Two of the classes are juniors, while second period is AP English. What's unexpected is that the students in the AP English class are sophomores. I've written so much about AP Calculus on the blog, especially in the traditionalists' posts (and yes, this is yet another traditionalists' post -- I already told you that you-know-who was about to post over the weekend). But I've said very little about how AP English classes work.
There are actually two AP classes -- AP English Language and AP English Literature. Back when I was a young high school student, I enrolled in AP English Lit as a senior -- actually, my high school didn't offer AP English Lang at all. Most schools that do offer English Lang consider it to be a class for juniors, who then move on to take English Lit as seniors. This district (or school) is thus rare in that it offers English Lang to sophomores instead.
I wonder what class the English Lang sophomores will take next year as juniors. The junior classes I cover today aren't listed as honors, much less AP. It could be that sophomores take English Lang and seniors take English Lit, so that 11th grade is a gap between AP English courses. Or it might be that these students will take English Lit next year, but the junior classes I see today aren't for AP students.
Traditionally, the first AP taken by a high school student is a sophomore history class -- in California, 10th grade is World History, and so AP Euro or AP World History are common. I ask some of the sophomores today, and they tell me that they're taking AP World this year as well. So instead of a "starter year" with just one AP, these students are taking two AP exams this year. With May being just a couple of months away, I wish these students luck on their two tough AP tests that are coming up soon.
Once again, I entered my magnet school late -- not until my junior year. Recall that I had to take two English classes as a senior, since 11th grade English outside the magnet is considered equivalent to honors 10th grade English inside the magnet. I can only imagine what would have happened if my district had offered both English Lang and English Lit -- would I have been forced to take two English classes simultaneously with both of them being AP courses?
All of this talk about AP courses piqued my curiosity, and so I decided to revisit the website of my old magnet school. Apparently, now both English Lang and English Lit are offered at my school -- with English Lang being given to juniors, as is typical. For magnet sophomores, honors junior English is still offered. AP History classes haven't changed from my high school days -- but my school offers AP US History to sophomores and AP Euro to juniors (the reverse from when most students take this courses).
But no, US History isn't the first AP exam students in my magnet currently take. That honors goes to one of the newest exams -- AP Environmental Science. Apparently, students in my magnet take the AP Enviro exam as freshmen. This test wasn't administered by AP until I was already a junior -- and it was probably a few years later before my magnet declared it to be a freshman course.
This past weekend was the transition to Daylight Saving Time. It is my blog tradition to write about clock-related issues on the day we spring forward. Today's post will discuss Proposition 7 here in California and its goal of establishing Year-Round Daylight Saving Time.
There are still two more things that must happen before Year-Round DST can begin. The state legislature must approve the time change, and then so must Congress. So far, a bill has been introduced in the State Assembly. It requires a supermajority (2/3 of all legislators) to pass. Here is a link to the bill, first proposed by Assemblyman Kansen Chu (the author of Prop 7):
https://leginfo.legislature.ca.gov/faces/billTextClient.xhtml?bill_id=201920200AB7
Recall that Florida was the first state whose legislature approved Year-Round DST. A senator and a congressman from the Sunshine State introduced bills to Congress as well. If the bill passes, the president has indicated that he'd sign the bill:
https://www.washingtonpost.com/politics/trump-says-hes-okay-with-adopting-daylight-saving-time-year-round/2019/03/11/0df3e1a2-43ec-11e9-90f0-0ccfeec87a61_story.html
Once again, here's my own opinion of this issue -- I have no problem with the biannual clock change, but of the two clocks, I prefer DST to Standard Time. Thus I promised on the blog that if there was the opportunity to vote for Year-Round Standard Time I'd oppose it, but if it was for Year-Round DST then I'd vote for it. Originally, Chu supported Year-Round Standard Time, but later he changed it to Year-Round DST instead. Since this is the clock I said I preferred, I kept my promise and voted for the proposition.
My favorite plan for a single clock year-round is the Sheila Danzig plan. On this plan, some states would have Year-Round DST and others would have Year-Round Standard Time. This would reduce the number of time zones in the Lower 48 to just two, separated by two hours.
Unfortunately, Florida -- Danzig's home state -- is headed towards Year-Round DST, even though her plan recommends Year-Round Standard Time for her home state. The Panhandle, which is currently on Central Time, would keep its clocks forward while the rest of the state would keep them back. The proposed bill instead places the whole state, including the Panhandle, on Eastern DST. This might lead to especially late winter sunrises in the Panhandle.
I assume that the rapid progression towards a single year-round clock is being driven by the desire to have DST year-round, with more sun in the evenings. Notice that any state could choose to have Year-Round Standard Time even without the approval of Congress, but few (only Arizona and Hawaii) actually do so. But it's the allure of Year-Round DST that's driving the current legislation, with at least half the states proposing Year-Round DST bills.
If Year-Round DST passes nationally, I assume some states might still prefer Standard Time. For example, Arizona already has a single year-round clock, and it will probably keep it. The net result will be that Arizona would essentially now be in the Pacific Time Zone -- the same clock at the West Coast year-round. Certain other states on the west side of their respective time zones might also keep Year-Round Standard Time.
An interesting case is in the Northeast. Massachusetts is considering Year-Round DST. If MA chooses DST, then so should Connecticut (since suburbs of Boston are in that state). If CT chooses DST, then so should New York (since suburbs of NYC are in CT). If NY chooses DST, then so should New Jersey (since suburbs of NYC are in NJ). If NJ chooses DST, then so should Pennsylvania (since suburbs of Philadelphia are in NJ). But Pennsylvania is far enough west in its time zone that Year-Round Standard Time is preferred in Pittsburgh, not Year-Round DST -- and in fact, there is currently a Year-Round Standard Time bill proposed in the PA legislature.
It's actually more important to keep metro areas, not states, in the same time zone. If Pittsburgh prefers Year-Round Standard Time and Boston prefers Year-Round DST, then at some point a state must be divided in order to keep metro areas together -- either PA (between Pittsburgh and Philly), NJ (between Philly and NYC), or CT (between NYC and Boston). Of course, the entire nation could just adopt the Danzig plan, which keeps the eastern half of the country in one large time zone.
But once again, the Danzig plan isn't the current proposal in Danzig's home state, FL. Even though Danzig herself would prefer Year-Round Standard Time to Year-Round DST in her home state, I'm sure that she would rather have Year-Round DST than the current biannual clock change.
As for CA and Prop 7, we didn't mind changing our clocks forward to DST this weekend because DST is what we want to be year-round. The only question is, will the Assembly and Congress cooperate by November 3rd so that we won't have to change the clocks back to Standard Time?
By the way, you might ask, were there many tardies in class today due to the time change? Actually, about a third of the class was late today -- to third period. In this district first period is like zero period and so second period is like first period. Fortunately, Mondays at the high schools in this district are late days, so that eliminates some of the sleep problems due to the time change (but tomorrow will be a different matter).
But there's no excuse to be late to third period today. Due to the tardies, I was more vigilant in trying to catch tardies to fourth period. I lock the doors when the bell rings, and I end up catching two girls who are late to fourth period. I end up naming second period the best class of the day -- not just due to no one being tardy, but because they work hard today on an essay to prepare for AP. The junior classes are supposed to take a quiz on The Great Gatsby, but no copies of the quiz are available.
Today on her Mathematics Calendar 2019, Theoni Pappas writes:
How many capital non-serif letters of the English alphabet have a vertical line of symmetry?
There are eleven such letters -- A, H, I, M, O, T, U, V, W, X, Y. Reflections and symmetry appear in Chapter 4 of the U of Chicago text, especially in Lessons 4-2 and 4-7. And of course, today's date is the eleventh. (From A to S there are just five symmetrical letters, and so reaching eleven letters seems to be impossible. Then suddenly there are six symmetrical letters in a row!)
Almost every Pappas this week is related to Geometry, so be prepared!
Lesson 12-7 of the U of Chicago text is called "Can There Be Giants?" This is one of those "fun lessons" that we can cover if there's time, but in the past we bypassed it to get to 12-8 and the all-important SSS Similarity.
As I wrote above, Lesson 12-7 naturally lends itself to an activity. The whole idea behind it is that while dilations preserve shape, they don't preserve stability. This is because of the Fundamental Theorem of Similarity -- a dilation of scale factor k changes lengths by a factor of k, areas by a factor of k^2, and volumes by a factor of k^3. Weight varies as the volume, or k^3, while strength varies only as the area (as in surface or cross-sectional area), or k^2. Therefore, the answer to the question in the title of the lesson is no, there can't be giants because their k^2 strength, couldn't be strong enough to carry their own k^3 weight.
Notice that the monomial worksheet from today's lesson somewhat fits this lesson. Some of the problems ask the students to find the area of a square or volume of a cube -- with a particular monomial as one side, so that the students can practice squaring and cubing monomials.
This is what I wrote last year about today's lesson:
As I wrote above, Lesson 12-7 naturally lends itself to an activity. The whole idea behind it is that while dilations preserve shape, they don't preserve stability. This is because of the Fundamental Theorem of Similarity -- a dilation of scale factor k changes lengths by a factor of k, areas by a factor of k^2, and volumes by a factor of k^3. Weight varies as the volume, or k^3, while strength varies only as the area (as in surface or cross-sectional area), or k^2. Therefore, the answer to the question in the title of the lesson is no, there can't be giants because their k^2 strength, couldn't be strong enough to carry their own k^3 weight.
Notice that the monomial worksheet from today's lesson somewhat fits this lesson. Some of the problems ask the students to find the area of a square or volume of a cube -- with a particular monomial as one side, so that the students can practice squaring and cubing monomials.
2019 Update: Today is not supposed to be an activity day. But it's almost impossible to give this lesson without making it an activity. Indeed, it's just like Lesson 9-8 on the Four Color Theorem. We just happened to luck out that Lesson 9-8 landed on an activity Friday, but we aren't so fortunate with today's Lesson 12-7.
By the way, here's one of my favorite questions to ask about this lesson. Today's lesson provides an indirect proof that giants -- Brobdingnagians -- don't exist.
Prove: Brobdingnagians don't exist.
Indirect Proof:
Assume that Brobdingnagians exist. In each of the three dimensions, a Brobdingnagian is 12 times as large as a human. So each bone of a Brobdingnagian would have to carry 12 times as much weight as a human bone. Thus a Brobdingnagian standing is like a human carrying 12 times its own weight. But no human can carry 12 times its own weight, a contradiction. Therefore Brobdingnagians can't possibly exist. QED
But there's a problem with this proof -- it can be used to prove that humans don't exist:
Prove: Humans don't exist.
Indirect Proof:
Assume that humans exist. In each of the three dimensions, a human is 12 times as large as a Lilliputian. So each bone of a human would have to carry 12 times as much weight as a Lilliputian bone. Thus a human standing is like a Lilliputian carrying 12 times its own weight. But no Lilliputian can carry 12 times its own weight, a contradiction. Therefore humans can't possibly exist. QED
The proof is clearly invalid, since humans do exist. My question is, which step is invalid?
Let's get to the traditionalists. Actually, Barry Garelick posted twice over the weekend. The first post is dated Saturday, yet somehow I was able to read it on Friday. (Hmm, maybe Garelick started DST or Prop 7 time on Friday -- he set his clock so far ahead it was Saturday!)
https://traditionalmath.wordpress.com/2019/03/09/the-so-called-instructional-shifts-of-the-common-core-and-what-they-mean/
Long-winded Introduction/Preamble
The San Luis Coastal Unified School District is in the central coast area of California. It includes schools in San Luis Obispo and the nearby towns of Morro Bay and Los Osos. The district, under the direction of the current superintendent, follows the trend of teaching that adheres to constructivist-oriented approaches; i.e., inquiry type lessons, with teachers facilitating rather than teaching. The math text used starting in middle school through sophmore year in high school is CPM, an inquiry-based program.
OK, since Garelick admits that this is "long-winded," let's skip to the important parts.
Inside Common Core’s “Instructional Shifts”
The “shifts” in math instruction are discussed on Common Core’s website. There are three shifts defined: 1) Greater focus on fewer topics, 2) Coherence: Linking topics and thinking across grades, and 3) Rigor: Pursue conceptual understanding, procedural skills and fluency, and application with equal intensity.
Which brings us to the third shift, “rigor” to which I want to devote the most attention and focus. The website translates “rigor” as “Pursue conceptual understanding, procedural skills and fluency, and application with equal intensity.” The site also mentions that students should attain fluency with core functions such as multiplication (and by extension, multiplication of fractions): “Students must be able to access concepts from a number of perspectives in order to see math as more than a set of mnemonics or discrete procedures.” Again, a nod to the notion that before Common Core, math was taught as a set of procedures “without understanding” using, yes, rote memorization.Now Garelick mentions the EngageNY curriculum, which I blogged about last week. I was writing about the Geometry curriculum, but here Garelick is discussing arithmetic:
I learned of the connection between these “instructional shifts” and the current practice of drilling understanding in a conversation I had with one of the key writers and designers of the EngageNY/Eureka Math program. EngageNY started in New York state to fulfill Common Core and is now being used in many school districts across the United States. I noted that on the EngageNY website, the “key shifts” in math instruction went from the three on the original Common Core website to six. The last one of these six is called “dual intensity.” According to my contact at EngageNY, it’s an interpretation of Common Core’s definition of “rigor.”
There are certain words and phrases that traditionalists don't like. One of these that we've seen before is "number sentence." Apparently, another word they hate is "regrouping":
In our discussion, I pointed to EngageNY’s insistence on students drawing diagrams to show place value in adding and subtracting numbers that required regrouping (a.k.a. “carrying” and “borrowing”—words now anathema in this new age of math understanding). I asked if students were barred from using the standard algorithm until they acquired “mastery” of the pictorial procedure.
What Does This All Mean?
What this means for me is that I do not subscribe to this philosophy. I believe it is injurious to students and defeats the purpose of providing understanding by burdening their overloaded working memories.
Let's look at the comments. Traditionalist Wayne Bishop tells us what he thinks about "regrouping":Wayne Bishop:
Borrowing and Carrying:
My first association with the onus associated with these familiar terms within self-respecting mathematics educators was as an undergraduate nearly 60 years ago. My yet-to-be wife was taking the required mathematics for education sequence from a renowned expert, E. Glenadine Gibb, later of UT Austin and president of the NCTM, and I was helping her decode the jargon. Ever since, when people use “authentic” terms such as “regrouping”, I play dumb and act as if I do not understand. They keep trying until finally in exasperation they say, “You know, borrowing and carrying.” My response? “Yes I do know and so do the parents of most lower elementary school students. I also know “regrouping” and some other alternatives for these familiar concepts that many of those parents do not. Why do you avoid standard terms that make it harder for them to help their children with these important and straightforward concepts?”
One thing I observe is that both Saxon Math and Singapore Math -- curricula that traditionalists hold in high regard -- use the word "regrouping" in their texts. Then again, Bishop can easily counter that I'm looking at the new editions, and these have been corrupted by the reform movement. I don't have access to any of the old 1980's and '90's versions of these texts. (Google searches mainly give the new editions of these texts.)
But as usual, the main commenter is you-know-who:
SteveH:
I find it striking how this is really all about K-8 and not about high schools. Middle schools (mostly 7th and 8th grades) are the weird changeover battle ground to high schools that are dominated by proper and traditional AP and IB math courses.
I subbed in an IB math course last week -- yes, SteveH has much respect for the IB program. And yes, today I sub in an AP course, except that it was AP English Lang, not Calc or Stats.
SteveH:
I call this a two+++ generational statistical approach to poverty that puts a huge onus on parents. It’s not about equal individual opportunity or leveling the academic playing field.
I just skipped to this part since the rest is the usual same-old. Actually, it's been a while since SteveH mentioned his "2+ generations" trope. His idea is that Common Core promotes upward mobility in at least two generations -- the original generation enrolls their children in public schools, they learn Common Core math, and then they enter community college. Then this first filial generation gets a job that pays enough to hire math tutors for the second generation. The math tutors teach enough math for the second generation to get into a prestigious university and win a high-paying job.
SteveH contrasts this with his "one-generation" solution -- just teach the first generation traditional math in the public schools. Then they'll learn enough math to get into the prestigious university.
As usual, SteveH ignores the reason why math tutors work. Many young children find traditional math boring. They leave the traditional p-set blank -- at least in a classroom where there are twenty or thirty other kids. When there's a tutor sitting inches away from them, they can't escape as easily.
Recently, SteveH wrote that charter schools shouldn't be necessary, but notice what he writes now:
SteveH:
Unfortunately, in K-8, students and parents do not have a choice. If they want to get rid of the 19th century factory model of education, then they need to get rid of their monopoly over choice.
Today I'm posting the Lesson 12-7 worksheets. These are as far from traditionalism as you can get -- it's a lesson that students may find interesting. You could replace this with a traditional p-set on similarity, but the kids might think it's boring and leave it blank.
Oh, and let me answer the question from above. Which step of the proof is invalid?
Answer: "But no Lilliputian can carry 12 times its own weight, a contradiction."
This step is invalid, because in the real world, Lilliputians can carry 12 times their own weight -- indeed, much more than 12 times their weight. (Real-world Lilliputians are often called "ants.")
Here are the worksheets that I've created for this lesson:
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