Monday, April 1, 2019

Lesson 13-7: Exterior Angles (Day 137)

Today I began my first day as an English teacher. The reason I took over for this teacher is that the school day here is very short -- just three hours! It's worth changing my subject from math to English at this high school to get such a short teaching day.

Here is "A Day in the Life" for my new school:

11:30 -- This class is senior English. The class has just twelve students. Today I show the students a movie -- Freedom Writers -- to prepare for reading the book in full starting tomorrow.

12:35 -- This class leaves for lunch.

1:20 -- This class is junior English. The class has 21 students. Today I show the students the same movie -- Freedom Writers -- to prepare for reading the book in full starting tomorrow.

2:25 -- This class leaves, thus ending my short day.

Another reason for my transition to math to English is traditionalism. After I read Barry Garelick's post from yesterday, I became a full traditionalist:

https://traditionalmath.wordpress.com/2019/03/31/count-the-tropes-dept-6/

After I read about the success of Garelick's middle school students, I suddenly realized everything I once thought I knew about teaching math was wrong. And so in order to escape progressive reform math completely, I decided to switch to a new subject, English....

APRIL FOOL!

I can't believe you almost fell for that one! No, I didn't give up math, and no, I don't suddenly agree with everything the traditionalists say. The day I described here was actually subbing in a high school special ed English class, not my new permanent job.

But the part about the day lasting just three hours is genuine. That's because this high school is now in the middle of SBAC testing week. From 8:00-10:00, the juniors take the multiple-choice section of the English SBAC. In theory, I should have helped proctor the SBAC since my regular teacher was assigned to do so. But at no time today does anyone in the office direct me to a room for proctoring.

This is followed by snack and a block schedule with all odd classes meeting for 65 minutes each. The day thus starts with first period -- but in this district, "first" period is like zero period, which most students don't have. Thus juniors get a break from 10:00 to 11:30, when third period starts, and most of the non-juniors don't arrive until 11:30.

The day also ends with seventh period, which meets for 30 minutes each today and tomorrow. This is similar to schools with regular seven-period block schedules -- the seventh class meets everyday, but for half as long as the other classes. But today's regular teacher, just like last Friday's music class, has straight periods 2-6 only. Thus I really did teach only two classes today.

Today I also play some April Fool's Day jokes on the students. Before the video, I tell them that they must write three pages of movie notes. Also, at the end of class I tell them that I'll become the permanent teacher for this class, as their regular teacher isn't returning (as I said here on the blog.) It works because the regular teacher was also absent last Friday.

This reminds me of the last time I was in a classroom for April Fool -- four years ago, which was also the first year of this blog. That day I was also assigned to play a video -- this time, it was a science video on earthquakes. My prank was to claim that they would have an earthquake drill that day rather than an earthquake video.

Three years ago, April Fool's Day fell during spring break. Two years ago, April Fool's Day fell on the weekend. Last year, April Fool's Day fell on Easter -- which, of course, meant that it was both the weekend and spring break (in both of my districts). It's much less likely for April 1st to be a school day than, say, March 1st or May 1st, since April 1st can fall during spring break.

In the LAUSD, schools are closed today for Chavez Day. Because Cesar Chavez was born on March 31st, the fact that Chavez Day is a holiday means that LAUSD schools are even less likely to be open on April Fool's Day. Obviously, if April 1st is Saturday or Sunday then schools are closed, and we see that if it's on Monday than it's likely to be closed as well.

If March 31st falls midweek, then the holiday often moved to a nearby Monday or Friday. In some years, it's moved to add an additional day to spring break (always the week before Easter, or Holy Week, in this district). This last happened in 2016 and will occur again next year.

Those changes allow LAUSD schools to be open on April 1st in 2016 and 2020. Since my old charter school observes the same Chavez Day as the district, it means that even if I hadn't left the charter, I wouldn't have been able to play any April Fool's pranks on my students. The existence of Chavez Day means that schools are closed on April Fool's Day in more than 50% of years.

I actually don't have much to say about the latest Garelick post. Most of it is all about reformist jargon that he doesn't like, such as calling students "learners." I assume he'd hate what my old charter school called them -- "scholars."

But I do want to discuss the film that I show the class today -- Freedom Writers. I've played this film in the classroom before, but it was years ago, well before I started this blog. In fact, I should consider this to be one of the big four inspirational teacher movies that have come out in recent years -- along with Akeelah and the Bee, McFarland USA, and Stand and Deliver. I've played the other three in classrooms since I began blogging, and now it's time for me to write about Freedom Writers.

Actually, all of the big four take place in Southern (or Central) California. Of the big four, only Akeelah and the Bee is fictional, and its location might have been chosen due mainly to its proximity to Hollywood. But the other three stories are all based on true California stories, including Freedom Writers, which takes place at a real high school called Wilson. Indeed, when I was student teaching one of my fellow candidates graduated from Wilson in 1998 -- the same year as the Freedom Writers.

The main character is a first-year English teacher, Erin Gruwell. Actually, one of the students -- a Latina named Eva -- can also be considered a protagonist. The movie opens with Eva as the narrator as she tells of her father being shot and killed by the police. This already makes this a much more intense movie than McFarland USA, where there is one violent scene but no one is killed.

When Mrs. Gruwell meets Eva on the first day of freshman year at Wilson, she mispronounces the girl's name. This, by the way, is a result of the Great Vowel Shift in English. Back around the 15th or 16th century, English speakers started pronouncing vowels differently. It's because of the Great Vowel Shift that English is isolated -- we pronounce vowels differently from almost everyone else. So Mrs. Gruwell pronounces "Eva" with an English long "e" sound, but the girl corrects her by saying it with a Spanish (international) "e" sound, which is more like an English long "a" sound.

The pronunciation difference is more noticeable when I look at the Portuguese subtitles (which for some reason I can't get rid of when I play the movie today). These subtitles spell Mrs. Gruwell's pronunciation as "Iva," since the English long "e" sounds like an international "i" sound.

Back at the old charter school, our English teacher was describing the CSET exam that prospective teachers must pass. She told me that she was stumped with a question on her exam because she'd never heard of the Great Vowel Shift. But the Great Vowel Shift is important for all teachers -- not just English teachers -- to know. It explains why English speakers often have trouble pronouncing the names of their minority students.

When subbing, I've noticed that many Hispanic students prefer the English pronunciations of their names, so that "Jorge" usually becomes "George." And recently a girl named "Abril" on my roster told me that her name was "April."

Oops -- I mentioned race in this post. That's back-to-back racial posts on the blog -- and this one is worse because neither of my schools is on spring break. But race is a major theme of Freedom Writers (as well as the rest of the big four teacher movies), and it's impossible to write about the film without mentioning race. (Fortunately I'm protected here by the "traditionalists" label.)

A turning point in the movie occurs when Gruwell is trying to teach a lesson on The Odyssey, which is a standard part of the freshman English curriculum. But there are racial tensions in the class, since there are several Hispanic, Asian, and black students as well as a single white student. One of the Latinos draws an insulting caricature of one of the black guys, and the other students laugh.

This causes Gruwell to launch a big argument about racial stereotypes and the Holocaust. During the argument, Eva asks, "Why do we have to learn about grammar?" And one black guy (not the victim of the caricature) adds, "Why should we respect you, just because you're a teacher?"

This is in itself a question worth answering, but "just because you're a teacher" quickly turns into "just because you're white." He points out that there's no reason for him to do well in her class, since the only paths to success for blacks are performing rap or playing sports. When Mrs. Gruwell asks him whether there are any others, he replies, "I don't know," yet he's sure that getting A's in English and his other classes has nothing to do with his future success.

And Eva adds that she doesn't like whites because of the white cop who shot her father at the start of the movie. Thus she says that she owes Ms. Gruwell no respect at all.

But let's return to the black student. I know all about students who doubt the importance of algebra, and I can see why one might think that reading The Odyssey is irrelevant. But in my last post, I wrote about the teacher Jasmine Lane, who discusses the importance of learning grammar. There are currently at most hundreds of black rappers and basketball players (perhaps surpassing 1000 if we add in football players), but there are thousands -- if not tens of thousands -- of blacks who followed Lane's advice. They learned grammar -- how to speak Standard American English -- and convinced employers to give them high-paying jobs.

Thus unlike Algebra I or The Odyssey, grammar more obviously correlates with future success. I wonder whether the black student who complains about Gruwell's grammar lesson would have accepted one from a black teacher such as Lane.

Many traditionalists lament the decline of the Western canon (which includes The Odyssey). They complain that young students would rather write about themselves and read about people like themselves, when education should be about learning about people different from themselves.

But of course, the movie is all about the students who write about themselves and their struggles in the journals that Gruwell gives them. That's what makes the students "Freedom Writers." We only have time to finish the first part of the movie today, but of course, the rest of the movie is all about how writing the journals inspires the students to improve their lives.

In many ways, the English teacher at my old charter school was a bit like Gruwell. At first she had trouble engaging with the students (especially the mostly black eighth graders). But by the time I left, I notice that the students complained less about her than about either the history teacher or me. I believe she was able to convince them that she deeply cared about them, and that's why they ending up respecting her much more than me.

Lesson 13-7 of the U of Chicago text is called "Exterior Angles." In the modern Third Edition of the text, the content of this lesson has been split. Exterior angles themselves now appear in Lesson 5-7 (which, just like the same numbered lesson in the Second Edition, is on corollaries to Triangle Sum), while Unequal Sides and Unequal Angles now appear in Lesson 6-2 (as the scalene analogs of the Isosceles Triangle Theorem).

This is what I wrote last year about today's lesson:

Unequal Sides Theorem (Triangle Side-Angle Inequality, TSAI):
If two sides of a triangle are not congruent, then the angles opposite them are not congruent, and the larger angle is opposite the longer side.

Given: Triangle ABC with BA > BC
Prove: angle C > angle A

Proof:
Statements                                     Reasons
1. Triangle ABC with BA > BC     1. Given
2. Identify point C' on ray BA       2. On a ray, there is exactly one point at a given distance from
    with BC' = BC                               an endpoint.
3. angle 1 = angle 2                       3. Isosceles Triangle Theorem
4. angle 2 > angle A                       4. Exterior Angle Inequality (with triangle CC'A)
5. angle 1 > angle A                       5. Substitution (step 3 into step 4)
6. angle 1 + angle 3 = angle BCA  6. Angle Addition Postulate
7. angle BCA > angle 1                  7. Equation to Inequality Property
8. angle BCA > angle A                  8. Transitive Property of Inequality (steps 5 and 7)

The next theorem is proved only informally in the U of Chicago. The informal discussion leads to an indirect proof.

Unequal Angles Theorem (Triangle Angle-Side Inequality, TASI):
If two angles of a triangle are not congruent, then the sides opposite them are not congruent, and the longer side is opposite the larger angle.

Indirect Proof:
The contrapositive of the Isosceles Triangle Theorem is: If two angles in a triangle are not congruent, then sides opposite them are not congruent. But which side is opposite the larger angle? Because of the Unequal Sides Theorem, the larger side cannot be opposite the smaller angle. All possibilities but one have been ruled out. The larger side must be opposite the larger angle. QED

In the new Third Edition of the text, not only is Unequal Sides proved right after the Isosceles Triangle Theorem, but both converses (Unequal Angles and Converse Isosceles Triangle) are proved all in the same lesson.

I've also seen -- and mentioned numerous times on the blog -- a theorem order that's completely different from either the Second or Third Editions of the U of Chicago text. The Triangle Exterior Angle Inequality is proved first -- not as a trivial corollary of the Exterior Angle Equality, but as a separate theorem a la Euclid. Then TEAI is used to prove Unequal Sides and Angles just as is done in this lesson. Finally, Unequal Angles is used to prove the Triangle Inequality of Chapter 1.

As I've written before, using TEAI to prove the other theorems could be interesting, but this year we're following only the U of Chicago text. (Yes, my blog is all about going by the book -- now you can see why I chose to have books in the background!)

Before we leave April Fool's Day, I point out that no, there still is no new April Fool Theorem posted at the Metamath website. Since we're in Chapter 13, I've been linking to Metamath lately, but not for anything to do with April Fool's Day.



END

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