Baptism Sunday Post (Yule Blog Challenge #12)
Introduction
Today is Baptism Sunday on the Christian Calendar. It is defined as the Sunday after Epiphany, and is based on an interpretation of the Bible that Christ was baptized around his 30th birthday. Thus Baptism Sunday is the last holiday of the "Christmas season."
Orthodox Christians celebrated Christmas two days ago, and their Epiphany (or Theophany), will be twelve days later, on January 19th. This is also their day to celebrate Baptism -- indeed, it's the Baptism, not the Three Kings, that is more significant in Eastern Churches.
What are my Hispanic students celebrating today? After doing some research, I did read about how some Spanish-speakers observe Octavitas, an eight-day celebration for Epiphany and Baptism. But this is mainly observed in the Caribbean, not Mexico. Thus, unless I find out that one of my students is of Caribbean descent, I shouldn't assume that my mostly Mexican-American students are celebrating any holiday today. In Mexico, the Three Kings are more significant than the Baptism.
And as for nonreligious observances, yesterday there was a Google Doodle for the king's birthday -- no, not Elvis, but Stephen Hawking, who worked in physics (the king of the sciences). On the old blog, I discussed Hawking several times -- first in connection with the movie Theory of Everything, and then while side-along reading a comic strip about the famed scientist.
Yule Blog Prompt #17: My Goals/One Word Challenge for 2022
Last year, Shelli -- the leader of the Yule Blog Challenge -- came up with a "one word challenge" for the new year. In other words, we should select one word to describe the entire year. And she's doing the same this year -- for 2022, she chooses "journey" as her one word.
Last year, I selected "homage" as my one word. I got the idea from 365 New Words-a-Year Calendar, where "homage" was the word for January 2nd. I definitely wanted to pay "homage" to the heroes of 2021 -- from developers of vaccines and other technology to the students who were able to learn math during the pandemic.
This year, I turn to that same calendar to choose a word for 2022. I don't like the January 1st word ("flotilla"), which doesn't really describe a year at all. So once again, I turn to the January 2nd word, which is more appropriate.
And so my one word for 2022 is (drumbeat) --
travail
And "travail" means hard work or toil. Just when we thought the pandemic was waning, omicron surged just as 2021 became 2022. And so making our way through this stage of the pandemic will depend on the travails of all of us -- that is, our hard work.
Last year, the first week of January was also the last week of my long-term assignment. (It seems hard to believe that yesterday marks one year since leaving that middle school.) The other Math 8 teachers and I found a Desmos assignment that replicates Shelli's One Word Challenge. Here's a link to a Desmos "One Word Resolution" assignment, though I doubt it's the same one we found last year:
On Twitter, I listed some of the words my eighth graders selected -- "consistent," "strive," "breathe," and "confident." One student chose "joy," and another even chose "vaccine."
I haven't decided whether I'll assign One Word to my students this year or not. In my last post, I wrote that I might have more Desmos lessons in my classes, and so I could give this activity. But the one above is all about equations of lines, which is not what any of my students are learning.
This might also serve as an activity to do in Advisory, which is all about social-emotional learning and making connections. But again, do I really want to discuss equations of lines in Advisory -- not to mention set up Desmos accounts for a class other than math? Well, I'll have to make a decision soon.
But "travail" is definitely my one word of the year, and my travails will take me back to school tomorrow as winter break comes to an end. For those of you who missed the EDIT that I made to my last post, it has been announced that students won't return to school until Wednesday, in order to give them enough time to get a mandatory COVID test. (Note: I've already received my test results from yesterday -- fortunately, they were negative.)
This means that tomorrow and Tuesday have become de facto PD days. And the principal has already emailed the teachers' main task for those two days -- to prepare two weeks of emergency lessons in case there needs to be a transition between in-person and -- you guessed it! -- a return to distance learning.
Hmm, they already made us write two weeks of emergency lessons just in case one of us is suddenly absent for two weeks (due to COVID, of course) and we can't supply lessons for the sub, so I can just use those lessons -- at least for Calculus and Ethnostats. I wrote those emergency lessons early in the first semester, so I don't have any emergency lessons for Trig yet.
That being said, perhaps this might lead to my getting the Trig textbook more quickly. All I have to do is tell the principal, "Gee, I'd love to write the two-week emergency plans for Trig, but I can't do so unless I have the textbook."
Suppose I do finally get the Trig text tomorrow or Tuesday. How does this affect what the first few days of Trig class? If I follow the plans I mentioned in my last post, I might start Wednesday with an activity (such as the Desmos One Word activity) and then assign Section 1.1 as homework -- which is possible, since 1.1 is most likely some sort of review lesson. Then on Thursday, I go over some HW questions (but not collect the HW yet) and start teaching Section 1.2. Then it's the three-day weekend for MLK Day, and then on Tuesday the 18th the students take the first quiz -- on Section 1.1, the only section that the students will have "completed" by then (even if I never actively teach that lesson).
Of course, this can work if 1.1 is just review. Then again, we know that in reality, many students forget the math they've learned in previous courses -- and that's even more the case during the pandemic. So giving this quiz so soon after the delayed reopening might be setting up the students for failure. (And again, even if I get my textbook, it doesn't mean that the students will have one.)
Then again, since I'm trying to keep the points and percentages equal in all my classes, I won't give the Trig quiz unless Calculus is taking a Chapter 4 quiz as well -- and whether I give the Calc quiz depends on whether there's a monthly minimum day in January. It might be decided that after losing the first two days of school, we can't afford to have a minimum day in January. Then there's won't be a Calc quiz, and so I can skip the Trig quiz as well. In other words, many of my plans will be determined as soon as they reveal when the minimum days are.
(Again, what do minimum days have to do with quizzes? It's because I want to give quiz corrections on all minimum days. I'm trying to avoid student complaints down the road where someone asks, "Why aren't you letting us do quiz corrections?" -- because there's no minimum day. "But back when there was a minimum day, you didn't give a quiz!" Then again, this is what I set myself up for when I didn't want to weight grades in the computer -- suddenly everything turns into "chasing points" and "making the points and percentages equal.")
Anyway, this is what "travail" means. I definitely don't look forward to the possibility of a big mess coming up on Wednesday. During to delayed COVID test results, I'm expecting lots of absences that day -- and that includes students and teachers. I wouldn't be surprised, if all classes meet tomorrow, if I must cover a teacher's class during first period -- and another teacher during sixth! And that will be another factor in the timing of quizzes -- suppose that of the three students in Trig, two (or even all three) are absent both Wednesday and Thursday. Then it would be difficult to justify giving them any sort of quiz next Tuesday.
Thus whatever sort of assignment I give on Wednesday, I must anticipate lots of students being absent that day. So I shouldn't really have any substantial lesson that day.
Cheng's Art of Logic in an Illogical World, Chapter 14
Chapter 14 of Eugenia Cheng's The Art of Logic in an Illogical World is called "Equivalence." Here's how it begins:
"One long-standing myth about mathematics is that it is all about 'getting the right answer.' That everything is simply right or wrong. Another pervasive myth is that it's all about equations."
And of course, one group of believers in those myths are the traditionalists. But Cheng mentions equations here to lead us to the subject of this chapter, equivalence. Equations tell us that two mathematical objects are equal, and now we wish to find out when two thoughts are equal:
"This idea continues into research-level math, where the senses of 'sameness' become more and more subtle, and increasing amounts of technical effort have to be put into finding and describing appropriate notions of sameness."
Cheng's first example involves handwriting:
"If I write the letter 'a' several times they'll all look slightly different, but a handwriting expert should be able to tell that they're all written by the same person."
There's no point in my trying to reproduce the author's a's here. So instead, let's proceed to her next example, which is all about Geometry:
"You might remember that two triangles are called congruent if they are exactly the same shape and size, that is, they have the same angles as each other and the same length of sides. If they have the same angles as each other but possibly different lengths of sides then one is a scaled version of the other and they are called similar."
Cheng includes a picture of two similar triangles -- you don't need to see that one. She also draws one more triangle:
"It's just the first triangle but flipped over sideways. Does flipping a triangle make it a different shape?"
We learn that two objects are congruent if there is an isometry mapping one to the other. A reflection is an isometry, and so two mirror images of each other are indeed congruent. The idea that reflection images aren't "the same" is encapsulated by the idea of "orientation." The author's example includes a backwards S -- it doesn't have the same orientation as a forwards S.
Now Cheng begins to describe the famous recently solved Poincare conjecture. Last year, we had a side-along reading book all about Poincare, so I don't need to repeat it here. Recall that the Poincare conjecture is all about topology, and interestingly enough, Cheng starts writing about that field without ever using the word "topology." She even gives the example of a doughnut being equivalent to a coffee cup without any form of the word "topology":
"It doesn't mean that those spaces are the same; it just means that viewed in this particular light they can be seen as the same."
At this point, Cheng moves on to false equivalence as used outside of mathematics. She writes about how some people argue that boys and girls can play with the same toys if they want, while others declare that we should just "let boys be boys and girls be girls":
"It seems to me that they are equating the argument 'boys and girls can play with the same toys' with a desire to turn boys into girls and girls into boys. This is a false equivalence."
Again, I remind you that Cheng writes about race and politics throughout her book. If you prefer not to read this, then I suggest that you avoid this blog for the next week and skip all posts that have the "Eugenia Cheng" label.
Most of the time, B => A is true, but then people try to conclude the converse A => B. This is a logical error.
I like doing X every day.
I think everyone should do X every day.
If X is "playing the piano" then the first statement is true while the second statement is false (for Cheng, that is). But if X is "brushing one's teeth," then both statements are true (for the author):
"So much for the logic of the situation. It is an example of how I can always be right, by restricting my statement to my own personal taste or aspirations about myself."
Cheng now moves on to damning accusations, many of which are based on false equivalence:
"A sign that someone is about to make a false equivalence is when they launch in with 'You're basically saying...' which is a sign they're about to twist your words into something they're not."
Her examples include equating not wanting to be fat with fat-shaming/misogyny, and finding inheritance of large amounts unfair with desiring confiscation of all wealth at death. In general, an antagonistic argument driving by a false equivalence goes like this:
You are saying A.
A is equivalent to B.
B is bad.
Therefore you are a terrible person.
The logical error could appear in the second line, or third line, or even both. Cheng finds this to be the case for comprehensive sex education. (This issue is all over the news here in California due to a bill that comes into effect this year.) She writes:
"I don't think it is equivalent to condoning sex outside marriage, but I also don't think sex outside marriage is evil."
Cheng's next example of a logical fallacy is false dichotomy. For example:
A: Label some toys "for boys" and others "for girls."
B: Force boys to be girls and girls to be boys.
According to the author, a false dichotomy is in fact a false equivalence between one statement and the negation of the other. Another example is:
A: I am skinny.
B: I am fat.
Cheng draws several diagrams to illustrate this. In her first example, she shows a true dichotomy, with the universe shown as a pie divided completely between A and B halves. Then she draws two types of false dichotomies -- one in which A and B are two circles in the universe with a large "neither" region outside them both, and the other where A and B are two overlapping circles with a "both" region in between. She tells us that it's possible to be a false equivalence in both ways.
Cheng’s example of a false dichotomy involves dieting:
A: Some people should watch what they eat (because it helps them stay healthy)
B: Some people should not watch what they eat (because it hinders them)
She explains that this is a false dichotomy because both A and B are true – some people should indeed diet while others shouldn’t.
Now the author draws a new type of diagram. The following four phrases are in the four corners of this diagram:
Upper-Left: some people should watch what they eat
Upper-Right: nobody should watch what they eat
Lower-Left: everyone should watch what they eat
Lower-Right: some people should not watch what they eat
Along the top and bottom are double-arrows labeled “true dichotomy.” That’s because the UL and UR really are negations of each other, as are the LL and LR. Along the left and right are double-arrows labeled “false equivalence.” That’s because UL and LL aren’t equivalent, and neither are UR and LR (but detractors on both sides make these equivalences). Along the diagonal from UL to LR is a double-arrow labeled “no disagreement.” That’s because these two statements don’t contradict each other, yet Cheng writes:
“The really funny thing about this argument is that it usually turns into a meta-argument about whether or not we’re disagreeing. I try to point out that we’re both making the same point, and the arguer usually insists that we’re not.”
In other words, we go from the reasonable points:
A: Some people should watch what they eat (because it helps them stay healthy)
B: Some people should not watch what they eat (because it hinders them)
To these two absurd and antagonistic ones:
A: Everyone should watch what they eat.
B: Nobody should watch what they eat.
Cheng now redraws the diagram but highlights the other diagonal, from LL to UR. Another double-arrow is placed there, labeled “needless antagonism.” She writes:
“I suppose in many cases people are criticizing different choices, but it doesn’t have to be that way, if we don’t let false dichotomies push us to extremes.”
She now proceeds to discuss straw man arguments. False equivalences are a source of these, as people replace their opponents’ arguments with “straw men” that are easy to knock down. One example is dear to our hearts – the STEM debate. This stems from a more fundamental false dichotomy between:
A: Being creative.
B: Being logical.
That is, some people oppose our emphasis on STEM because they fear that they don’t allow students to be creative. The author draws another chart:
UL: creativity
UR: logic
LL: art
LR: science
Once again, there are false equivalences on the left and right. But this time, the top and bottom are false dichotomies. In reality, we aren’t forced to choose between creativity and logic, and neither must we choose between art and science.
Now here’s the big one that Cheng discusses: “Black lives matter” and “All lives matter.” She explains this in more detail:
“What the slogan ‘Black lives matter’ really means is ‘Black lives matter just as much as other lives, but are currently being treating as if they do not matter as much, and we need to do something to correct this injustice.”
But unfortunately, opponents of “Black lives matter” set up and attack a straw man instead – they interpret the name to mean “Black lives matter and other lives don’t.” So once again, Cheng draws a chart:
UL: black lives matter
UR: black lives don’t matter
LL: some lives don’t matter
LR: all lives matter
Once again, there are false equivalences on the left and right. Just as with the dieting chart, the top and bottom are true dichotomies. The diagonal from UL to LR is “no disagreement.” But again, she redraws the chart with the diagonal from LL to UR as “needless antagonism.”
Cheng tells us that opponents of “Black lives matter” should really debate the following:
A: Black lives matter just as much as other lives.
B: Black lives are currently being treated as if they do not matter as much.
C: We need to do something to correct this injustice.
The argument being made is:
A and B and C.
Cheng has little respect for those who refute A – she regards them as explicit racists. As for the other two statements, we can discuss why they disagree with B and C:
“Is it because they think that black people are bringing it on themselves? Is it because they do not think it is anyone’s responsibility to help other people, in general?”
She also tells us that we may need to have a discussion about:
1. Whether or not the Black Lives Matter movement is really synonymous with anger and aggression, and
2. When anger and aggression are reasonable.
But unfortunately, such discussions are too complex for interactions on social media:
“It is also too complex for people who are riled up by anger or fear. Complex arguments require a certain level of calm.”
The author now tells us that analogies often lead to false equivalence:
A is (falsely) equivalent to B.
B is true.
Therefore, A is true.
Or more likely, we’ll see:
A is (falsely) logically equivalent to B.
B is good/terrible.
Therefore, A is good/terrible.
Cheng returns to an example from earlier:
Saying we should remove gender labels from children’s clothes (A)
Is logically equivalent to
Saying we don’t want to just let girls be girls and boys be boys (B).
B is terrible.
Therefore, A is terrible.
She returns to the diagrams from the last chapter. We might have A and B be linked directly by X, or we might have A linked to Y first, and then have Y and B be linked to X.
Her next example is all about “mansplaining.” She writes:
“But sometimes the evidence that you don’t need the explanation is that you already said that very thing yourself.”
Some people try to make the counterargument that women might try to explain things to men just as much as men explain things to women. And Cheng draws a diagram. “Mansplaining” is first linked by “a man telling a woman something she already knows as part of a general pattern of men failing to give women credit for intelligence.” Then this, along with “a woman being patronizing to a man,” are linked by “a person being patronizing to a person.” Hence here’s how she addresses the counterargument:
“If we go all the way to the top level of this diagram then [mansplaining] is indeed analogous to women being patronizing to men, but this is a level of abstraction too high.”
The author warns us to be aware of false accusations of false equivalence. For example, she writes about a discussion over whether government should pay for higher education, as compared to government paying for healthcare. The difference would seem to be that higher education is “optional,” while going to the doctor isn’t “optional,” which is why government should pay for the latter but not the former. But is it as simple as it seems?
“I don’t think it’s as clear cut as ‘hypochondriacs vs. normal people,” and ‘sick people vs well people.’”
She now draws two charts. The first one (black and white logic) has rows for “hypochondriac” and “normal” and columns for “well” and “sick,” with “no doctor” in the normal-well cell and “doctor” in the other three. The second chart (fuzzy logic) contains “worrier” between “hypochondriac” and “normal.” “ropey” between “well” and “sick,” and “maybe doctor” between “no doctor” and “doctor.”
Returning to education vs. doctor, Cheng goes back to the arrow charts. On one hand, we might link “education” to “you decide whether to go” and “doctor” to “you go when it’s necessary,” but on the other hand, someone else might link both “education” and “doctor” to “you go when it’s necessary.” She agrees with the latter, but:
“I will concede that there might be some exceptions – rich people who go to university just for the sheer fun of it, as they will never need to depend on their education in their lives.”
Cheng’s final example involves manipulation. Recall that she’s British, and so one issue important to her is Brexit. Proponents regard their opponents as “unpatriotic,” but they counter that they think that Remain is best for the UK:
“It then comes back to an argument about what is best for the UK, which is what the argument should be about, rather than simple name-calling.”
For an American example, Cheng also discusses kneeling during the national anthem and whether or not this is “unpatriotic.” In the end, this is really an emotional argument.
Therefore, as usual, Cheng concludes the chapter with review and preview:
“Unfortunately, because of the power of emotions over logic, there are many people who are either unable to think logically enough, or prevented from doing so once their emotions are stirred up. In the next chapter, we will explore what a better interaction between emotions and logic could be.”
There are two chapters left in Cheng's book, Since this is the last winter break post, I'll cover the last two chapters during spring break.
Conclusion
With everything going on, you might be wondering what my upcoming blogging schedule is. Notice that I posted every other day during winter break -- I did this so that I could make it to twelve posts by today, the last day of winter break. But this was assuming that the students would be returning to school tomorrow -- now with the extension, I have actually time for a 13th Yule Blog post. But I won't make a 13th post -- twelve is enough.
Also, I've been making "A Day in the Life" posts on special days, following the old schedule given by Tina Cardone (the original leader of "A Day in the Life"). One of her special days is "A PD day" -- which Monday and Tuesday will be. Still, I likely won't post either day.
Instead, my next post will be Wednesday. And once again, this semester my plan is to post whenever my largest class meets -- that's fourth period Ethnostats, on Mondays, Wednesdays, Fridays.
This year all of us teachers expect to have many travails as we work hard to get through the year. I hope that we'll all be ready for whatever 2022 throws at us.
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