This school follows a block schedule. Mondays are normally Common Planning/All Classes days, but once a month, there's a special Monday minimum day. It's a special ed class with some history and English classes. The classes are extremely small, except for gen ed sophomore World History class that I must cover during the conference period.
I've subbed for this class before, and I wrote about it back in my March 8th post. Today, the World History classes (both special and gen ed) are learning about the Russian Revolution, while the English classes complete a worksheet on sentences and fragments.
Today on her Mathematics Calendar 2019, Theoni Pappas writes:
...nothing, actually. All the givens are in the diagram, with none of the points labeled. So once again, I must label the points myself.
In Circle O, the chord
We just covered arc measure in Chapter 8 last week, but the main theorem to use isn't until Chapter 15 -- the Angle-Chord Theorem of Lesson 15-5. In particular, Arc (AB + CD)/2 = Angle CED, from we find that (AB + 146)/2 = 156, or AB = 166. Now since
(Actually, there is an error in this problem. Pappas also tells us that Arc DA = 32 degrees. But this would imply that Arc DAB, a semicircle, has measure 32 + 146 = 178 degrees. I simply leave out the measure of DA as it's not really needed for this problem, but I do note that this is the first error of the 2019 Pappas calendar.)
Today is the Chapter 8 Test. It is also Day 90, the mathematical midpoint of the year. As we already know, most Early Start schools don't actually begin early enough in August to have a true semester of 90 days before winter break.
Two years ago at the old charter school, the mathematical second semester was when SBAC Prep began. Indeed, the bell schedule was changed so that SBAC Prep would replace most of P.E. time. Since we'd lacked a real conference period anyway, things truly became tough for me once SBAC Prep began.
Oh, and before I write about the test, you might point out that today's a lousy day for the test -- especially since I state that my calendar is based on the district where I sub today. Not only is today Monday, but at least one district school has a minimum day today. In other words, not only am I expecting students to study over the weekend for the test, but now they have only 35 minutes per class to finish the 20-question test.
Yes, I work for this district, but I don't sub here enough to know about minimum days at individual school sites. You might ask, why was today chosen for the "once a month" minimum day schedule? Well, there are only two Mondays in January to choose from -- last week the students didn't return from winter break until Tuesday, and next Monday is MLK Day. Usually, the minimum day is as early in the month as possible, and so today's it.
And so I can't help it that blindly following the digit pattern unfortunately makes the test land on the worst possible day, a minimum day Monday. If I were really teaching Geometry at this school, I'd probably push the test back to Tuesday or Wednesday, and then resume the digit pattern on Thursday or Friday. Chapter 9 is an introduction to space figures, and so this isn't as important as Chapters 8 or 10. Thus there's nothing wrong with skipping or combining lessons in Chapter 9.
This is what I wrote last year about today's test:
1. This is a triangle tessellation. The triangle is isosceles, so it shouldn't be too hard to tessellate.Let's worry about the Chapter 8 Test that I'm posting today on the blog. Here are the answers:
2. One can find the area by drawing a square grid and estimating how many squares are taken up on the grid. Since the shape happens to be an ellipse, one can also find its area using the formula for the area of an ellipse -- pi * a * b, where a and b are the major and minor axes. That's right -- I had to slip in a reference to pi this week.
3. 5/2 or 2.5.
4. 12 square units.
5. 40 square units.
6. 6 mm. This is a trick if one forgets the 1/2 -- especially with 3-4-5 right triangles featuring in the last few questions, but here the legs are 6 and 4, not 3 and 4.
7. 10 feet.
8. 4.5s.
9. One can find the area by drawing a diagonal to triangulate the trapezoid. Then one adds up the area of the two triangles.
10. Answers may vary. The simplest such rectangle is long and skinny -- 1 foot by 49 feet.
11. Choice (a). The triangles have the same base and height, therefore the same area.
12. 3s^2.
13. 13 feet.
14. 6 minutes.
15. 780,000 square feet.
16. 133 square feet.
17. 1/4 or .25. Probability is a tricky topic -- the U of Chicago assumes that the students already know something about probability. Then again, it should be obvious that the smaller square is 1/4 of the larger square.
18. 4,000 square units.
19. 13.5 square units.
20. a(b - c) or ab - ac square units.
But here's a 2019 update: again, the test I wrote last year was based on Lessons 8-4 to 8-9 (which is what we covered that year), rather than Lessons 8-1, 8-2, and 8-6 to 8-9. It's awkward to make the students answer so many questions about skipped lessons of the chapter. And so if teachers wish, they may replace two questions on the test with the following:
9. Give the circumference and area of a circle with radius 10: a. exactly; b. estimated to the nearest hundredth.
10. Could the numbers 1, 2, sqrt(3) be the lengths of sides of a right triangle?
Answers:
9. a. 20pi units, 100pi square units
b. 62.83 units, 314.16 square units
10. Yes. (Notice that c here needs to be 2, not sqrt(3).)
Today is a test day, and so as usual I'm labeling this post "traditionalists." And now it's finally time for me to address the elephant in the room. I live in Southern California, and the big news affecting education in our area is the LAUSD teacher strike.
I'm not directly affected by the strike. I currently sub for two districts, neither of which is LAUSD (since after all, I subbed in one of those two today). So there's no reason for me to blog about the strike at all. Yet as a Southern Californian writing an education blog, I feel that it's my duty at least to address the issues surrounding the strike from my local perspective.
Math teacher bloggers have previously discussed recent strikes in their own states. This includes Sarah Carter of Oklahoma and Joanna Burt-Kinderman of West Virginia:
https://mathequalslove.blogspot.com/2018/04/five-things-volume-15.html
https://problematizingmathteaching.com/2018/05/11/through-the-math-forest/
Hmm, that's interesting -- they both mention how "tired" the strikes have left them feeling.
It's been said that the one thing that distinguishes the LAUSD strike from the others is that it's the first teacher strike during the current presidential administration that's taking place in a state that didn't support the current president. In other words, the main issues surrounding the strike transcend party politics. Thus I'll try to avoid politics throughout the rest of this post.
But I am tying this to traditionalists. Yes, it just so happens that the first day of the strike coincides with my regularly scheduled traditionalists' post. Yet traditionalists have often criticized teachers' unions for not supporting traditionalist ideas in the classroom. As a former teacher and current sub, I wish to defend and support my fellow educators during the current strike. But as usual, I will point out that some of the traditionalist ideas have merit.
One frequent teacher critic I've mentioned recently is Floyd Thursby. He strongly condemns teacher unions at the following EdSource link:
https://edsource.org/2018/high-court-ends-mandatory-fees-collected-by-public-unions/599702
Floyd Thursby:
[Supreme Court Justice] Kagan should have said that the unions had 41 years of good faith and blew it by being extreme and making no progress on the achievement gap or U.S. international scores, in fact fighting most reforms that would lead to progress on those fronts. No money for tutoring poor kids, across the board raises. If you get a gift like Abood, show some good faith, pressure teachers to stay late and tutor poor kids, not call in sick, decline to defend a Berndt, encourage charters that help kids learn the work habits of the upper 20% of this country, the only people with a really good life, etc.
Fight to fire bad teachers. If the union had fought for 95% of teachers and pressured the rest to work harder, focused on test score improvements, and shown good faith, they’d have won today. I’m glad Kagan is in the minority. I’m not personally willing to wait another 41 years till I’m maybe dead in the desperate hope one day the union gets a clue. They’ve been a force for bad lately, and got what they deserved. They haven’t prioritized poor children. They’ve prioritized an adult jobs program. Yey for this decision!
Here Thursby is actually writing about the recent Janus Supreme Court decision, but I quote it because he makes his opinion of unions here.
For example, he mentions "across the board raises." Yes, the teachers union in LA (UTLA) is fighting for a 6.5% across the board raise. But Thursby argues that many teachers don't deserve an increase -- he mentions "not call in sick." This hearkens back to "Floyd Thursby Day" -- the Tuesday before Thanksgiving when, he argues, too many teachers call in sick.
This debate comes up over and over again during teacher strikes. While unionists argue that teachers are underpaid, their opponents argue that we're overpaid because we get many days off during the year -- most notably summer break.
This complaint typically takes one of two forms. One involves paychecks -- the fact that teachers often receive twelve monthly paychecks despite not teaching in the summer. Of course, a teacher usually responds that she receives only five-sixths of her hourly pay during the ten months that she teaches, then receives the remaining amount during the two months of summer. In the old days, teachers really did receive only ten monthly paychecks. But deferring some of the payment to the summer (so that there are twelve paychecks) appears to be the standard practice now.
Of course, there's nothing stopping schools from having ten monthly paychecks and teachers from saving one-sixth of each check away for the summer. Perhaps this is the only way to get teacher critics to support us more -- seeing teachers going three months between paychecks (even if they're living on saved money). Just knowing that if a teacher hasn't seen the inside of a classroom in months then said teacher hasn't seen a check with her name on it in months might be enough to satisfy some.
The other argument involves the total annual pay. Teacher critics argue that since teachers only work part of the year, we should receive only "part-time pay" -- but "part-time pay" isn't completely defined, only that it's less than what we're getting now. I wonder how deep a pay cut we'd need to get for their tune to change from "They're overpaid!" to "They're finally earning the correct pay for their hours worked."
Instead of annual salary, let's focus on hourly pay. Then we can compare how much a teacher is paid per hour to how much an office worker is paid per hour, instead of getting hung up over how many hours a teacher actually works.
Let's look at the LAUSD salary table, since this is ultimately what the strike is all about:
https://achieve.lausd.net/cms/lib/CA01000043/Centricity/Domain/280/Salary%20Tables/Salary%2018-19/T%20Table.pdf
The first row shows us that the minimum pay is $50,368. When we scroll down to the bottom, we see that this is based on 1224 hours worked (204 days * 6 hrs./day). We divide and see that this works out to be $41.15/hr. So this is the amount we should use to determine whether teachers are overpaid.
Of course, that's the minimum salary. The maximum pay (fourth career increment) is $87,085, which works out to be $71.15/hr. (There are also B- and A-basis tables based on working more hours, and so the hourly pay works out to be the same.) By comparison, minimum wage in California is now $12/hr, and so the range is from about 3.5 times the minimum wage to about six times the minimum.
No matter what the pay is, some teacher critics will never respect teachers as long as teachers get long breaks off. We can assume that the typical office worker works eight hours per day year-round, and receives only six paid holidays -- the three winter holidays of Thanksgiving, Christmas, and New Year's Day, and the three summer holidays Memorial Day, Independence Day, and Labor Day. There are probably a few extra floating days that most workers take off -- Black Friday, Christmas Eve, New Year's Eve (judging by how crowded the stores are those days). Many workers likely took the Eves off since the holidays themselves were on Tuesdays this year. But then we notice that stores were also crowded the day after Christmas, so that many workers took that day off too. To claim that workers took off only December 25th and January 1st and worked all the other days is disingenuous (but of course most workers took off many fewer days than the three-week LAUSD break). We'll also assume that the office worker gets two weeks of vacation at some point during the year.
Of course, that's just office workers. We know that retail workers aren't even guaranteed to get Thanksgiving off any more, judging by how many Black Friday sales start on Thursday now. And of course, first responders must work around the clock and are always on call. I know it's pointless to argue that teachers work many more weekly hours than the 30 that we're paid for (grading papers, etc.) since teacher critics counter that they work more than the 40 that they're paid for -- if they're always on call, they might even work nearly 100 hours in a week!
So sometimes I wonder, does this mean that teacher critics won't respect teachers unless we work as many hours in a year as private sector workers?
Imagine telling all school-aged children that from now on, every hour that Mommy and Daddy goes to work, the children must go to school -- since after all, it's not fair that the parents must work while the teachers get to relax. Sorry kids, you don't get summer break any more because it's not fair that your parents still have to work over the summer. Sorry kids, you must go to school on Thanksgiving because Mommy has to work at the Black Friday sale. Sorry kids, your school day is now 16 hours because Daddy has to work a double-shift to cover for his sick coworker. And since your parents are always on-call, you kids should have do your homework after midnight, so that you can call your teachers in the middle of the night to ask for help. After all, it's not fair that the teachers get to sleep while your parents have to stay awake.
And emphasize that all of this is to make sure that teachers work hard, not necessarily the students -- but of course, the teachers can't work unless they have someone to teach, so in the end, it's the students who have to work harder too. Now guess what your kids' response would be. I want to guess what the teacher critics' response would be -- would they finally say, "OK, we respect teachers now"?
Thursby points out that at the very least, most teachers should miss zero hours per year. For example, doctors' appointments should be after the last class of the day so that no time is missed. Of course, this means that there's now a greater demand for late afternoon appointments. During my last two days of subbing, I had a late afternoon conference period when I had to cover another teacher -- and at least one of those was for a teacher with a doctor's appointment. It was just for one period -- so what most likely happened was that the teacher asked for a 3:00 or later appointment and the doctor replied that only, say, 1:00 was available. The teachers didn't take the whole day off -- they even chose days when their conference period rotated into the afternoon (Friday's teacher) or a minimum day (today's teacher) so that only one period is missed. But that's not enough for Thursby.
I've also mentioned days taken off for cross-country flights to see family. Airline prices increase on the days that teachers have off due to increased demand. Disneyland just announced yet another ticket price increase. Due to lower demand, most "value days" are on school days. (In my new district, the only day off in the next four months that's a "value day" is Lincoln's Birthday. I suspect that in the LAUSD, at least one of the Jewish High Holidays will be a "value day," though the autumn price schedule isn't posted.)
Office workers get only two weeks off, but they have more flexibility as to when exactly those two weeks will occur. Thus they can choose days when airline or amusement prices are low, whereas teachers can't. I suspect Thursby might argue that this is fair -- in exchange for getting more weeks off, teachers are stuck with higher ticket prices. Those with fewer vacation days have more say in when they want those days off.
Oh, and notice that I'm currently a sub. If most teachers worked as hard as Thursby wants and take zero days off, I'd hardly make any money at all.
During the holidays, I posted several versions of Calendar Reform. Many of these calendars are based on uniting the school and office work weeks -- by reducing the number of office days, not by increasing the number of school days. Some of those calendars are based on having half the week be weekdays and the other half be the weekend (such an eight-day week with four days of work and four days of rest, or a 12-day week with six days on, six days off). On these calendars, both the work and school years are around 180 days. There's no room for a summer break on the school calendar, and there never was a summer break on the work calendar.
A compromise might be the nine-day week with five days on, four days off. There are about 40 weeks in the year, so that's 200 weekdays. We can reduce this to 180 by assuming that there are approximately ten holidays. The other ten days can make a two-week vacation to equal the two weeks that office workers get. Something similar is possible with my own Eleven Calendar (a six-day workweek, with a midweek day off and a four-day weekend).
By the way, it's possible to come up with workweeks like these without reforming the Gregorian Calendar at all (since such Calendar Reform is unlikely, not to mention far beyond what either a district or a union can accomplish). Similar to my Eleven Calendar is a 14-day "week" (fortnight) with eight workdays, a midweek day off, and a five-day weekend. The midweek day off can line up with Sunday (for Christians), Saturday (for Jews), or Friday (for Muslims). A simpler version is a four-day workweek (Monday-Thursday, thus respecting all three Abrahamic religions). Extended year-round this provides us with 208 workdays. Only eight days need to be dropped to provide both teachers and office workers a two-week break, leaving us with some wiggle room for holidays or other vacation days (for both teachers and office workers).
OK, that's enough about school and work calendars. There are other issues raised by the strikers and their opponents besides pay and number of workdays.
Floyd Thursby:
Fight to fire bad teachers. If the union had fought for 95% of teachers and pressured the rest to work harder, focused on test score improvements, and shown good faith, they’d have won today.
So Thursby wants to get rid of "bad teachers." This phrase is ill-defined -- but considering that he mentions "test score improvements" in the next sentence, it's clear what he means. "Bad teachers" are those who fail to improve test scores -- standardized test scores, that is.
The union counters that having to "teaching to the test" is a burden for many teachers. LAUSD and UTLA are powerless to eliminate Common Core or the SBAC, but at least LAUSD could eliminate the tests that the district does control -- the triannual district assessments.
Some Eugenia Cheng-style logic is in order here. (Recall when we first read Cheng's book that I said I'd use her logic to settle contentious debates -- and what's more contentious right now than the LA teacher's strike?)
Thursby and the traditionalists want "some accountability." They believe that teachers should ultimately be evaluated on standardized test scores. On the other side, the teachers in the union want "some autonomy." Teachers believe that there is too much pressure on them to teach to the test. Now we can join "some accountability" and "some autonomy" with Cheng's "no disagreement" diagonal, since it's possible to have both some accountability and some autonomy.
But then we negate these. "Some accountability" becomes "no accountability," which is what the traditionalists believe the unionists want. And "some autonomy" becomes "no autonomy," which is what the unionists believe the traditionalists want. We can join these along the opposite Cheng diagonal, "needless antagonism."
We can also apply Cheng's concepts of "false positives" and "false negatives" to this debate. The traditionalists' biggest fear is the "false positive" -- a teacher who intentionally takes many days off and makes no attempt to improve his students' learning, yet is labeled an "effective teacher" who gets to keep his job. The unionists' biggest fear is the "false negative" -- a teacher who works hard everyday and improves her students' learning, yet produces low test scores, for one reason or another.
Traditionalists often deride unions, especially public-sector unions, as "socialist." (Yes, that's a political comment, but it's indirectly related to the class I subbed for today -- today the World History classes learned about the Russian Revolution and the origins of socialism as a major influence.) On the other side, the unions argue that it's the "billionaires" who wish to take away the autonomy of many teachers. (These billionaires include Bill Gates -- a financial backer of Common Core -- as well as LAUSD superintendent Austin Beutner.) I wish to take the middle path here -- no, the unions aren't trying to take us back to the Soviet Union. And while Gates and Beutner are indeed rich, it's not just the rich who want more teacher accountability. It's the average taxpayers who only want to be sure that their tax dollars are being spent wisely.
I wish to get back to the "no disagreement" diagonal. I believe that their should be some sort of evaluation system that respects both teacher accountability and teacher autonomy -- an evaluation system that minimizes both false positives and false negatives.
I already know of one way to reduce false negatives. One example of a false negative is a teacher (usually high school) whose students learned a lot from their teacher, yet score low because they make no effort to answer the questions (because they see the standardized test as pointless). And my idea to resolve this is, if test scores are included as a certain percentage of the teachers' evaluation, then they should be included as the same percentage of the students' grade.
Now suddenly the teens have a reason to excel on the standardized test, and so there should be fewer false negatives. And there's an added bonus -- since test scores are included in the grade, there's more correlation between test scores and grades. Traditionalists fear the false positive of students who receive A's yet score below average on the standardized tests -- partly because parents pressure the teachers to lower their standards. If part of the grade is out of the teachers' hands, then suddenly the parents will be demanding "Teach my kids better!" instead of "Lower your standards!" -- that is, it eliminates a conflict of interest.
Thursby supports standardized tests such the Common Core tests. Many traditionalists believe that the Core doesn't go far enough -- its standards are too low (especially with regards to eighth grade Algebra I and senior-year Calculus). By the way -- notice that I keep conflating Thursby and the teacher critics with "traditionalists." Thursby strongly criticizes teachers and their unions, but most of our main traditionalists so far haven't commented on the teacher's strike.
But this is a "traditionalists" post. The values of the teacher critics and traditionalists are clearly aligned, as both fear false positives more than false negatives. And so I feel justified in writing about the teacher's strike in this traditionalists' post.
One tweeter I've discussed recently goes by the username "CCSSIMath." I've referred to this tweeter as a traditionalist, since he/she regularly attacks Common Core as lacking rigor. Just last week, this person tweeted a so-called "10th grade problem" about quadratic equations that goes well beyond anything taught in Algebra II, or even Pre-Calculus.
Yet CCSSIMath also tweeted about a "false negative" -- in New Hampshire, the SAT is now used as an accountability test for juniors instead of SBAC. But the bar for proficiency in math is set to 530 -- which is above the average (500, by design). So in other words, a junior must be above average in order to be considered proficient. Unionists should rightly be concerned if a teacher is evaluated on how many students she can get over the 530 bar.
Yet it's interesting that CCSSIMath would criticize the 530 SAT bar and then post the so-called "10th grade problem" a few days later. Most juniors scoring 530 or even above will have trouble with the 10th grade quadratic problem. It's difficult to tell exactly what CCSSIMath wants, since that person's ideas have a 280-character limit. If the bar for proficiency were set to 430, is that reasonable? Is a bar of 330 reasonable, or have we crossed into false positive territory (where students who know very little math are labeled "proficient.")?
OK then, so forget what CCSSIMath wants -- what exactly do I want? Well, I want some sort of compromise between the traditionalists' "more accountability" and the unionists' "more autonomy." I argue that Common Core itself might be such a compromise -- the traditionalists wish to replace the Core with a more rigorous test while the unions wish to drop the Core completely (especially as a part of teacher evaluations).
The key is -- what exactly is reasonable to expect students at each level to know? There's a fine line between "It's too much to expect teachers to teach this!" to "Any teacher who fails to teach this no longer deserves a job!" Many people have tried to come up with such a list (state standards, Common Core, Hirsch's Core Knowledge, etc.), but there's no universal acceptance of any such list.
There's another compromise that I once proposed on the blog -- there should only be Common Core Standards for high school, while K-8 standards should be relegated to the state level. After all, the unionists might ask, why do third graders in one state need to be compared to those in another? But it's easy to see why high school students in different states need to be compared -- many of them are competing against another for admissions to colleges across the country.
And then we can take this a step further -- there should only be state standards for middle school, while elementary standards should be relegated to the local (district) level. Notice that each state can decide for itself what exactly is "middle school." While nearly all states agree that eighth grade is middle school while ninth grade is high school, in some areas fifth grade is already middle school, while in others sixth grade is still elementary school.
Under this plan, we would adopt the opposite of UTLA's proposal in grades 3-5 -- LAUSD would keep the district assessments and drop the Common Core tests. But this is impossible, which is why UTLA reverses this. But dropping the district assessments in secondary school would be consistent with this plan. At all levels there would still be some standardized test (district, state, or national) that's sufficient to satisfy the traditionalists' desire for accountability.
And I agree with the union that we can eliminate redundant tests. I wrote that New Hampshire, along with some other states, drop the junior-year SBAC in favor of the SAT. Our outgoing Governor Brown suggested the opposite -- that we use SBAC as a college entrance exam. Either way we are reducing the number of tests. And we might even choose to keep the district assessment for high school if we give those instead of final exams, since that also reduces the number of tests while maintaining both teacher and student accountability.
(Speaking of governors, our new Governor Newsom has proposed a new budget plan that includes increased spending for schools. It might mitigate some of the financial issues involved in the strike.)
Once a set of standards have been adopted, they can be increased gradually over the succeeding years and generations. Perhaps someday America will produce a class of sophomores who really can answer CCSSI's "10th grade question," but that time definitely isn't now.
Let's return to Floyd Thursby's post:
Floyd Thursby:
...encourage charters that help kids learn the work habits of the upper 20% of this country...
Charters are another huge issue in the current teacher's strike. I've worked in both charters and traditional public schools, and so I don't take a side on this issue on the blog. Thursby clearly believes that charters are a net good, while the union disagrees. I don't take one side or the other here.
There's one more major issue involved in the strike that Thursby doesn't mention -- class size. The unionists argue that class sizes are too large in the LAUSD.
Today I subbed in another district, where I experienced a wide range of class sizes. The first period class today has only two students. Then again, it was a special ed class, and special ed clearly isn't representative of the how large gen ed classes can get. The one gen ed class I cover today during sixth period contains 32 students.
I've never mentioned this on the blog before, but the district where I completed my student teaching was in fact the LAUSD. I covered three classes, and one of them, a fifth period Algebra II class, had 41 students enrolled. At least the other two classes were closer to normal-sized. I once wrote on the blog that the sixth period Algebra II class is the most successful class I've ever taught -- and I believe that one factor that made sixth period better than fifth was class size. So I can attest to the power of smaller class sizes.
Traditionalists counter that there is little evidence of a relationship between class size and learning. I think back to the old charter school, which is indeed chartered with the LAUSD. (Again, charters are a separate issue in the strike -- right now, let's focus only on class size.) Classes were small, but only because the entire school was small and there were very few in each grade level. There were only 14 eighth graders in the entire school.
Was eighth grade my most successful grade at the charter due to its smaller size? That's a tricky one, since my overall experience was unsuccessful. Because eighth grade was smaller, different issues came up in that grade as opposed to the sixth and seventh grades. For example, eighth grade usually wasn't as loud as the lower grades, but many of them still didn't pay attention to me. This was the grade that usually tricked me into neutering some of my class rules ("I'm not chewing gum -- I'm chewing paper!" and "That's not a phone -- that's the phone case!") My problems with science occurred mostly with eighth grade since that's the year of the NGSS test. And of course, Grade 8 was the grade with the special scholar and all of her issues.
The New Year's Resolutions that I wrote in my Epiphany post address some of my problems. But that only proves the traditionalists' point -- it's classroom management, not class size, that matters. A strong manager can handle a class of 41 with no problems at all, while a weak manager will struggle even with a class of 14.
I'll take the middle path again -- both management and class size matter. Given two teachers with the same group of students, the the more effective manager will be more successful. But given a single teacher with two different classes, students will learn more in the smaller class.
I don't know exactly what the ideal class size is. Clearly 14 is better than 41, but what about the sizes in between, such as 32 (today's World History class) vs. 23 (Grades 6-7 at the old charter)? So far, I've heard that UTLA is striking for smaller classes, but I don't know how small. It probably depends on the grade level and other circumstances (such as special ed vs. gen ed).
Here's an interesting question related to the strike. Suppose I were an LAUSD Geometry teacher. So what exactly would I teach the week before the strike? Obviously, the worst thing I could do is what I did on the blog -- schedule a test for today. If there's anything worse than a test on a minimum day Monday, it's a test on a strike Monday. The students -- who already know that the strike is coming -- will avoid studying for the test since the test was obviously going to be cancelled by the strike. In fact, it might have been difficult to get the students to do any work at all last week. They might even find a way to use the strike against me -- why should we students do our jobs and study math when you teachers aren't going to do your jobs next week?
One idea is to do something that the students enjoy doing anyway -- activities and math games. Last week, I made a big deal out of not including too many activities. But if I knew that a strike was coming, I'd include even more activities to fill the entire week.
Notice that unlike my district, most LAUSD schools were open last Monday. Officially, the district allows schools the option of having a PD day between the semesters, but most didn't. (Once again, it all goes back to the Jewish High Holidays. When either Rosh Hashanah or Yom Kippur falls on a Saturday, the last day of school in June is on Thursday, and so some schools might take the PD day in January and end school on Friday. But if both High Holidays fall during the week, then the last day of school is Friday even without the PD day in January, and so hardly any school will take that PD day.)
And yes, I know that I'm writing about activities in a post labeled "traditionalists." CCSSIMath complains that teachers play too many games in math class. OK, I'd like to see CCSSIMath teach a traditionalist lesson the week before a strike, when students are likely to use the impending strike as an excuse not to pay attention to you.
So here's a possible week full of activities:
- Monday, January 7th: Golden Rectangles (as this is the closest we get to Phi Day)
- Tuesday, January 8th: Lesson 8-4 activity from last year (areas of irregular figures)
- Wednesday, January 9th: Lesson 8-7 Pythagorean Theorem activity from two years ago
- Thursday, January 10th: Lesson 8-8 Circumference activity
- Friday, January 11th: Lesson 8-9 Area of a Circle activity
In this case Friday's circle area activity hearkens back to Tuesday's irregular figure activity, thereby linking the two.
Of course, there's no reason why there must be a different activity each day. This is the opportunity to have several multi-day activities. Notice that the strike was originally planned for last Thursday before it was delayed to today. Thus I might have planned for one activity to span three days, up to Wednesday, and then once the strike was delayed, set a second activity for Thursday and Friday.
But all of this presumes that the LAUSD second semester Geometry curriculum starts with Chapter 8 of the U of Chicago text (measurement and area) or the equivalent chapter in another text. If I'm going to assume a counterfactual (What if I were teaching in LAUSD?) then I should take that assumption to its full conclusion. So we should look at the LAUSD curriculum:
(Yes, this is the same site I should have looked up two years ago for the science curriculum.) We see that the year is divided into four units. It's logical to assume that each unit corresponds to a quarter, and thus the current third quarter should be Unit 3.
But Unit 1 is the Common Core unit on congruence. Notice that this unit spans the first seven chapters of the U of Chicago text -- nearly half of its 15 chapters. (In the modern Third Edition where there are only 14 chapters, the congruence unit is fully half of the text.) Unit 2 is on similarity (Chapter 12 U of Chicago), which I like to save for second semester.
In fact, I'd have no problem with spreading Unit 1 to the first semester and squeezing all the rest of the units into the second semester. But I suspect that most districts don't do that. Unit 1 is only one of several units in Common Core Geometry, and so most districts won't let it span a semester. And so we'll assume that the third quarter is indeed Unit 3:
This unit corresponds roughly to Chapters 11 and 15 of the U of Chicago text. (And so today's Pappas question would fit in this unit.) Let's scan the Exploration Questions in these sections for some suitable activities:
Chapter 11:
1. (Section 11-1) Three vertices of parallelogram are given (coordinates). Where is the fourth vertex?
2. (Section 11-2) The distance from point X to a given ordered pair is specified. Where is X?
3. Give an equation for a circle for which there are no lattice points on the boundary or interior.
4. Find the point where a cardboard polygonal region will balance on the tip of a pin.
5. Draw at least five quadrilaterals with different shapes. Describe their midpoint quadrilaterals.
6. Set up a coordinate system in your classroom and determine the coordinates of lights and windows.
Chapter 15:
1. Experiment with various circumscribed polygons.
2. Find a schedule for teams in a league involving your school or community.
3. Examine a camera in your household or in a store. What is its normal picture angle?
4. Each of the three circles overlaps the others. Are the three chords common to each pair concurrent?
5. What is the sum of the measures of the angles of a regular pentagram?
6. What is the angle covered by sun and moon during a solar eclipse?
7. Is the Secant Length Theorem true if the secants intersect on the circle?
8. Give dimensions of a polygon whose perimeter is 100 feet and whose area is greater than 625 ft.^2.
9. Research the Isoperimetric Inequality and Dido, the queen of Carthage.
In Chapter 11, the only questions students might find interesting during pre-strike week are those for Lessons 11-4 and 11-6. These will have the students moving around the classroom. It might be interesting to start with one of those old graphing worksheets (like Frosty the Snowman -- and emphasize that a snowman is a symbol of winter, not Christmas) and then use coordinates to predict the shape of a figure given the vertices of its coordinates.
The questions from Chapter 15 aren't introductory. The Lesson 15-2 question (from the lesson "Regular Polygons and Schedules") is somewhat interesting, but even though it's in our book, it's only indirectly related to circles. Lesson 15-3 is based on an analog camera -- a dated question these days when many people just use the cameras on their phones. The Dido question might be interesting in a class of mostly girls, to emphasize that women have been doing mathematics for millennia.
Another possibility is to dispense with the textbook altogether and find activities online. One teacher, Julie Reulbach, works at a school whose calendar includes "Winterm" -- a special week of electives that takes place after winter break. Since the pre-strike week in LAUSD is essentially a "Winterm," we might follow Reulbach's suggestion -- she has her class create their own blogs:
Here are some of my favorite student blogs from Reulbach's class:
(Oh, the answer to his question "Who can stop the 'Boys?" is our local Rams.)
(Unfortunately, our other local team, the Chargers, didn't do as well.)
(So that I don't choose only sports blogs, here's a poetry blog.)
In our math class, we might choose to have the students first blog on something they enjoy (like football/sports) and then add another post showing how math related to what they like. (For example, how do stats prove that Elliott is the best running back?)
I think back to New Year's Day. In many years, it's been a Pappas tradition to use the digits of the new year on the first day. Last year, her New Year's problem was:
(2018!)^0
but this one, unfortunately, includes an extra 0 that has nothing to do with the year. This year she started with a polynomial long division problem that has nothing to do with the year's digits. Her question on January 2nd was:
(2^0)(2^1)((1/2)^0)
which ironically fits the new year better than the January 1st problem as the digits 20 appear. This suggests that a good problem for January 1st this year would have been:
(2^0)(1^9) = 1
And if we really wanted another year problem for January 2nd, we can change it to:
(2^0) + (1^9) = 2
Now here's an interesting question -- can we come up with a similar Pappas-style problem using the digits of the year for the entire month of January? That is, can we write all the numbers from 1 to 31 using only the digits of the year?
This actually isn't an original problem at all. I once wrote about the "for four 4's" problem that I once found in my old TI-34 calculator manual. It turns out that some teachers actually use the "for four 4's" problem in their classrooms. And other teachers start the first week after winter break with a similar problem involving the digits of the new year.
It appears that the originator of this annual challenge is the same blogger who started so many other math ideas that I still use from time to time -- Sarah Carter:
Actually, Carter attributes the idea to a British teacher, Mr. Collins, who first used it for 2015. But as usual, Carter is the one who made it famous. Most tweets referencing the challenge state that it comes from Carter.
Notice that this post is from last year, so the digits to use are 2, 0, 1, 8. Forget a five-day pre-strike week -- Carter writes that due to PD and snow days, she must often begin the new semester with a one-day week! (Compare this to the teacher who had a one-day week on Floyd Thursby Day a few years ago. Maybe Floyd Thursby himself should read about these teachers who are dedicated enough to come in on one-day weeks, instead of assuming that all teachers want to take extra days off!)
So anyway, Carter would set up the challenge for something for kids to do on the lone day. She writes that her students usually enjoy the activity. At any rate, I'd have plenty of activities to choose from for the pre-strike week.
By the way, a related question is, what would the pre-strike week look at if I had still been working at the old charter? I assume that it would be no different from a regular week. Most charters don't participate in strikes -- after all, the union opposes many charters. But there are actually some charters whose teachers are unionized. My charter wasn't one of them, and so I assume that my charter is open for school today.
But two years ago, my charter was co-located with an LAUSD elementary school. My school's schedule was thus dependent on the districts -- for example, we had the same three-week break as LAUSD, with a few extra days (the Thursday/Friday before and the Monday after) for PD or various other meetings. (This year, the charter is no longer co-located, and so the winter break was apparently just two weeks plus at least two of Thursday, Friday, and Monday.)
Thus two years ago, if a strike had broken out then we might have been forced to close, since it wouldn't have been safe for us charter teachers (and our students) to cross the picket line to reach our co-located school. So it's possible that if there was a week before the strike, then I could have used some of the activities that I posted here. I also could have just set up an activity from the Illinois State STEM text instead.
To close this traditionalists' post, I do point out that Barry Garelick posted over the weekend. He's a Northern Californian, and so he makes no mention of the LAUSD strike. Instead, he writes about a "wish list" -- a wish for more studies supporting the traditionalist position.
https://traditionalmath.wordpress.com/2019/01/13/wish-list-dept/
Like most traditionalists, Garelick writes about possible false positives, such as students who get straight A's in high school but can't do college math because of grade inflation. But he also mentions a possible false negative:
That ends this post, but the great LAUSD teacher strike has only just begun.
By the way, a related question is, what would the pre-strike week look at if I had still been working at the old charter? I assume that it would be no different from a regular week. Most charters don't participate in strikes -- after all, the union opposes many charters. But there are actually some charters whose teachers are unionized. My charter wasn't one of them, and so I assume that my charter is open for school today.
But two years ago, my charter was co-located with an LAUSD elementary school. My school's schedule was thus dependent on the districts -- for example, we had the same three-week break as LAUSD, with a few extra days (the Thursday/Friday before and the Monday after) for PD or various other meetings. (This year, the charter is no longer co-located, and so the winter break was apparently just two weeks plus at least two of Thursday, Friday, and Monday.)
Thus two years ago, if a strike had broken out then we might have been forced to close, since it wouldn't have been safe for us charter teachers (and our students) to cross the picket line to reach our co-located school. So it's possible that if there was a week before the strike, then I could have used some of the activities that I posted here. I also could have just set up an activity from the Illinois State STEM text instead.
To close this traditionalists' post, I do point out that Barry Garelick posted over the weekend. He's a Northern Californian, and so he makes no mention of the LAUSD strike. Instead, he writes about a "wish list" -- a wish for more studies supporting the traditionalist position.
https://traditionalmath.wordpress.com/2019/01/13/wish-list-dept/
Like most traditionalists, Garelick writes about possible false positives, such as students who get straight A's in high school but can't do college math because of grade inflation. But he also mentions a possible false negative:
- What effect has the emphasis on understanding been on students who have been identified as having a learning disability?
- And a more difficult question, is there evidence that such emphasis has resulted in students being labeled as having learning disabilities?
That ends this post, but the great LAUSD teacher strike has only just begun.
OK, here is the Chapter 8 Test:
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