The calendar is designed so that certain holidays do not fall on certain days of the week. Indeed, neither Rosh Hashanah nor Yom Kippur can fall on Friday or Sunday -- that is, the day before or after the Jewish sabbath. (Either holiday can fall on Saturday, the sabbath itself, though.)
This means that there are four possible "gates" on which a Jewish year can begin:
- Monday
- Tuesday
- Thursday
- Saturday
For gates 1 and 2, both Rosh Hashanah and Yom Kippur fall on school days, and so the LAUSD closes for both of them. But for gates 3 and 4, one holiday falls on Saturday. Unlike for secular holidays such as Veteran's Day, the district doesn't observe a holiday on Friday or any other day -- instead, the district closes for only the holiday that isn't on Saturday.
But how does this affect the length of the year? If the school year had 180 days for gates 3 and 4, then it would have only 179 days for gates 1 and 2. But if the school year had 180 days for gates 1 and 2, then it would have 181 days for gates 3 and 4. So how do schools fix it so that the year always contains 180 days?
Well, in LAUSD it's simple. For gates 1 and 2, the last day of school is on Friday, but for gates 3 and 4, the last day of school is on Thursday. Sometimes students and teachers alike might get confused as to why the last day of school is sometimes Thursday and sometimes Friday. They forget that it all had to do with Jewish holidays that occur nine months before the last day of school.
But in other districts, such as my new district, the last day of school is always Thursday. For gates 1 and 2 when both High Holidays are on school days, the district closes only on the more important holiday for Jews -- Yom Kippur. Therefore only for gate 3, when Yom Kippur is on the sabbath, does the school close for Rosh Hashanah. Even though I wasn't hired in my new district until February, I was given a school calendar which indeed showed a recess day on Rosh Hashanah, since the Jewish New Year was on Thursday in 2017.
But this year, the new district was open last week for Rosh Hashanah. And since the district is closed today for Yom Kippur, I don't sub today. (In theory, I could have subbed at my old district today -- but that was always unlikely. I almost never sub thrice in a month there -- and I was just there twice last week.)
And as I've mentioned several times recently, today's Yom Kippur holiday has delayed the PSAT -- normally the second Wednesday in October -- to next week. This is why I suddenly have an extra day in the calendar between Chapters 3 and 4 as compared to last year.
So let's fill this open day with an activity. As usual, I like to go back to the Exploration Questions in the U of Chicago text. Well, here is the last question of Lesson 3-6:
Because the rules for constructions are quite specific, there are some figures that can be drawn but cannot be constructed. The Greeks were very puzzled by this and three problems became famous. They are called "squaring the circle," "duplicating the cube," and "trisecting an angle." Find out what one of these problems was.
Interestingly enough, I found an article written just yesterday about these three problems:
https://www.laphamsquarterly.org/roundtable/beware-cranks
The four impossible “problems of antiquity”—trisecting an angle, doubling the cube, constructing every regular polygon, and squaring the circle—are catnip for mathematical cranks. Every mathematician who has email has received letters from crackpots claiming to have solved these problems. They are so elementary to state that nonmathematicians are unable to resist. Unfortunately, some think they have succeeded—and refuse to listen to arguments that they are wrong.
I've discussed "cranks" on the blog twice before -- once in discussion with Poincare's Conjecture and the other was about Lyndon LaRouche and his ideas on C256 and A432 (the so-called natural frequencies of the earth). Unlike the three Geometry problems listed above, Poincare really was proved, so just claiming a proof of Poincare doesn't make one a crank. (The crank's "proof" of Poincare was much simpler than the real proof turned out to be.)
On the other hand, anyone who claims to solve the trisecting, doubling, or squaring problems really is a crank, because they have already been proved impossible. The proof is indirect -- that is, we assume that the construction is possible, and then that assumption leads to a contradiction. Thus it's more like the Bridges of Konigsberg problem of Lesson 1-4 -- Euler proved that a solution is impossible.
How can we convert this into an activity that we can give our high school students? Well, I found this old post from 2014:
https://mikesmathpage.wordpress.com/2014/12/14/geometric-constructions-with-origami/
The author, Mike Lawler, quotes Evelyn Lamb, whom I've mentioned on the blog before. Lamb tells us that it's possible to double a cube and trisect an angle -- not with a straightedge and compass, of course, but with origami:
http://www.cutoutfoldup.com/409-double-a-cube.php
Unfortunately, the angle trisection link is dead, so only cube duplication is listed here. (The third construction, circle quadrature, can't be solved with origami -- probably because it's impossible to fold paper into a circle.)
And so this is the activity that I have made into a worksheet. Notice that one of the commenters in this thread at this link above is a crank who claims to have doubled the cube using a classical (that is, with straightedge and compass only).
Yesterday, I did say that this would be a traditionalists' post, so let me start it now. The traditionalist who has been the most active lately is Bill at the Joanne Jacobs site. Let's see what he has to say:
https://www.joannejacobs.com/2019/10/no-justice-for-bullies-victim/
Julia Carlson describes restorative justice gone wrong on Project Forever Free. Her sixth-grade son was targeted by three bullies — threatened, insulted, robbed and beaten — for a month before a teacher told her what was going on.
Here's what Bill has to say here:
Bill:
A better solution is to sue the bullies and their idiot parental units for every penny they’ve got in a civil court, along with subpoenas for student discipline records and any thing else a lawyer can use against a school district if they’re a knowing party to said abuse and did nothing to stop it (not counting namby-pamby solutions that don’t fix the actual problem).
Usually when the cost of lawsuits gets prohibitive, the school district usually will fix the problem (along with the appropriate amount of bad press and public shaming)…
But notice that Bill doesn't explain exactly what a real -- as opposed to "namby-pamby" -- solution to the bullying problem actually is. We might think that suspending the bully is an effective punishment, but last month I linked to an article arguing that a three-day suspension is just as "namby-pamby."
Of course, the article isn't about suspensions, but about "restorative justice." This is hard to define -- for example, I once heard the 150-word essays that I once assigned at the old charter school (see for example, my posts from January 2017) as "restorative justice."
In this thread, Bill also writes:
Bill:
In my day, we’d kick the crap out of bullies and their friends, and we did it off campus so the school idiots (administration) couldn’t interfere (but perhaps in this case, it would be easier to sue the school administration which allows this to go on.
Perhaps they need (the administration) needs to be bullied by fed up parents
Sad indeed
Whenever I see this, I think about The Simpsons and its first season episode "Bart the General." In this episode, Bart does exactly as Bill suggests -- gather an "army" to defeat the bullies Dolph, Jimbo, and Kearney.
But here Bill refers to the "school idiots," or administrators. He implies that if only the administrators would do the right thing, there'd be no need to beat up bullies after school -- and certainly no need to sue the administration. Once again, though, he never explains what the "right thing" to do is.
Our next Bill thread involves whether there should be an untimed SAT exam or not:
https://www.joannejacobs.com/2019/10/untimed-sats-for-all/
Many more students, especially the children of well-to-do parents, are getting extra time to take the SAT, reported the Wall Street Journal in May.
Bill writes a little about computer-adaptive exams. He mentions one such test where your score is reported immediately after the exam. If only the SAT -- or even the SBAC -- were as rapid in reporting the scores, since that is an advantage of taking tests online in the first place. The SBAC was given last spring, but the scores weren't released until -- today.
That's right, today is SBAC score report day. Let me reveal the scores for my old charter school, eighth grade -- the last cohort that I actually taught. I prefer to reveal the Hispanic scores, since I use "Hispanic" as a proxy for "was taught at my charter as opposed to our sister charter" (which was nearly 100% black), since the SBAC website combines our scores:
4 -- nobody
3 -- 1 student
2 -- 5 students
1 -- 7 students
We can't compare these scores to last year, since there were ten or fewer Hispanic seventh graders last year (and so the scores were blocked by an asterisk).
In case you're curious, among blacks there are more 1's, but also the only 4 score. The scores look even more dismal if we look at gender -- the lone 3 and 4 are both male, and there are slightly more 1's among the female students.
This is the first year that the eighth grade science scores count -- but the science scores won't be released for at least three more months. Once again, I wish that the CAST released the instant score reports that Bill describes.
Returning to Bill, he also writes:
Bill:
Only in Academia does this nonsense persist, due to the fact in the real world, there exist things known as deadlines, which usually have to be met on a regular basis.
Sigh
Of course, the whole debate is whether certain students (special ed students) should receive extra time on the SAT. The problem is that if we allow special ed students extra time, some gen ed students would lie and claim that they're special ed to get the extra time. The proposed solution is just to give everyone the extra time, so no one would have to lie.
But Bill describes this as "nonsense," because deadlines (on the job, say) exist. Instead, he believes that there should be a hard time limit, and anyone (even special ed students) who can't answer the questions in time should be given a failing score (based on the questions answered in time), period.
I think back two months to the math teacher I blogged about here. She wrote that as a young student, she was good at math, but not necessarily fast. Given unlimited time, she'd get a perfect score on the math test, but under Bill's hard time limit, she'd get a failing score. In other words, she'd say that it's wrong to equate "good at math" with "fast at math," but according to Bill, "slow at math" equates to "unable to meet deadlines."
This is a tough one. Bill mentions an IT Cert exam with 60-70 questions in 80-90 minutes. So I ask, is it possible that there's a potential IT worker who knows all her stuff and can easily fix computers and meet deadlines, yet simply can't answer 60-70 IT questions in 80-90 minutes? If such a worker exists, an IT department that fails to hire her would be missing out on an excellent worker, simply because she can't answer questions quickly. After all, IT workers should be judged on how well they can fix computers, not answer questions on them.
Or is Bill right, in that no such worker exists? A worker who can't answer 60-70 questions in 80-90 minutes can't possibly be able to fix computers and meet deadlines.
Our last post is about another hot topic -- the Harvard affirmative action lawsuit. I know -- it seems as if it's impossible to get through a traditionalists' post without getting into race! Anyway, Harvard has won its lawsuit and so affirmative action lives on, but the decision is expected to be appealed and heard at the US Supreme Court.
The following link isn't about Harvard, but about the UC system right here in California:
https://www.joannejacobs.com/2019/10/university-of-california-may-drop-sat-act/
Some University of California regents want to stop requiring SAT or ACT scores without waiting for a faculty study, reports Teresa Watanabe in the Los Angeles Times.
One possible alternative is to use the Smarter Balanced test, which is aligned to Common Core standards.
And the traditionalist who posts here isn't Bill, but Ze'ev Wurman:
Ze'ev Wurman:
“The way to stop discrimination on the basis of race is to stop discriminating on the basis of race.”
Justice John Roberts.
Notice that Wurman is quoting the Chief Justice here. In this context, "stop discriminating on the basis of race" means eliminate the use of affirmative action.
The article points out that officially, affirmative action no longer exists in the UC system. But it points out that the UC's circumvent this ban by considering other factors in admission that have the same de facto effect as affirmative action itself.
Is it possible to follow the suggestion of Chief Justice Roberts and completely "stop discriminating on the basis of race"? This is another tough one -- and the only answer I have is political. I believe that it's impossible to stop discriminating on the basis of race -- because conservatives and liberals cannot agree on what constitutes a level playing field.
For example, suppose that there exists a number N such that everyone with an SAT score higher than N is admitted to UC, and everyone with an SAT score lower than N isn't. Then Wurman and Chief Justice Roberts would agree that such a system would be non-discriminatory and thus would fulfill the line "stop discriminating on the basis of race," even if this results in a class that is almost 100% Asian and almost 0% black (say).
But the progressive would counter that an admitted class that is almost 0% black is, a priori, discriminatory on the basis of race, even if Wurman and Roberts don't think so. And likewise, if a class that's admitted that a progressive would consider to be non-discriminatory, Wurman and Roberts would consider it to be discriminatory (affirmative action).
Therefore, until we can get those on both sides of the spectrum to agree on what it means to end discrimination, we can never end discrimination.
Here is today's worksheet:
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