Mathematics Day Post (Yule Blog Challenge #3)

Table of Contents

1. Introduction

2. Yule Blog Prompt #4: How to Build Student Relationships/SEL Needs

3. Cheng's Art of Logic in an Illogical World, Chapter 5

4. Conclusion

Introduction

Yes, today really is Mathematics Day. Here "Mathematics Day" actually refers to the birthday of Srinivasa Ramanujan, the famous "man who knew infinity." In his homeland of India, today is observed as a day to learn math, but its proximity to Christmas makes it difficult to celebrate in schools.

It's also the last of the palindrome dates this month. In the mm/dd/yy format, today is 12/22/21.

This is the third Yule Blog post, but I'm doing the fourth prompt from Shelli's list today. That's because there are 17 prompts for only 12 days, so I'll be skipping some of the prompts. (Notice that the post titles will be counted out of 12 while the prompts are numbered out of 17, so this is Yule Blog post #3/12 and Yule Blog prompt #4/17).

Yule Blog Prompt #4: How to Build Student Relationships/SEL Needs

Even though I know that building student relationships will be especially important during the current pandemic, I admit that I've always struggled to do so. Indeed, as a Stats teacher, I had the students survey each other, and they got to choose the questions. Some asked, "Who's your favorite teacher?" I already know that no one selected me as a favorite.

Of course, if I wanted to be liked, I would have chosen a different profession. My job is to make the students learn, not to make friends. I'd rather have every student hate me and learn lots of math than hate me and learn nothing. But what this does show is that in response to Shelli's prompt, the only honest answer is that no, I haven't done a good job building student relationships.

There are several reasons for my lack of popularity. One is that I teach math, which many students have grown to hate by this point. Some students probably hated me the instant they looked at their schedule and saw my name next to the word "math." But I believe that at least one student named the other math teacher at our school -- which leads to a second reason, namely that I'm a new teacher, while the students already have existing relationships with the teachers who have been at our school. Moreover, I'm not sure whether any student outright hates me (except, perhaps, for one guy who was really upset with me last week due to technical issues with the final exam).

As a matter of fact, I know the main reason why I'm having trouble connecting with the juniors and seniors I've been assigned to teach. It's because I've always had trouble communicating with students of this age, even when I was a young high school student myself.

Back in my November 30th post, I wrote that it was the anniversary of the day that I was suspended in the eighth grade when someone dared me to hit the teacher. The incident made me distrust my fellow students, and so I was eager to avoid others when I moved to my new high school as a freshman. By the time I reached my junior and senior years, I hardly spoke to anyone (except possibly my teammates on the Cross Country team).

To this day, I have trouble communicating with others, period. During lunch, I rarely speak to my fellow teachers in the lounge. (This is partly because schools have stopped serving lunch in the cafeteria to teachers during the pandemic. So I must spend every moment of lunch driving out to a store or restaurant to buy something to eat.) And this even extends to Twitter -- sometimes I purposefully seek out tweets on the MTBoS that have received no likes or responses, only to find out that the only such tweets are my own. In other words, my communication skills are so bad that I don't know what things I should say that will get others to read my tweets.

Recall that back on November 17th, I observed an experienced teacher teach Calculus. But there's something else that I observed -- as each student arrives, he's able to have conversations with them. I suspect that if I were to ask those kids who their favorite teacher was, some would name him. He, unlike me, knows how to build relationships with his students.

Fawn Nguyen is a well-known member of the MTBoS. In her post for the first day of school, she wrote:

https://www.fawnnguyen.com/teach/dear-new-teachers

Tell your students an everyday story. This is not something you force or make up. You either have something light to say or you don’t.

And here's my problem -- almost anything I say would sound forced. I'm simply not the type of person who easily engages in light conversation.

So what should I do? Well, there's one class when building relationships and SEL lessons belong at the forefront -- my morning Advisory class. This class (which is often called "zero period," but it's at the regular start of the day and counts as a homeroom) has ten seniors -- seven guys and three girls.

Once a week, every Advisory class in the district is supposed to give a special SEL lesson known as "Character Strong." There are 25 lessons to give throughout the year, but our school only gave four of them in the first semester (due to spending time on college and financial aid applications instead). The first four lessons are all about having the students meet each other and having them come up with classroom rules/norms. They agreed upon one norm -- that it's important for the students and the teacher to listen to each other.

Yet many of them don't listen to me or their classmates. Many of the students spend the entire period drawing pictures and using their phones (often to look for pictures to draw). They tell me that these drawing technically are assignments for their art class, and that Advisory class is supposed to be only for doing work for other classes (even though they actually get a letter grade from me for this class).

Still, this is the class where I'd like to work on communication skills -- both for myself and for the students in the class. I want to greet each of them by name as they enter my room -- I sometimes do so, but not consistently. And I did follow Shelli's suggestion of giving the students special birthday pencils on their special day. (This is quite new to me, as most of my own teachers didn't acknowledge birthdays when I was young -- only my first grade teacher, with her "Birthday Tree," and my seventh grade teacher for English/history did.)

But this won't be enough. I need to improve my communication skills completely -- with all of my classes (not just Advisory), my colleagues, and teachers I meet on Twitter. Only then will I be able to build effective relationships with my students and others.

Cheng's Art of Logic in an Illogical World, Chapter 5

Chapter 5 of Eugenia Cheng's The Art of Logic in an Illogical World, "Blame and Responsibility," begins as follows:

"On 9 April 2017 United Express Flight 3411 was overbooked. The airline bumped a particular passenger off the flight, but he didn't go voluntarily and was dragged off by security officers, sustaining injuries along the way."

Cheng asks us, whose fault was it? There are two opposing viewpoints:

1. It was United's fault for their unreasonable use of force.
2. It was the passenger's fault for refusing to leave his seat when asked.

Her next example is about a certain comic strip. Often appearing in traditionalists' debates, it's about students who fail classes.

"In the panel for the good old days, a parent and child are in a teacher's office, and the teacher is scolding the student for their bad grades. In the panel for today, the image is the same except now it's the parent scolding the teacher for the student's bad grades."

Cheng's point is that the student's contribution and the teacher's contribution combine to cause the outcome -- as she shows us:

the student didn't work hard enough}

and                                                    } => the student failed the exam

the teacher didn't teach well enough}

The main idea of this chapter are logical connectives. Cheng writes:

"For example, 'The student didn't work hard enough and the teacher didn't teach well enough.' The connecting word here is 'and.' How could the student have passed? Perhaps if 'The student worked harder or the teacher taught better.' The connecting word is 'or.' These two words are the two basic connectives in logic."

The general situation is that given two statements A and B, we get two new statements by using "and" and "or":

1. A and B are both true.
2. A or B is true.

Cheng tells us that "and" works the same in logic and English -- although in English we might leave the word "and" out in certain situations. But the word "or" could be exclusive or, which means "one or the other but not both," or it could be inclusive "or." Here's her example:

"Similarly you have higher social status if you are rich or male (or both). You are an LGBTQI person if you identify as lesbian, gay, bisexual, transgender, queer or intersex, or more than one (for example, transgender and lesbian)."

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 three weeks and skip all posts that have the "Eugenia Cheng" label.

In logic, we tend to use the inclusive "or," even though we might use exclusive "or" more often in speaking English.

At this point Cheng shows us some Venn diagrams. She illustrates the set of black women in the region where the circles for "black people" and "women" overlap:

"In the language of sets and Venn diagrams this is called the intersection, and in this case it consists of black women."

(By the way, lately we've heard the word "intersectionality" in recent news articles pertaining to the social sciences. I believe that the word "intersectionality" here goes back to exactly the sort of intersection that Cheng is describing here, as in "black women.")

In her next diagram, Cheng shows us the set of people who are either black or women:

"This gives us the region shown in the following diagram, which in the language of Venn diagrams is called the union of the two sets."

Unions and intersections -- hey, this is exactly what yesterday's Lesson 2-6 was all about! For the second time this week, Cheng and the U of Chicago are out of sync by one day. (If this occurs a third time next week, I'm seriously considering combining Chapters 1-2 and editing the posts so that the Cheng topics line up with U of Chicago lessons.)

Now Cheng shows us how to find the negation of a statement containing "and" or "or." In her first example, the set of white men (that is, those who are "white" and "men") is the intersection of the sets of white people and men. Its negation consists of three regions:

1. white people who are not men
2. men who are not white, and
3. people who are neither white nor men.

In general:

(A and B) is false means A is false or B is false (or both).

She also negates her earlier example involving "or" -- the negation of the set "black or women" consists of those who are both non-black and non-women:

(A or B) is false means A is false and B is false.

To sum up:

Original statement: You are black and female.

Negation: You are not "black and female." So you could be black but not female, female but not black, or neither.

Original statement: You are black or female.

Negation: You are not "black or female." So you are not black and you are not female. In more natural language you are neither black nor female.

The author now moves on show how to assign blame. Cheng writes that if she breaks a glass she might say there were two contributing factors:

A: I dropped the glass.

B: The floor was hard.

The glass broke because of A and B. So to prevent the glass from breaking, we must invoke the negation -- A is false or B is false. This extends to more "ands":

(A and B and C and D) is false means A is false or B is false or C is false or D is false.

Cheng expands upon this idea:

"I heard an interesting talk by software developer Jessica Kerr who summed this up as understanding the system rather than blaming the individual. So instead of arguing about trying to attribute blame individually, it is more productive to understand how the system makes all those factors interact with each other to cause that outcome."

This applies, for example, when considering who's to blame for a divorce:

A: Alex had an affair.

B: Sam does not forgive Alex.

X: Alex and Sam split up.

Cheng points out that often we forget to consider other contributing factors:

C: they both refuse to go to couples therapy, or

D: they went but the couples therapist wasn't very good.

The author's next example is all about the education system. Once again, many of her ideas have been mentioned earlier in some traditionalists' debates. Cheng writes:

"The education system is full of problems, in my opinion. There are problems to do with funding, expectations, objectives, standards, and so on. Problems with the education system is where I believe math phobia comes from."

She points out that one source of this math phobia is the pressure placed on teachers -- pressure caused by standards and tests (such as Common Core and SBAC). But she adds:

"This causes children to lose interest in it, often towards the end of elementary school, when the math has become to hard for general elementary teachers to be comfortable with, but specialist math teachers have not yet been invoked."

Cheng now returns to the example of the United passenger. She repeats the simplest argument:

1. It was United's fault for their unreasonable use of force.
2. It was the passenger's fault for refusing to leave his seat when asked.

But then she points out that there are many additional factors involved:

1. The flight was unexpectedly overbooked.
2. Some crew needed to get to Louisville to work on another flight, so the airline decided to remove people from the flight.
3. Nobody accepted the offer of money to get off the flight.
4. United decided not to offer more money.
5. United chose a particular passenger to be asked to leave the flight.
6. The passenger decline.
7. United staff called security officers.
8. The security officers used excessive force to remove the passenger.

She draws a fairly complicated diagram containing these and even more possible factors. Of course I won't include this diagram, but she does write:

"I think identifying important factors is an aspect of powerful rational thinking, related to knowing when to stop asking or explaining 'why' in a given situation."

And then the author adds in more complex diagrams explaining the result of the 2016 US presidential election (on the bottom of course is "Trump won the electoral college vote" => "Trump was elected") and why she gained weight ("take in more energy than I burn" => "gain weight").

"So who is to blame? It is possible futile even trying to answer that question. A better question is: who is going to take responsibility for changing it?"

And so Cheng concludes this chapter as follows:

"It is tempting to point the finger of blame at one factor or person, especially if that exonerates ourselves, but I believe it is much more productive to understand the connections of the system. Outcomes are always caused by whole systems, but we can still as individuals take responsibility for change."

Conclusion

Indeed -- I need to take responsibility for changing my communication habits. Today is Ramanujan's birthday, but it's more important to celebrate my students' birthdays than Ramanujan's. And effective relationship building only starts there.