And this definitely includes both of my districts. Both announce two weeks of school cancellations starting next week. For my old district, this includes spring break, and so it will actually be closed for three weeks, with schools possibly reopening on April 6th. As for my new district, it will be closed for two weeks, with the students returning just one week before that district's spring break. I won't be surprised if it's closed for the additional week to make it four straight weeks of closure.
This means that the Big March has suddenly been reduced to four weeks this year, after I've sung about the 5-7 weeks of Big March.
I'll detail what this means for the blog near the bottom of this post. But first, I want to look at today's third and final day of subbing at the special ed high school English class.
I'm wondering whether it's even worth doing "A Day in the Life" today. I did it for the first two days of this assignment, but today has a strange feeling to it. All day, teachers and students wonder whether our district will be closed. It sort of has a "last day before spring break" feeling to it.
Not much work is done today in English class. This is partly due to the coronavirus -- if school's closed for four weeks, the regular teacher won't see how much (or little) they accomplished for about a month, by which time his main concern will be getting back on track, not what the sub writes in the notes to the teacher. (Even when it's just before winter break, the students know that the regular teacher will see the note in just two weeks.) It's also partly due to my Pi Day (Eve) party, where passing out food and playing songs makes it feel like a no-work day anyway.
I'll write out "A Day in the Life" just for completion, but I'll only focus on major behavior issues:
9:15 -- Second period is the first senior class. This class doesn't receive pie, but I do have cookies for the classes that don't win the pie. Students must have completed at least as much as the winning class's average (in this case, six vocab words and definitions) to get the cookies. Two students who don't have enough words get it done today to get the cookies.
Oh, and after yesterday's tardy-fest, today there's just one tardy. That let's-all-hang-out thing only seems to happen on 10:20 testing days.
10:00 -- Second period leaves. Third period is conference period leading into snack.
11:10 -- Fourth period arrives. This is the second senior class. At the store, I find only one pumpkin pie on discount, and so I add apple and cherry pies to give three pies to fifth period only. Last year, there was a pie sale on Pi Day, and there might very well be another one tomorrow. If today had been March 14th instead of the 13th, I might very well have declared it a tie and awarded pies to both fourth and fifth period.
11:55 -- Fifth period arrives. This is the winning senior class. But only two-thirds of the 18 students in this class are present, so I could have gotten away with buying only two pies (or letting fourth period get one of the pies). They finish all of the pumpkin pie and leave parts of the other two pies.
Today, one student tries to leave a minute early for lunch again. This time, I tell him that if he remains in my sight (that is, not turn a corner) when the bell rings, I won't mark him. I won't fuss over one minute when we have several 20- or 30-minute violators to worry about today.
12:45 -- Fifth period leaves for lunch.
1:30 -- Sixth period arrives. This is the first junior class. Some pie is left over, and so sixth period eats it, even though it's the least deserving class.
And they continue to misbehave yet again. After I sing two of the Pi Day songs, one student turns up the volume and plays YouTube on a laptop. The teacher next door tells him that she's giving one of her students a test today -- which makes him only turn it up even louder, and he keeps it loud for the rest of the class. (This happened last week at the middle school, except this time all that student did was stomp his feet loudly for a few seconds.)
Oh, and the same student who was severely tardy yesterday arrives 25-30 minutes late again.
2:15 -- Seventh period arrives. This is the winning class. Only five of the seven students are present today (just like yesterday), so two medium pizzas (one pepperoni, one cheese) are enough. Each student gets two slices, leaving the last two slices for me.
One student asks for a restroom pass and is out for 25-30 minutes, not returning until there are less than five minutes left in the day.
3:05 -- Seventh period leaves. It's actually a few minutes after school when we get the message that the coronavirus has forced the school closure.
On my calendar, today is Saturday, the second day of the week:
Resolution #2: We make sacrifices in order to be successful in math.
Of course, this is an English class, so there's not much chance to discuss this one. The only math I mention today is in the Pi Day songs.
Today's Pi Day songs include Bizzie Lizzie's "American Pi" and "Digit Connection," along with the standards "Ode to Pi" ("Oh Number Pi...) and "Number Pi" (to the tune of "This Old Man"). I also decide to play a simple song on the ukelele, "Solve It." I sing it in the key of C major, and the song requires only the I, IV, and V chords (C, F, G7), so it's easy to play on a less familiar instrument.
After the songs, one student in seventh mentions that he's studying some "real-world math" -- by which he means Business Math. So at least he knows the importance of learning that math. Also, with regards to the resolution, it's not really a good idea to discuss sacrificing to learn math, considering what's going on with the coronavirus.
Indeed, today ends up being a better day to look up the millennium resolutions on communication. I mentioned that on Wednesday, we three subs were stuck in the lounge during state science test. On Thursday, there were twice as many subs there, and the conversations went flying. We were talking about what we'll do during the impending school closure -- regular teachers will be paid during the closure, but subs only get paid when we work. One lady tells me that she also works for DoorDash, so she hopes that she can pick up some income then.
Another sub tells me that like me, he's a former charter teacher. He used to teach elementary school, but now he's hoping to become a high school Spanish teacher. He discusses tricks of the trade -- what to do to get students' attention as a sub. I, of course, tell him about my songs. His trick is that he tries to joke around and communicate well with the students.
Indeed, I also feel that for me, communication with students is also a weakness. Today, for example, might have been a good time to discuss the coronavirus with the students. In particular, I can tell that some of the seniors are worried about the prom and graduation. Of course, it would completely stink to wait your entire life for these activities, seeing older students graduate ahead of you, and then have your end of senior year be ruined like this. I briefly mention this to some of them, but that's not the same as having a heart-to-heart conversation that my fellow sub would have.
There's also one more opportunity to communicate with fellow teachers. On Fridays, one teacher in the math department brings snacks. I often just go in and eat with them on days that I sub, even if I'm not subbing in this department that day. So today, I make it up by buying an extra Pi Day pie (peach, this time) and placing it next to the regular teacher's snack pile (donuts, oranges, and veggies).
Then I stay to hear the other teachers' conversation. By now, the other teachers have heard of the LAUSD and SDUSD closures and wonder whether our district is next. Many teachers look forward to the long break -- for them, it's paid time off. For students, it's a longer spring break. It's mainly us subs who are affected the most negatively. (Of course, I know the ones actually most affected are those who catch the virus, along with their family members. I'm referring to which staff members are most affected regarding their employment situation.)
With everything else going on, the Rebecca Rapoport calendar is the last thing on my mind. But I notice that she makes another error on her calendar:
x + y = 24
y + z = 26
x + z = 28
For the second time on this calendar, she gives a system of equations, but neglects to state which variable we're to solve for, x, y, or z.
Of course, knowing that today is Friday the thirteenth helps. That second equation, y + z = 26, sticks out like a sore thumb because twice 13 is 26. But if one of the addends in that equation were 13, then so would the other, so y = z = 13. Yet y can't equal z, since x + y doesn't equal x + z (24 vs. 28).
Thus x must be 13. But that's not really solving a system -- that's cheating by already knowing that the answer is the date. Of course, if we solve for x by eliminating y and z, we do obtain x = 13, but still, we cheated. Then again, if Rapoport didn't want us to cheat, she should have just specified in the first place that we are solving for x.
OK, so here are my plans for the blog. This blog follows my old calendar, which we know will be closed for three weeks (with spring break as one of the three weeks). Thus the next three weeks will follow a de facto spring break schedule.
I'll make at least three posts during the "vacation" period. The first one will be tomorrow, Pi Day, since I like to post on the special day, even when it's on the weekend. (Just as I did on Leap Day, I would have posted tomorrow anyway, even if there had been no coronavirus outbreak.) Only once have I missed a Pi Day post -- that was in 2017, amidst the chaos of leaving the old charter school and the "Great Posting Purge of 2017" when I deleted many posts to avoid confusion.
Since two weeks of school will be missed, today, Day 131 will be followed by Day 142, assuming that school resumes on April 6th as scheduled. This means that following the digit pattern, we skip directly from Lesson 13-1 to 14-2. (But note -- if it's announced that school must be extended two weeks in June to make it up, then April 6th will be labeled Day 132 instead.)
Before the coronavirus, spring break would have divided the quarters for the first time this year. In the past, even though the Chapter 12 Test was given before the end of the third quarter, some teachers might not have it graded before the end of the quarter, so it ends up as a fourth quarter grade. This year, I have no idea what's going on with third quarter grades.
Meanwhile, in my new district, today is Day 122. If only two weeks are canceled, then school will resume on Day 133. If, as I suspect will happen, a third week is blacked out, then the return date after spring break will be Day 138.
In a way, it means that we're unwittingly following the Third Edition text, which doesn't include the equivalent of the old Chapter 13. I was going to make a joke about triskaidekaphobia, beginning Chapter 13 on this Friday the 13th. Well, I'm still giving Lesson 13-1 today (since it's still Day 131), but that's all we're getting out of Chapter 13 this year.
This is what I wrote last year about today's lesson.
This lesson focuses on mathematical logic, which ultimately helps the students write proofs. I mentioned earlier that the Law of Detachment is often known by its Latin name, modus ponens. In fact, I pointed out that on the Metamath website -- a website full of mathematical proofs -- modus ponens is one of the most used justifications:
http://us.metamath.org/mpegif/ax-mp.html
Notice that I only mention the Metamath website for general information. This website is definitely not suitable for use in a high school math classroom. At Metamath, even a simple proof like that of 2+2=4 is very complex:
http://us.metamath.org/mpegif/2p2e4.html
In fact, believe it or not the proof was once even more complicated because it tried to use pure set theory to prove that 2+2=4, and then later on more axioms (postulates) were added to make the proofs easier -- similar to the postulates for real numbers mentioned in Lesson 1-7. To repeat, the basic idea is that one makes a proof simpler by adding more axioms/postulates.
This is when students often ask, "Why do we have to learn proofs?" Of course, they ask because proofs are perhaps the most difficult part of a geometry course. The answer is that even though mathematical proofs may not be important per se -- but proofs are. Many fields, from law to medicine, depend on proving things. We don't want to guess that a certain person is guilty or that taking a certain medicine is effective -- we want to prove it. For centuries, the dominant way to learn how logical arguments work was to read Euclid. Let's learn about how Honest Abe learned about logical arguments from Euclid:
http://the-american-catholic.com/2012/08/16/lincoln-and-euclid/
Unfortunately, the above link is a political and religious website. Well, I suppose it's impossible to avoid politics when discussing Lincoln, but the webpage is also a Catholic site.
Last year, we read Eugenia Cheng's third book, which is all about logic. Thus some ideas from Cheng's book are explored in this chapter.
Today is an activity day. The Exploration questions for Lesson 13-1 are based on a famous puzzle called "Who Owns the Zebra?" I decided to include a description of the puzzle -- but instead of typing it in by hand, I cut-and-paste from the following link:
https://sites.lsa.umich.edu/inclusive-teaching/2017/08/16/who-owns-the-zebra/
As the U of Chicago text notes, "This puzzle dates from the 1950's, before the dangers of smoking were widely recognized." By now, of course, we understand the perils of smoking. And so the U of Michigan link above replaces "the Old Gold smoker" with "the aerobic exerciser."
2020 update: Since today is suddenly the last day before "spring break," we might skip the main lesson and give the logic puzzle as a pre-spring break activity.
EDIT: Also, I'm treating this as a "last day of school" post. Thus I'm following my typical protocol for the last three days: yesterday was the last test of the year (even though it's the Chapter 12 Test rather than a final), tomorrow is all about future blogging plans (and Pi Day of course), and today is the spring MTBoS post.
Yes, the Queen has spoken! Here is what Fawn Nguyen has to say tonight:
http://fawnnguyen.com/math-worksheets/
I often create worksheets for my students, even though every district-adopted math curriculum we’ve had has worksheets for students. I do this for two reasons:
- I teach differently — sometimes slightly, sometimes quite a bit — than what the curriculum writing team was thinking.
- There’s a particular structure/scaffold that reflects how I see the content can unfold for learners.
Here’s a sequence of practice questions for my 8th graders on rigid transformations.
"Rigid transformations" are the same as what the U of Chicago text calls "isometries." As we know, isometries are at the heart of Common Core Geometry (including Math 8).I'm fascinated by how much thought Nguyen puts into her worksheets:
Everything about this is intentional.
- Item #1 is a completed sample of what’s to come. This is a practice worksheet, not a problem-solving task, so I will be clear about what is expected.
- I remove certain parts in item #2, while keeping it similar to item #1.
- Item #3 comes before item #4 because I think it’s easier to follow the stated transformations than to say what they are.
- Item #6 asks for more flexibility but with an ending constraint.
- Item #7 opens up the problem and allows for peer exchange.
Other math teacher bloggers are making special Pi Day posts. Sara Vanderwerf (the "name tents" teacher) writes all about circles and pi today:
There is a High School in the district I worked in for my entire career that is notorious for putting math content questions on their list of interview questions if you are interviewing to be a math teacher there. A favorite question of this type for many years (until word got out that they used this question) was, ‘What is the definition of Pi?‘. Off the record and according to several people who were part of these interviews, more than half of all secondary licensed math teachers who applied struggled with this question. They could talk about the number pi (3.14159….) & that this number is irrational. They mentioned ‘Pi Day’ and named formulas for the circumference of a circle and the area of a circle, but when pressed for more they could say little. How sad that so many math teachers struggle with a basic concept in mathematics.
Wow, Vanderwerf sounds just like a traditionalist here, except instead of complaining about how little math students understand, she writes about how little math teachers understand.
But her view of this problem, of course, is anything but traditional. A traditionalist complains about too much understanding and too little skills, but Vanderwerf says it's the opposite problem -- too much of the pi unit is devoted to skills:
Too much of how Pi Day is celebrated is connected to low level memorization and not the beautiful relationships in Pi. There are so many other wonderful things you could do on March 14th – than just memorizing digits of Pi. If you need one small way to start this – Check out video #2 where I have students start to build an intuitive idea of Pi – you could expand the ideas in this video to really do something special with Pi.
I'll just let you view the videos directly from their source at Sara Vanderwerf's website.
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