Today I subbed in a high school English class. Thus there is no ¨Day in the Life" today.
Two of the classes are freshmen. No, there is no persuasive essay today -- they actually worked on the essays yesterday, and those who still need more time are finishing it at tutorial today. Instead, they are studying The Odyssey by Homer. One of the classes is special ed with an aide.
The other two classes are sophomore AVID. Believe it or not, this is my first time subbing AVID here. The last time I covered an AVID class was three years ago -- before I started working at the old charter school. (There were a few close calls -- I co-taught with AVID teachers during their non-AVID classes.)
In AVID classes, tutors typically work with students on Tuesdays and Thursdays. Since today is neither Tuesday nor Thursday, there are no tutors today. In the past, I mentioned the special boards -- VNPS -- that are used with the AVID tutors. I see the seven boards today, but the students do not use them on Wednesdays. Instead, they have two assignments -- one written, one on Chromebooks.
This teacher is out both today and tomorrow, but I am already locked in to cover the same middle school class tomorrow as yesterday. Since I will not return to this class tomorrow, I instead did my holiday incentive by giving out Valentine-themed pencils and candy to the top students in each class.
During tutorial, I help several students out in math, including Geometry. Many of these students are preparing for a quiz to be given before the four-day weekend. Chapter 7 of the Glencoe text (the first chapter fully in the second semester) is on similarity. I notice that one of the review questions is:
True or false. Corresponding angles in similar triangles are proportional.
One girl writes false as the answer to this question. Technically, the correct answer is true, since the angles are proportional -- it just so happens that the constant of proportionality must be 1. But I refrain from correcting her, as common sense implies that false is the intended answer. The question is meant to distinguish between angles and sides (the latter of which are proportional, while the constant may or may not be 1).
I help her and a few other Geometry students with their review. I always tell them about the Geometry student I once tutored years ago -- I asked him how he knew that a certain pair of triangles was similar, and his reply was that they were similar because we were in Chapter 7. This time, I make sure the students know why two triangles are similar before they try to set up a proportion. And of course I warn about the common trick (Triangles ABC and ADE are similar, but some might try to set up a proportion with BD or CE).
I continue to help students during AVID after they finish their assignment. This includes one Algebra II student who is learning about exponential functions, including e^x. Thatś right -- the Algebra II text used at this school is the one where exponential functions start the second semester. This is timed perfectly for e Day, which was last week on February 7th. (No, I avoid asking him whether his class celebrated e Day or not.)
1. 4.
2. 24 square units.
3. 9pi cubic units.
4. sqrt(82) * pi square units, 3pi cubic units.
5. 48,000 cubic units.
6. 98 square units.
7. 28,224pi square units, 790,272 cubic units.
8. 5.5. Section 10-3 of the U of Chicago text asks the students to estimate cube roots. If one prefers to make it a volume question, simply change it to: The volume of a cube is 165 cubic units. What is the length of its sides to the nearest tenth?
9. Its volume is multiplied by 343. This is a big PARCC question!
10. Its volume is multiplied by 25 -- not 125 because only two of the dimensions are being multiplied by 5, not the thickness.
11. The volume of Neptune is 64 times that of Earth.
12. A ring -- specifically the area between the the circular cross section of the cylinder and the circular cross section of the cone. This is Cavalieri's Principle -- recall the comments I made about Dr. Beals?
Instead, today is my "traditionalists" post. Actually, I already mentioned a traditionalist in this post -- Dr. Katharine Beals. Actually, Beals is no longer an active blogger -- instead, she's focusing on writing her own book about traditionalism and language.
But four years ago, Beals wrote a post attacking Cavalieri's Principle as fluff and a waste of time in high school Geometry classes. Since I reblog my old posts from past years every time I write about Cavalieri, I keep dragging up her name and the old debates.
Instead, let's look at today's active traditionalists. On February 6th, the tweeter CCSSIMath wrote about a sixth grade problem about the area of an irregular rectilinear polygon (to be found by dividing the polygon into rectangles). But according to CCSSIMath, this ought to be considered a fourth grade problem (as it would be in Japan) instead of a sixth grade problem.
https://twitter.com/CCSSIMath
We know that CCSSIMath likes to push Common Core recommendations down into lower grades. I point out that this requires elementary teachers with multiple subject credentials to be more comfortable with this sort of math. Two years ago at the old charter school, this problem appeared in the fifth grade text, and the fifth grade teacher had to ask me to help her solve the problem. Yet CCSSIMath tells me that I should have been helping the fourth grade teacher with this problem, not the fifth grade teacher!
On the other hand, in my current district sixth grade is still elementary school. And so even the sixth grade teachers might be uncomfortable with the problem if they lack math on their résumé. I like the idea of protecting teachers with multiple subject credentials from having to teach difficult math problems regardless of CCSSIMath and his/her preferences.
Ironically, five days later CCSSIMath gives a Common Core fraction problem that is "quite difficult for 5th grade arithmetic":
Leonard spent 1/4 of his money on a sandwich. He spent 2 times as much money on a gift for his brother as on some comic books. He has 3/8 of his money left. What fraction of his money did he spend on the comic books?
OK, I see what's going on here. The boy spent 1/4 on lunch and has 3/8 at the end, and so that leaves him with 1 - 1/4 - 3/8 = 3/8 for the gift and comics. Since he spent twice as much on the gift as the comics, it means that 2/8 was for the gift and 1/8 for the comics. The correct answer is 1/8.
Also, for this traditionalist post, let me write about something other than math. l address the subject I cannot help but think about lately -- English. Not only have I not subbed much math lately, but I have yet to see history or science since 2019 began. For some reason, I keep ending up in English classes -- even when it is special ed, it is English. And as we already know, English lately has been nothing but the district Performance Task.
During the LAUSD strike, I explained how district assessments were a point of contention. According to the settlement, district assessments would be reduced by 50%. My district is not LAUSD, and so that settlement has nothing to do with me. And this Performance Task is basically a district assessment, just like the ones the union wants to reduce.
Why do districts give these sorts of assessments, anyway? I assume the main rationale is to prepare the students for the SBAC. The name ¨Performance Task" gives it away -- this is supposed to be similar to the Performance Task portion of the SBAC.
We can see what the districts are thinking -- they want to prepare the students for the SBAC so they will earn a high score on the big test. But this is what exactly the union wants to reduce -- not just standardizing testing itself, but all the time devoted to preparing for standardized testing. If the sole purpose of giving the district test is to prepare for the SBAC, then we are justified in counting all of the time devoted to it as test prep. Thus English classes just spent the last six weeks on nothing but test prep.
The ideal situation would be for there to be no test prep -- teachers just simply teach the curriculum and the students get high scores on the test. For math, this would entail eliminating tricky questions that require extra test prep to solve, but what sort of questions these are is debatable. All this week, I wrote about Katharine Beals and Cavalieri. Beals would count Cavalieri as such a ¨test prep¨ question, since many Geometry teachers might not cover it had it not been for its presence on the test. (I wonder whether she would count ¨derive the area of a sphere¨ as a test prep question.)
Hmm, even though the Beals math blog is no longer active, she does currently write a blog with another Katharine -- to be precise, another Catherine (Johnson). Their blog is less about math and more about writing:
But still, I am not sure what such traditionalists would say about writing Performance Tasks. My guess is that they would tell us to teach good writing early, starting in elementary school. I do see the two Kates telling us about examples vs. non-examples at the link above, so this could help. And I suppose that even making a claim, researching evidence, and citing evidence is also something students can learn early as well. In theory, no test prep time is needed -- the students can enter the classroom on test day, receive the prompt, write a persuasive essay, and get a good score without knowing anything about the prompt until the they arrive that day.
Earlier, I did say that there should be three levels, with only one test at each level -- district for elementary, state for middle school, and Common Core for high school. But how do we know that, if we have state or national writing tests for secondary students, the district will not throw its own writing tests on top in the name of ¨preparing¨ the students for the main test? And as we have seen firsthand, the test prep needed for writing can be extensive.
Once again, I am a math teacher, not an English teacher (despite all my Jan.-Feb. subbing), and so I recognize what is too much testing in math more than English. This is why I can say that the standardized math test should be reduced to no more than a standard class period. I cannot be sure how much time should be devoted to a proper writing test for ELA.
So let us just get back to math. Is that fifth grade question fraction above fair? I suppose that in the end, the best way is just to ask students and teachers. It is very possible, for example, that my fifth grade teacher at the old charter could solve the fraction problem, even though she was unable to solve the rectilineal area problem.
What the students and teachers can handle -- whether it is English or math -- is how we should ultimately determine what is grade-level appropriate. (When tests are inappropriate, we wind up with situations such as the Atlanta cheating scandal, which has returned to the news today.)
By the way, let me conclude this post by mentioning the death of Lyndon Larouche. He was a controversial presidential candidate, but I mentioned him on the blog only in order to discuss his music theory. He suggested that middle C on a piano should be tuned to 256 Hz (hertz).
Since 256 is a power of two, C256 is compatible with Kite and his color notation. We may refer to C256 as white C. Then the other otonal colors (yellow, blue, lo, tho) correspond to the other integral hertz values (since hertz/frequency is an otonal system). No, I definitely do not agree with Larouche and his reasons for C256 (the so-called natural frequency of the earth), but at least his system and the Kite colors are somewhat compatible.
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