I'm torn as to whether to do "A Day in the Life" today. As I mentioned in October, two of the classes have a co-teacher (and indeed, I've subbed for that co-teacher too). But just like the first of October, there's a shortage of subs, and I'm pulled away from co-teaching to cover a special ed class. This time, it's science.
Half of the classes have another teacher or adult involved -- first, the AVID class has a snowman bingo game that's combined with the second AVID teacher's class next door. Then one of English classes still has a co-teacher. And one of the special ed science classes has an aide. Thus half of my six classes have someone else in charge. Today, it just so happens that the aided classes come earlier in the day, so I can observe those teachers to see what the later classes should be doing.
Three classes would ordinarily be worth describing in "A Day in the Life" (and I did indeed write one up for October 1st, a day similar to today). But this time, I want to keep the class description short because it's a long-overdue traditionalists' post.
I will briefly describe the science lesson, as usual to compare to the old charter school. This is actually an eighth grade class, and the students are learning about electricity -- including protons, neutrons, electrons, static electricity, and so on. If you recall, I made very little effort to teach this to my eighth graders that year.
There are several behavior problems in the classes that I cover solo. In the science class, one student keeps playing a few seconds of loud music on a Chromebook. The regular teacher's lesson plan devotes almost 15 minutes each to a review worksheet (for tomorrow's test), going over the answers to said worksheet, and free time to listen to music with headphones. I try to give extra time for going over the answers (since I want these students to pass tomorrow, plus there are four errors on the answer key for the worksheet), but still, that's no excuse to play loud music on the laptops.
In English, the students are reading A Christmas Carol due to the season. The students have a project where they decorate a Victorian-era house with quotes from the novel. In both classes, there are more problems with cleaning up at the end of class. Usually one of two things happens -- either I have the students start cleaning too late (and the bell rings with a big mess left in the room), or else I have them start too early (and the room gets clean, but then there's extra time and students leave the class before the bell). Today, both of those occur -- I call time late in the honors class and then early in the non-honors class. (Just like October 1st, the honors class is loud -- too loud for them to hear me when I say it's clean up time.)
I sing various songs today. For science I sing "Earth, Moon, and Sun" (as I did on October 1st), and for English I perform both "One Billion Is Big" and "Twelve Days of Christmath." I probably should have chosen only one song and used it for a clean-up incentive. (The co-teacher earlier called time with about 3-4 minutes to go -- which is about right, assuming that the students are actually listening and paying attention to me. The projector and timer could have helped me here.)
Today on her Mathematics Calendar 2019, Theoni Pappas writes:
The volume of this circular cone is 108pi cubic units. If its height is 4 units, what's the diameter of the cone's base?
The cone volume formula comes from Lesson 10-7 of the U of Chicago text:
V = (1/3)pi r^2 h
108pi = (1/3)pi r^2 (4)
27pi = (1/3)pi r^2
81 = r^2
r = 9
The cone has a radius of nine. Therefore the desired diameter is 18 -- and of course, today's date is the eighteenth.
OK, so today is final exam day as well as traditionalists' day. Actually, our main traditionalists have been more active lately, ever since Floyd Thursby Day and especially since my birthday. But I was distracted that week -- and not just because it was my birthday. Indeed, I wrote very little about my birthday this year, for several reasons:
- My birthday fell on the weekend this year -- a non-posting day. It also meant that I didn't have the opportunity to make a big deal about it in school (as in playing Conjectures with "Guess my age" on my birthday,
- My birthday fell on the day of the Putnam exam this year. Indeed, that's what I ended up posting about that week instead -- the Putnam competition.
- This year isn't a significant milestone birthday. Hmm, this year I turned 39 = 3 * 13. Unless I'm going to call it my "third Bar Mitzvah birthday," I've got nothing.
I didn't really mention traditionalists until yesterday's post, when I preserved some old traditionalist discussions about tessellations. But today, it's going to be traditionalism in earnest. (Otherwise, had it not been for the Putnam, I might have blogged about nothing but traditionalists last week.)
As usual, we begin with Barry Garelick. Here is his most recent post:
In a recent column in the Washington Post, Jay Mathews has written what has become the emblematic anthem against algebra II in high school
I can understand the argument against requiring algebra II for graduation, since at one time that was the case. Students only needed two years of math, and that usually consisted of algebra I and geometry. But his argument seems to be to get rid of it altogether and in its place have courses that are more relevant like statistics.
He ignores the fact that if you really want to pursue statistics, you will have to have some facility in the topics taught in algebra 2. So what is he suggesting? Students should take that in college?
So here we go again with Statistics and its prerequisites. Here's the problem -- many students sitting in Algebra II students ask, "When will I use this in real life?" And so Mathews wishes to reduce how often that question is asked by replacing it with another class, such as Stats.
But Garelick insists that Algebra II is necessary to understand Stats fully. And as a traditionalist, he's on the mild side here -- some traditionalists insist that Calculus is needed to understand Stats as well.
If the traditionalists are correct, then this is what we'd conclude:
- Stats is necessary to understand big data we encounter in the real world.
- Algebra II (or Calc) is necessarily to understand Stats.
- Thus Algebra II (or Calc) is necessary to understand big data we encounter in the real world.
- Therefore Algebra II (or Calc) is necessary in the real world -- and so the question "When will we use this in real life" should never occur, since it's use is so obvious.
Yet this question is asked by real Algebra II (and Calc) students. How about answering this, traditionalists -- how can people who can't pass Algebra II (much less Calc) be made to understand and interpret big data?
As a Geometry-focused blogger, I know what a big jump it is from our course to Algebra II. I'd love to reassure students at the end of our class that next is Stats, not Algebra II. And so I must side with Mathews, not the traditionalists here.
As usual, the main commenter in this thread is SteveH:
SteveH:
Jay Matthews doesn’t see or make the distinction between graduation requirements and requirements for all. He’s a Harvard educated fool. How many students does he think will get accepted to Harvard who can’t even pass Algebra II? How many degree programs in all colleges will be unattainable by these students? How many careers? How many careers require degrees containing classes and subjects that they might never use? How often do I need to use thermodynamics or reference a steam table? How often do I need to rebalance the flow of water in a piping system? Do I really need to know the molecular restructuring that happens when steel is annealed? Why should I know all the stuff I needed to know to pass the EIT test and then the Professional Engineering test? Never mind a rounded education when careers are, apparently, only about on-the-job vocational education needs.
Yes, SteveH, we teach many things that students might never use. Yet "When will we use this in real life?" mostly occurs in math classes. Therefore, math is the main class whose requirements we wish to reduce.
SteveH:
These people can never, ever admit that what they want in math is not what is needed by any STEM career path. They can’t admit that they are just talking only about those students who, for whatever reason, can’t handle math up through Algebra II. They would then have to explain why this low slope starts in Kindergarten. They desperately want to have the high ground on thinking and understanding and mathematical behavior. They don’t have it and they never will. Reality will bite them in the butt, but maybe they will just get students to accept that the “process is the product” so it will only bite them in the butt.
As usual, SteveH writes about the "low slope" of Common Core. His assumption is that had it not been for "low slope" Common Core, more students would be able to pass Algebra II, thus rendering my question (what about those who can't pass Algebra II) moot. Once again, SteveH, would your "high slope" math lessons make the question "When will we use Algebra II in real life" vanish?
By the way, the original Washington Post article to which this links has over 200 comments. There are some commenters who agree with Matthews and others who side with the traditionalists. Let me include some of these statements here:
nvamoderate:
A colleague's dissertation included a section where professionals were interviewed on the extent to which they used algebraic skills, especially Algebra 2, in their careers.
Doctors, nurses, lawyers & other professionals agreed almost to a person: nil, nope, nothing. Don't use those skills in my work.
Algebra as part of U.S. education goes as far back as Colonial America, but took hold in public education as early as the 1880's. It's past time for change.
All sorts of justification exist for teaching Algebra--but requiring Alg.2 for graduation is utterly ridiculous. Other, more practical classes in applied math, econ or other skills entirely should take the place of Alg.2 as a requirement to graduate HS.
By the way, the original Washington Post article to which this links has over 200 comments. There are some commenters who agree with Matthews and others who side with the traditionalists. Let me include some of these statements here:
nvamoderate:
A colleague's dissertation included a section where professionals were interviewed on the extent to which they used algebraic skills, especially Algebra 2, in their careers.
Doctors, nurses, lawyers & other professionals agreed almost to a person: nil, nope, nothing. Don't use those skills in my work.
Algebra as part of U.S. education goes as far back as Colonial America, but took hold in public education as early as the 1880's. It's past time for change.
All sorts of justification exist for teaching Algebra--but requiring Alg.2 for graduation is utterly ridiculous. Other, more practical classes in applied math, econ or other skills entirely should take the place of Alg.2 as a requirement to graduate HS.
My response: I agree. Algebra II should not be required for graduation.
Molly Rogers:
Statistics and all its components can't effectively be taught if you don't understand complex algebra. Something that's taught in algebra II. I'm a hopeful statistics major, and the degree requires all the way up to calc 4.
Things such as research or engineering also require higher mathematics. Hell, physics itself requires atleast precalculus.
Americans are already extremely bad at math. No, not everyone will need it, but we're going to have a bleak future if none of our kids learn it.
My response: Rogers is clearly on the traditionalists' side. OK, so Calculus IV is needed to be a Stats major, but what about the stats that people encounter everyday in real life? Surely Algebra II can't be necessary to understand and interpret real-life stats, much less Calc IV.
Robert from Melbourne, Australia:
Students who study Algebra II, or indeed any other subject in Mathematics at High School level mostly do not know what they want to do when they grow-up. Can't these people who want to continue this dumbing down of education; this time by removing Algebra II from the syllabus, see this? If students wish to study at university, inter alia, certain branches of engineering, physics or mathematics, then they will need these topics.
I think that 'all doors should remain open' for students for as long as possible while they are at school. If students are obviously not capable of studying these topics in mathematics then they should be 'streamed' into a group where they are not required to study them. Other students should be given the privilege of studying these important mathematical topics.
My response: "All doors should remain open" reminds me of SteveH, who often uses the phrase "closing doors" to refer to what he accuses the Common Core of doing. (Of course, Robert states that he is Australian, so he's unaffected by Common Core.) To SteveH and Robert, Algebra II opens doors, but to others, the subject closes doors by lowering their GPA and blocking them from studying a non-STEM subject. They'd hardly call studying Algebra II a "privilege" at all.
physicsteacher:
It's not easy to predict what someone will "need" in the future. Imagine someone who decides to major in engineering in their senior year of HS having already missed the boat.
When I was a teacher I was trying to get chem certification and so I was taking chem classes at NOVA. In a biochem class most of the students there were trying to become physician's assistants, but their insufficient math (and physics) skills severely impaired their learning in biochemistry. In the rates of reaction section, a little bit of algebraic manipulation was necessary, but that task was so far beyond the students in that class that the instructor dropped that topic entirely.
My response: And what did that hypothetical senior who "missed the boat" say when he or she was taking math in Grades 9-11? Was it something like "When will we use this in real life?" This commenter states that math and physics are very useful to the Biochem students -- and yet back when they were in math class, they complained that math was irrelevant. How does this physics teacher plan to make "When will we use this in real life?" vanish from math -- and Physics -- classes?
padnactap92:
I struggled mightily in Algebra II, such that I no longer remember what we were suposed to learn but the sheer struggle of not failing because I couldn't figure matrices and probability out. (It didn't help that our teacher couldn't do the assignments herself.) I did fine in Algebra I, Geometry, even trig and calculus (I excelled at calculus, though I no longer remember it.) I was ok at statistics when I got to graduate school. I think that in terms of intellectual rigor and problem solving skills, geometry is the most useful, especially working out unknowns with 2 or 3 intermediate steps and writing out proofs.
My response: This Geometry blogger agrees! It's interesting that this poster would struggle in Algebra II yet did fine in Calculus. Then again, the two topics mentioned there (matrices and probability) aren't generally relevant to introductory Calc classes.
That's enough for this article. Here are more recent traditionalists' threads that are worth discussing:
Molly Rogers:
Statistics and all its components can't effectively be taught if you don't understand complex algebra. Something that's taught in algebra II. I'm a hopeful statistics major, and the degree requires all the way up to calc 4.
Things such as research or engineering also require higher mathematics. Hell, physics itself requires atleast precalculus.
Americans are already extremely bad at math. No, not everyone will need it, but we're going to have a bleak future if none of our kids learn it.
My response: Rogers is clearly on the traditionalists' side. OK, so Calculus IV is needed to be a Stats major, but what about the stats that people encounter everyday in real life? Surely Algebra II can't be necessary to understand and interpret real-life stats, much less Calc IV.
Robert from Melbourne, Australia:
Students who study Algebra II, or indeed any other subject in Mathematics at High School level mostly do not know what they want to do when they grow-up. Can't these people who want to continue this dumbing down of education; this time by removing Algebra II from the syllabus, see this? If students wish to study at university, inter alia, certain branches of engineering, physics or mathematics, then they will need these topics.
I think that 'all doors should remain open' for students for as long as possible while they are at school. If students are obviously not capable of studying these topics in mathematics then they should be 'streamed' into a group where they are not required to study them. Other students should be given the privilege of studying these important mathematical topics.
My response: "All doors should remain open" reminds me of SteveH, who often uses the phrase "closing doors" to refer to what he accuses the Common Core of doing. (Of course, Robert states that he is Australian, so he's unaffected by Common Core.) To SteveH and Robert, Algebra II opens doors, but to others, the subject closes doors by lowering their GPA and blocking them from studying a non-STEM subject. They'd hardly call studying Algebra II a "privilege" at all.
physicsteacher:
It's not easy to predict what someone will "need" in the future. Imagine someone who decides to major in engineering in their senior year of HS having already missed the boat.
When I was a teacher I was trying to get chem certification and so I was taking chem classes at NOVA. In a biochem class most of the students there were trying to become physician's assistants, but their insufficient math (and physics) skills severely impaired their learning in biochemistry. In the rates of reaction section, a little bit of algebraic manipulation was necessary, but that task was so far beyond the students in that class that the instructor dropped that topic entirely.
My response: And what did that hypothetical senior who "missed the boat" say when he or she was taking math in Grades 9-11? Was it something like "When will we use this in real life?" This commenter states that math and physics are very useful to the Biochem students -- and yet back when they were in math class, they complained that math was irrelevant. How does this physics teacher plan to make "When will we use this in real life?" vanish from math -- and Physics -- classes?
padnactap92:
I struggled mightily in Algebra II, such that I no longer remember what we were suposed to learn but the sheer struggle of not failing because I couldn't figure matrices and probability out. (It didn't help that our teacher couldn't do the assignments herself.) I did fine in Algebra I, Geometry, even trig and calculus (I excelled at calculus, though I no longer remember it.) I was ok at statistics when I got to graduate school. I think that in terms of intellectual rigor and problem solving skills, geometry is the most useful, especially working out unknowns with 2 or 3 intermediate steps and writing out proofs.
My response: This Geometry blogger agrees! It's interesting that this poster would struggle in Algebra II yet did fine in Calculus. Then again, the two topics mentioned there (matrices and probability) aren't generally relevant to introductory Calc classes.
That's enough for this article. Here are more recent traditionalists' threads that are worth discussing:
https://traditionalmath.wordpress.com/2019/12/10/puff-piece-dept/
Just read a rambling article in the Atlanta Journal Constitution by Maureen Dowd that points fingers and doesn’t come to any conclusions. Main point: math ed has been bad in GA for many years so why blame Common Core.
Let's skip down to what Garelick says about Integrated Math:
Lastly, she talks about Japan’s “integrated approach” to math, which Georgia will emulate. Japan isn’t the only country to take an integrated approach to math in high school; many European countries do this also. But they do it fairly well. The U.S. has done a horrible job of it; one need only look at the integrated approaches used here: IMP, Core Plus, MVP math.
Hmm, I wonder what makes Japan's and Europe's Integrated Math good and ours "horrible." I also wonder whether Garelick would consider Saxon Math -- a curriculum many traditionalists like in the elementary years but is integrated in high school -- to be "good" or "horrible."
Let's see what SteveH has to say about this article:
SteveH:
There are so many problems and so many layers and these people can’t separate them. It’s all guess and check. They claim to know about mathematical understanding and problem solving, but they fail at it miserably, especially the part that requires them to be honest about all of their cargo cult assumptions.
At this point SteveH goes on to discuss "Everyday Math" (U of Chicago elementary texts) and says nothing about the high school curriculum. Of course, we already know what he believes about Integrated Math -- that it "already lost the battle" (despite its prevalence in Japan and Europe).
Here is my birthday post:
Just read a rambling article in the Atlanta Journal Constitution by Maureen Dowd that points fingers and doesn’t come to any conclusions. Main point: math ed has been bad in GA for many years so why blame Common Core.
Let's skip down to what Garelick says about Integrated Math:
Lastly, she talks about Japan’s “integrated approach” to math, which Georgia will emulate. Japan isn’t the only country to take an integrated approach to math in high school; many European countries do this also. But they do it fairly well. The U.S. has done a horrible job of it; one need only look at the integrated approaches used here: IMP, Core Plus, MVP math.
Hmm, I wonder what makes Japan's and Europe's Integrated Math good and ours "horrible." I also wonder whether Garelick would consider Saxon Math -- a curriculum many traditionalists like in the elementary years but is integrated in high school -- to be "good" or "horrible."
Let's see what SteveH has to say about this article:
SteveH:
There are so many problems and so many layers and these people can’t separate them. It’s all guess and check. They claim to know about mathematical understanding and problem solving, but they fail at it miserably, especially the part that requires them to be honest about all of their cargo cult assumptions.
At this point SteveH goes on to discuss "Everyday Math" (U of Chicago elementary texts) and says nothing about the high school curriculum. Of course, we already know what he believes about Integrated Math -- that it "already lost the battle" (despite its prevalence in Japan and Europe).
Here is my birthday post:
Dana Goldstein, a New York times reporter, asked on Twitter if there were any teachers willing to be interviewed for an article she was writing. I responded (I was on Twitter at this time), suggesting she view the video of a talk I gave in which I mention some of the problems with Common Core. https://www.youtube.com/watch?v=RlLbXZOoAMU (I even told her to start at minute 19:24 to save her some time).
At this point, Garelick complains about "strategies" the Common Core emphasizes for addition -- and how they are taught when the traditionalists would prefer standard algorithms and memorizing tables:
For example, while the process of “making tens” is used in Singapore’s “Primary Math” first grade textbook, it is one of several strategies presented that students may choose to use. (See figure below for how “making tens” was explained in my 3rd grade textbook—and introduced after mastery of the standard algorithm for addition).
(I omit the figure. Click the link above if you really want to see it.)
There is no requirement that I’ve observed in Singapore’s textbooks that forces first graders to find friendly numbers like 10 or 20. This is probably because many first graders likely come to learn that 8 + 6 equals 14 through memorization, without having to repeatedly compose and decompose numbers to achieve the “deep understanding” of addition and subtraction that standards-writers feel is necessary for six-year-olds.
Here's what Garelick leaves out here -- at the start of the year, the first graders know 0 (none) of their addition facts, and by the end of the year, they know 100 of them (that is, the entire addition table from 0 + 0 to 9 + 9). They don't magically memorize these facts -- there is a process. And during this process, there's a point where they've memorized some of the facts -- more than 0 but less than 100.
And so we ask, which facts are they likely to memorize first? That's right -- among the more easily memorized facts are those involving "friendly numbers" like ten!
Garelick tells us that first graders should have learned 8 + 6 through "memorization" -- that is, any other method is inferior. OK then, so we ask Garelick, in what order do they memorize 8 + 6 as compared to the other 99 members of the addition table? Do they learn 8 + 6 before 9 + 5, or do they memorize 9 + 5 first? (After all, there's likely some point in the memorization process where they've memorized one so far, but not the other yet.)
And of course, the claim I make is that among the ones memorized first during the process are the ones involving ten, such as 8 + 2. Doubles are also more easily memorized, so not only do we expect 6 + 6 to precede 8 + 6, but even 8 + 8 might precede 8 + 6 as well.
Instead, Garelick states that this making ten process should be taught "after mastery of the standard algorithm" (and the addition table). But by then, the process of memorization is complete -- there's no need to make tens to find 8 + 6 by then. Instead, making tens should be taught during the process of memorizing the table.
Let's just go straight to SteveH now:
SteveH:
Why are parents even looking at the worksheets? My parents never did that at any grade level or go to any “open house” on math. There were none. I got to calculus in high school, but my math brain son needed our help in K-8. Why is that?
OK, I concede that a math "open house" was unnecessary before Common Core. But now suddenly for parents even to look at the worksheets is bad! Parents help their students all the time in many subjects, not just math, before and after the advent of Common Core. Proclaiming that he "got to Calculus" (without any help) starts make him sound exceptional, not typical of the pre-Core era.
And not to leave traditionalist Bill out, here's one from the Joanne Jacobs website:
Unemployment rates are very low. College costs are very high. Instead of four, five or six years of higher education, more young people are seeking white-collar and “new collar” apprenticeships, reports Farah Stockman in the New York Times.
And here's what commenter Bill has to say here:
Bill:
It probably takes more training to be able to cut and style hair that it did for me to work in information technology at my first job, and I didn’t need any type of certification when I started many years ago
IMO, arbitrary license/certificate requirements by the state is simply asinine (just another regulatory method to chisel money out of people who would like to work in those professions)
Of course Bill has a point that not everyone needs to go to college -- good, high-paying jobs need to exist for those without a college degree.
But then Bill also refers to licenses to cut hair. This is now a political and economic argument -- do licenses protect consumers by increasing the quality of hair stylists, or do they only block qualified stylists from getting a job? At this point, this is no longer an educational discussion, and so I make no comment one way or the other.
Bill's comment, though, is partly in response to another commenter, SAG:
SAG:
This is how entry into the professions use to be. President Lincoln apprenticed to become an attorney. It wasn’t until the early 20th century when professional organizations formed such as the ABA began putting caps on who can become an attorney. That’s why it is so difficult to find quality, affordable attorneys. Everything is out of wack now. Licensing regulations have made it difficult for those with limited education, or an inability to spend thousands of dollars to obtain degrees, to gain employment. It’s like a vicious circle: schools no longer offer apprenticeships as a viable option.
I've mentioned Lincoln's education on the blog in the past. I was impressed by how he taught himself to make sound, logical arguments -- by reading Euclid's Elements on Geometry.
The original argument is about whether law school should be needed to become a lawyer. This is a tricky one. Students currently must take Algebra II to be considered as lawyers -- only because they need a degree to become a lawyer and Algebra II to get a degree. The solution proposed by the traditionalists here is to drop the degree requirement to become a lawyer -- not to drop the Algebra II requirement to get a degree.
According to the link, "some college" is required to join the alternate program here in California, but I don't know how much math that is. I hope that Algebra II isn't required -- but hey, let's at least make them take Geometry, since it worked for Lincoln.
SAG:
There has been a lot of lawsuits against states and their licensing boards forcing ethnic hair braiders out of business because they don’t have a cosmetology license; despite the fact that beauty schools do not teach ethnic hair braiding!!! That’s just one issue that is so egregious. However, it seems everything requires some ridiculous credential. This is creating a serious problem because schooling has become bureaucratic and beholden to the dictates of the Democratic party, they are not willing to offer creative ways to prepare students for adulthood.
This is why Bill mentioned hair stylists -- in response to SAG here. This comment has become political (as many traditionalists' posts do) since SAG mentioned "Democratic party" -- but this can also be interpreted as an indirect reference to teachers unions. Again, I consider the question of whether licenses are truly necessary to become a stylist to be off-topic for this blog. (This post has also become racial, as many traditionalists' posts also do. The original article to which Jacobs links mentions both race and gender.)
OK, I guess I can't avoid the elephant in the room -- today the imp****ment is official. Well, this is a traditionalists' post, and I already mentioned politics in this post. So I may as well write the political word out -- today the impeachment is official. For only the third time in our history, a President has been impeached -- A. Johnson, Clinton, Trump.
But now I must post the first semester final exam. Here are the answers to the questions on the final:
BBBCA AADAB BBADA CADBC ABBAA BDDAC DDBCC ADBBA BDABC ADDCA
BBBCA AADAB BBADA CADBC ABBAA BDDAC DDBCC ADBBA BDABC ADDCA
No comments:
Post a Comment