Some of the classes have an aide, and many of the classes are not math. Therefore I won't be doing "A Day in the Life" today.
But in the first class, a few students comment on the date, September 11th. The regular teacher has written "Never Forget" on the board. This is a great time for me to cut-and-paste last year's post, where I describe where I was on that fateful day when the towers fell.
In the year 2001, I was an undergrad student at UCLA. I had just completed my second year and decided to take two classes over the summer. (These summer classes, along with my AP credits, would allow me to complete my bachelor's degree in just three years.)
Notice that since UCLA is on the quarter system, summer classes extended into September. We see that the fall semester typically begins in late August so that an entire semester is completed before Christmas (the same reason that high schools also now have an Early Start Calendar). But at quarter schools, only one quarter (not one semester) needs to be completed by winter break, and so they can afford to start later. The fall quarter at UCLA began the last week of September, and so summer classes start and end later.
Summer at UCLA was divided into two halves, called "A Session" and "C Session." Each session was six weeks. (Officially, "B Session" refers to a few special one- or two-week seminars only in certain departments, such as art.)
If you check the UCLA website nowadays, you'll see that math courses could be offered either A Session or C Session. But back in 2001, summer math courses were eight weeks long -- the six weeks of A Session plus the first two weeks of C Session. The class I took in Summer 2001 was MATH 132, Complex Analysis. (I still have a copy of a test I took that summer -- a perfect 300/300 score.)
The second course I took that summer was Geography 5, "People and Earth's Ecosystems," which I used to fulfill my general ed requirements. This was a C Session course that met twice a week, on Tuesdays and Thursdays. So by September, I had finished Complex Analysis, but was still attending the Geography 5 course.
Meanwhile, during my years at UCLA, I earned money by working part-time at the library. During the summer, we worked a fixed schedule for A Session and C Session. Since my math and geography classes overlapped for the first two weeks of C Session, my library hours for that session would have to accommodate both classes. If I recall correctly, my schedule was like 8-10 for Geography 5, then noon-2 for math, and afterwards I worked at the library from 2-6. Once the first two weeks of C Session had passed, I was left with a long gap between geography class ending at 10 and work not starting until 2 for the final four weeks.
September 11th, 2001 fell on a Tuesday -- and just like this year, it's the sixth and final week of C Session. And so I had to wake up early for Geography 5. I commuted a long distance to UCLA back then -- I woke up around 5-something in order to leave by 6-something.
When I first turned on the news that morning, I heard that a plane had struck one of the Twin Towers in New York City. Originally, I assumed that it was an accident. I took an early morning shower -- and by the time I came out of the shower, a second plane had hit the other tower. I knew that the probability of two planes having accidents about a half-hour apart, with each plane hitting the World Trade Center, was infinitesimal. The plane crashes were clearly intentional!
I began the long commute to UCLA. On the way there, I hear about the events of the East Coast on the radio. I reach the campus in time for my 8:00 Geography 5 class. I arrived expecting a long lecture followed by review for the final -- to be held two days later, on Thursday.
As the title of the class implies, the subject material of the class is all about what effect humans have on the planet and its ecosystems -- indeed, how we cause the ecosystems to change over time. And so this is what the professor said to open the class:
"This summer, we've learned how the world can change over a period of many years. But today, we see that the world can change a whole lot in a single day."
He dropped the lecture format for that day, and instead allowed the class to discuss what was happening in New York. Some students had grown up on the East Coast, and they were undoubtedly fearful of what was going on. Not until the last few minutes of class did the professor remind us of what would be on Thursday's final.
Class ended, and it was time for my long break between class and work. I walked to the library (the same one where I worked) and studied a little for Thursday's final. Then I went to the computers and decided to play around on the Internet. It was only then when I realized exactly how much the world had changed that day.
You see, there was a huge bank of computers on the first floor of the library. But on the second floor, there was a lone computer in walking distance of a restroom. I knew about the computer mainly because I worked there -- so most of the time this computer was open. Because of its proximity to the restroom, I liked to use that computer. Yet I was afraid that by the time I'd return from the restroom, someone would take that computer. So I had a bright idea -- I'd leave a window open on some website and leave my backpack behind as I went to the restroom. Hopefully, other patrons would get the hint that the computer was taken.
When I returned from the restroom, a security guard was standing at the computer waiting for me. He asked me, "Is that your backpack over there?" When I nodded, he continued, "Someone had called in a bomb threat, so we had to make sure that it was yours."
I knew that the "bomb threat" was the general events occurring on the East Coast. In other words, because it was 9/11, the security guards were afraid that my backpack contained a bomb and that I'd walked away before it exploded. Only then did I know that the world had changed -- and it was a world full of fear, uncertainty, and doubt.
After the encounter with the security guard, I was no longer in the mood to use the computer. It was approaching lunch time anyway, and so I left the library and walked to the student union. As I ate, I saw the news continue to cover the events of New York -- and Washington DC. I recall reading the scroll bar on the bottom of the TV -- all sporting events had been cancelled, not just the games in the two cities that had been attacked.
I thought about the people -- the people on the planes, the people in the towers. I began to shed tears for all of the victims.
When it was time for work, I returned to the library. It goes without saying that my boss and student coworkers were discussing the tragic events. After work, I took the long walk back to the car. I glanced at the TV in the student union along the way and saw burning buildings on the screen -- and I was afraid that downtown LA had been attacked as well. It wasn't until I listened to the radio along the drive home that I learned that the West Coast had been spared after all.
On Thursday, September 13th, I took the Geography 5 final and passed the class. During the long break between class and work, a group of students were gathering in front of Royce Hall. A moment of silence was held for all the victims who had died two days earlier -- just as a moment of silence is held at the school where I sub at today.
And that's my answer to the question, "Where was I on 9/11?"
Today is the Chapter 1 Test. This is what I wrote about the test last year:
I am now posting my first test. It is actually the Chapter 1 Quiz that I posted in the past, but now I'm considering it to be a "test." This is mainly because in my semester plan at the start of the year, I refer to the first day of school up to Labor Day as the first "unit," and then the month starting with Labor Day as the second "unit." Each test that I post corresponds to one of these "units." Still, I don't want to overburden the students with a hard test at the start of the year, so this still has only 10 questions.
Even though my series "How to Fix Common Core" is over, I will often use these quiz and test days to post links to articles about the Common Core debate, including recent traditionalist arguments. I will start by rewriting what I wrote last year about today's test (including my rationale for including the questions that I did), and then link it back to the Common Core debate.
There is a Progress Self-Test included in the book. But even if I threw out the questions based on sections 1-6 through 1-8, there are some questions that I chose not to include.
For example, the first question on the Self-Test asks the students to find AB using a number line. This is very similar to some of the questions that I gave on the Wednesday and Thursday worksheets. But there is one crucial difference -- this one is the first in which both A and B have negative coefficients.
Now I know what the test writers are thinking here. The test writers want to know whether the students understand a concept. There's not enough room on the test to give both easier and harder questions. If a student gets a harder question correct, we can be sure that the student will probably get a much easier question right as well. But if the student only answers an easier question correctly, we can never be sure whether the student understands the more difficult question. Therefore, the test should contain only harder questions, since anyone who gets these right understands the simpler concepts too.
But now let's think about this from the perspective of the test taker, not the test maker. Let's consider the following sequence of hypothetical conversations:
Wednesday:
Student: The distance between 4 and 5 is 9.
Teacher: Wrong. You're supposed to subtract the coordinates, not add them. The distance is 5 - 4 = 1.
Student: Oh.
Thursday:
Student: The distance between -4 and 2 is 2.
Teacher: Wrong. When subtracting, change the sign. The distance is 2 - (-4) = 6.
Student: Oh.
Friday:
Student: The distance between -8 and -4 is 12.
Teacher: Wrong. You forgot the negative in front of the 4. The distance is -4 - (-8) = 4.
Student: Oh.
And we can see the problem here. The teacher wants the student to be able to find the distance no matter what the sign of the coordinates are -- not just when they're positive. But the problem is that the instant that a student finally understands how to solve the first problem, the teacher suddenly makes the problem slightly harder, and the student becomes confused.
Of course, you might be asking, why only give one problem on Wednesday? Why can't we give more problems to check for student understanding of the all-positive case, then move on to negatives? But you see, I'm imagining the above hypothetical conversations as occurring during, say, a warm-up given during the first few minutes of class -- and warm-ups typically contain no more than one or two questions. The student is never allowed to taste success, because each day a little something is added to the problem (like a negative sign) that's preventing the student's answer from being completely correct. The student never hears the words "You're right." And that's just with negative signs -- the U of Chicago text includes questions with decimals as well. I immediately threw all decimals out of my problems -- since decimals confuse the students even more, most notably when we draw number lines and mark only the integers.
Well, I don't want this to happen, especially not on the quiz or test where most of the points are earned. I want the student to taste success -- and this includes the student who's coming off of a tough second semester of Algebra I and is now in Geometry. Sure, if you feel that some students need to be challenged, then challenge them with all the negatives and decimals you want. But I don't want to dangle the carrot of success in front of a student (making them think that they've understood a concept and will get the next test question right), only to jerk it away at the last moment (by adding extra negative signs that will make the student get the next test question wrong), all in the name of challenging the students.
And so my test questions are basically review questions rewritten with different numbers. My rule of thumb is that the test contains exactly the same number of negative signs as the review. Some teachers may see this as spoon-feeding, but I see it as setting the students up for success. Any student who works hard to prepare for the test by studying the review will get the corresponding questions correct on the test.
Of course, some questions about the properties are hard to rewrite. I considered using the question from the U of Chicago text, to get from "3x > 11" to "3x + 6 > 17." But notice that the correct answer -- Addition Property of Inequality -- is difficult to remember and will result in many students getting it wrong. So even here I changed it to the Addition Property of Equality. After all, the whole point of learning the properties is to be able to use them in proofs. The Addition Property of Equality is much more likely to appear than the corresponding Property of Inequality. All including Inequality on the test accomplishes is increasing student frustration over a property that rarely even appears in proofs.
As I mentioned earlier, today is a traditionalists' post. Let's start our traditionalists' discussion by revisiting the one math class that I sub for today -- "Business Math." This class consists mainly of special ed juniors, and it's one of the classes that doesn't have an aide. There are three worksheets for the students to work on today:
- Lesson 6: Tips
- Lesson 8: Rounding Money
- Lesson 9: Salary
Officially, I 'm supposed to begin with Lesson 8, but the regular teacher knows that most students haven't finished Lesson 6 yet. So instead, I devote half the class to Lesson 6 and the other half to Lesson 8, leaving out 9 completely.
Relevant to the traditionalists' debate is the fact that according to the regular teacher, calculators are allowed for this assignment. Here is an example of a problem from the Lesson 6 worksheet:
- Alyssa is a server and earns $4.25 per hour. In one week she earned $250 in tips while she worked 40 hours. Find her total income for the week.
A traditionalist might argue that this problem is doable without a calculator. The product 4.25 * 40 is done via the standard algorithm for decimal multiplication. Since this product works out to be $170, the ensuing addition involves no decimals -- it's just two three-digit numbers, both of which are multiples of ten.
Meanwhile, someone like Ruth Parker (of Number Talk) fame might point out that $4.25 can be doubled twice, first to $8.50 and then to $17. This is equivalent to multiplying by four, so all that remains is to multiply $17 by ten, which is easy. But this method isn't traditionalist-approved.
Now Lesson 8, on rounding, asks students to round each amount to the nearest cent:
- $5.01785
Of course, this problem shouldn't need a calculator at all -- and of course, most simple calculators don't even have the ability to round. There is a rounding function on the TI-83:
round(5.01785,2)
But most likely, no one would ever use this function in isolation. Indeed, the rounding function would most likely be used in a program:
PROGRAM:PLUSTAX
:Disp "COST"
:Input C
:Disp "RATE"
:Input R
:Disp "YOU PAY"
:Round(C(1+.01R),2)
As a sub, it's difficult to judge the ability of special ed students. Perhaps these students could have done Lesson 6 without a calculator, but the teacher has them using calculators. But of course, there's no excuse for needing a calculator to complete Lesson 8.
Now this is where lesson presentation and classroom management come into play (especially since this class has no aide). The regular teacher has a strict no cell phone rule -- and indeed, she has pockets near the door in which to place phones. But for some reason, there aren't quite enough calculators for all the students, and so naturally students would want to use phones here.
I decide to let the students keep their phones for Lesson 6. Then when it was time for Lesson 8, I adhere to the regular teacher's "no phone" rule, since calculators aren't needed for that lesson. But there are still two guys who have trouble putting the phones away when it's Lesson 8 time. It might have been easier just to follow the regular teacher and have them put phones in the pockets, but then they wouldn't have had calculators for Lesson 6.
As a sub, it's difficult to deal with this sort of situation -- but if I ever return to the classroom as a regular teacher someday, I can plan for this. I can decide in advance whether an assignment requires a calculator, count how many calculators and students there are, and then consider whether to allow students without a calculator to use phones (and what to do if they use phones for off-task stuff).
For example, let's say that I'm teaching our favorite math class -- Geometry. We're in the lesson on the Triangle-Sum Theorem, and students are completing a worksheet with many problems where they are given two angles of a triangle and are asked to find the third. Thus for each problem, two steps of arithmetic are required:
- Add the measures of the two given angles.
- Subtract this sum from 180.
Most likely, the numbers to be added will contain two digits each, and we're subtracting this sum from the three-digit number 180. A traditionalist will say that no calculator is needed here -- the standard algorithm can be used for both the addition and the subtraction. But as I've mentioned on the blog in the past, some students haven't done arithmetic without a calculator since sixth grade -- and they're now in high school Geometry. I refer to students who can't do one-digit arithmetic as "drens," but two-digit arithmetic is a gray area. Notice that since 180 ends in zero, the standard algorithm for subtraction will involve "borrowing" unless the number being subtracted also ends in zero.
Here's one way I can organize such a lesson. On the first day, no calculators (and thus no phones) are permitted, but all the angles are multiples of ten degrees. This for the most part eliminates borrowing, since instead the students will need to subtract 180 - 80 or 180 - 110 -- and these are essentially equivalent to subtracting 18 - 8 or 18 -11 (definitely in the "dren" range). The only case that arguably counts as borrowing is 180 - 90 or 18 - 9. (There is a recent meme which shows a student trying to "borrow" to find 18 - 9.) Even in this case, since 90 degrees is a right angle, the hope is that students will recognize this special case quickly even without having to find 18 - 9.
Then the next day, calculators are allowed and the angles no longer need to be multiples of ten. In this case, I count in advance how many calculators there are. If there are enough calculators, then phones remain forbidden. If there aren't enough, then phones are allowed -- and in this case, I know in advance to double-check that students aren't playing games on the phones.
I believe I do an OK job in explaining how to solve the Lesson 6 problems. But when it comes to Lesson 8 and rounding, I fear that I don't explain these problems in class well enough. The worksheet does break down this process into steps. Round $92.0769 to the nearest cent:
- Locate the digit to which the number is to be rounded. In this case, the KEY DIGIT is 7. The key digit is the number to be rounded and is underlined in the example ($92.0769).
- Check the digit to the right of the key digit. This digit, 6, is boldfaced in the example ($92.0769).
- If that digit is 5 or greater, add 1 to the key digit (round up). If that digit is less than 5, then the key digit remains the same.
- Drop all the digits to the right of the key digit. $92.0769 rounded to the nearest cent is $92.08.
Students get confused when I use the phrase "round down." For example, some students try to round $1.333 to $1.32 because I've told them to "round down" in that situation. Notice that the steps above use the phrase "round up," but never "round down." That's why I should have followed the script that is clearly written above. ("Round down" makes more sense with rounding whole numbers. It's more obvious to see why rounding 33 to 30 is called "rounding down" than it is with $1.333 to $1.33.)
Notice that this is the perfect lesson for a Square One TV song -- "Round It Off." But I've never sung this to the old charter school students, so I never blogged or wrote down the lyrics -- and Barry Carter doesn't list this song at his site either. Without the lyrics, I can't sing the song. I do remember a few of the lines -- the ones that actually explain how to round:
Five and over, just increase it,
Under five, you just decrease it.
Then again, "decrease it" might have had the same problem as "round down." Still, the parts of the chorus/refrain that I remember fit this lesson very well:
Make it hundredths, make it tenths,
You can use your common sense,
To round it off! Round it off!
To the nearest whole number.
That's because the back side asks students to round to the nearest cent, dime, and dollar -- that is, to the nearest hundredth, tenth, and whole number, just like the song. By the time we reach the back, the class is almost over. Instead, I have the students focus on answering the front side correctly.
One of these days, I need to write the words of the song, since who knows when I'll be in the next math class where students need to round? (It could be an algebra class where students need to round square roots, for example.)
Certainly, what I need to practice is presenting lessons one step at a time -- and having strong enough classroom management to keep the students quiet while I present the steps. It's possible for me to call upon students to complete each step. If I have the song available and feel that it makes a difference, I can use the song as an incentive for the students to get quiet.
(In the end, the only song I sing today is during the last class of the day -- the girls soccer team. There is no practice today and the girls must work in the classroom. Once again, I default to the time of year and sing "Meet Me in Pomona," as the LA County Fair is still open.)
I never reach Lesson 9 at all. Students are asked to fill in the chart for several workers' salaries:
Worker: Dominic
Annual Salary: $26,000
How Often Paid: Weekly
Times per Year:
Amount per Pay Period:
Students are told that "weekly" means 52 pays per year, "biweekly" means 26 pays per year, "semimonthly" means 24 pays per year, and so on. ("Biweekly" and "semimonthly" may seem to make a little difference, with 26 paychecks vs. 24. But to those of us who worked at the library -- as in the one I mentioned in my 9/11 story above -- it made a huge difference. We were paid biweekly, but deductions were taken from our check semimonthly! Thus there were two checks per year that were worth more money -- and we always looked forward to those. These occurred in whichever months had three paydays.)
Returning to traditionalists, these Lesson 9 questions would almost certainly be done with a calculator or phone. All of these questions involve division.
And yes, it's been a while since one of our main traditionalists, SteveH, has posted anywhere. But if we check out the Joanne Jacobs website -- no, SteveH didn't post there. But here's a link to a Jacobs post -- and several of the commenters actually mention SteveH here:
https://www.joannejacobs.com/2019/09/exemplary-parents-so-so-schools/
After 10 years in Hong Kong, Shanghai and Tokyo, Teru Clavel and her husband returned to the U.S. with their three children. They chose Palo Alto for its top-rated schools — and were disappointed to discover “the schools weren’t doing an exemplary job educating the kids,” she writes in her book, World Class: One Mother’s Journey Around the Globe in Search of the Best Education for Her Children. Palo Alto students excel because they have “highly educated, ambitious and wealthy” parents, she concludes.
The first commenter to mention SteveH is Momof4 (a traditionalist in her own right):
Momof4:
Steveh, a longtime commenter on kitchentablemath and traditionalmath blogs, has been saying for years that “good” schools ignore what parents do outside of school to ensure that their kids are academically well-prepared. Schools point to SAT/AP scores and elite college admissions as results of curriculum and instruction inadequacies like “balanced literacy”, spiral math programs, etc; usually while refusing to acknowledge the huge impact of widespread tutoring; by parents, private tutors (in some cases teachers from their own schools), Kumon, Mathnasium etc. I see it in my grandkids and their peers, in a high-performing – and very complacent – district.
(By the way, I've used to link to kitchentablemath before. But around the time I started teaching at the old charter school, that blog closed down. Its authors created a new blog where the main topic isn't math, and so SteveH doesn't post there.)
Of course, Momof4 repeats the same comments that SteveH always says -- the students are learning traditional math from tutors, because the teachers won't teach traditionally. And to the traditionalists, what's sad is that this is happening in a high-achieving district where one would expect the teaching to be excellent -- Palo Alto. (Yes, this is the same district to which Coach Jim White applied before he decided to stay at McFarland.)
Another commenter disagrees with SteveH (and thus probably isn't a traditionalist). At this point, race appears in the comment thread again -- this is inevitable in a thread about tracking. Then again, the original article begins by mentioning three Asian school systems. Then the commenter argues that it's mostly Asian-American students who are using the tutoring centers. This is echoed by another traditionalist, Ann in L.A.:
Ann in L.A.:
I’d love to see a graph by zip code of standardized test results vs density of tutoring centers. I’m on the edge of Koreatown in L.A., and there are tutoring centers on almost every block, with many blocks having multiple.
I must admit that when I tutored about five years ago (during the first year of this blog), the students there were mostly born in Korea. Then again, I've seen more tutoring centers showing up within a few miles of my house -- and I live nowhere near Koreatown.
Of course, you already know what I have to say about the tutoring centers. Of course, traditional math works when the tutor is sitting inches away from the student, so that the student who's bored by the traditional lesson can't escape or be distracted. In a classroom with many students, it's easy for bored students to get off-task -- as I observe today when I try teaching the traditional worksheet on rounding to the special ed juniors.
Before we leave the traditionalists, noted traditionalist Ze'ev Wurman posted in this thread as well:
Ze'ev Wurman:
I very much subscribe to what this mom says. Most of the teachers for the four of my kids over the years were OK, but not great. The curriculum was mostly OK too, but rarely stood out. There were a few exceptions, but they were just that — few and exceptional. The push for the successful kids came mostly from home — parents & siblings.
And that explains perfectly why Palo Alto is WORSE for educating its disadvantaged kids than is Gilroy school district, a much more disadvantaged district 30 miles south of here. Palo Alto schools rely mainly on the parents rather than on its school curriculum, but take the credit. Gilroy relies on the school curriculum.
That's right -- Wurman mentions the exact same Gilroy where there was a mass shooting last month.
No comments:
Post a Comment