Today I subbed in a middle school special ed history class. It's in my first OC district -- and in fact, it's the exact same class that I subbed in last week.
I mentioned this class in my February 9th post. That was a Tuesday, but the school followed Wednesday's schedule due to the Friday holiday. Thus I see the same students both that day and today -- and so I don't need to spend that much time describing the classes.
The fourth period co-teaching class is still studying Japan. Fifth period, while also a seventh grade World History class, has finished West Africa and has moved on to China. Sixth period, an eighth grade US History class, is about to begin a -- you guessed it! -- CER district assessment. It's about the nineteenth century young women who worked at the textile mill factories in Lowell, Massachusetts. Students must discuss whether the opportunities these women received outweigh the hardships they faced, or vice versa.
Today is Saturday, the second day of the week on the Eleven Calendar:
Resolution #2: We make sacrifices in order to be successful at math.
Well, there's one eighth grade girl who doesn't make sacrifices to be successful at history today. She's an online student who has opted out of hybrid. She logs into Zoom, but then she's completely unresponsive to either me or the aide, and does no work on the prewriting assignment. It's obvious that she's logged in merely to get credit for attendance.
I don't communicate with her at all, but we can easily imagine what she'd say if pressed to give an honest answer as to why she does no work today. School's boring, history's boring, we make her go to school too many days and for too long each day, she's already learned everything she needs to know to have a great adult life and so she needs no more education. At any rate, she definitely doesn't want to make any sacrifice in order to be successful at history.
The irony, of course, is that today's lesson is all about a time when we didn't force young people to go to school when they don't want to learn. A young girl around her age who lived anywhere near Lowell, MA 200 years ago would have worked in the mills.
This girl thinks we make her work too long at school. She only has to attend online school five days a week, from 8:30 to 2:00 -- actually 12:05, since after lunch is academic support, which is optional (and a student who pretends to be engaged in regular class is the last person you'd see at optional tutorial). In Lowell, the young ladies worked six days a week, 12 hours a day -- from sunrise to sunset.
Today I sing the "Big March" song, which reinforces the idea that seven weeks between holidays is much too long. In 1821, there were no federal holidays -- Lowell mill workers would have been lucky just to get Christmas, New Year's Day, and the Fourth of July off. (Thanksgiving wasn't established until Lincoln.) Thus their "Big March" would have lasted from January to June. I admit my guilt here to the students who are engaged today -- we students and teachers complain about the Big March, but imagine how many young women in 1821 would gladly trade places with us.
I won't make a habit of comparing the youths of today to 1821 to reinforce the second resolution, but I will bring it up if it's directly related to the lesson. (Since eighth graders will spend the next few weeks on this CER, I will bring it up in their history classes.)
Here is the Chapter 10 Test. Let me include the answers as well as the rationale for including some of the questions that I did.
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 -- and it's a big one. Today I'll discuss the book that our main traditionalist, Barry Garelick, has published. And several other traditionalists -- yes, including Katharine Beals -- mention the new book on their own blogs.
Let's start with the author himself. Garelick mentions his new book in his February 7th (e Day) post:
https://traditionalmath.wordpress.com/2021/02/07/as-you-havent-been-told-dept/
I teach math at a small Catholic school in California. I teach 7th grade math and 8th grade algebra. For those who have read my latest book, you know that I use a 1962 version of Dolciani’s “Modern Algebra” as my textbook. The students like the simplicity of its presentation, and so do the parents. I have had parents tell me they like the book, and one in particular said that it is how she learned algebra, and it allows her to help her daughter. She thanked me, and said “I can’t stand that Common Core stuff.”
The title of his book is Out on Good Behavior: Teaching Math While Looking Over Your Shoulder. He's linked to excerpts of his book earlier, and now his complete book has been published.
In this post, Garelick discusses the standard algorithms for addition and subtraction, and his belief that they should be taught earlier than suggested by the Common Core:
Therefore it is of interest to hear William McCallum’s view of this aspect of Common Core. He was one of the two lead writers of the Common Core math standards. When I wrote an article that was published in the online Atlantic about Common Core, I pointed out that the standard algorithm for multi-digit addition and subtraction did not appear until 4th grade. Until then, teachers and students were saddled with “strategies” which included pictures and inefficient methods in the name of “understanding”. The view of reformers is that teaching standard algorithms first eclipses the conceptual underpinning of why the algorithms work as they do—this in spite of the pictorial explanations that appeared in early textbooks from the 60’s, 50’s and earlier that provided such explanation.
I've already devoted many posts to that Atlantic article years ago, so we don't need to revisit it again.
Let's skip down to the comments. As usual, SteveH posts several times in the comments:
SteveH:
Ultimately, the fuzzies failures have to do with no enforcement of individual mastery at any level. Whether its traditional algorithms first or last, they fail to understand the deeper levels of understanding learned by doing and mastering lots of individual homework variations.
And as usual, the traditionalists fail to understand that many students would rather leave those individual homework p-sets blank. Students who leave assignments blank don't master any math.
SteveH:
K6 schools need to be explicit about what mastery (slope) is needed to meet their 7th grade split to Pre-Algebra and then full Algebra in 8th grade. They need to AT LEAST publish their requirements/test they use. I saw kids (and parents) dumbstruck that they were not selected for the advanced classes after years of “exceeding expectations.”
We already know that Algebra I is the only class that SteveH recommends for eighth grade, so of course he wants to know what the requirements for getting into that class are.
On one hand, most schools do make the requirements for getting to such classes explicit. For example, at my new district where I completed my long-term assignment, sixth graders must earn at least AAAB for the four quarters of Math 6 and at least a B on the Math 6 final exam, to get to Math 7X. There's another pathway with slightly lower quarter grades, but then an A must be earned on the final. (It's also possible to jump directly from regular Math 7 to eighth grade Algebra I, also via AAAB grades, but with a placement test instead of the final (I told my top Math 7 kids about this). There's even a link to a study guide for the final exam and placement test, so that counts as "publishing the requirements/test they use."
Then again, SteveH does begin by mentioning elementary schools -- and this betrays what SteveH is really driving at here. I assume what he wants is for, say, third grade teachers to say something like, "Your child needs to have learned" -- or to use SteveH's word -- "mastered the times tables and standard algorithms for addition and subtraction, even though this is beyond Common Core. Unless your child masters these very soon, he/she won't be on the right slope to get to the A's and B's needed three years from now to get into Math 7X or Algebra I."
In his next comment, SteveH finally acknowledges that yes, students do leave assignments blank:
SteveH:
By the time their students get to high school, they lack mastery of the basic skills AND the ability to finish a homework P-set.
I tutored many high schoolers who thought homework was something that you just made a stab at. Even after we had tutoring sessions where I got them to explain things in words, I told them to go back and do the homework themselves. Few did so.
Then of course, SteveH assumes that if math had been taught the traditionalists' way in mid-elementary, these high school students wouldn't be leaving their p-sets blank now. To me, it's just as logical to make the opposite conclusion -- if math had been taught traditionally earlier, these students would have left their mid-elementary school p-sets blank. He continues in this comment:
SteveH:
When I was growing up, kids not only had the standard algorithms, we had homework and tests and report cards that gave understandable feedback to parents. If you didn’t get a fixed passing grade, you were subject to summer school or being held back a year.
Should students be held back a year for failing to make the Algebra I in eighth grade "slope" easily, even if they can pass the easier "Algebra I in high school" slope with flying colors? Meanwhile, according to him, the standard algorithms aren't enough:
SteveH:
However, even if they decide to teach just the standard algorithms, they still have the underlying problem of low expectations and no enforced mastery at any one point in time. That’s the classic Everyday Math line – “Trust the Spiral” which turns into repeated partial learning. Our schools probably point to my son as their poster boy for Everyday Math, but nobody asked us parents what we had to do at home EVEN for our “math brain” son.
As we already know, SteveH likes to criticize the U of Chicago elementary math text (Everyday Math).
Barry Garelick mentions the much maligned San Francisco district. The SF district has made the news lately for other reasons which I choose not to discuss here -- here we're focusing only on the math policy, where all eighth graders take Common Core 8. SteveH wonders whether it's still possible to take AP Calculus in San Francisco:
SteveH:
I found it. They created a Junior year class called:
CCSS Algebra 2 + Precalculus Compression to lead to AP Calculus as a senior.
Really!?! My math brain son didn’t just twiddle one thumb during separate years of Algebra 2 and Precalculus that they now combine into one.
I'll partially agree with SteveH here, since Algebra II is such a tough class. I suppose that if any two classes should be combined, it should be Algebra I and Geometry. It's also possible to have the students take Geometry over the summer, or simply two math classes as freshmen. (It helps that here in California, freshmen don't need to take history, and so there's space for a second math class.)
This thread so far has been one huge echo chamber for the traditionalists. Then again, there is one poster who tries to stand up to them:
Ramani:
No time to dig into details – but there is a lot of ignorance of math research across various domains here. Please hold your opinions people and study a little more.
Here's SteveH's response:
SteveH:
“Ignorance”??? You’re guessing.
“Opinions”???? Maybe that’s all YOU have.
I’ve taught and tutored math and I watched and helped my son survive “Trust The Spiral” EM and CCSS over the last two decades.
If most students were like SteveH's son, I'd be 100% in favor of traditionalist math. The problem is that most students aren't like his son. His son thrives with traditionalist p-sets. Most other students find traditionalist p-sets boring -- and when something is boring, they leave it blank -- and when something is left blank, no learning occurs.
SteveH:
Are you assessing “executive functions”, developing “low-cost mobile app technology,” or both? Does the assessment include finding out whether kids have mastered their adds and subtracts to 20 or the times table? Do you need a mobile app to do that or does that just help you get funding?
I do agree with the traditionalists that students should learn the times tables. To me, third grade is right around the border -- I agree with traditionalism up to around this point.
SteveH mentions "funding" here because he finds a research paper with "Ramani" listed as one of the authors -- he suspects that Ramani is more interested in money than what works for students. Then again, I can turn it around on the traditionalists -- do they sincerely believe in their methods, or are they just trying to sell books (such as Out on Good Behavior)?
Here's my own research, based on I see in my class today -- a girl who pretends to be engaged in history, but in reality she just leaves her assignment blank. Before you counter that this is history and not math, notice that SteveH also pivots to another subject, music:
SteveH:
If you want to see what works for under-privileged groups – as equals, see El Sistema for music. They take kids from the barrios and get them to play at Carnegie Hall and the BBC Proms by the end of high school. The key to it are the private lessons that enforce mastery of skills and start in the earliest grades and NOT the mixed-ability orchestra classes in school. These musicians do not have just mere facts or rote skills. Mastery drives understanding and excitement and hard work – NOT they other way around.
Here's the difference between music and subjects like math and history -- people enjoy music, and musicians are granted a higher status than mathematicians or historians. Therefore students are more likely to make sacrifices for music than they ever will for math or history.
This is why I incorporated this into one of my new rules -- the need to make sacrifices in order to be successful in math. I expect that it will be difficult for me to convince students to do so -- they won't suddenly make sacrifices just because the traditionalists say so.
On Presidents' Day, Barry Garelick makes another blogpost about his new book:
https://traditionalmath.wordpress.com/2021/02/15/faqs-about-out-on-good-behavior/
I'll quote only some of Garelick's FAQ here:
Is “Out on Good Behavior” about the Zen of teaching math?
Nope. Just the usual rebelling against the edu-fads and how I make it look like I’m on board with the current educational lunacy.
You mention your use of the 1962 algebra book by Dolciani. Do you ever get complaints from parents about your use of that book?
Any and all reaction from parents about the Dolciani book has been positive. One parent told me “This is how I learned algebra, and I’m able to help my daughter.” Others like the simplicity of the format and the problems. I also hear from the students who like it because “It doesn’t have those real-world problems.”
I must comment here. As we already know, many students ask "Why do we have to learn math?" or "When will we use this math in the real world?" A proper answer lists real-world examples of math -- and so the question implies that students want to see more real-world examples in order to justify their need to learn math.
Now Garelick is telling us that his students don't want to see real-world examples -- that in fact, they like the old Dolciani text specifically because it doesn't contain such examples! Once again, I must give Garelick credit for being in a real math class and hearing this from a student. I still can't see why his students don't ask "When will we use this in the real world?" and insist on seeing real-world examples when most of the rest of us teachers hear this question all the time.
I did say earlier that I'd get to the other traditionalists regarding Garelick's new book. I specifically mentioned Katharine Beals. Well, let's see what she has to say:
https://catherineandkatharine.wordpress.com/2021/02/03/out-on-good-behavior-is-out-heres-my-review/
It is, among other things, a fascinating insider account of the struggles and insights of a novice grade school teacher who is also a seasoned mathematician and a proponent of traditional, evidence-based math instruction. We watch Garelick in action as he teaches struggling, under-motivated students how to subtract negative numbers and factor polynomials. We eavesdrop on the often awkward feedback sessions he has with mentors and other supervisors who are sometimes taken aback by Garelick’s commitment to traditional teaching methods—and by the compelling case he makes for them.
At this point, Beals discusses "critical thinking," and what Garelick means by the term versus what his BTSA mentor meant.
As usual though, my biggest concern with the traditionalists is their emphasis on p-sets that students are likely to leave blank. One comment on her blog is interesting here:
terri:
My daughter’s AP Physics C teacher has unfortunately drunk the koolaid hard (boy, do I have stories) and she’s completely demoralized. (Students ask for help;he tells them to go watch a YouTube video or ask their peers to help them. He sends them into zoom breakout rooms to work together on the problem sets that he hasn’t explained how to do, and her classmates disappear and play video games instead. It only halfway worked last year in APPhys1 in person, and it’s a TOTAL disaster this year over zoom.)
This science teacher assigns p-sets, and the students play video games instead -- in other words, the students do leave the p-sets blank. Is this supposed to be an argument in favor of assigning p-sets?
The implication here is that if the teacher had explained how to do the assignment, the students would have done it. Who's to say though that the students wouldn't have played video games during the teacher's own explanation?
Meanwhile, Darren Miller of Right(-wing) on the Left Coast has also discussed Garelick's book:
https://rightontheleftcoast.blogspot.com/2021/02/good-book-by-good-math-teacher.html
Here Miller discusses a phrase that traditionalists dislike, "growth mindset":
You might wonder, how can someone possibly object to "growth mindset"? Barry answers that on page 14:
I believe it's the other way around: success causes motivation more than motivation causes success.
Or, as I've worded that sentiment for years: self-esteem is the result of accomplishment, not the cause of it.
If success causes motivation, then what causes success? That's what traditionalists tend to forget. In addition, I think of "motivation" here as "not leaving p-sets blank." If students leave p-sets blank, then they will never taste success, no matter what the traditionalists believe.
Miller proceeds:
My favorite line comes from page 52:
You don't have to like math; you just have to know how to do it.
Students who don't like math tend to leave p-sets blank. Also, a reason that students say they don't like math is because they have to do p-sets all the time. I'd rather search for something that students like and, more importantly, won't leave blank.
That's all I have to say about Garelick's newest book for now. Don't expect Out on Good Behavior to be a side-along reading book on the blog at any time soon, if ever.
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