Review for Final Exam, Continued (Day 80)

This is what Theoni Pappas writes on page 45 of her Magic of Mathematics:

"The list of mathematicians with their discoveries and uses or misuses of infinity extends through the centuries."

This is the second page of the section "The Worlds of Infinities." Pappas writes about mathematicians left and right here -- and this being a Geometry blog, we might as well start with the founder of our branch of math:

"Euclid (circa 300 B.C.) showed that the prime numbers were infinite by showing there was no last prime. But the phenomenal work of Georg Cantor (1845-1918) on set theory was a major breakthrough. He determined a way to compare infinite sets by developing transfinite numbers -- numbers that dared to cross the realm of the finite. His work and proofs on these topics are ingenious."

And of course, yesterday I reblogged one of David Kung's lectures on the infinite -- and of course I mentioned Cantor's transfinite numbers.

There is one picture on this page. Here is the caption:

"This field of sunflowers in the Spanish countryside gives the illusion of infinity."

In the LAUSD, today is the last day before the three-week winter break -- and last year, my charter school added a few extra teacher PD days to the LAUSD winter break. But I'm at a new district -- and like most districts, this one has a two-week winter break. The difference is that the last week of each semester is a three-day week, since only three days are needed for six periods of finals.

This means that the last day before winter break on the blog calendar will be Wednesday. This is later than the LAUSD, but slightly earlier than many other area districts.

Let's continue our review for the final exam. This is what I wrote two years ago about the second half of the review worksheet:

Most of the questions on this half, which cover Chapters 5 through 7 of the U of Chicago text, are mostly self-explanatory. Notice that in Question 47, we are given that ABCD is a trapezoid with one pair of opposite angles congruent and we are to prove that it is a parallelogram. In other words, we are using the inclusive definition where a parallelogram is a trapezoid. If teachers prefer the exclusive definition, they can change the Given section to: AB and CD are parallel and angles A and C are congruent, to prove that ABCD is a parallelogram.

So far, this is a very short post -- so it's the perfect day to cover Fawn Nguyen's most recent post:

http://fawnnguyen.com/send-doughnuts/

Here Nguyen writes about a teacher she meets at a workshop in Orange County, California. I will post some excerpts from her post:

I had a wonderful time working with a roomful of teachers over two days at my Grassroots Workshops last week. During a morning break, I talked with a teacher who was concerned about not being able to reach all her kids, that there was a handful of students who were failing the course, and that she’d tried everything. I said, “But you are reaching the other 25 or 30 kids in your class.” She said, “Please tell my principal that.”

So,

Dear Principal,

Your teachers are working really really hard at this thing called teaching. The role of a teacher is not unlike that of a parent. And if you’re not a parent, then think of being a neurosurgeon or an astrophysicist, being a parent is way harder than that.

It’s practically guaranteed that your teachers have not reached all their students today. But, there is tomorrow and the day after that. Please remember that Teacher A in room 23 may not have reached all her students in the academic sense, but she smiled and said hello to Melissa, gave Joey a granola bar and Jake a sharpened pencil, laughed at Amanda’s joke.

Your teachers need your implicit trust and continued support to thrive. Show them you have their back and give them feedback frequently, but wrap each feedback in kindness, empathy, and humor. This makes all the difference in whether or not they want to show up for work tomorrow.

Dear Principal,

Please stop being evaluative, start being helpful and send doughnuts. 

When I read this post, I think back to last year in the middle school classroom. The teacher Nguyen meets ["Teacher A"] was criticized by her principal for not "reaching" the five students who were failing her class, even though she was reaching all the other students. Unfortunately, last year I was the opposite of this teacher -- I'd only reached a handful of students and failed to connect with the majority of the students -- even those with passing grades.

I wrote about the last day before winter break last year -- and I definitely had trouble connecting to the seventh graders:

11:45 -- Now here's where that Wednesday scheduling confusion comes in. Ordinarily, right after nutrition is music for seventh graders, and the lessons take place in my classroom. But today we had the Aspiration Assembly. We try telling the music teacher that we have the assembly today, so the seventh graders can have its music lesson afterward. Anyway, the seventh graders go up to my room so that they can wait for the music teacher -- but he never shows up, probably completely confused by the whole schedule.

I could pass out the snowman graph, but I don't because I'm expecting the music teacher to arrive at any minute. While the class is waiting, a terrible incident occurs.

I see what appears to be one seventh grade girl using a cell phone. When I call her out on it, she pulls the common trick of taking out the case and making it appear that she was playing with the case, not the phone. But then several other students begin to complain that the girl was taking photos or videos of them on the phone.

While this was going on, two students are playing with a broken broomstick. I ask them to surrender the stick, but instead they decided to run around the classroom because they are entertained by my chasing them. According to the student sitting next to the girl, this is what she is trying to record on the phone. Yes, at this point I'm definitely feeling the Disillusionment of being a first-year teacher.

I'm sure that Teacher A has much better classroom management than what I showed that day. I'm the one who deserved rebuke from a principal -- not Teacher A.

Nguyen writes about how teachers like Teacher A "said hello to Melissa, gave Joey a granola bar and Jake a sharpened pencil, laughed at Amanda's joke." (I hope that Melissa, Joey, etc., are pseudonyms and not names of actual students.) In my classroom, I had no problem saying hello to students as they enter, and I gave students red vines (not granola bars) for earning good grades. But I was strict on giving out pencils (though right before winter break I'd give Christmas pencils) and often had trouble getting my two pencil sharpeners to work properly. And I was afraid to laugh at jokes because I'd had such a tenuous grip on classroom management, and worried that allowing students to laugh at jokes would make me lose control of the class (as actually occurred in that post from last year).

By the way, I was also recently reading some old posts from two years ago, around finals week (while I was looking for today's review worksheet). In January 2016 I actually wrote a "day in the life" post as a sub -- and I see how that day went much more smoothly than the December day. In a way, I connected with students better that particular day as a sub than I did my own class as a teacher -- and I should look into those old posts in more detail to figure out what I did right and wrong.

Meanwhile, when principals criticize teachers just because five students are earning F's, this makes the teacher want to inflate the grades in order to avoid that criticism. And this is the traditionalists' biggest fear -- students are passed along and end up in college unable to do elementary math.

Here is the Review for Final, Part II.