alternative is to drop January, in order to maintain the Latin names.)

December, the tenth month, now begins on Gregorian December 23rd. If we decide to transfer all holidays so that they remain close to their Gregorian equivalents, then Christmas now becomes the third day of December. If we declare this date to be Sunday (the Christian sabbath) to guarantee that it's an off day, then the first of December (and hence of every month) becomes a Friday. (If you prefer, we might call the numbered days 4-10 instead of 1-7.) Then it's now possible to take either the week before or the week after Christmas off, allowing for some flexibility. (Recall that New Year's is now March.) Some schools might even choose to take off weeks far away from Christmas, just as they often now ignore Easter.

(It's also possible to declare the 25th of December to be Christmas, even if this is much later than Gregorian December 25th. This is 22 days or two weeks later, hence it's still good to start all months on Friday if we wish to keep Christmas on the sabbath.)

Loose Ends with the Eleven Calendar

We're essentially done with our Calendar Reform posts for the year. But there are a few more things I'd like to say about the Eleven Calendar before we leave it.

So I've stated that for now, my favorite version of the calendar has weeks beginning with the three Abrahamic Sabbaths (Friday, Saturday, Sunday) followed by generic number names -- Day 4, Day 5, and so on to Day 11. I should probably make these names look more like weekdays -- Fourday, Fiveday, up to Elevenday.

And the eleven months go March, April, May, and so on up to January. March 1st, New Year's Day, is on the same named day in the Gregorian Calendar. The last 2-3 days (February 27th, 28th, 29th) are blank days so that every week starts on Friday, March 1st. Each month begins in the Gregorian month with the same name, which is why there is no February -- no month starts in Gregorian February.

At this point, you may wonder about the rule for Leap Days. When I first posted the Eleven Calendar, I mentioned a 33-year cycle with eight Leap Days per cycle -- yet today, I state that each year begins on Gregorian March 1st (thus implying the Gregorian leap cycle). Anyway, the intended leap cycle is indeed the 33-year cycle. But since I can't implement the Eleven Calendar single-handed in the real world, in reality I must convert from the actual calendar in use (the Gregorian Calendar) to my own Eleven Calendar. Hence in reality I have to use the Gregorian leap rules. (It would certainly be desirable to start my calendar on March 1st on an established calendar that actually use a 33-year cycle, such as the Dee-Cecil Calendar.)

The school week in each 11-day week goes 3 on, 1 off, 3 on, 4 off. But each school operates on a different shift (in order to beat airlines, amusement parks, etc., raising prices on the weekend). As I've explained, all shifts will have a day off on the sabbath of the majority religion in a given country -- thus in the majority-Christian US, all shifts will be closed on Sunday. This leaves five logically possible shifts. Let's label each of these five shifts in a way so that members of each religion can be off on its respective sabbath, with the weekend starting on its respective Day of Preparation:

Muslim shift: on Fourday-Sixday, off Sevenday, on Eightday-Tenday, off Elevenday-Sunday
Jewish shift: on Fiveday-Sevenday, off Eightday, on Nineday-Elevenday, off Friday-Fourday
Christian shift: on Sixday-Eightday, off Nineday, on Tenday-Friday, off Saturday-Fiveday
Librarian shift: on Sevenday-Nineday, off Tenday, on Elevenday-Saturday, off Sunday-Sixday
Atheist shift: on Elevenday-Saturday, off Sunday, on Fourday-Sixday, off Sevenday-Tenday

The "Librarian shift" is so-called because many libraries are closed on Sundays and Mondays, so this is the equivalent in my calendar. The "Atheist shift" is off on Sundays because all shifts are, but for this shift, Sunday is the midweek day off. The assumption is that this shift is less interested in religion (hence no extra days off surrounding Sunday) and perhaps even more interested in avoiding weekend prices at businesses (hence observing the Sevenday-Tenday weekend, far away from Sunday).

Now the school year will be divided into three trimesters of ten weeks each (to give the usual total of 180 school days), each followed by a week off (33 total 11-day weeks in the calendar year). We place Christmas on Sunday, December 3rd, since this corresponds to Gregorian December 25th. Since New Year's is on March 1st (far away from Christmas), schools now have the option of taking the week before Christmas or the week after Christmas off (similar to Easter and spring break). Again, the idea is for there to be shifts rather than having every school take its breaks at the same time.

In fact, Easter should now be eleven weeks after Christmas, which works out to be April 25th in my calendar (April 27th Gregorian). Even though this is a bit later than Gregorian Easter, it works out so that schools that take the week before or week after Christmas off can also take the corresponding week of Easter off, and thus fit exactly one trimester between the holidays.

Notice that it's possible to take a week off that's not adjacent to Christmas, just as many schools do now with Easter. Thus it's possible for there to be four vacation shifts:

Penultimate week before Christmas/Easter
Week before Christmas/Easter
Week after Christmas/Easter
Second week after Christmas/Easter

And just as there's a fifth weekly shift (the "Atheist shift"), we might even have a fifth annual shift that takes no week near Christmas nor Easter off, but the week halfway in between instead. This week turns out to be close to March 1st, New Year's Day, so those who would prefer to take New Year's off than Christmas/Easter might choose this fifth shift.

Thus there are 25 possible shift combos, five for the weekly cycle and five for the annual cycle. But we might reduce this to five, since some weekly/annual cycles might go together. For example, the Librarian shift might choose the week before Christmas off to avoid working on Christmas Eve. (It's also possible for the shift that's off Elevenday-Sunday likewise to choose the week after Christmas off to avoid working on Boxing Day, but some workers on this shift might be Muslims for whom Christmas/Boxing Day aren't important holidays.)

Those on the "Christian shift" are off Saturday-Fiveday, and thus they are automatically off from Christmas Eve to the second day after Christmas. I'm not sure which they would prefer -- to take the week before Christmas off (to avoid working on Christmas Adam, as well as Good Friday in spring), or the week after off (to avoid the actual 12 Days of Christmas, and Bright Week in spring).

If I were to choose a shift, which one would I personally choose? This is an interesting one. Recall that in my "radical version" of the calendar, everyone gets the birthday month off. It's possible for me to take my birthday into consideration and choose a shift which will allow me to get my birthday off.

Notice that while only the March dates are aligned with their Gregorian counterparts, the first eleven days in Gregorian December likewise fit into an 11-day week starting with Friday (although these dates are now labeled November 12th-22nd). Thus I know that my December 7th birthday will fall on Sevenday in the new calendar.

I can get Sevenday off as my midweek day off if I take the "Muslim shift" above. (Disclaimer: I am not Muslim.) Moreover, if I take the penultimate week before Christmas off as my vacation week, that week includes my birthday, so I'd get my entire birthday week off. I'm actually torn here between taking my birthday week off and taking the week after Christmas off. (Since this shift is off from Elevenday-Sunday, I'd get the days leading up to Christmas off anyway, so it's more important to get the days after Christmas, including the day after the holiday, off.)

Another choice for me is the "Atheist shift," since it has Sevenday-Tenday off. It thus gives me my birthday and the next three days off. My assumption is that the "Atheist shift" is also the one that takes New Year's off instead of any week near Christmas (or my birthday).

Oh, and speaking of New Year's, there are some anomalies around that week. On most calendars with blank days, we expect those blank days to be days off for everyone. But notice that on my calendar, the blank days appear at the end of the week (between Elevenday and Friday). Thus someone on the "Christian shift" would have 3 on (Sixday-Eightday), 1 off (Nineday), 3 on (Tenday-Elevenday), 2-3 days off (blank days), 1 on (Friday), and then 4 days off. That lone workday on Friday sticks out like a sore thumb (especially when it's New Year's Day itself, which should be a holiday).

Instead, we should treat the first blank day like Friday, and the second blank day like Saturday, for those shifts that work on Fridays or Saturdays. The third blank day (Leap Day) is truly a day off for everyone, as are the first three days of the New Year, Friday-Sunday. (This affects the Librarian shift, but not the Atheist shift if we assume that they get the entire week surrounding New Year's off.)

So far, we moved Christmas to Sunday since it's the one day of the week that everyone gets off. If we wish to observe US federal holidays as common days off, then they must also be moved to Sunday (as there are no weeks off other than the three vacation weeks and first three days in March). We'll find each federal holiday in the Gregorian Calendar and then convert it to the nearest Sunday in the new Eleven Calendar. (All Sundays are on the 3rd, 14th, 25th in my calendar.)

MLK Day: January 16th (Gregorian), December 25th (Eleven Calendar)
President's Day: February 18th (Gregorian), January 25th (Eleven Calendar)
Memorial Day: May 30th (Gregorian), May 25th (Eleven Calendar)
Independence Day: July 2nd (Gregorian), June 25th (Eleven Calendar)
Columbus Day: October 9th (Gregorian), September 25th (Eleven Calendar)
Veteran's Day: November 11th (Gregorian), October 25th (Eleven Calendar)
Thanksgiving: November 22nd (Gregorian), November 3rd (Eleven Calendar)

It's actually interesting that so many of these holidays land on the 25th. (This is actually something I once noticed about the distribution of US federal holidays.)

Holidays when businesses don't close thus can fall on days other than Sunday. For example, we can convert Valentine's Day (February 14th Gregorian) to January 21st, a Tenday. (That's right, even though February no longer exists in my calendar, Valentine's Day still does.) St. Patrick's Day is easier, since dates in March are aligned. March 17th is a Sixday in my calendar. We might wish to keep Mother's Day and Father's Day on Sundays anyway -- the closest dates that fall on Sundays are May 3rd (May 8th Gregorian) and June 14th (June 21st Gregorian).

Halloween is an interesting one. October 31st Gregorian converts to October 14th, a Sunday. But Halloween on Sunday isn't necessarily desirable -- indeed, we might prefer to have All Saints' Day on that Sunday instead, and move Halloween to the previous day (a Saturday, plus it's the 13th -- a fearful day that's fitting for Halloween). So we might make this change anyway, even though it places Halloween on October 30th Gregorian.

You might notice that I haven't placed Labor Day yet, even though it's a federal holiday. We see that August 25th on the new calendar corresponds to September 6th Gregorian -- and it even fits the pattern that most federal holidays land on the 25th.

But here's the problem -- I haven't placed the third holiday break (in addition to Christmas/winter break and Easter/spring break) yet. In order for the trimesters to be equal, there can be a holiday near August 14th on the new calendar (August 26th Gregorian). Then schools can close the week before or week after this day for a short summer break (depending on which week before and after Christmas and Easter is the vacation week at that school).

We might even place a Christian holiday on that date -- perhaps the Assumption of Mary (which is also used as an anchor in the Andrew Usher Calendar). Then Christmas, Easter, and Assumption divide the year into equal thirds, and these are used to determine the trimesters and vacations).

But if we place Assumption on August 14th and Labor Day on August 25th, then schools will be tempted to take the week after Assumption off, which then forces the weeks after Christmas and Easter to be vacations as well (thus taking away the flexibility to take the weeks before off instead).

My solution is to define both Assumption and Labor Day to be August 14th, but this isn't necessarily the best solution. (Also, notice that Assumption on August 14th is awkward, only because the actual Assumption -- August 15th Gregorian -- becomes August 3rd, which is already a Sunday anyway!)

Finally, I wonder where to place Pi Day on the new Calendar. We might keep wish to keep March 14th as Pi Day, but 3/14 now means May 14th (since March is the first month, May now becomes the third month). In any case, the 14th of any month is a Sunday, so there can never be school on Pi Day.

Conclusion

This last version of the Eleven Calendar is my favorite. It's a compromise of all the different versions that I previously mentioned. Celebrating the third of December (in this calendar) as Christmas also addresses the reality that no one is really going to implement this calendar. So I can't just pretend to the rest of the world that my own December 25th (Gregorian January 16th) is Christmas.

Anyway, this concludes my Calendar Reform posts for the year. I wish you a Merry Christmas, Happy Hanukkah, New Year, or whatever you celebrate. And I'll see you next decade!

Boxing Day Post

Table of Contents

1. Introduction

2. Christmas Adam and other Adam Holidays

3. Darren Miller's Long Weekend
4. My Own Calendar Experiences
5. Possible Solutions Within the Gregorian Calendar
6. Possible Calendar Reform Solutions
7. The Gaia Calendar, Revisited
8. Conclusion

Introduction

This is the first of my three winter break posts. Today is December 26th, the day after Christmas -- also known as Boxing Day in some English-speaking countries.

One week ago today, one of the last classes I subbed in was a special needs class. These students had a short reading assignment on holiday traditions around the world. That day, they read a letter from an Australian pen pal who described how his family celebrated Christmas -- and Boxing Day. I learned that in Australia today, many people had barbecues and attended cricket matches. (Of course, we must remember that down under, Christmas and Boxing Day are summer holidays.)

I devote today's post to the late brother of Fawn Nguyen. It's always sad to lose a family member, especially around the holidays:

http://fawnnguyen.com/whats-in-a-name/

In Nguyen's post, she describes an academic award she received four decades ago (in math, of course) and tells the story of how her Vietnamese name Phuong became the Anglicized Fawn.

Christmas Adam and other Adam Holidays

It is my tradition to celebrate New Year's Day by discussing several calendar-related topics in my posts between Christmas and New Year's. This year is no exception. I'm adding the "Calendar" label to this post. (Note: I try to avoid religion on the blog, except in Calendar-labeled post. So expect religion to be mentioned here aplenty.)

In my last post, I mentioned how December 23rd is sometimes known as "Christmas Adam," because it's the day before Christmas Eve. We can generalize this idea -- the Adam of any holiday falls two days before the holiday, while the Eve of that holiday is the day before that holiday.

Sometimes the Adam of a holiday has a special name of its own. We've already encountered one such day -- Christmas Adam is also known as "Festivus." Here are a few more interesting Adam days:

• Valentine's Adam is also Lincoln's Birthday. (Before the creation of "President's Day," the 12th itself was a day when businesses closed.
• St. Patrick's Adam is the Ides of March.
• Easter Adam is Good Friday. (According to Christians, the crucifixion occurred on the Adam of the resurrection.)
• Independence Adam is July 2nd -- the day that our President John Adams originally foresaw as the anniversary festival before it settled on the fourth. (In that case, we should probably call it Independence Adams after the President.)
• And of course, Thanksgiving Adam is Floyd Thursby Day.

Sadly, Pi Day just barely misses being St. Patrick's Adam. But third Pi Day in November is usually Veteran's Eve, but Leap Day causes Third Pi Day to land on Veteran's Adam instead.

Most of our other holidays fall on Monday, so each has an Adam on Saturday. This is significant only when dating events that take place over the three-day weekend -- for example, the first day of college football for most teams is Labor Adam (though a few start earlier).

I'll get back to Adam holidays later in this post.

Darren Miller's Long Weekend

I'm loath to bring up politics again. But since I read the Joanne Jacobs website (in order to see what traditionalists are thinking) and Darren Miller of (political) Right on the Left Coast is a frequent contributor there, I end up reading so many of Miller's posts. Anyway, back in October he blogged about the school calendar, and so I wish to bring it up in today's Calendar post:

https://rightontheleftcoast.blogspot.com/2019/10/long-weekend.html

I've been thinking about what the ideal school calendar might look like. Indeed, this is how Miller begins his post -- thinking back to the days when school started after Labor Day. Now his school starts in August, but with more holidays:

In 1975, my aunt and I returned from visiting my mother in Germany.  We landed on August 27th, my aunt's birthday (her geburtstag, as it were).  When I got home there was still time to go school shopping for new clothes for the upcoming school year, and to adjust to the time zone.

Whether to start school in August or September is an example of a change to the school calendar that can be made within the context of our Gregorian Calendar. Other possible changes require actual Calendar Reform. For example, we might wish to keep the five-day week but extend every weekend to three days. This requires a Calendar Reform with eight-day weeks.

I enjoy Calendar Reform, but this is an education blog. With every proposed calendar, I like to see what its effect would be on the school year. In this post I'm considering the reverse -- first, what is the optimal school calendar, and second, what sort of Calendar Reform is needed to implement it?

Anyway, Miller describes a long weekend that his school held in October -- and the problems that it led to:

A few years ago, someone in my district administration noticed that, since school started in mid-August, both teachers and students started taking days off in October.  Thus was born the idea of giving a 4-day weekend in early October; we get a chance to recharge the batteries, so the theory goes, and should be able to make it until the next holiday, Veterans Day.  By giving teachers the days off we eliminate a spate of days of not having enough substitute teachers, and by giving students the days off we cut down on unexcused absences and avoid losing state funding, which depends on attendance.  What can go wrong?  Any economist could have predicted that there would be a number of teachers out last Thursday, and those economists would have been correct!

OK, so Miller mentions subs and unexcused absences here. This suggests a definition of "ideal school calendar" -- it's one that seeks to minimize the number of teacher and student absences. Calendars with many days of work without a day off, or many weeks of work without a vacation, are prone to absences because teachers and students get tired.

We know that Fridays often lead to more subs because teachers who get sick on Thursday don't wish to return to work on Friday. It's easy to see how a long weekend (such as the four-day October weekend mentioned in the post above) can lead to even more absences -- a teacher who gets sick the preceding Wednesday definitely wouldn't want to return on Thursday. So that's one reason for the number of absences to spike the Thursday before the long weekend.

But notice that we still haven't quite defined what the ideal school calendar is. Suppose Miller's district has 1000 teachers. Suppose that before the four-day weekend was introduced, about 5% (that is, 50) teachers were absent each of the four Fridays in October. But then with the long weekend, 15% (or 150) teachers were absent on the Thursday before the long weekend.

So which is worse -- 200 absences on the four Fridays, or 150 absences on a single Thursday. On one hand, 150 is less than 200 total absences. But on the other, the single Thursday requires 150 subs -- and suppose that there are only 100 subs in the district. In other words, there's a difference between minimizing the total absences (over a month) and minimizing the peak absences (on a single day). In fact, we see that introducing the four-day weekend reduces the total absences, but having the long stretch without holidays reduces the peak. In his post, Miller mentions both the total and the peak, but it might be that the twin goals of minimizing them both are at odds with each other.

But notice that Miller begins this paragraph by mentioning the August school start. Thus he implies that if school still began after Labor Day, teachers can make it all the way to Veteran's Day without taking extra days off or needing a four-day weekend in October. That is, the way to minimize both total absences and peak absences is to start after Labor Day.

Yet we already know why more schools start in August. It's not October that's the problem -- it's December and January, and the problems associated with having finals after winter break. But I don't see any simple way to eliminate this problem. We could insert an extra month between Labor Day and Christmas (either via Calendar Reform with a new month somewhere between September and December, or keeping the Gregorian Calendar but changing Labor Day to August). That solves the finals problem, but it doesn't reduce the urge to take off extra days in October.

My Own Calendar Experiences

I've been subbing a lot lately, including the last day(s) before breaks and first day(s) after break. So we ask, have I observed any spikes in absences (whether teacher or student) on those days?

Well, this year I spent the last days before both spring and winter break at a continuation school. It's known that many students their have poor attendance records (part of the reason that they've been sent to a continuation school). There were many absences those days, but not significantly more than a typical day at that school.

The last day before Thanksgiving break was different. That day (a Friday) I was at a comprehensive high school, but there was a credible threat made at the school on Thursday. Thus there were many student absences both Thursday and Friday, and there was additional police presence. Thus it's difficult for me to gauge student attendance leading up to the breaks since there were extenuating circumstances in each case.

On the other hand, I do know something about teacher absences during those weeks. I subbed for a math teacher who was out the entire week after Thanksgiving. She was out because her daughter was in the hospital in another state. I also heard of another teacher who had scheduled surgery for the week before winter break.

That's another thing that Miller doesn't mention in his post -- teacher doctor visits. Both he and Floyd Thursby criticize teachers who take days off to go to the doctor instead of going during break. But they forget that doctors wish to take days off as well. Think about it -- there are ten weekdays this year during winter break, from December 23rd to January 3rd. But two of those days are holidays on which no doctor will work (December 25th and January 1st). The Eves are likely to be taken off by doctors -- and possibly the Adams as well, since they fall on Mondays. That doesn't leave many days during the break when doctors' offices are open.

Moreover, if a teacher knows that she will need three weeks for surgery and recovery, then it's smart to schedule it for the week before winter break, so that the three weeks needed include two weeks of break and only one week of school. The problem is that the extra week will invariably be the week before the break, thus contributing to the peak of subs needed to cover the last week. It's impossible for a teacher to take three weeks to recover from surgery -- two weeks of break and one week far away from the break.

This suggests that some schedule problems are impossible to avoid. When it comes to recovering from illness or surgery, it's actually better to take extra days off near breaks to do so in order for the break to contribute to the recovery time. While that reduces the total number of days lost to subs, it increases the need for subs on peak days surrounding the breaks.

And of course, notice that Miller mentions economics in his post:

Any economist could have predicted that there would be a number of teachers out last Thursday, and those economists would have been correct!

We're discussing workers and their schedules, hence the relevance of economics here. But another issue related to economics is supply and demand -- as in airline tickets. During holidays, demand for tickets often exceeds supply. Passengers often have to book flights on the Adams of major holidays when flights on the Eves are sold out. This usually isn't a problem for Thanksgiving in my districts, since we get the entire week off, but it is a problem for Floyd Thursby's district, where school is open on Thanksgiving Adam. And as we're well aware, in New York there is school on both Thanksgiving Eve and Christmas Adam (in years when the 23rd falls on Tuesday-Friday), which adds to the travel nightmare for teachers, students, and parents.

Possible Solutions Within the Gregorian Calendar

Our goal here is to schedule a 180-day school year such as to minimize both the total number of teacher (and student) absences and the peak number of absences.

Two possible but impractical solutions jump out at us. One way to minimize the peak absences is just to have 180 straight days of school followed by a 185-day vacation. Let's see -- January through June add up to 181 days, so let's just start on January 2nd. Most of the major holidays fall between Independence Day and New Year's Day anyway -- and with only one long break, there's only one "last day/week before break" that would encourage teachers to take extra peak absences.

Of course it won't work. No one wants to work 180 consecutive days, even with six months off. And it also ignores the concept of sabbath -- a day off every week for religious purposes.

The other impractical solution is to alternate the whole year between work and rest. For example, we might have school on even days and take odd days off. This almost gives us 180 days (twelve months with 15 days of school each month), except that there's no February 30th, so it's only 179 days. As a bonus, many major holidays are on odd days anyway (January 1st, November 11th, December 25th, and others like both October 31st/November 1st as a bonus). Every day is the last day before an off day, so there's no reason to take an extra day off as a bridge to the weekend.

But of course it won't work either. We like having more than one (occasionally two) days off at a time for vacations and so forth. And of course, this plan doesn't respect the sabbath either.

One realistic solution in this mold might be to reduce the school week to four days. Since 180 equals 45 times 4, this leaves 52 minus 45, or seven weeks for vacation. We might spread these out so that we have one week off at Thanksgiving and two weeks off for winter, spring, and summer breaks. If we choose Tuesday-Friday as the work week, then this takes care of Monday holidays. Assuming that the two weeks of summer break include the Fourth of July, this leaves only Veteran's Day (which can fall on any day of the week) as the only problematic holiday. (Of course, we can solve this simply by redefining Vets Day as the second Monday in November.)

The hope here is that with every weekend having three days, there's less need for a breather when there are long stretches between holidays (such as Labor Day-Veteran's Day or the Big March). And so perhaps both the peak and total absences can be minimized with this solution.

Possible Calendar Reform Solutions

This last solution fits within our Gregorian Calendar -- specifically its seven-day week. That's because it's based on four school days and three rest days. If we wish to improve upon this solution, then we must abandon the seven-day week.

For example, perhaps a three-day weekend isn't enough -- even if every weekend were three days, teachers might still wish to take extra days off. So let's make the weekend four days. This still might not be enough -- consider Miller's Thursday in October problem, but maybe if every weekend were four days, there would be no need to take a fifth day off on one particular weekend in October.

The "sick on Thursday" problem that I mentioned above (that is, teachers take an ordinary Friday off if they get sick on Thursday) will persist regardless of the week length -- no solution can make it disappear completely. But maybe we can at least reduce it by extending the week length -- if there were a six-day workweek, then only 1/6 of those days would be "Friday" rather than 1/5, so only 1/6 of the days would require as many subs as an ordinary Friday.

But six days makes for a long workweek. Teachers and students might take extra days off midweek to avoid having six days of school in a row (similar to Miller's October problem). So let's now add an extra day off in the middle of the week.

That gives us three days of school, one rest day, three more rest days, and a four-day weekend. This gives us a grand total of eleven days per week. So what we need, then, is a Calendar Reform that's based on eleven-day weeks.

And I know one such calendar -- my Eleven Calendar, first published on this blog.

OK, I admit this is partly an excuse to mention the Eleven Calendar again. But when I first came up with that calendar, I had something like this in mind. I wanted there to be six days per school week in order to make it fit block schedules more easily, but I knew that six-day weeks would be tough unless we either extend the weekend, add a midweek day off, or both. Oh, and I wanted the total to be eleven since it would be a truly original calendar -- no one else had a 11-day week. Hence I invented the Eleven Calendar.

Of course, my solution is still not a perfect solution. For example, I added the midweek rest day in order to avoid having six straight school days. But would that result in the day before the rest day becoming a second Friday (that is, with as many teacher absences as a Friday)? If so, then that would defeat the purpose of having six-day weeks. (The answer might be intermediate -- it could be that there are fewer absences on the midweek "Friday" than on the real "Friday," yet more than the other days of the week -- enough to outweigh the advantage of having 1/6 of all school days being true "Fridays" instead of 1/5.)

Then again, there's no way to experiment to see whether 11-day weeks might work, since I can't change the length of the week to 11 days just to find out.

If 11 days per week isn't optimal, perhaps we might be able to tweak it a little. I notice that there are a number of new 10-day calendars at the Calendar Wiki website:

https://calendars.wikia.org/wiki/Alternative_and_Proposed_Calendars

Maybe ten days will work better than eleven. The question is, do we eliminate a school day, the midweek rest day, or a weekend day to get to ten days? Again, which week length will minimize the total and peek absences?

The Gaia Calendar, Revisited

Last year for my Calendar Reform post, I linked to several lunisolar calendars and mentioned the Gaia Calendar as a possible calendar. It had an interesting but complicated Leap Month rule -- and I made several suggestions to simplify the Leap Month rule, based on another calendar that I had read about (the Meyer-Palmer Solilunar Calendar).

Well, the inventor of the calendar has taken my suggestions to heart. Here is a link to a new version of his calendar:

https://www.peristanom.org/p/calendar.html

This marks the second time that I've helped out a Calendar Reformer. (The first time was for the Andrew Usher Leap Week Calendar.) In both cases, my contribution was to simply the Leap Unit (that is, Leap Week or Leap Month) rules. My real baby is the Eleven Calendar.

Conclusion

And that is my goal for my next post, to be posted tomorrow. I will continue to develop the Eleven Calendar by adding suggestions for day names, month names, and what the 11-day week looks like.

I wish you many condolences for your recent loss, Phuong Nguyen.

Semester 1 Review and Semester 2 Preview (Day 85)

Today I subbed in a continuation high school English class. Thus there's definitely no need for "A Day in the Life" today.

I haven't subbed in this classroom before, but I have been to the continuation school. Indeed, I wrote about the school back in my April 12th post -- the last day before spring break in this district.

Today, the students only need to make up any missing assignments. The only real issue with classroom management is in the fourth class, which is a bit loud. The third class, which counts as homeroom, earns a doughnut party for having one of the best holiday door decorations. (Our door has a poster based on the movie Elf -- as in Buddy the "Elf.")

Both April 12th and today are Fast Fridays -- all students go home early except those with any D's or F's, who must attend tutorial instead. On April 12th, there were only three students who needed tutorial, but today there are a whopping ten. One of them is a girl who somehow has a D-, not in English, but in AVID (the regular teacher's first class). It almost seems as if tutorial is the largest class of the day -- it isn't, but they do outnumber the nine students in the AVID class.

But unlike April 12th, today tutorial is suddenly cancelled. Because I'm a sub, somehow I don't get the message. (Is it sent directly to teachers' email accounts.) Some students receive a text from other friends that they get to leave early, and finally an administrator confirms the cancelling of tutorial. So at 12:40 when I finally get the message, my winter break officially begins.

Today is the third and last day of finals week. It has been my tradition on the blog on the third finals day to post a review of the old semester and preview of the new semester.

Last year, when I was searching for MTBoS blogs, I did find the following blog:

http://cheesemonkeysf.blogspot.com/

The blog belongs to a Northern California high school math teacher. (Apparently the letters "sf" in the URL stand for "San Francisco.") Even though the blog is anonymous, a commenter I quoted yesterday referred to this author as "Elizabeth." Thus I'll refer to cheese monkey by the name Elizabeth (and use feminine pronouns to her).

[2019 update: I wrote this last year, but I wish to preserve this discussion. And I'll also mention one of Elizabeth's posts from this year.]

Anyway, Elizabeth is a Geometry teacher, and she refers to Geometry proofs in these posts:

http://cheesemonkeysf.blogspot.com/2018/11/proof-portfolios.html

http://cheesemonkeysf.blogspot.com/2018/11/proof-portfolios-revenge-of-immersive.html

And so for our review, let's compare our U of Chicago course to Elizabeth's to look for any key similarities and differences.

Let's start with the first semester plan from the U of Chicago text:

1. Points and Lines
2. Definitions and If-then Statements
3. Angles and Lines
4. Reflections
5. Polygons
6. Transformations and Congruence
7. Triangle Congruence

In her November 6th post, Elizabeth writes:

So this year, when I had to be out of school for a few days, I designed a Proof Portfolio project for them to do in my absence.

Each day had four small, reasonable proofs students had to do — and they could collaborate on these. But then... they had to write a number of short-answer reflections to analysis questions based on their own proofs in the day's set.

And by "a few days" she means "four days," since she links to four worksheets -- a grand total of sixteen proofs. The first worksheet includes proofs about parallel lines (Chapter 3 of the U of Chicago text), while the other three are the more common triangle congruence proofs (that would have to wait until Chapter 7).

Did Elizabeth's students enjoy the project? Well, that's not exactly the case:

When I returned, there was a great deal of wailing and moaning and gnashing of teeth about How Hard This Project Was and How Hard They All Worked.

Yet she declares the project a success:

But as I'm reading their work, I am blown away by how much they seem to have learned!

The following week, Elizabeth blogs about this project some more:

The complaints and lamentations were filled with drama. "OH MY GOD, DR. S — THAT ASSIGNMENT WAS HARD." But they could tell that they had accomplished something.

(OK, so apparently Elizabeth's last initial is S.) She explains how she grades the assignment:

My assessment strategy was to be rigorous about completion but merciful with points. It was only worth a quiz grade (100 points), and my default score for students who completed every section was a 95. There are rewards for following instructions. Missing sections or components left blank cost more points.

She concludes the post as follows:

I am excited to see what happens on the next major test that includes a proof. Photos of student work to follow.

But unfortunately, she hasn't posted anything on Geometry since then, so we don't know yet how her students fare on the next major test.

Notice that the cornerstone of this project is the peer review. Elizabeth feels that feedback from peers is more effective than that from teachers. Traditionalists would disagree -- they believe that feedback from the teacher (someone who knows math) is better than that from another student (someone who doesn't know as much math). But traditionalists make the assumption that students will actually listen to the teacher just because she says so. Elizabeth's project is based on the possibility that the traditionalists' assumption is false -- that students are more willing to listen to each other than to the "sage on the stage."

Our first semester plan contains some activities, but nothing as ambitious as Elizabeth's four-day proof project.

Here is our second semester plan. We'll begin with Chapter 8:

8. Measurement Formulas (January 7th-13th)
9. Three-Dimensional Figures (January 14th-28th)
10. Surface Areas and Volumes (January 29th-February 12th)
11. Coordinate Geometry (February 13th-27th)
12. Similarity (February 28th-March 12th)
13. Logic and Indirect Reasoning (March 13th-April 2nd)
14. Trigonometry and Vectors (April 3rd-20th)
15. Further Work With Circles (April 21st-May 4th)

Since the new semester begins on Day 86, we start with Lesson 8-6, "Areas of Trapezoids." It means that Lessons 8-3 (rectangles), 8-4 (irregular figures), and 8-5 (triangles) are omitted. But I'll find a way to squeeze in the missing lessons.

Is there anything on Elizabeth's blog about second semester Geometry topics? Well, I did find a link to the following post from over two years ago:

http://cheesemonkeysf.blogspot.com/2017/07/things-that-work-1-regular-vocab.html

This post is all about Geometry vocabulary. Her example is on circles, This appears to be more like the basic circle lessons of Chapter 13 than the more advanced work in Chapter 15 (where we have to deal with inscribed angles, power of a point, and so on).

Our worksheets refer to vocabulary. But Elizabeth takes the extra step of actually giving her students a vocabulary quiz. She writes:

At some level, I recognize that this sounds stultifying. But at another level, it was incredibly empowering for the students. Everybody understood exactly what was being asked and expected. And everybody saw it as an opportunity to earn free points. Students gave each other encouraging written comments and cheered each other on. They saw their scores as information—not as judgment. They used what they knew to make flash cards or Quizlet stacks. They quizzed each other. They helped each other.

And nobody ever complained about the regularly scheduled vocab quiz. It was a ritual of our course.

And apparently, she gives these quizzes every week:

It also ensured that everybody spent a little quality time on the focus task of preparing for the vocab quiz on Thursday or Friday. And this, in turn, meant that everybody was a little more ready to use the correct and appropriate mathematical vocabulary in our work. They noticed more because the owned more.

On the circle answer, Elizabeth gives a term, "2. concyclic points," that doesn't appear anywhere in the U of Chicago text. I believe the correct answer is "N. points that lie on the same circle" -- that is, "concyclic" is to circles as "collinear" is to lines. Also, the answer to "7. party hat situation" is "J. the situation where two tangent segments are drawn to a circle from a point external to the circle." This situation (which does indeed sort of look like a party hat) occurs often on the Pappas calendar, yet the U of Chicago text never gives it a formal name.

Elizabeth writes:

• There should be many more definitions in your right-hand list than there are terms in your left-hand list. Also definitions can be re-used. This way there isn't a zero-sum outcome if someone misses an answer.

Yet in her given circle unit example, there are exactly 16 terms and 16 definitions. But perhaps she follows her own advice on the other vocab quizzes.

I know the importance of vocabulary to any math class, especially Geometry -- particular these days of the Common Core when students must explain their answers. But I've never considered giving students a weekly Geometry quiz.

And Elizabeth has written more about Geometry tips since her endorsement of "word walls" (as the Illinois State text would call them). As I promised, here's one of her posts from this year:

http://cheesemonkeysf.blogspot.com/2019/10/building-feel-for-major-moves-in-proof.html

Here she gives some hints for setting up proofs in Geometry class.

This has meant that we are developing students' intuition that that these sub-assemblies are knowable and predictable. We call these our "major proof moves." Some of our major categories of major proof moves include:

• the relationships between parts & wholes
• a sense of bisectors and "half-ness"
• parallels and the results of parallels
• perpendiculars and their results
• right angles and their results.

It's working out surprisingly well.

There are many other examples of "things that work" on Elizabeth's blog. It definitely gives me something to consider if I ever return to my own classroom someday.

OK, so it's now time for winter break and the holidays. This year, we have not just Christmas but the Jewish Hanukkah, which is so late that it overlaps Festivus, Christmas Eve, Christmas Day, and Boxing Day this year.

Festivus -- that's the name for December 23rd mentioned on the TV show Seinfeld. (It's celebrated with a long metal pole instead of a Christmas tree.) But it's come to my attention that December 23rd is also known by another name: "Christmas Adam." That's because Adam comes before Eve (in the Bible), so Christmas Adam comes before Christmas Eve.

Note that while "Christmas Adam" seems to be a recent invention, it actually goes all the way back to the Middle Ages:

https://aleteia.org/2017/12/24/happy-adam-and-eve-day/

Originally both Adam and Eve were celebrated on December 24th, in order to make a connection to the celebration of Christ on the 25th. With "Christmas Adam," we now have Adam on the 23rd and Eve on the 24th.

So whether you celebrate Festivus, Christmas Adam, Christmas Eve, Christmas Day, Boxing Day, Hanukkah, or any other holiday, I wish you the very best.

Expect three posts this year during winter break this year.