But in the district where I actually sub today, it's only Day 14, so we still have a ways to go before the end of the first quaver. It is another middle school special ed class, with the focus on English.
Two of the classes are eighth grade classes and two are seventh grade classes. The eighth graders are reading Hunger Games while the seventh graders are reading Esperanza Rising. Like most special ed teachers, this teacher also co-teaches one period. It's another seventh grade English class, but these kids are studying The Outsiders.
As usual, an aide is in charge of most of the classes, so there's no "Day in the Life" today. But the aide must leave for one period, thereby leaving me in charge. This is third period, which is one of the English 7 classes. As always, middle school periods rotate, but today the rotation actually starts with first period. Let's look at this class in a little more detail.
Ten students are enrolled in this class, and one of them is absent. The students are supposed to complete a worksheet with questions from the first four chapters of Esperanza Rising -- and they're supposed to do it with a partner. Based on the seating chart, it's actually more natural to have the students divide into groups of three.
But in one of the groups, one boy doesn't want to work with his two neighbors. So he answers the questions quickly and puts his head down. The other students inform me that his head is down, but right at this moment, the regular teacher arrives in the classroom. (She has on-campus meetings all day and decides on a whim to drop in right between two of her meetings.) She speaks to the student, and they agree that she would take him to the nurse on the way to her next meeting.
Near the end of class, another group of three finishes their worksheets. Since the regular teacher has left an answer key, I decide to let one girl check her answers. But while this is going on, her two partners -- another girl and a boy -- start playing with some "chimes" on the teacher's desk.
In the lesson plan, the regular teacher tells me that the best class of the day (or best two classes, one in each grade) will be rewarded with donuts on Monday, while any student on the bad list will receive a detention on Monday instead. So I tell the class that I will choose the other seventh grade class to get the donuts reward. The two students keep denying that they're playing with the chimes, even though they are the only two standing nearby. In the end, I tell the regular teacher during lunchtime that they deserve a detention.
There is one mistake in classroom management that I make here. Between telling the two students about the donuts and giving their names to the teacher, I should have given them a warning by saying the name of each student aloud -- especially since a seating chart is available. If the students continue to deny ringing the chimes, then I should have used teacher look. This might have been enough to get the students to stop ringing them and sit down -- and then maybe third period would have received the donuts reward instead of the other class.
It's a habit that I need to establish -- say the name of the student during teacher look. I will keep repeating this over and over on the blog until I actually establish this habit.
Lesson 2-2 of the U of Chicago text is called "If-then Statements." This is what I wrote two years ago about today's lesson:
Lesson 2-2 of the U of Chicago text continues the study of logic by focusing on "if-then" statements. I certainly agree with the text when it writes:
"The small word 'if' is among the most important words in the language of logic and reasoning."
There are a few changes that I will make to the text. First of all, the text refers to the two parts of a conditional statement as the antecedent and the consequent -- although it does mention hypothesis and conclusion as acceptable alternatives. I'm going to follow what the majority of texts do and just use the words hypothesis and conclusion. Actually, Dr. Franklin Mason doesn't even use the word hypothesis -- he simply uses the word given -- since after all, the hypothesis of a theorem corresponds to the "given" statement in a two-column proof.
When I teach or tutor students in geometry, one of my favorite examples is "if a pencil is in my right hand, then it is yellow." So I pick up three yellow pencils, and we observe that the conditional is true. But let's suppose that I pick up a blue pencil in addition to the three yellow pencils. Now the conditional is false, since we can find a counterexample -- the blue pencil, since that's a pencil in my right hand yet isn't yellow.
Notice that I decided to replace the word instance with the word example -- so that the connection between examples and counterexamples becomes evident.
The text has to go back to an example from that dreaded algebra again. Of course, it's an important example, since students often forget that 9 has two square roots, 3 and -3. But I decided to include it anyway since it's simple -- it's not as if I'm making students use the quadratic formula or anything like that.
Then the book moves on to a famous mathematical statement: Goldbach's conjecture, named after the German mathematician Christian Goldbach who lived 300 years ago:
If n is an even number greater than 2, then there are always two primes whose sum is n.
At the time the book was written, the conjecture had been verified up to 100 million, but the conjecture had yet to be proved. But what about now -- has anyone proved Goldbach's conjecture yet? As it turns out, the answer is still no -- but now the conjecture has been verified up to four quintillion -- that is, the number 4 followed by 18 zeros.
But there has been work on a similar statement, called Goldbach's weak conjecture:
If n is an odd number greater than 5, then there are always three primes whose sum is n.
This is called weak because if the better-known (or strong) conjecture is true, the weak is automatically true because we can always let the third prime just be 3. Ironically, when Goldbach himself actually stated his conjecture, he stated the weak version of the conjecture. It was a letter from Euler -- you know, the same Euler who solved the bridge problem that we discussed as an Opening Activity -- that convinced Goldbach to state the strong conjecture instead.
Now as it turns out, someone has claimed a proof of Goldbach's weak conjecture -- namely the Peruvian mathematician Harald Helfgott. Last year, Helfgott's proof was still being peer-reviewed -- that is, checked by other mathematicians to find out whether the proof is correct. By now, Helfgott's proof has finally been verified. Yes, mathematicians are still proving new theorems everyday.
Dr. M also mentions Goldbach's conjecture, on a worksheet for his Lesson 2-1. Often students are fascinated when they hear about conjectures that take centuries to prove, such as Goldbach's conjecture or Fermat's Last Theorem. I often use these examples to motivate students to be persistent when trying to come up with proofs in geometry -- if mathematicians Helfgott and Wiles didn't give up even after centuries of trying to prove these conjectures, then why should they give up after minutes?
The final example in this section has students rewrite statements into if-then form. With the newly released Common Core scores still fresh on my mind [...]
[2018 Update: Notice that the 2018 SBAC scores still haven't been released yet. Apparently, at this time last year the scores had been released, but for some reason, this year the release of the scores is even slower than last year. This is one reason for opposition to Common Core and its associated computer-based standardized tests -- they take too long to score. To me, this defeats the main purpose of taking tests on the computer. Once again, I believe that (at least for math) computer scores should be given instantaneously. Any math question that can't be scored immediately isn't worth asking. So instead, let's skip to the next relevant part of last year's post.]
If you thought that there would be no "spilled milk" in this post, guess again. That's because today's the day my old school made its annual field trip to the LA County Fair. So I can't help but think about the trip to the fair from two years ago.
This is what I wrote two years ago about the field trip:
1) Teachers make a lot of decisions throughout the day. Sometimes we make so many it feels overwhelming. When you think about today, what is a decision/teacher move you made that you are proud of? What is one you are worried wasn’t ideal?
I think that the best decision I made during the first 22 days of school was to include a music break as part of my daily lesson. As I wrote in my First Day of School (August 16th) and August monthly posts, I try to sing a math related song three times a week. This motivates the students to want to sing along -- and by learning the words, they are learning math without realizing it. One of my most popular songs is the one I mentioned in my August monthly post, Count on It. Music break is ten minutes out of an 80-minute block -- but as an incentive, I extend the break to 15 minutes if the students are singing along.
As for the worst decision I made -- well, the field trip to the LA County Fair was two days ago, and so it's still fresh on my mind. There were a number of poor decisions I made on that trip. I know that this isn't supposed to be a Day in the Life post, but here is a brief overview of my field trip:
10:00 -- We arrived at the fair. All groups -- including mine of half a dozen sixth graders, five boys, one girl -- walked through the Jurassic Planet exhibit. My students were hungry and wanted to eat their lunch, but I tell them that all groups would eat near Mojo's Wild and Crazy Island.
12:00 -- The students eventually spent all of their money on the Extreme Thrills tickets. Since all of the other rides were now open, we walked towards the Carnival section -- only to find out that all of the rides require purchasing tickets. The kids kept walking hoping to find a free ride, but we didn't.
2:00 -- As we get ready to board the bus to leave, I met my Support Staff aide, who had a small group of sixth graders of her own. She told me that her group had taken a tram to the farm area, rode a few extreme rides, and still had money left over for the carnival rides!
At that point, one of my group members proceeded to blame me for giving them such a miserable day at the fair -- even though I wasn't the one who wouldn't let them ride. (That would be the carnies who told them that they needed tickets to ride.) On the other hand, he had a point, as there actually were a few things that I could have done to improve my group's experience at the fair.
Until I arrived, I didn't even know that there was a tram. That was something I should have looked into ahead of time -- when I was doing research for my song "Meet Me in Pomona, Mona." Finally, I should have found out that all of the rides require tickets -- perhaps if I'd told my students this, they would have saved money for the Carnival section.
OK, let's return to 2018. First of all, I wrote that when I was writing the music break song, "Meet Me in Pomona, Mona" (as in Pomona, the city where the fair is located), I should have looked up info about the tram and how to get to the farm area.
And so let me fix that error today. Today I'll post a new, better version of the song. Two years ago, I was so obsessed with trying to match the lyrics of the song I was parodying ("Meet Me in St. Louis, Louis") that I kept writing about a "janitor" instead of the field trip itself. In this new version, I keep the first verse but change the second verse to reflect what the kids would see at the fair. Some of that info was included in my original refrain, and so I must change the refrain as well:
MEET ME IN POMONA, MONA
First Verse:
When Mona came up to the school, as she sat,
She hung up her coat and her hat.
She gazed around, but no teacher she found,
So she said "Where can the class be at?"
She remembered the noted, she flipped,
She saw it was a permission slip.
It said, "Hear, hear, it's too slow to learn here,
So let's go on this crazy field trip."
Refrain:
Meet me in Pomona, Mona,
Meet me at the fair.
Don't tell me that I'll learn science,
Any place but there.
The bus will leave for the fair soon,
We can stay there all afternoon.
Meet me in Pomona, Mona,
Meet me at the fair!
Second Verse:
At the fair Mona said, "Here I am!
So first I will get on this tram."
She went to the farm and she saw at the barn,
Cows, pigs, chickens, and even a ram.
And then Mona wanted to go,
To see the monkey named Mojo,.
Peacocks and giraffes and a whole lot of laughs,
And when to leave there she didn't know.
(Repeat Refrain)
While I'm at it, I might as well fix the Fraction Fever song as well, to add the extra verses that I was discussing last week:
FRACTION FEVER
First Verse:
Hey, if you've never
Played Fraction Fever
Here's how to get the action
You gotta get the right fraction!
Choose the wrong one and down you fall
(Down you fall!)
Through the hole and that's not all!
(That's not all!)
If you find the right one later
(Right one later!)
You'll go up in the elevator!
(Elevator!)
When you get to Floor 20
(Floor 20!)
You'll win plenty!
(Win plenty!)
Fraction! Fever!
Fraction! Fever!
Second Verse:
Hey, if you've never
Played Fraction Fever
Here's how to do addition
And also subtraction!
To go up in the elevator
(Elevator!)
Find a common denominator
(Denominator!)
Add or subtract the numerators
(Numerators!)
That will lead you to the elevators!
(Elevators!)
When you get the answer, always try
(Always try!)
To simplify!
(Simplify!)
Fraction! Fever!
Fraction! Fever!
Third Verse:
Hey, if you've never
Played Fraction Fever
Here's how to multiply
And also to divide!
Multiply the numerators
(Numerators)
Multiply the denominators!
(Denominators)
Don't forget when you divide
(You divide)
Flip the second one down upside!
(Down upside)
When you get the answer, always try
(Always try!)
To simplify!
(Simplify!)
Fraction! Fever!
Fraction! Fever!
Moreover, now that I found out what day the field trip, this makes a difference in thinking about how I would have organized the class if I had still been at my old school. Recall that the first two weeks school are for Opening Week Activities and Benchmarks.
[2018 Update: Two weeks ago I wrote a hypothetical letter to myself and described what the first five weeks of school -- up to the day of the fair -- should have looked like in 2016. In today's post, I'm writing about what the first five weeks would have looked like in 2018 if I were still there now. The difference is that in 2016 I needed to teach science, but in 2018 there is a separate science teacher and so I'd only need to teach math.]
Meanwhile, in past posts I pointed out that my students struggled to learn many standards during the school year. I linked to the blogs of other teachers, who suggested that to overcome this, have a lag of one week (or even two weeks) between the introduction of a standard and its assessment. This means that in the Illinois State suggested weekly plan:
Monday: Coding
Tuesday: STEM Project
Wednesday: Traditional Lesson
Thursday: Learning Centers
Friday: Weekly Assessment
the standard to be assessed each Friday is the one introduced in the traditional lesson nine days earlier, not two days earlier.
In earlier posts I was noncommittal regarding whether I wanted to do this. But now that I know the exact date of the field trip, this makes the decision easier for me.
Here's a summary of what the first five weeks of school would look like, from August 14th all the way to today:
First Week of School:
Tuesday, August 14th: Opening Week Activity (VanDerWerf name tents & Bridges)
Wednesday, August 15th: Opening Week Activity (Classroom Rules)
Thursday, August 16th: Opening Week Activity (Buildings)
Friday, August 17th: Opening Week Activity (Sequences)
Notice that even during Opening Week, it's possible to enforce the Illinois State weekly pattern. So on Tuesday, the students work in groups as if it were a STEM Project. It would still be a reverse of the first day of school last year, starting with [2018 update: VanDerWerf name tents followed by Bridges in groups]. On Wednesday, the students write down the rules required for effective traditional lessons. On Thursday, the kids use manipulative blocks to form the buildings -- and manipulative blocks are one part of Learning Centers. On Friday, students complete the sequences as if it were a quiz -- but of course I don't grade the quiz.
Notice that we don't discuss the rules until the second day of school. Of course, I must still enforce the rules starting the first day of school -- especially rules relating to sitting down and being quiet. I enforce these rules exactly as I implied in many recent posts.
During music break, I sing "The Dren Song" on Tuesday, and [2018 update: "Respect the Teacher," an Aretha Franklin tribute/parody] on Thursday and Friday. [Also, notice that Count on It, which I mention earlier in this post, is blocked by "Respect the Teacher." There might be an opportunity to sing this song in the next few weeks.]
Second Week of School:
Monday, August 20th: Benchmark Tests
Tuesday, August 21st: Benchmark Tests
Wednesday: August 22nd: Benchmark Tests
Thursday: August 23rd: Fraction Fever
Friday, August 24th: Dren Quiz
This week is a repeat of the second week of school in 2016. But again we follow the Illinois State weekly plan -- Fraction Fever should be completed using DIDAX manipulative blocks as required during Learning Centers.
On Friday, we follow the weekly plan again and give a Dren Quiz. Since nothing this week is graded, I might as well let it be a 1's Dren Quiz. Alternatively, I could count it as the first graded assignment of the year, in which case it should be a 10's Dren Quiz -- just as I began with 10's last year.
During music break, I sing "The Benchmark Test Song" on Monday and Tuesday, and "Fraction Fever" on Thursday and Friday.
Third Week of School:
Monday, August 27th: First Coding Monday
Tuesday, August 28th: First STEM Project
Wednesday, August 29th: First Traditional Lesson
Thursday, August 30th: First Learning Centers
Friday, August 31st: Admissions Day Holiday
This week is not a repeat of the third week of school in 2016. Instead, I strictly enforce the pattern from Illinois State. Also, as per Illinois State, we follow the naive Common Core order of standards, so the standards to be taught are 6.RP1, 7.RP1, and 8.NS1.
If there was no school on September 1st, then I could squeeze in the Dren Quiz on the 7th. Since I definitely want all activities this week to be graded, it would be the 10's Dren Quiz.
Notice that I do not sing "Need for Speed" (the mousetrap car song) from last year, even though I sang it last year during the third week of school. "Need for Speed" was the first project in the STEM book, but we're now following the pacing guide, which has the projects in a different order (as I mentioned last year). In fact, mousetrap cars only appear in the sixth grade pacing guide -- and it's not the first project of the year (it might have been the third or fourth project).
Setting up the Learning Centers this week would be tricky. Most likely, I'll try to find a few usual DIDAX assignments to return to regularly -- usually algebra tiles or fraction blocks -- and I can even sing "Fraction Fever" on days that we use the fraction blocks.
Fourth Week of School:
Monday, September 3rd: Labor Day Holiday
Tuesday, September 4th: Second STEM Project
Wednesday, September 5th: Second Traditional Lesson
Thursday, September 6th: Second Learning Centers
Friday, September 7th: First Weekly Assessment
The quiz on 6.RP1, 7.RP1, and 8.NS1 is during that fourth week, on September 7th. The first Illinois State online assignment will be on the 4th -- and it will be on the standards to the assessed that week (not the standards to be taught that week). So the "lag" applies to both homework and assessment. The standards to be taught that week are 6.RP2, 7.RP2a, and 8.NS2.
Notice that for the fourth week of school, there is a die cut assignment that's perfect for eighth grade (the square root project) as it lines up with 8.NS2. Otherwise, I'd just have to wing it to make sure that the students are receiving sufficiently many die cut assignments.
Fifth Week of School:
Monday, September 10th: Rosh Hashanah Holiday
Tuesday, September 11th: Third STEM Project
Wednesday, September 12th: Third Traditional Lesson
Thursday, September 13th: Third Learning Centers
Friday, September 14th: LA County Fair Trip
Here I assume that my charter school is observing LAUSD holidays, including Rosh Hashanah. If Rosh Hashanah isn't a school holiday, then it would just be Coding Monday anyway. There's no special Rosh Hashanah earth/moon/sun lesson as in 2016, since I don't need to teach any science.
The standards to be taught this week are 6.RP3a, 7.RP2b, and 8.EE1. That's right -- there are only two 8.NS standards, so we already jump into 8.EE.
Just as in 2016, this fifth week is when I sing the new version of "Meet Me in Pomona, Mona." I don't specify songs for the third and fourth weeks here -- "Ratios" and "Another Ratio Song" from 2016 fit here. The tunes for these songs aren't completely developed, and so it's possible for me to use the new musical scales that I developed over the summer.
Two weeks ago, I wrote that Thursdays should be project days, but in this post I'm giving Tuesday as the project day. Actually, to me Thursdays are more logical, but projects on Tuesdays conform more closely to the pacing plan provided by Illinois State. The exact order would depend on the exact Wednesday bell schedule -- which I don't know. If one grade doesn't meet on Common Planning Wednesdays, then it would be a bad idea to have traditional lessons that day. This is why I'd move the traditional lesson up to Tuesdays and the project back to Thursdays, so that Learning Centers would be given only to the grades that do meet on Wednesdays.
Finally, for today -- the day of the fair -- the students wear special fair T-shirts. One problem I had two years ago was that it was too hot to walk -- which made my poor planning and inability to find something free for the students to do even worse. (One sixth grader almost felt like passing out!) I hope that these fair T-shirts are cooler -- as in temperature -- for the students to wear.
OK, that's enough crying over spilled milk for now. I know that I kept writing about my old class everyday this week, since my subbing this week (especially the multi-day in the art class) reminded me so much of my old class from two years ago.
In addition to today's worksheet, I'm restoring my old pattern of posting a weekly activity. In a way, nearly all of Chapters 0 and 1 are activities, so I resume this tradition here in Chapter 2. Our first activity from last year is a list of logic puzzles, to go along with the logic that we learn here in this chapter. Yes, I know I just wrote a few lines above that for Illinois State, I do projects on Tuesdays (or maybe Thursdays) and assessment on Fridays, but for now I'm posting tests on Wednesdays and activities on Fridays.
Here's a little of what I wrote last year about the logic puzzles:
As it turns out, I've seen a version of this puzzle before last spring. It is a similar brain teaser known as the "Sum and Product Puzzle." The next link contains a statement and solution of the puzzle:
http://www.qbyte.org/puzzles/p003s.html
Notice that in describing the solution, the author actually uses Goldbach's conjecture -- the unproved conjecture that I mentioned earlier in this post. Of course, the numbers involved in this problem are much too small to be counterexamples to Goldbach.
I'll repeat the same activity worksheet from last year, although it might be interesting to replace the old Puzzle #10 with Cheryl's birthday problem. The sum and product version of this puzzle might be suitable in an algebra class, especially near the lesson on factoring quadratic polynomials.
No comments:
Post a Comment