New Year's Day Post (Yule Blog Challenge #8)
Introduction
Today is New Year's Day 2022. When 2021 began, many people thought of 2020 as an annus horribilis, a Murphy's year in which anything that could go wrong did go wrong. Of course, this was mainly due to the ongoing pandemic. But this was all based on the assumption that the pandemic would end in 2021, so that labeling 2020 as the Murphy's year would distinguish it from 2021.
But the pandemic didn't end in 2021, and now many consider 2021 to be a Murphy's year too. Case in point, when legendary actress Betty White died yesterday, many people tweeted that it was just one last bad thing that had to happen in 2021.
That being said, why should we believe 2022, the third year (n + 3) of the pandemic, to be any better than the first two years? After all, the year begins with omicron raging more strongly than ever. As far as I know, some celebrity will die on December 31st, 2022, and the response will be that it's one last bad thing to happen in 2022 -- a year to be just as horrible as its two predecessors.
Of course, I hope that's not what 2022 has in store for us, but as of now, I'm wondering what will change to prevent it from being yet another Murphy's year.
Yule Blog Prompt #11: What I Learned in 2021
So what did I learn during this second pandemic year? Well, I learned that I need to work harder making sure that my students know how to use their calculators. On Back to School Night (Day 11), I showed my students how to use their TI calculators, but they still struggle to use advanced functions. So whenever I give my students a calculator assignment, it takes too long because I must go around to each and every student to make sure that all of them know how to use them properly.
Thus in my largest class -- fourth period Ethnostats -- we regularly run out of time during each of the calculator lessons. And my third period Calculus students will struggle on the calculator sections of the AP if they don't know how to use them properly.
Back to School Night was also the week when I learned that one of my favorite teaching strategies from previous years -- singing math songs -- would fail. During the early weeks of the school year, many of my introductory songs were on soft math skills. One parent didn't understand the purpose of these songs, and so due to that parent complaint, I could no longer sing them.
I do admit that even prior to 2021, I didn't always sing for older juniors and seniors, who didn't always have fun with these songs that younger kids in Grades 6-10 did. So with only juniors and seniors this year, I don't really need to rely on singing as much. Depending on what direction our magnet school takes in the fall, I might end up with freshmen and sophomores -- so I'd definitely like to reintroduce music break if that happens.
New Year's Resolutions for 2022: The HONOR Code
In past years on the old blog, I'd post New Year's Resolutions that serve as rules for my students and me to follow in the classroom. The most recent resolutions were dated January 1st, 2020 -- and then I had to modify some of those resolutions to describe pandemic teaching. I continued to use those rules during the recently completed first semester.
But now my school is introducing a new matrix based on the acronym HONOR:
H -- Honesty
O -- Organization
N -- Nobility
O -- Ownership
R -- Respect
Teachers are supposed to personalize their HONOR rules for their own classrooms and introduce them in the second semester. The deadline for teachers to submit their HONOR rules is the first Friday after winter break.
And so the timing is perfect for me to introduce, as New Year's Resolutions for 2022, new rules based on the HONOR acronym. Most of the following rules were suggested by more experienced staff members (and I'm even including some of them verbatim). Since the rules listed under Organization matched those in other sections, so I found them unsatisfactory. Instead, I'm including some of my old 2020 resolutions for math -- that is, keeping the mind organized.
On the other hand, the new tenth resolution is now about respecting others, whereas the old rule was "We are not truly done until we have achieved excellence" (which is subsumed in some of the other rules anyway). The old Resolution #8 was "We follow procedures in the classroom" (including COVID procedures), while the new rule is more specific, focusing on books and materials. My seventh rule changed several times -- originally it was about singing math songs to help us learn, but now that I can't sing, I replace it with working hard to earn grades.
Resolution #4 was based on one of my own rules -- "We need to inflate the wheels of our bike" (that extends the metaphor from the bike in the third rule). This has also been made more specific -- now the third rule focuses on mental math (say with one-digit numbers) and the fourth rule on using the TI calculators properly. In either case, mental math and calculator math need to come as easily to our students as riding a bike in order for them to be successful.
I admit that I had trouble enforcing these rules -- sometimes I would redirect an off-task student, but I didn't always tie their behavior back to these rules. But all teachers will soon be enforcing the HONOR code, and so I'll need to do so as well. In my last post I wrote that I must still work on improving my classroom management, and the best way to do so is to enforce these resolutions consistently.
Links to Others: My Eleventh Resolution
Cheryl Leung continues to be a strong Yule Blogger. Over New Year's, she made two more posts about the lessons she learned during the pandemic. These lessons are on student anxiety and self-care:
https://matheasyaspi.wordpress.com/2021/12/31/pandemic-lessons-anxiety/
https://matheasyaspi.wordpress.com/2022/01/01/pandemic-lessons-taking-care/
Of these two posts, the one on anxiety really resonates with me. Leung can easily tells that her students are feeling much more anxious due to the pandemic. She writes that anxious students definitely have trouble learning math:
Some students would freeze when they did not immediately understand everything about a new concept or process when it was first introduced. Some students would freeze when it came to taking a quiz or test. They would take two, three, or four times as long as normal to complete the assessment.
My students are juniors and seniors, unlike Leung's sixth graders trying to get used to middle school during a pandemic. Thus my students should be less anxious than hers -- and likely they are. But there's one thing that my students and hers have in common -- they both need extra time for assessments.
How can I tell whether my students are anxious or not? I'm not sure -- but then again, how can Leung tell whether her students are anxious or not? For one, she can see it through their actions, but there's another way she probably figured out their feelings -- she asked them.
As I wrote in an earlier Yule Blog post, one of my biggest weaknesses is communication. I have trouble communicating with my students in person (in the classroom). I had trouble communicating with my students online (in distance learning last year). I have trouble communicating with my fellow teachers in person (in the lounge). I have trouble communicating with my fellow teachers online (on Twitter, where my tweets are consistently the least popular on the MTBoS). And I had trouble communicating with my fellow students (back when I was a young high school student myself).
My communication struggles are so deep that I once wrote a New Millennium's Resolution (all the way back in the year 2000) that I would improve my communication skills. And I consider that resolution to be active, since it's still the third millennium and I still need to work on it.
Therefore there is an eleventh resolution, "I will improve my communication skills." Notice how this resolution begins with "I," not "we" -- I am the only person who needs to follow this rule. It's not part of the HONOR code that students need to follow.
I will work on my communication skills with students. I do greet my students when they enter the classroom and when they leave it, but I need to do so consistently. When students seem to be anxious or struggling, then I must reach out and ask them, so that I can help them out the same way that Leung helps her kids. Advisory is the main class for working on communication skills and listening to what my students have to say, but I also want to be attentive to my math students' needs as well.
Last year as a long-term sub, I believe that many of the middle school students liked me as a teacher -- mostly because they enjoyed the math songs I sang. But I can't perform this year -- and older students don't always enjoy my songs anyway. Indeed, I believe that with older students, they'd much prefer a teacher who is real with them (by communicating with them) than one who just sings all day.
I definitely want to improve my conversations with my fellow teachers. There's not much I can do about the lounge -- ever since cafeterias stopped serving lunch to adults on campus, I've been forced to spend most of my break going out to get something to eat. (At least I was able to mingle a little during the two parties -- a baby shower and the Secret Santa party -- the last week before winter break.)
Communicating with teachers online is another story. Not many people read this blog, but I've already accepting that Blogger is declining in popularity. It's Twitter where I want to make sure that I'm posting interesting things that people want to read and react to. (Indeed, Shelli, the leader of the Yule Blog challenge, once suggested that I join Twitter when I was teaching at the old charter school, to get tips from other teachers who could have helped me. But I know exactly what would have happened -- my tweets would have been largely ignored, and so I still wouldn't have become a better teacher.)
- like three tweets
- retweet two tweets (a pure retweet, not a quote tweet)
- follow one new tweeter
And once school starts up again, my designated Twitter days will also be for 3-2-1 -- liking, retweeting, and following. (Right now I'm leaning towards blogging on days when my Ethnostats class meets in the second semester -- Mondays, Wednesdays, Fridays -- since this is a Stats blog. This leaves Tuesdays and Thursdays for Twitter.) Only once in January will I initiate my own message -- next week, when I announce that I've made my twelfth and final Yule Blog. Otherwise, I'm only a responder, not a talker.
In February, I might tweet a few photos of my classroom. (To encourage my students to send me tweetable photos, I'll count them as homework passes.) And during spring break, I'll proceed to the next level -- responding directly to questions asked by members of the MTBoS. I should only reply if an explicit question (with a ? mark) is asked, and then only to answer that question. Hopefully by the end of the school year, I'll know how to be a better communicator and improve the quality of my tweets.
Calendar Reform: 11-Day Calendars
Let's continue looking at Calendar Reform -- again, this year we're focusing on calendars that can support a three-day school week. This time, let's move up to eleven days per week. This is my favorite calendar, because I created my own Eleven Calendar on the old blog:
http://commoncoregeometry.blogspot.com/2016/01/an-original-calendar-reform-proposal.html
Simplest Version of the Eleven Calendar
(Maximizes Compatibility with Gregorian Calendar)
The 363 days are divided into 33-day months, as follows:
Month 1: March 1st - April 2nd
Month 2: April 3rd - May 5th
Month 3: May 6th - June 7th
Month 4: June 8th - July 10th
Month 5: July 11th - August 12th
Month 6: August 13th - September 14th
Month 7: September 15th - October 17th
Month 8: October 18th - November 19th
Month 9: November 20th - December 22nd
Month 10: December 23rd - January 24th
Month 11: January 25th - February 26th
Blank Days: February 27th, 28th, 29th
Each month is divided into 11-day weeks, with days numbered 1 to 11.
I was originally inspired by theAbysmal Calendar -- a calendar which can accommodate various week lengths, from three to ten days and then from 12-14 days. Since there was no 11-day calendar, I decided to create my own.
Last week, the author of theAbysmal Calendar visited my old blog. Since then, he's added an 11-day version of his calendar (and announced some changes to it since last year), but he acknowledged that I had beaten him to the 11-day calendar. So my Eleven Calendar really is an Original Calendar Reform.
Of course, this post is all about what the school calendar should look like on11-day calendars. The ideas I mention here can be applied to either my Eleven Calendar or theAbysmal 11-day calendar.
Just like the 9-day "A Calendar for Time to Come," we can have six days per school week. But instead of having a five-day weekend, we use one of these off days for a midweek break. So the school week goes 3 on, 1 off, 3 on, 4 off.
On my version of the calendar, I once labeled the first three days of the week as Friday, Saturday, Sunday rather than Oneday, Twoday, Threeday. Then the three Abrahamic religions can all have their respective Sabbaths. Schools are open Fourday-Sixday, the midweek break is Sevenday, then open again Eightday-Tenday. The weekend includes Elevenday and all three Sabbaths.
Meanwhile, the author of theAbysmal Calendar likes to start his counting from zero, and he likes to emphasize symmetry in his calendar. Thus the midweek break should be Day 5, with schools open on Days 2-4 and Days 6-8. The weekend includes Days 9, 10, 0, and 1.
The year includes 33 weeks, with only 30 weeks of school needed to reach 180 days. So we can insert three holiday weeks. There are several ways to do this. If we assume that one holiday week falls near my New Year's Day (March 1st), then the other two holidays weeks fall near (Gregorian) July 1st and (Gregorian) November 1st.
There are two active versions of theAbysmal 11-day calendar -- 363-A and 363-B. They differ in where they place the blank days -- 363-A places them September 7th and April 5th, while 363-B places them October 21st and February 20th. New Year's Day on both calendars is June 22nd, while Leap Day falls on the last day of the year, June 21st. Thus 363-B, unlike 363-A, is designed to divide the year into three equal parts (terms).
Notice that the terms on both of our calendars nearly line up -- in fact, if I choose the last week of my terms to be vacation week while theAbysmal Calendar selects the first week (Week 0), then the vacation weeks line up almost perfectly. Both calendars would have the vacation weeks around the last week of Gregorian June (between Juneteenth and Fourth of July), the last week of October (around Halloween), and the last week of February (just after Presidents' Day, a sort of Ski Week).
Of course, in the name of symmetry, theAbysmal Calendar might prefer the last three days (Days 6-8) and first three days (Days 2-4) to be the vacation week. Notice that my current district likewise has a short first week of school (Wednesday-Friday) and ends with three days of finals.
But then there would be no traditional winter or spring breaks. I once considered placing a Christmas on my calendar (near its Gregorian equivalent), but there's no guarantee that a Christmas even belongs on this calendar (as it doesn't fit well with the declared New Year's Day).
It's also possible to make this into a hybrid calendar, with different cohorts on off different days. Notice that unlike the 9-day "A Calendar for Time to Come," any two cohorts are guaranteed to have at least one day off in common. (On your four-day weekend, your partner works at most three of those days.)
Before we leave Calendar Reform, let me mention a few extra calendars. In addition to the 11-day calendar, there is now a 17-day calendar posted at theAbysmal. The author defines a week at any period of 17 days or less -- any period of 18 days or more is considered a month. (Perhaps the reason for the 17/18 border is that 17 is slightly closer to 7 -- the traditional length of a week -- while 18 is slightly closer to 28 -- the length of February, and of each month in the main 13-month calendar.) With the new 17-day calendar, every possible week length is now possible in theAbysmal Calendar.
The 17-day week is also the longest possible week where my "midweek" day off is possible -- the week is 5 on, 1 off, 5 on, 6 off. But some people may object to having just one day off between two stretches of five days -- it might be better to go 5 on, 2 off, 5 on, 5 off. There are 21 weeks in the year, with only 18 needed to reach 180 school days, so again we have three vacation weeks.
Believe it or not, this isn't the first 17-day calendar. There is also a Dove Calendar:
https://calendars.fandom.com/wiki/Dove_Calendar
The reason the author, Karl Palmen, chose each dove to be 17 days is that he wanted there to be a Leap Day cycle of 33 years (the Dee-Cecil cycle) and 12053 days, and 12053 has 17 as a factor. While the Dove Calendar is a Leap Week (or Leap Dove) Calendar, all versions of theAbysmal Calendar are based on blank days. So there are eight blank days in theAbysmal 17 calendar (but he doesn't specify when any of those eight days are).
Once again, any of these calendars that modify the 7-day week (including the 11- and 17-day calendars) are pipe dreams. It's unlikely that any calendar that modifies the 7-day week will be adopted. That's why I wrote about 7-day hybrid plans earlier this week.
My favorite 7-day plan is the Andrew Usher Calendar:
http://commoncoregeometry.blogspot.com/2020/02/leap-day-post.html
This Calendar Reform proposal (named for its original author, Andrew Usher) adds a hidden Leap Week Calendar to the Gregorian Calendar -- the only change is to the Gregorian Leap Days to make them fit the Leap Week portion.
Not only do I think it's possible for the Usher Calendar to be adopted, I believe that it's already in the process of it! That's because the first step of adoption is for the NFL to add a 17th game to the schedule, which already happened. The next step will occur in 2027, when Super Bowl Sunday will fall on February 14th, which is both Valentine's Day and Presidents' Day Eve. Then the calendar will change so that the Super Bowl will always fall on Presidents' Day Eve (by adding an 18th game) yet never again on Valentine's Day (by changing the definition of Prez Day so that it can fall on Washington's actual birthday, the 22nd, rather than the 15th).
Read the rest of the link above to see how this leads to the Usher Calendar. While the three-day hybrid schedule is possible on the Usher Calendar, most likely the standard five-day schedule will remain.
Cheng's Art of Logic in an Illogical World, Chapter 10
Chapter 10 of Eugenia Cheng's The Art of Logic in an Illogical World, "Where Logic Can't Help Us," begins as follows:
"Cardiac surgeon Stephen Westaby writes in Fragile Lives about the fact that if the heart stops, the brain and nervous system will be damaged in less than five minutes. So he often had five minutes or less to decide how to perform surgery."
As the title implies, there are just some situations where logic just can't help us. Clearly, surgeons don't always have enough time to do a full logical analysis. Cheng writes:
"It's important to understand how far logic gets us and where emotions have to help, rather than pretend that logic can get us all the way there. But we'll start by thinking about where logic can start to kick in, which is only after some help with finding starting points."
Cheng's first example involves language. She points out that there's no logical reason, for example, why the word for "cat" is, well, "cat." Indeed, she contrasts this with her native language:
"'Cat' in Cantonese is a high-pitched 'mow' (rhyming with cow), which does sound quite like the sound a cat makes. More than 'cat' does, anyway."
Of course, English speakers would render the sound a cat makes as "meow." Anyway, young infants learning how to speak the language must figure out for themselves what a "cat" is, since for most words there's no logical connection between the word and the object -- again, except for certain imitative words like English "cuckoo" and Chinese "mow."
The author moves on to discuss flashes of inspiration. She writes:
"You might argue whether they really exist or not, but I have definitely had moments that I would describe it like that. Perhaps it would be less melodramatic to call them an 'idea.'"
Cheng tells us that art and music are all about such flashes of inspiration. Only occasionally would a musician use "logic" to compose a song:
"Some composers, famously Bach and Schoenberg, use symmetry to transform parts of their composition into new but related music."
According to the author, even math often begins with flashes of inspiration:
"Once we have had the idea we proceed using logic, but that part comes afterwards, when we test and exhibit the robustness of our idea."
Having shown us where logic begins, Cheng now proceeds to tell us where logic ends. She presents us the following menu:
Marinated Roast Breast of Chicken -- $18.50
Pan Fried Ostrich -- $21.00
Char Grilled Fillet Steak -- $26.95
Smoked Haddock Fish Cake -- $16.95
Roasted Summer Vegetable Tart -- $17.95
Cheng explains:
"Perhaps you've decided that you can't spend more than $20, and also you don't like fish. This logically narrows down your options to the chicken and vegetable tart, but beyond that, logic can't tell you anything."
And of course, there isn't always time to think logically in an emergency:
"If there is a fire you will, I hope, have an instinctive reaction 'I must get out!' If this is an instantaneous reaction, it probably wasn't exactly processed logically."
But Cheng tries to write it out logically anyway, as follows:
A: There is a fire.
X: I must get out.
It might go like this:
A is true (there is a fire).
A implies X (If there is a fire I must get out)
Therefore X (I must get out) by modus ponens.
The author also inserts additional steps in case we need to explain this to a child:
Let A = There is a fire.
Let B = I stay here.
Let C = I burn.
Then we have:
A is true.
A and B implies C.
C implies bad.
Therefore I must make sure B is false, i.e. I must get out.
On the other hand I think we can all agree that this would not be a logical deduction:
There is a fire.
I will stay here.
(Consider recent news events. Google: refuse to evacuate colorado.)
Cheng continues to write about how insufficient time leads to insufficient information to make a logical decision:
"This can happen in an emergency but it can also happen in sport, where the trajectory of a ball is in principle entirely governed by physics, but we can't take all the necessary measurements in time to do the calculation before needing to hit the ball."
And she adds:
"Any consequences involving human reactions to things are almost certain to be guesses about human behavior rather than logical conclusions."
This applies to both economics and voting.
In fact, there's one very famous conundrum in which insufficient information leads directly to people making an illogical decision -- the prisoner's dilemma. So I'll try to explain it better using Cheng's book today. Alex and Sam are two prisoners, and the prosecutor asks each of them separately to testify against the other:
- If neither testifies, each get a year in jail.
- If both testify, each gets five years.
- If exactly one testifies, the snitch goes free and the other gets ten years.
Cheng points out that this is counterintuitive. And so she comes up with a clarifying example by assuming that there are more than two people involved. (I've done the same in the past with the Monty Hall paradox -- imagine that there are more than three doors.)
- If no one betrays the group, each gets $500.
- If more than one betrays the group, each traitor gets $0 and everyone else loses $1000.
- If exactly one betrays the group, that traitor gets $1000 and everyone else loses $1000.
"This shows us that in all scenarios for other people's behavior, you get a better outcome if you betray. In game theory this is called a dominant strategy and the logic says that this is the strategy that you should take for the best outcome in either scenario."
- If no one defects, there is some cost but the benefit is global.
- If everyone defects, the effect on the world could be drastic.
- If exactly one country defects, then that country benefits the most -- they reap the benefits of conservation without any of the costs.
(This is even though Cheng never names the country which would defect from the agreement.)
"Now according to the logic of the prisoner's dilemma, we should expect everyone to defect. It is perhaps heartening that this isn't universally the case."
As the author explains, it's all about trust:
"I think what this is actually saying is that if a community is infused with enough trust to act as a coherent whole rather than as a collection of selfish individuals, then the logic of the situation changes, and becomes one that can benefit everyone rather than everyone suffering as a result of a few selfish individuals."
Prisoner's Dilemma
I claim that the Prisoner's Dilemma is one of the most commonly played games by the teenagers in our classes -- except it's the Lover's Dilemma:
- If I like my friend, and my friend likes me back, then we can start a relationship.
- If I don't like my friend that way, nor does my friend like me, then we don't start a relationship, but at least we can remain friends.
- If I like my friend, but my friend doesn't like me back, then our friendship is ruined. My (former) friend gets to laugh at me -- the best of all situations for my (ex-)friend, the worst for me.
And Cheng concludes the chapter similarly:
"We have seen that logic cannot explain and decide everything in the world, so we are going to have to do something when it runs out. We should not pretend that those non-logical things are logical, but we should also not assume that those non-logical things are bad."
Conclusion
Even though the Eleven Calendar will never be adopted, I still use the Eleven Calendar for fulfilling New Year's Resolutions. The first day after winter break, January 10th, is an Eightday on the Eleven Calendar, and so I'll get my students to focus on Resolution #8 (minding books/materials). Elevendays on the Eleven Calendar are for my Resolution #11 on communication skills in person.
But I'm working on my online communication skills starting today. By the time I post this to the blog, I have already liked, retweeted, and followed on Twitter for the day.
I hope you all have a Happy New Year, and a much better 2022 than 2020 or 2021.
Comments
Post a Comment