Bob, Gwen, and Lines of Best Fit

I have no excuse for this article. Except the new Fosse/Verdon ads are showing up. Also, consider “lines of best fit” a descriptive, not technical, term.

“Hey, Gerardo. Take a look at this.”

Gerardo, my new TA, reluctantly removed his air pods. Like all my graders, he’d been my student for three classes before asking if I could take him in third block, but the rest of my TAs were chatty folks. Gerardo grades with fantastic efficiency, but the rest of the time he’d really rather be somewhere else working on his English essay.

“What the hell…heck is that?”

VerdonFosse1

“Well, this is an image from a famous dance. I took some images from it and started comparing movement lines for fun.”

Gerardo shot me a look. “Fun? You’re so weird.”

“Yeah. But it beats grading. So take a look. What do you notice?”

“You mean, what are the red lines telling me?” Gerardo did look, and think. But shook his head. “I don’t see anything.”

“Who’s taller?”

“What, that’s a trick question? The guy is.”

“Yep. The guy is Bob Fosse, one of the most famous choreographers in history, and Google says he’s 5’8″.  The woman is Gwen Verdon, his wife, and she’s 5’4″.”

“So what does….wait a minute. Gerry looked again. ” You’ve got the other lines at their butts and knees.”

“Yep.”

“And they’re, like, the same.”

“Exactly. So what does that mean?”

“She has to have really long legs. Yeah, I see it now. Look how far below her shoulders are. Her body’s a lot shorter.”

“Good! Try this one.”

VerdonFosse2

Gerardo was interested, now. “Okay, I get this. Her hips are way, way out. His aren’t. But what’s the line for…oh, I see. You have the lines right on their hips, and there’s all this space between her body and the line. But the line goes right through his body. So that means…he can’t push his hip out as far.”

“Nice. Now here’s two at once. What do they have in common?”

FosseVerdon3FosseVerdon4

Gerardo was hooked, now, leaning into my desk closely. Ideally, my trig students were getting some work done, but we were pretty intent on this.

“Okay, so the top red line on this one is about their height…it’s the same. How is that happening?”

“Good catch.”

“Their knees are lined up, their heads are lined up…wait. Their…what, hips? His is lower!”

“Look at his feet.”

“Oh, wow. He’s got way more give in his feet. So he’s using his feet to push up while his knees are bending down. Oh, you have it circled in the next one. So he’s able to bend down to her height on his toes using only his knees.”

“It’s unusual, because she’s clearly more flexible than he is in the hips, but he’s got very bendy feet. Try this one.”

fosseVerdon6

“Okay, those vertical lines are showing the distance.”

“Yeah. Later on I do slopes to show the difference.”

“What, you’ve got more?”

“You could always grade.”

“No, no. But on this one, I can’t figure out what it means. Her leg is straight up and down. His is all bent forward…oh, I see. He has to bend forward, to do that thing with the shoulder. But she can keep her whole body straight.”

“Neat. Next up.”

fosseVerdon5

“Oh my god. How does she do that with her leg? And she’s almost straight up. She is straight up. He’s kind of tilted just to try and get his leg up nearly as much. Not that I could lift my leg more than an inch.”

Despite his complaints, Gerardo had moved far in to check out the pictures.

fosseverdon7

“He’s way higher.”

“Yep. Fosse was a jumper.”

“But the other lines show his leg is below his waist. Hers is above…hey, she’s lower than he is in the air, but her leg is higher–not just relatively, but like higher than his. ”

“How about this one?”

FosseVerdon8

“These are getting easy. She’s standing straight up, while he’s having to bend to get the same results. And this one, she’s got the flexible hip thing going, while his is straight.”

fosseverdon9

“Here I was trying to show that she is turning faster. But I honestly don’t know if that’s a problem, if they’re supposed to time it perfectly, or what. I was just trying to show the turn.”

FosseVerdon12

“Yeah, you can see he’s barely started when she’s halfway around.”

FosseVerdon13FosseVerdon15

“So he’s having to bend to get the same positions that she can do standing straight up. What part of the body allows that?”

“Hips, definitely. Knees? Good question. Here’s a sequence of three that probably look strange, but it’s like a fake exaggerated run.”

FosseVerdon16FosseVerdon17FosseVerdon18

“Jeez, her leg is at 90 degrees, and her body is tilted over. What is she holding herself up with–just her foot?”

“And some pretty impressive legs and abs, I’m thinking.”

“He’s solid on that one, too. But in the next ones, her body is practically an L.  He’s balancing. Like throwing his weight forward to get his leg up. In the last one, he has his leg up as high as hers but tilts over a bit to do it.”

“Well, keep in mind that on relative terms, she outranks him. Gwen Verdon was probably the best dancer ever seen on Broadway, and the rest of the best were trained by her. In her prime, no one was better at that time. Fosse was a groundbreaking choreographer and an excellent dancer, but not in the same league as a performer or star. I know nothing about dancing, so I can’t tell you how the two of them are rated by others, nor do I have any clear idea of who was “better”.

“So this was a long time ago?”

“Yes, Damn Yankees is sixty years old. Try this group of pictures of a sequence of two jumps.”

FosseVerdon19FosseVerdon20

“He’d have been a damn good basketball player.”

“I know, his vertical jump stats had to be amazing. ”

“You know what else? And you didn’t red line it, so maybe I’m getting good at this. He’s the one who’s straight up. She’s the one bending to balance and get more flight.”

“Whoa. I didn’t catch that. You’re right.”

“Unless maybe the middle picture is just her on the way down?”

“No, I caught the first two on the way up and the last one, after they’d switched sides, at as close to peak as I could. That’s another sign that he’s much more comfortable at jumping than swinging his hips.”

“Well. As it is for most guys.”

“Ha. True.”

FosseVerdon21

“This is obvious. She’s got a straight leg, up and down, and then just a tilt of her body. He’s tilting his body one way to get the hip out, then the other way for the…whatever you call it, the show. Hey, you know, this really is a good use of slopes.”

“Thanks.”

“What the fuck…oh, sorry. What is happening with her leg!”

FosseVerdon22a

“I love this one, because it’s related to the reason I became fascinated with this dance.”

“But man, look at it! He’s at his highest point and she’s got a whole additional gear yet!”

“And the funny thing is it makes Fosse look almost clumsy, which he wasn’t. Not many male dancers could do anywhere near as well.”

“How come you got so interested in this dance you’re breaking it down image by image?”

“My interest was first.  I made the images for math class, but much later.   I was watching a documentary once years ago where Gwen was talking about this dance and how Bob Fosse was always yelling at her to jump! because she can’t fly like he does.  I’ve been watching musicals my entire life, but I never really considered comparing dancers. When I was a kid, I always wondered why Cyd Charisse was brought in to dance with Gene Kelly…”

“Who?”

“Remember that movie we watched with Princess Leia’s mom at Christmas?”

“Oh, and then  she died! Yeah, the musical about silent movies. That was good.”

“So you remember how in the big dance number at the end, it wasn’t Princess Leia’s mom?”

“The brunette lady with the legs.”

“Exactly. I used to wonder why they brought her in. But when I grew up, I realized it was because Debbie was a  movie hoofer, while Cyd Charisse rivals Verdon as the best there is. So when I found the dance on Youtube, I analyzed the whole dance and noticed differences that went both ways.”

“You do that with a lot of dances?”

“No. Most famous dances with men and women aren’t doing identical steps–and most of the ones that do exist are tap dances.”

“So you made these pictures?”

“I was having trouble sleeping one night and  watched Cabaret, which he directed. That got me thinking about this dance, and wondering if I could capture their differences in a way a student could analyze.”

“For class?”

“Yeah, maybe. It was just a whim.”

fosseverdon23

“How does she hold that balance? Even for a second? I mean, he looks good, but normal.”

“Here’s another spin. This time, it goes from a spin into her going on the floor into a goofy tug and him pulling her by the leg. I should say that some of their spins were perfectly synchronized. I was more curious as to what it meant.”

FosseVerdon24

“Ha, I like that little arrow you put! He just jumps like it’s nothing.”

“Wanna see the actual dance?”

“Wait. That’s all the pictures? You mean, there aren’t like, five hundred?”

But Gerardo watched the clip closely, despite the clear implication that I’m a tad, oh, obsessive.

“OK, I get it now. If I’d watched this first, I’d say they were completely identical. But looking through those pictures lets me see the differences.”

“Thanks. Now. You’ve been a really good sport, but can you do me one more favor?”

Gerardo looked warily skeptical. “What?”

“These pictures are from a recreation of that dance from a new show coming out on their lives. I don’t have any red lines drawn, but do you notice anything?”

FakeFosseVerdon2

He snorted. “Yeah, right, like I’m going to see any  differences…wait a minute. Their hips and knees aren’t even. She doesn’t have the long legs.”

“And?”

Gerardo sighed, but complied. Suddenly he leaned forward, and smiled. “Got it. He’s the one dipping his hips! She’s holding them straight.”

I startled him, and the class, by thumping my desk. “I am justified.”

“What?”

“That’s the whole reason I asked you to look through those pictures. Because when the new trailer came out, all I could think was hey, they’ve got it backwards! and I wanted to have someone else know. Thank you, Gerardo. I’ll give you an A.”

“All TAs get an A. Is the guy a better dancer than the lady, or just more flexible?”

“Well, they’re both actors, not dancers. But Sam Rockwell, who’s playing Fosse, has danced in almost all of his movies and you can see he’s really loose-limbed, with hip action. Michelle Williams famously recreated one of Marilyn Monroe’s dances and got nominated for it, but it may or may not be significant that they cut away during a lot of the dips and weaves. Or maybe these few seconds aren’t representative, of course.”

(Note: I didn’t bore Gerardo with this picture, but hey, this is my blog so I’ll bore you. Here’s one example:

MichelleMarilyn

Williams, on the right, has to turn her entire body back to kick backwards. Monroe, who had been well-trained to use her body in dancing, can turn her head and neck, kick her leg back–farther, no less– while keeping her body straight.)

I’d like to tell you that Gerardo then asked me dozens of questions about movie lore, but instead he went back to modern music on his air pods. But I felt better for the validation, and got some grading done. While I told the story uninterrupted,I did take some time for student trig questions, pesky though they were.

If you’re unfamiliar with the story, “Who’s Got the Pain” is a throwaway number from “Damn Yankees”. For years, it was considered a time-waster and often cut out of TV broadcasts. But dancers and choreographers treat the scene like the Talmud, studying it endlessly. And over time, “Who’s Got the Pain” became known as the only time Fosse and Verdon danced together in a production movie number. Definitely watch the dance all the way through if you’ve made it this far into the read.

 


Lawton Chiles Middle Academy: When the Cop Shows Up

Our school has a ritual, a long-standing one. We start the announcements with the pledge. For the first five years of my employment, it was an enjoyable thing. Everyone stood up. If a kid didn’t stand up, the teacher exhorted him or her jovially, and the kid stood up, whining. It took less than a minute.

Cue Colin Kaepernick and his foolish, self-destructive campaign. Many football players started “taking a knee”, which was fine. Stupid, but fine. But then other kids would just refuse to stand up.  Teachers would, as usual, exhort the kids to get up, and they usually would. Until a parent got the superintendent involved, and the superintendent sent out a note saying that under no conditions could a teacher require a student to stand up. These kids, by the way, are not even remotely interested in the NFL and why Kaepernick is taking a knee. They have all sorts of reasons from “I hate Trump” to “The flag’s racist” to “I just want to sit and look at my phone”.

To me, that’s bullshit. It’s our school ritual. If we can’t tell the kids to stand, or kneel, and the kid is allowed to sit on his or her phone during the Pledge, then what’s the point of the Pledge? So I take phones away from kids and they go screaming to the admins, but the admins are firm, so far–the teacher can’t tell you to stand, but the teacher can take your phones.

Most of the time it’s been ok, and I’ve gotten around it, but this semester I’ve got a class of kids who literally refuse to stand. Just 12 of 35 get up at all. That’s far too many to police, so now I just say the Pledge with the kids who stand and randomly remove phones, which keeps that violation in line.

Most teachers in our school agree; I’m not alone in arguing that if we can’t enforce minimum behavior for a school ritual, one that’s been going on for decades, then a) that’s a bad thing and b) we should stop the Pledge and “let the Commies win”, as a particularly right of center student of mine used to call it.

I used to be annoyed at the Pledge for “under God”–as an agnostic, I think the rebuke to non-believers is a deliberate slur that came out of the anti-Communist era and would still be happier if the phrase was dropped. But in today’s world, with an immigrant population that increasingly takes America for granted, the Pledge had become an enjoyable ritual until Kaepernick and the NFL ruined it all.

If schools are not allowed to insist that students simply stand or kneel respectfully during the Pledge, then it should be dumped. At this point, I hate the first five minutes of class, and have asked that the Pledge be dropped from announcements.

All that is prelude to this story about a Florida kid “getting arrested for refusing to say the Pledge”. Key details:

  • This was a substitute teacher.
  • The substitute teacher was a Cuban immigrant.
  • The kid refused to leave the room without disruption.
  • The kid was arrested for threats.

So the media headlines are, essentially, lying. The kid was not arrested for refusing to say the Pledge, unless the police want to speak to Jussie Smollett for buying a Subway sandwich.

The shocking part, to me, was the teacher’s comment to the kid, until I read well into the newspaper stories. As is usually the case when demographics conflict with the narrative, the media holds back or delays release of demographics. So it’s well into the story before you learn  the sub, Ana Chavez, is an immigrant, while the kid in question is, I think, a non-immigrant African American.

We come, once again, to the clash of “Who/Whom?”. Normally, immigrants can say things that white Americans can’t, so Ana Chavez probably thought she was secure in her ability to criticize a snotty little kid who wouldn’t stand for the flag. Notice that she actually put her comment in the report!

But no one warned Ana of the dire fate that awaits the loser of a narrative clash. On the plus side, Ana Chavez is a common name, so she can leave town and sub somewhere else.

The administrator decision to remove the student from the classroom isn’t surprising. We have a nationwide sub shortage. If the sub had said “remove this kid because he’s wearing a blue shirt that’s hurting my eyes”, he probably would have removed the kid and took him to another room saying “Sorry, don’t worry, this is no big deal.” Maybe dump the sub, maybe not, depending on the scarcity, the sub, and the kid.

What I don’t understand, and can’t without more information, is why the school resource officer was called in.  I can think of two possibilities off hand. First, the administrator came, the kid refused to go, and then the SRO showed up. Second, the administrator and the SRO came together, and I can only conceive of that occurring if the student was utterly out of control–or the substitute teacher made it sound that way.

Then I looked up the school and considered a third possibility:  Lawton Chiles is a fairly rich, very high-achieving middle school (supposedly ranked 11th in the entire state) and is also 15% black, with  most  blacks scoring proficient on state tests. Perhaps they don’t have many discipline problems, so the dean and SRO are twiddling their thumbs waiting for each call. Unlikely, but I offer it up.

However, this part seems quite clear:

The student was asked more than 20 times to leave the classroom by the dean of students and the school resource officer intervened, asking the student to leave the classroom and the student refused, the police say.

Police say the student eventually left the classroom and created another disturbance, making threats while he was escorted to the office at the school.

They didn’t walk into the room and arrest him. They asked him to leave. More than twenty times. Many, many school officials read about the events at Spring Valley and learned their lesson well. They made no effort to physically force the boy from the room.

Eventually, the sixth-grader did leave, probably making threats. But it took a long time, and during that time, that student had directly disobeyed a police officer. Once he left, he apparently made more threats.

Do I think he should have been arrested? Absolutely not, on the evidence.

But my primary reason for writing this short piece is to remind people, once again, that the underlying issue becomes irrelevant once a cop shows up. Students–particularly  black students, it seems–need to learn a fundamental truth: don’t treat a cop like a teacher.  The minute the cop walks into the room, the facts on the ground shift unalterably.

I wish more of the media coverage would focus on this, which is of course a foolish dream. The media wants to convince everyone that schools are racist, that black children are deliberately put on a school-to-prison pipeline because of white teachers’ intolerance and bigotry.

Perhaps consider this: the Lawton Chiles Middle Academy case is a big step up from Spring Valley. The dean and the SRO acted with restraint in removing the recalcitrant student from the classroom. Perhaps they arrested the young boy because they can’t allow students to holler violent threats with impunity. Whatever their reason, reports make it clear they didn’t just charge in and lock the kid up.

Perhaps people should tell Dhakira Talbot, the boy’s mother, that while she might wish the school had handled things differently, her most pressing responsibility is to tell her son that no matter what he feels about the flag, or his unjust treatment, he must understand the facts on the ground once a cop shows up to talk to him. Obey the cop. No matter what. Things will get straightened out later.

They can tell her white parents tell their kids the same thing, if it helps.


Not Really Teaching English Once More

Have I ever gone through the steps that led to my teaching ELL?

Year 1

Back in August 2016, the day before school started, my principal walked into my classroom, which he rarely does, and I said, fearfully, “you’re not taking my pre-calc class, are you?” because I rarely get to teach precalc and principals only walk into your room when they’re asking for something you won’t like, and the only thing I wouldn’t like was losing my precalc class. The other upper math teachers complain, which isn’t fair, because the state tests show my kids do as well as theirs on average (their top kids do reeeeeeally well, but the rest of the kids do horribly, while my top kids do well, but everyone else does respectably.)

But no, he wasn’t taking my precalc class, he was taking my prep period. The non-tenured mostly ELL teacher who was on track to for termination in the upcoming year had taken a new job with less notice than is legally allowed. It’s not well known, but teachers aren’t allowed to quit without some degree of notice, usually between 30 and 60 days, unless the district gives permission. Otherwise, they won’t be able to teach anywhere else in the state. My principal and the English department felt the rejected teacher should be allowed to take a new job under the circumstances. English teachers hate taking extra preps, but they scrounged up two volunteers and suddenly, someone remembered I have an English credential.

So with no notice, I started ELL instruction. I had four classes planned for the following semester. But despite an ongoing hiring campaign, no one would accept the job. With a whole bunch of juggling,  Bart was handed one of my trig classes and I taught ELL the entire year. That was year one. Articles: The Things I TeachNot Really Teaching English,ELL isn’t Language Instruction

I expected it to be an anomaly. I loved the kids, and my first, large, ELL class remains my favorite both for the students and the experience. I’m currently teaching Marshall and Kit (from the Things I Teach), both of them juniors, doing well. Juan, Anj, and Tran are all academic rock stars, with several AP classes (including English) to their credit. But the political and instructional aspects of ELL bothered me tremendously, and I was happy to be out of it.

Year 2

Then almost exactly a year ago right now, an AVP walked into my classroom just a week before the first term ended, just as I had convinced myself I was actually going to get the pay cut of a normal prep period, to ask me if I’d help them out by teaching the ELL Connections class. She didn’t say why. In fact, I’d asked the principal a month earlier to confirm that there’d be no additional class coming my way, and he assured me there were no plans to use me. Which, well, wasn’t true. He couldn’t mention that he was in the process of firing the primary ELL teacher, the 20 year expert, which he achieved in three months from start to finish, including investigation. They collapsed two of her courses into one, and gave me the other.

The second year (2017-2018) wasn’t particularly enjoyable. The kids had hated the fired teacher, and had enjoyed three months of substitutes and movies. None of them had any particular interest in learning English. I had two Chinese boys who wouldn’t (and won’t) stay off their phones, one Afghani girl who liked (and likes) to cause trouble, a German girl who was seriously pissed off at her dad for bringing her to America (I hear she’s forgiven him), a Mexican boy from my previous year who went from being the weakest student to the second strongest simply because all the others moved on, a Salvadoran girl who was friendly and helpful and hardworking unless she wasn’t, and three Guatemalans who chattered constantly in Spanish, generally refusing to even try to speak English.

Simply getting them to enjoy being a class, to tolerate each other, took a long time, although I’m pleased to say that the Disney/dead animals day was the turnaround I took it for. But as far as actual progress in learning English went, there was none. In fact, I didn’t spend much time teaching them English at all, not directly. I taught content in other areas and got them thinking and talking, which trust me was more than enough of an accomplishment. But even if I’d wanted to teach actual English, I had no curriculum.  No books. All the stuff from last year disappeared from my old room (I was using the previous teacher’s room, until the kids asked if we could just stay in mine).

One significant improvement over the year before, though, was Miko.

Miko was a science teacher with an English credential. But he loathes the new state science curriculum. So he volunteered to be the permanent replacement that I’d been temporarily, and now he’s an English teacher with a science credential. He likes running things, he likes after-school activities, teaching drama, cheerleading, stuff like that. You might have noticed that between the two of us, we could open a school. He could be in charge, even.

So after the 20 year expert got fired, Miko was put in charge, and made changes that I’d advised the year before. He reduced the infuriating “three English classes” requirement, arguing as I had (but more successfully) that just two classes would give students needed time to build credits towards graduation. He was considerably more aggressive about moving students up into second year, ending the absurd practice of forcing highly educated students who read English at a 9th grade to learn “cup”, “stand”, “pencil”, and “sit”.  And, as a guy who likes to be in charge, he took a very hands-on approach to the kids’ status, so I had someone to talk to about behavior problems and frustrations.

I apparently impressed him, too, because he asked me to teach two courses of ELL in the next year (2018-19). How to put this politely? I demurred, saying that I’d be happy to help out if another teacher quits (hahahaha! What are the odds?), but that math was my bag, thanks.

I didn’t see much need for me. The other, brand new, ELL teacher was let go. The ELL specialist (non-teacher) was leaving and we’d hired a new one. The principal decided to use experienced English teachers, non-ELL, to take over the classes rather than try to hire new teachers again.  So Miko would teach first year and Connections, Karinna, who taught AP English, would pick up second year, and Joanne, also an honors teacher, would take third year.  A full-fledged ELD department would be created, with Miko and the newly hired ELL specialist, and Karinna and Joanne in both.

So I left for summer thinking I’d be teaching two precalc classes, or even three, which I’d strongly requested, maybe a trig or algebra 2. Four blocks again, definitely–the 33% premium now for nine semesters running!–and no ELL. Alas, no history either. We’ve been hiring up in that area, so I won’t be teaching US History possibly ever again. Sad.

While I wasn’t crazy about the kids, I still felt the year finished productively, given where I started. At the time, I felt it was a good way to leave the topic.

Year 3

We teachers were notified of our schedule for the year by email, from yet another AVP, the week before school started. My note said:

  • Trig
  • ELL 1
  • Algebra 2
  • Algebra 2

WHAT THE HELL! I sent off a cranky–too cranky–note to that AVP and hurt her feelings, which wasn’t my intent and I apologized later, saying I wasn’t blaming her. I was just pissed off, having been reassured that my agitation for more pre-calc had been heard.  Why no pre-calc? Well, because one of the pre-calc classes was second block, and they needed me to teach ELL. OK, we’ll get back to that. Why no pre-calc? Well, because Chuck had though the fourth block class was mostly juniors and seniors and better suited to me than Wing, who got the pre-calc class. I gave her a look, and she thought it a good idea to give that pre-calc class to me.

Now, why was I teaching ELL again?

Well, the newly hired specialist had quit. Not quit, but gone…oh, I don’t know, fishing. I don’t remember the details. Off to another school somewhere. But we needed a specialist. So Miko stepped up. Told you, he likes to run things. He is still teaching the Connections class, and his drama class, but being specialist takes time, so he gets a block off. And so, here I am. Out of the tree, but still in the car.

I told Miko I wanted curriculum and a reasonably homogeneous class. I eventually got curriculum. I’ll discuss the class another day. But for all the frustrations, this year has been much more enjoyable. Miko is in charge, and moves over-qualified students out of my first year class at a gratifying pace. I have a curriculum with textbooks and workbooks, as well as an online program. We have an over-arching framework that allows us to focus in on kids who need a particular skill. For example, second and third year students who needed grammar focus get additional time in small group instruction, while others got practice time listening to long, involved stories and answering questions about it, just like they would in “real school”.

We’ve had several days of professional development which has been reasonably useful. And having a small department that allows us all to discuss the craziness that is ELL policy has been most cheering. I’m part of a group, one that considers me valuable as opposed to a dangerous renegade, which is a pleasant change.

Note well that the school hired two ELL teachers and fired both of them, then fired its 20 year expert, then hired and lost a specialist–all in less than two years.

I say again–hiring, not firing, is the pain point.

Here’s irony: As a math teacher, I am longest-standing ELL teacher at my school. I speak no languages other than English, yet I am the designated entry class for students who speak no English at all.

Apparently, I’m pretty good at it.

 

 

 

 

 


What I did in January instead of writing

Until 10:00 Thursday night, I really thought I’d get in one post. But then I fell asleep.

Making January the only month in the seven years of this blog that I didn’t get in a single post. I shoot for four. Half the time I make three.  But every month I make one or two. My writing has just fallen off a cliff. Just 28 articles in 2018.

I’m not less interested. I’m just finding it much, much harder to write.

So what did I do in January?

Well, I spent a lot of time researching two different pieces on direct instruction. A movie gave me some interesting insights and more data to research. I read Zig Engelmann’s book again. I tried and failed to organize a way to discuss either article.

I found out how to search the ACS for high school demographics by state (to keep it manageable, I made it populations of 400+). These are stats I’ve wondered about even before I started (and abandoned) Everybody’s Second Favorite. Dick Startz spurred me on with this rather anodyne wail about integration in public schools (which he confuses with opportunity). So that led me to make interesting charts like this: CaSchoolsraceprofNYSchoolsraceprof

But while that was interesting, I was already halfway through January and this takes more time than I had.

I also spent some time at the DMV. My brother has two cars, but he carelessly allowed the registration on one to expire, and then he ignored the followups, and then he ignored the warnings, until he started to worry about how much it would cost. So he bought a new used car from a friend for cheap. The other car was parked at the curb until the city labeled it as unregistered and threatened to tow it. By this time, the battery was dead, so he put the batter from his other car into that one–and it started right up.

“Aww,” I said. “It missed you. You should get it reregistered.”

Until then, he put it in the driveway, where the city can’t get it. But the driveway is my spot–and a non-trivial amenity I pay for with my higher rent. He gets the bigger part of the house, despite paying less.  A lot less. I’m not bitter. I make more.

But it’s now well over a year later, and I want my damn driveway back. It’s often hard to park in the streets; people can (and do) park right in front of the house. So I made an appointment for him to find out what it would cost to reregister a car that hadn’t been paid for in three years. I told him about it and everything.

And I knew he’d forget, so I made a second appointment, on a Saturday, for me. So when he forgot, I spent an hour or so with a surprisingly nice bureaucrat finding out how much it would cost. The answer was much better than feared. My best case was $500, worst case $2000. It was $625. Plus a smog test.  And a battery. Plus by now the tire’s flat, so he needs to fix that. Still, about $1000 to get a second car that he could give to his kids. He’s got the money. He owes me $800 that he has in an account. He doesn’t live large. I told him he could pay me later if he’d get the car done.

It’s 3 weeks later. No fixes. I told my nephew that if he got his dad to fix the tire and buy a battery, I’d pay him $20. Hasn’t happened yet.

I’m sympathetic to people who avoid. I did it for years. Still do. And I want my damn driveway back.

Anyway. That took some time.

Then I read Robert Pondiscio’s article on, among other things, killing education myths and remembered very apt parallels between that particular myth and an Asimov short story. That’d be easy to write. I looked up the text, and promised myself I’d get it started.

But first I opened my mail. That’s….not something I do often. Let me give you an example. At the bottom of the large box of mail was a letter from my financial manager’s company alerting me to a $2500 account that hadn’t seen any activity for three years, and was in danger of being put into the state account. Please notify us before it gets sent to the state. The problem was, the form letter was from December 2017. So I had to call the office and admit I hadn’t opened the letter for over a year, but everything was okay and my money wasn’t at the state, right?  His assistant called me back, chuckling, to assure me that it had been issued in error and my money was safe.

Another half day gone. Then I thought about some Great Moments in Teaching articles I’d postponed, or one on my pedagogy for number sets. Multiplication is the Death Lord. Things like that.

But the major time suck was….

Grading. Jesus. Grading took over January.  I used to like grading. I still like it, really. A whole day of January winter break grading. Then more tests, more grading, rinse and repeat.I don’t know why it kicked my ass so badly this year.

I’ve taken on a lot of fascinating, challenging responsibilities at school that take time and energy. So when I get home, all I do is fall asleep.

In fact, I may be slightly burnt out. My job is fantastic, but I’m usually pretty energized in January. Not this time.

In celebration of my tenth year teaching, I won’t be working this summer. The original plan was 6 week tour of the English-speaking countries of Europe, but my father’s health has been going up and down, and I’d rather stay close. Hopefully, he’ll be up for some trout-fishing or a trip into Canada. Either way, I hope to buy a used SUV and tour the US.

I will try to write more. Hope that’s not a threat.

Hey, under 1000.

 


Direct Instruction Miracle? The Lewis Lemon Case

Back in February, I observed that Direct Instruction hadn’t failed because of teacher disdain, as Robert Pondiscio charged, but because educational leadership from superintendents on up through US senators had not only refused to support the program, but in some cases actively and systemically ripped out implementations that seemed to be successful.  As I said at the time, I considered it a real mystery.

So I dug deep into Zig Engelmann’s book, Teaching Needy Kids in Our Backwards System looking for an example of a success story I could independently verify. He goes on at some length about both San Diego and Baltimore schools, but not in any way I could pin down DI vs. Non-DI. Quite often Engelmann would cite a newspaper article as evidence.

The Ventura County Star carried an article on March 15, 2003, titled “Effective Reading Program Must Go”, which indicated that the only school in Ventura County and one of 109 in the state to receive a citation for achieving exemplary progress was forced to drop their [DI] program.

No mention of the school. Or the superintendent. Or the degree to which test scores increased. One gets the distinct impression that Zig….well, read about it in the paper. He uses virtually identical wording in this Edweek article. California keeps detailed, easily searchable records; with the name of the school, the specifics of the decision could be confirmed.

The exception is Lewis Lemon.LewisLemoncite

But then, as happened consistently through the decades, a new superintendent came in and demanded Lewis Lemon abandon Direct Instruction and adopt “balanced literacy”. The principal, Tiffany Parker, flatly refused. She was accused of cheating, so the students were tested again. They passed the new test.  The district actually had to give back Reading First federal funds because they dropped DI. Apparently, the district blamed the principal for informing the feds that the district was no longer using the program, and Parker was demoted. She sued, and settled.  If you google this, you’ll find a New York Times article, a New York Sun article, this Heartland article, and references to many Rockford Register Star articles by Carrie Watters, who from what I can tell now works at an Arizona paper. The Rockford Register Star archive goes back before 2003, and has other articles by Carrie Watters, but contains none of the many stories Watters did on the Lewis Lemon controversy. Even Joanne Jacobs’ blog entry on Rockford, “They Messed with Success” has disappeared, which had me really freaked until I learned she was had temporarily moved her archives.

The story made national headlines when the superintendent decided, in 2005, to force Lewis Lemon off of DI into “balanced literacy”, while the strong student performance of 2003 only got covered locally. The New York Times piece went into a bit more depth, mentioning that the fifth graders didn’t do as well. Also, the reports weren’t always specific. Was it math or reading? Or both? So I went digging for data.

If contemporaneous reports are scarce, the contemporaneous data survives. Illinois test scores comparing Lewis Lemon performance to the district and state by race are all online. Here they are, and please check my results:

2001–the year they implemented DI
2002
2003
2004
2005–the year they were forced to discontinue DI
2006

So now I’m going to go all graph heavy, like Spotted Toad. First up: the top level comparison of Lewis Lemon scores to the district and state level for both 3rd and 5th grade (reading down).

LewisLemonOverall

Note the big ol’ spike in 2003. Lewis Lemon 3rd graders had far more students meet or exceed standards than the district or state averages in that year. But then, third graders at Lewis Lemon outscored the district average  every year both before and after DI was implemented in  Notice, too, that the fifth grade scores aren’t nearly as impressive, but that both math and English show a spike in 2005, which is the year the third graders of 2003 would have been in fifth grade.  Then again, fifth graders had much better reading scores in 2002 than in any time after DI implementation.

Lewis Lemon officials blame the lower fifth grade reading scores on a less than perfect implementation, and students who were further behind. On the surface, this seems unlikely, given the high scores in 2002. But there may be other causes.

So I disaggregated, first by race. Here are black and white 3rd grade reading score scores compared at the school, district, and state level, broken down by achievement category.

Up first, 3rd grade blacks:

LewisLemonBlack3rdReading

Now remember, this is Lemon Lewis black students compared to other black students only (not the entire population). Blue is Lemon Lewis, and the more blue to the right of each graph, the better Lewis Lemon is doing. 2003 is the year of the Big Score. The blue clearly moves to the right from 2002 to 2003, and stays there for two years. Then it shifts back.In 2003, black students  at Lewis Lemon met or exceeded standards at 3 to 4 times the numbers that district or state black students did.

Third grade reading, white students.

LewisLemonWhite3rdReading

So this is interesting in a couple ways. First, it’s clear that in the pivotal year of 2003, white performance actually declined slightly. Fewer students failed to meet standards, but fewer students exceeded them. Not a lot. But there’s no tremendous spike in white student performance in 2003.

And then, something that has gone completely unmentioned: the white student population collapsed to below testing levels immediately after 2003. This explains some of the falloff of the graph above–if whites comprised a decent chunk of the high scores, then their disappearance would impact the overall “meets or exceeds”.

It’s not clear to me whether the DI implementation was reading only, or reading and math. The news accounts all focus on reading, but more than one account mentions improved math scores. So I’ll include them. Here’s third grade, African American.

LewisLemonBlack3rdMath

Here, Lewis Lemon was scoring better than blacks in the district and state before the DI implementation. The blue still shifts right, but it’s not as dramatic. In 2003, virtually every student met or exceeded expectations, but in every other year, both before and after the DI implementation, they were still doing very well.

Now white 3rd grade math:

LewisLemonWhite3rdMath

So in 2002 through 2003,  the school saw a good bunch of whites move from “meets” to “exceeds”. Unlike reading, third grade white performance saw a decent boost, but it started a year earlier. Whites at Lewis Lemon performed better than the district.

And now, the fifth grade. Reading, black fifth graders:

LewisLemonBlack5thMath

Scores actually declined in 2003. 2005, the year that the third graders from 2003 were in fifth grade, sees a slight improvement. But not much of one–more than half failed to meet standards.

Fifth grade whites, reading:

LewisLemonWhite5thReadingAgain, whites have their best year in 2002, and don’t show any particular spike. They also do better than black fifth graders (which is normal).

Fifth grade math:

LewisLemonBlack5thMath

Indifferent–except note the spike when the third graders of 2003 show up. It’s much more pronounced in math than it was in reading.

White fifth graders, to finish out.

LewisLemonWhite5thMath

So here’s one last way of looking at the data–compares blacks at Lewis Lemon to the whites at the school, district, and state level. Read down  on the left for 3rd and 5th reading, down on the right for 3rd and 5th math.

LewisLemonblktowhite

Once again a consistent pattern for  black third graders–big boost in 2003, slight fade in 2004, then tank. Black fifth graders see the boost exclusively in 2005, when the rock star 3rd grade class arrives,  holding on to their gains more so for math than for reading. Spike or not,  black third graders at Lewis Lemon do well in math compared to district whites from 2002-2005.

And here are the formal demographics reflecting the disappearance of white students from Lewis Lemon.

LewisLemonDemographics

That’s a stark drop in a short time. 47% or so from 2001 to 2003, and 50% from 2003-2005.  It may have just been a drop in new students, but the third grade and fifth grade classes ran out of whites at the same time–I’d have expected the fifth grade cohort to have more white students for longer, in that case.

So restating the observations:

  • Lewis Lemon black 3rd grade scores are stupendously high in 2003. The accusations of cheating were groundless, unless the cheaters carefully waited two years to boost the same kids’ scores when they hit fifth grade.
  • However, black 3rd grade scores at Lewis Lemon were consistently higher than black scores district and state wide, before and after the program.
  • White students saw no real benefit from the new program.
  • Fifth graders, white or black, saw no real benefit from the program. The one strong category, fifth graders in 2005, is the boost of the third graders from 2003.

Questions:

  • Is it possible that the 3rd grade class of 2003 was in some way extraordinary?
  • Were the white and black 3rd grade students practically (that is, for some legal reason) separated? Did the black students have a different teacher than the white students?
  • Did the white flight remove more high ability students? But even if it did, you’d expect the white kids to respond as well to DI as black kids,
  • Could parents “opt out” of DI?
  • Was the white flight out of Lewis Lemon exacerbated by the switch to DI? White students did not see the dramatic increases. Maybe they didn’t like the new regime?

Conclusions:

Well, it’d need a better analyst than me to evaluate the data. And if there’d been solid analysis and reporting at the time, we might have a better idea why the black third graders did so well. Clearly, the curriculum is a possibility for the higher reading and math scores.  But I can’t explain why subsequent third grade classes fell off in performance. And I really can’t figure why the white kids didn’t do well, unless it’s for the same reason that white kids don’t do KIPP.

Did the meta-analysis  include Lewis Lemon?

What I don’t see is a miracle. What I don’t see is  conclusive test evidence showing an obvious incremental increase in test scores at every level, in every demographic, or in every race. Given the actual, honest to god data, not a compiled version of it, broken down by both race and grade and score category, is easily available, I hope someone can go even deeper into the data and see if they find explanations or patterns that aren’t available in this surface level display of data.

Here’s what else I don’t see: any reason whatsoever for that domineering control freak superintendent to rip the program out of Lewis Lemon. I’m not a fan of D, but reading about this blatant obliteration of something that worked for the kids has been depressing. Shame on the media for not digging deep at the time and finding out why.

So there you go. Real data on Direct Instruction. Have at it. Draw your own conclusions.

Happy New Year.


The Students of My Christmas Present

“What..?”

On time for once, he trudged into the class pulling a small pine tree behind him, a stand in his other hand. His chin was set. His curly hair braided in two plaits instead of flying all around his head added to his air of determination.

“It’s a tree.”

“I see that.”

“I wanna make it a Christmas tree. I want a Christmas tree with lights and decorations. I want to know what it looks like, and see it looking pretty every day.”

“So you’re taking it home?” He rolled his eyes in my direction, and I grinned apologetically. “Just checking. I guess it’s haram?”

“Extremely haram.” Faisal has most of the brains, four times the looks, but far less of the focus and drive of his older brother Abdul, now in his sophomore year of a top 50 university.  Not unknown to the administrators for all the wrong reasons, Faisal nonetheless has held onto a 3.5 GPA and, barring a last semester senior catastrophe, a decent chance at a good college.

And so I acquired a tree.  I showed Faisal how to put the tree in the stand, and we steal some water from a classmate.

“The vendor across the street gave it to me for free! He’s Yemeni, maybe that’s why.”

“No, I’d guess his generosity is due to the trunk bending sharply forward before it goes up.”

“Do you have the..the lights? The things you hang on them?”

“Ornaments.” I looked sideways.  “You are expecting me to decorate?”

Faisal has a charming grin.

The tree was an instant hit with all my students, even sitting in the corner unadorned, as it did for a week. Someone noticed that the tilt kept pulling it over, so we snuck outside and grabbed some painted tiles from the garden to weight the stand down.  Students volunteered from their water bottles to keep the tree hydrated. I took three days and a weekend to bring in lights (one day to find them in my garage, one to pull the box down, one to sit by the door to be forgotten, weekend to put them in my car so I couldn’t forget them), another two days to bring in the ornaments.  Then one day four top students finished a quiz early and I assigned them “light” duty.  I have a huge collection of gorgeous ornaments, some hand-blown glass, others hand  made, some just utterly beautiful, that they all oohed and ahed over. Faisal got to select his favorites.

The vocational cooking teacher teased me for taking nearly a week to complete the tree, but she readily agreed my end product was far superior to the one her student put up in 30 minutes–and I still had it done two weeks before break. Each morning, I turned the lights on to twinkle cheerily throughout the day. Very festive. I have these old plastic window coverings, one with Santa peeking around the corner, one with bells, and on impulse taped them over my door windows, where they hung, unmolested and unbroken, for the better part of two weeks, the kids carefully closing the door without tearing them.

Four of my nine ELD students are either Muslim or Hindu, and they haven’t been here that long. I carefully explained “secular” as opposed to “religious”, reassuring them that the tree was in celebration of the former.  The other half of the class is Catholic, either Guatemalan or Filipino, so were surprised to learn that not everyone celebrated Christmas as a religious event. My math students needed no clarification. Our school is wildly diverse, but that’s never stopped us from openly celebrating Christmas. The kids sell mistletoe messages and Christmas wreaths through December.

I regret not capturing a picture of the tree at school, completely decorated. I’ve learned that it made any number of appearances on Snapchat and Instagram, as my students bragged about their Chrismassy room.

My family of origin has always centered celebration on Christmas Eve. For 45 years, December 24th means cheese, beef, and occasionally chocolate fondue.  When we were kids, we’d then go to bed and have Christmas in the morning. But once we hit our teens and late 20s, we’d just open presents Christmas Eve so we could sleep in. As we grew up and moved out, we turned Christmas Day into family unit, keeping Christmas Eve for fondue with everyone.

My ex and I did Christmas big. We both loved the holiday, both bought each other lots of gifts, bought other family members multiple presents, shopped together and separately.  I love presents. But it wasn’t just the presents. We had a party once, I remember, and always made plans to see friends or do something fun.

We divorced when our son was not quite three. Because of our fondue tradition, my son always had Christmas Eve and morning with me, then went to my ex’s for two or three days. So on Christmas Day, I was alone.

I wasn’t miserable. I still loved the Christmas holiday, even if the 25th was always a bit of a letdown.My son and I would always decorate, get a tree.  We’d drive around looking at lights, go to see It’s A Wonderful Life or Wizard of Oz at the revival theater. But after the divorce, I always felt as if I were watching others experience Christmas, rather than experience it myself. A good chunk of my loss was simply the presents. I’m not materialistic the rest of the year, but by god I like people buying me presents at Christmas. However, the larger sense of loss was due to the realization that while my family of origin is big, my own family unit was just two–and when my son was gone, I didn’t really have a family unit at all. Just me.

The post-divorce change in Christmas was as nothing compared to its utter disappearance after my son finished high school.   Before Faisal dragged that little scrubby pine into my room, I hadn’t put up a tree since 2005. My son would still come to fondue, we’d still have Christmas morning, but without him around during the lead-in, what was the point?

That amputated Christmas threatened to disappear entirely once he moved three states away with his girlfriend and eventual wife. I once had fond notions of visiting for Christmas and opening presents with my grandkids, but my ex and I have spent no small amount of time commiserating with each other about the truth of the maxim “A son is a son till he takes a wife, a daughter’s a daughter the rest of her life”. I am truthfully not bitter about this, although I would certainly have it otherwise. My son has a woman he adores, an excellent job he enjoys, two beautiful, loving children , a mortgage, and a marriage certificate (acquired in that order).  I have done my job well. Peace.

My son’s absence forced me to stare down a (hopefully very long) telescope looking towards old age wondering was this it? I’m going to be someone who doesn’t do Christmas? Will I just start peeling away holidays as I have fewer people to celebrate with? I’m still blessed with both parents and family of origin nearby, but the disintegration of my Christmas Day–now getting perilously near why-bother status–made me realize that I had to change my mindset and perhaps my practice as I move towards a time when family will be fewer and farther away.

So for the past few years, I’ve made a point to experience Christmas as a family unit of one. A married couple I’m close to often invites me over for dinner, where I have a wonderful time even though, god help me, she’s a terrible cook. I can dress up a bit, talk to people, drink wine, and mark the year’s passing. Sometimes I’ll go see the holiday film at the revival theater. I often go to a Starbucks, write, talk to people at the store or on the street, seek out a neighbor to chat.

I resumed putting up outdoor lights three years ago, slowly finding uses for the big pile of lights I’d acquired earlier, and then actually buying more. I love Christmas lights so much. And they’re outdoors, so it felt more like contributing to  neighborhood spirit, rather than decorating an empty nest. For three years now, coming home and seeing the house all lit up has been most cheering.

While I expected my new “experience” of Christmas to be limited to outside lights and activities,  Faisal and my students have reminded me of all the happy ornaments locked away in my garage, sitting there unused and unenjoyed. I have treasured the shared cheer of my classroom tree. If I ended my Christmas tree practice because there was no one to share it with, well, then, why not continue to have a tree at school for the season? So I will. When I told my students, they applauded.

I wonder if Julia Ioffe can possibly conceive of a Muslim Palestinian American  begging for a free tree, lugging it into his most familiar teacher’s room, simply because he wants to be a part of one of the best holidays ever created. Would she demand that he, too, see Christmas entirely in terms of Christ? Could she not see it as assimilation of the best sort, appreciation for what American culture has to offer?

I received an additional gift of recognition, one that involves the second best Christmas Carol. The finest is, of course, the Alistair Sim version, which you should run out and see right away, before Christmas season officially ends. But Patrick Stewart’s version holds its own very well.

One scene in particular has always resonated with me, and only recently have I understood why.  I’ll try to show it with pictures, but the difference is easier to see in action. Here’s Ebenezer before his transformation, sitting in front of his fire:

sadalonescrooge

His body language is all crunched up, his face is tense (granted, Marley’s said hello). Here he is after the three ghosts have visited:

happyalonescrooge

He’s alone both times. But in the second, he’s not eating dinner, shoveling it down as a utilitarian act, scrunched and sullen. He’s just sitting, enjoying the fire, with a nice drink. He’s experiencing Christmas, alone and happy.

I wasn’t Scrooge before, or now. I’m just an introvert who is perfectly content to be alone most of the time, but didn’t know how to celebrate Christmas if I wasn’t part of a  big family unit. I faked it–and faked it well–for a long time, but I’m learning how to keep the day in the spirit I’d like.

Faisal’s determined desire for a Christmas tree, and my students’ happy participation in creating one,  had one more surprise in store for me. When school ended for the year, I carefully took off all the ornaments, wrapped them up and put them back in the box. Next was the lights..but I stopped. I’d planned to put the tree in the dumpster but instead wrapped up the cords and carried the whole tree, lights and all, to the front seat of my car. I only felt a little bit silly.TreeatHome

I’m looking at it now, shining brightly in the front window. Maybe next year I’ll have two trees–one for school, one for home.

This year my friends had to delay their Christmas dinner until Thursday. So my brother and I ate standing rib roast, which cooked to rare perfection, and I made lemon meringue pie for dessert.  I’ll be rewarding myself with a hot toddy (Makers Mark) when I finish this.

I always give thanks for my students, past and present, and am grateful I’ve got many more students to enjoy in years to come. But this year, to students present, I thank you all for showing me how to bring back one more piece of my favorite holiday.

Merry Christmas.

 

 

 


Making Rob Long Uncomfortable

(Note: This is in the context of my multi-chaptered review of The Case Against Education, particularly the last, but I think it stands alone.)

I’m a big Rob Long fan; I listen to both his Ricochet  and GLoP podcasts. I’ve even subscribed to Richochet, and you should, too. I am not a Heather MacDonald fan, for reasons that puzzle others. But I like Long/Lileks/Robinson more than I don’t like her, so I was listening to their conversation a while back.

The three hosts were completely on board as Heather excoriated the college campus craziness documented in her new book. You can practically hear them nodding with approval as she outlines the various issues: the outraged feminist wars, the soft and whiny college students, the transgender insanities.

And then Heather turned the same withering sarcasm to race, talking about the delusional fools who think that African American disparities in college are due to racism as opposed to their low academic achievement….

Pause.

RobLongUncomfortable

I laughed and laughed.

You could practically hear Rob’s toenails shrieking against the tiles as he braked to a stop.  This was not the conversation he’d signed up for. He was there to lightly mock feminists and social justice nuts, not crack witty, on-the-nose jokes with Heather about the racial skills deficit.

Cognitive dissonance, anyone?

It runs all through the political and intellectual class, particularly on the right. So, for example, Charles Murray is a great social scientist and The Bell Curve an important work  (I agree!)–but  let’s blame crap teachers and low standards for black academic underperformance.

Recently, Megan McArdle added her voice to John McWhorter in calling for an end to research on race and IQ. This appears to be the new “informed right” position: if you’ve spent any time actually reading about race and IQ, it’s clear that only bad news awaits further research. So ban it.

Meanwhile, on the subject of recent campus craziness, Megan thinks that Evelyn Beatrice Hall’s formulation is one of “humanity’s noblest inventions” and John McWhorter routinely denounces the safe-space rhetoric on college campuses as absurd and “unhelpful”. Both of them are appalled at the idea that college students would want to shut down conversations they don’t like.

They’re reactionary fascists, you’re unreasonably censorious, I’m judicious in setting limits.

Ever notice how the same people who praise Caplan’s idea of restricting college are also those singing songs of praise about KIPP and “no excuses” charters in general–for sending more poor urban kids of color to college?

KIPP schools put their kids through hours and hours more school every week, all to get just 45% of them to graduate college “ten or more years” after 8th grade–that is, 6 or more years of college.

They’re the education blob who ignore reality to keep spending taxpayer dollars, you’re unduly optimistic about college readiness, I’m all for unqualified black kids going to college if it’s not unionized teachers sending them there.

I read many reviewers of The Case Against Education on the right or the intellectually honest left who discussed the book without ever observing the obvious implications of Caplan’s plan to cut back on college attendance. This perplexes me. I actually know a reviewer who gave a great analysis without mentioning race. I asked him why the omission. He replied the idea was  “far-fetched enough that the racial implications are a ‘cross that bridge when we come to it’ side issue.”

That sounds amazingly on point. Yeah, sure, Caplan’s proposal is pie in the sky, but it’s a great idea, you know? Interesting. Challenging. Controversial. Let’s engage it. Play with it. Not get into the nitty gritty details.

Of course, everyone’s totally into the nitty gritty when castigating the here and now.

“Failing schools” is an expression with bipartisan support–and the schools are always failing on the count of race. KIPP’s “Success for All” or Eva’s “Success” Academies are clearly talking about success by race. All the praise for Wendy Kopp giving Teach for America a chance to “expand opportunity” for kids is, again, talking about opportunities for black and Hispanic kids–and, by the way, pretty sure those opportunities include college. No Child Left Behind demanded that test scores be disaggregated by race, and only if all students of all racial and income populations achieved at the same rate could schools get out of academic probation. States dumped their test score standards and still couldn’t avoid putting all their schools in probation status, thus creating the need for waivers that allowed everyone to ignore the racial gaps while they Raced to the Top.

I don’t doubt the sincerity of my reviewer buddy. But come on. All the pro-charter, pro-voucher, anti-union policy wonks on the right are all about race when they can use it to beat teachers over the head. The nation itself defines its success in education almost entirely on how well it educates kids by race. But a guy writes a book proposing to restrict access to college and most public schools by choking off funding in ways that would be catastrophic to African Americans but hey, it’s just spitballing. No need to mention race.

Policy analysis a la Wimpy: I’ll gladly talk about race in today’s education if you let me ignore race in the education of tomorrow.

But despite my dismay, that is definitely how it goes. Everyone suffers from educational romanticism, as Charles Murray puts it:

Educational romantics of the Left focus on race, class, and gender. It is children of color, children of poor parents, and girls whose performance is artificially depressed, and their academic achievement will blossom as soon as they are liberated from the racism, classism, and sexism embedded in American education. Those of the Right see public education as an ineffectual monopoly, and think that educational achievement will blossom when school choice liberates children from politically correct curricula and obdurate teachers’ unions.

In public discourse, the leading symptom of educational romanticism is silence on the role of intellectual limits even when the topic screams for their discussion.

This silence from those who know better leaves the rest of the talking class, particularly those on the right, the ones who aren’t into policy, utterly unprepared for a serious discussion. They get very, er, uncomfortable with any mention of black underperformance that isn’t a de rigeur nod to shit teachers and corrupt schools. They haven’t really thought about it much or read the literature, but they quite like the basic GOP talking points (bad unions, bad! Charters! Choice!) and would much rather no one take away their comfort chew toys.

Fair to say I’d make Rob Long uncomfortable.

Notice that I did not (and do not) hold black culture  at fault for these academic results. As I mentioned once long ago when looking at the black/white gap in Praxis scores (teacher credential tests):

  • The white Millennial bonghitter with a 1.2 GPA who teaches sixth grade science after his parents booted him out of the basement ties the freshly-pressed hardworking black track star with a 3.8 GPA teaching special ed.*
  • The goofball wannabe [white] manicurist who loafed through Podunk U and went into teaching kindergarten after the tenth of her problematic boyfriends dumped her outscores the idealistic black welfare daughter success story on a full scholarship to Harvard who went into teaching sixth grade English to “give back” to her community.

Pace JD Vance, it ain’t culture. Your Middletown classmates who ended up dead or in dead-end jobs almost certainly outscored the rich black kids in, I don’t know, Delaware County, or wherever the wealthy black families live in Ohio.

As I’ve written before, all those placing great hope in KIPP are missing the big picture: the kids who need the hours of extra education and the forced discipline of No Excuses to get anywhere near 8th grade ability by 8th grade is simply not the same as the intellect that can eat Crispy Cocoa Puffs every day while watching TV or playing video games and bet at the 8th grade level by 4th grade.

MacDonald herself blames culture. In the podcast, she responded to Long’s plea with the offer of a thought experiment. If black kids have the same level of school attendance, same level of homework completion, and in ten years they still have lower achievement, she says, then and only then she’ll consider racism. Apparently MacDonald isn’t aware of the thought experiment known as Cambodians, Laotians, and Hmong who have the same dedication to education but wildly different academic results and graduation rates.

And given the frequency with which poor white kids outperform wealthier black kids, often at the same schools, it’s hard to reasonably argue that schools themselves are the result of black underperformance. Which doesn’t stop many people from unreasonably arguing it, of course.

What do I blame?

[Crickets.]

Look, it’s not a matter of “blame”.

But that’s an answer that gets one into hot water. People who talk about the test score gap without fingering responsibility–worse, who argue against the usual culprits–are giving the impression that there’s nothing to fix. Which isn’t true, but it’s closer to true than any hope of closing the racial achievement gap.

The discomfort has wasted billions to no real avail. Despite the demands to increase college readiness, we are sending far more students to college who are less prepared than ever. Colleges have responded not by tightening standards, but by ending them, giving college credit for classes teaching middle school skills. Employers routinely call for more unskilled immigrants to take on the tasks  “Americans won’t do” when in fact they mean jobs that won’t pay enough for Americans to do, and thus create more low-skilled populations we can let down in future generations–populations that are beginning to outnumber American blacks of slave ancestry, the people to whom America owes a great debt.

And yet. I can think of so many ways that accepting performance gaps and modifying education policy could create more problems–like, say, Bryan Caplan’s notion to end public education.

So it goes.  Bryan Caplan gets a book deal and fame for seriously arguing in favor of a policy that would block most blacks and many Hispanics from all advanced education. I’m anonymous, unpaid, and unbook-dealed, writing in favor of continuing public education for all. But Caplan ignores race, and I’m blunt about black academic results while refusing to blame acceptable scapegoats.

Despite his pose as a controversial intellectual, Caplan will never make Rob Long uncomfortable.

I wish I knew how to distill all this into something pithy. But I’m bottom up, not top down. Or is it the other way round?


The Case Against The Case Against Education: Average Was Always Over.

Part 5. (Parts onetwo, and three, and four.)

In his book, Caplan goes on at great length about what level of academic achievement predicts probability of success in attaining a credential.  But he complete ignores the fact that the probability of low academic achievement is skewed based on demographic attributes. While it’s fashionable these days to pretend that income is the great demographic divider, the mother of all disaggregations in America is race.

Let’s examine Caplan’s discussion of race in educational achievement. Go get your copy of Case Against Education and check the index. I’ll wait.

Huh.

Caplan mentions authors named “Black” about as often as he mentions blacks as a demographic category,  which he does three times .

What about Hispanics? No one has the last name “Hispanic”, or “Mexican” or “Puerto Rico”, much less “Dominican” or “Salvadoran”, so the sum total of their mention is uno.

And mind you, I mean mentions.  At no point does Caplan do anything so basic as discuss the  academic performance of different demographic categories. Blacks and Hispanics make a brief appearance in name only during the Griggs discussion and never show up again.

How do you write a book that argues for draconian cuts in our education system—and not discuss race?

Education policy in America is obsessed with race. Name a single problem in education and it’s a mortal lock that it was either caused by the achievement gap or caused by a policy put in place to end the achievement gap. Any attempts to solve educational challenges will be sued out of existence, or fail, or simply ignored to death because of its impact on the racial achievement gap.

But Caplan never once explores whether the implications of his proposals might unduly affect certain demographics. He simply uses median scores and percentages for the overall population. I am not a huge fan of Tyler Cowen’s dystopic fantasies but in education, there’s no doubt that average is over and has been for years. Averages hide too much. In Caplan’s book, averages hide the implications of his “ability archetypes”:

capstudentdef

Caplan advises people to use “ability archetypes” to ensure they are realistic about their goals:

capstudentselfish

Let’s consider the racial implications of his advice.  Once again, we’ll use the  NAAL report that Caplan discarded after culling a few shallow data points.

Here’s the results broken down by race in the four ability categories, from Below Basic to Proficient, for Prose and Document. For example, white comprise 70% of the population and 7% of the tested white population scored below basic in the Prose category.  So 4.9% of the tested population was white and below basic in Prose.  White scores are in gray, black scores in blue.

2003NAALproscomprace2003NAALdoccomprace

(I’ve been working on this forever, and just now noticed I didn’t put the percentage of each race’s contribution to each category. Sigh.)

Asian and Hispanic results are skewed by the conflation of immigrant and native results.  But it’s instantly obvious that blacks, who were only 12% of the tested population, contribute far more to the lower categories and are almost non-existent in the skill categories Caplan considers suitable for college.

The columns in the graph below list the median score by race in each education category. The horizontal lines are the overall population percentiles. So 14% got Below Basic, while “Basic” scores went from the 14th to 44th, Intermediate from 44th to 85th, and Proficient above that. The “Excellent”, “Good”, “Fair”, and “Poor” classifications are those that Caplan defined and are at (very roughly) the corresponding percentile location. (“Good” is a bit low, I think.)

naal2003raceandedNotice that white high schoolers and high school graduates have roughly the same scores as blacks with 4 year degrees or more. This is a very consistent finding in most test score data.

Caplan argues that only students from the Excellent or Good categories should invest in college. The NAAL report finds that only two percent of blacks read at proficient levels,  31% score at the intermediate level.  If blacks or colleges took Caplan’s directive and only went to college with that qualification (which is actually broader than Caplan would like) just 4% of the overall population would be black college graduates.

NAAL doesn’t disaggregate by race, education, and performance category. But another survey, done three years later, gives us some insight: The Literacy of America’s College Students. This literacy survey tested 25 randomly selected students from each of over 1800 universities.

This survey uses the same assessment as NAAL, and the same categories, to assess  college students in their last semester of an AA or BA degree. Again, I’m restricting the comparison  to blacks and whites.

First, I benchmarked the literacy data to the NAAL data for college graduates. 2006colllitmedian

The literacy survey data is much higher for blacks than the NAAL data, particularly for black AA holders. But it’s pretty close for BA holders. Moreover, standards change over time so it’s at least possible that looking at brand new AA degrees would differ from the overall population.

Here’s the breakdown by score category. Black AA and BA candidates are on the left, whites on the right. Blue and green are intermediate and proficient categories. 2006colllitmedian

And consistent with the first graph, these results seem quite high for African Americans. Only 5% of  blacks in 4 year schools scored below basic?  Blacks in 2 year colleges had no below-basic scorers? Really?

Still, this is fine for my purposes. 1 in 4 blacks about to get a BA had basic or lower reading scores, while less than 1 in 40 whites had the same low ability.

Caplan asserts “we” should  be shocked that  “under a third” of those with a BA or higher achieve Proficient levels in numeracy and literacy.  But close to half of the white college BA holders achieved Proficient levels in the three categories  ( 42%, 45%, and 40%).  The same black proficiency scores are 16%, 17%, and 5%.

Whites are achieving considerably higher than the results Caplan sniffs at, while black scores are far worse than “under a third” but rather “under a fifth”. Moreover, Caplan argues that he’s giving this advice to prevent low-skilled people from failing in college–but clearly, these blacks are about to graduate and made it through with skills he deems too low to succeed.

The college graduate data above would almost certainly be replicated in all the other education categories. Whatever Americans Caplan decries as low-skilled and incapable of succeeding in education, rest assured that he’s skewering a group that’s considerably more African American than the overall population.

Remember, too, that Caplan regularly dismisses the idea that our education system might be able to improve results.  He spent an hour debating Ric Hanushek arguing this very point.

But NAAL results over time (below) suggest that our k-12 system has improved results for African Americans. Asterisked scores indicate significant improvement. Blacks saw significant improvement in all three areas. (note again Hispanic performance declined rather spectacularly, thanks to increased immigration)

chgbyrace92to03

What educational categories saw the most black improvement?

chgbyedrace92to03

Well, hey now. Look at that. The blacks that graduated (or even dropped out!) of high school in the 10 years previous saw significant improvement in prose and quantitative skills.

Black proficiency scores on the NAAL survey are extremely low. But they have improved.

Caplan’s prescriptions run into all sorts of problems when evaluating black academic performance. If Caplan is correct about the skills needed for college, then why is the black college graduate average below the level that Caplan declares essential for college success? Certainly, as I’ve observed, colleges are lowering standards (for all admissions as well as blacks in particular). But while the average earnings of black college graduates are less than those of whites, black earnings increase with education nonetheless. So should they invest in more education even though they don’t meet Caplan’s criteria?

I pointed this out to Caplan on Twitter, and  he observed that the ethnic group improvements were marginal  and that the absolute level of basic skills were “terrible”. Which suggests he was aware of the ethnic group differences and just decided not to mention them.

Breaking down test scores by race can be incredibly depressing. No one likes to do it. But Caplan’s failure to include this information is simply irresponsible.

Caplan argues that people outside the top 30% of academic achievement should stop investing in school, the sooner the better. He sees this as both selfishly correct and also the correct government policy, so he thinks all funding for education past minimal skills should end. Those who are worth further investment can justify the expense to a bank or a parent. Meanwhile, we should end the child labor laws so that the very lowest academic achievers can get to work as soon as it becomes a waste of time to educate them.

Applying his policies to black Americans, around 25 percent would be in need of those changed labor laws, because Caplan wouldn’t spend a penny to educate them.

In his conversation with Hanushek, Caplan proposes giving low-skilled kids “more realistic” careers–the example being “plumber”, of course. Like most elites, Caplan uses  “plumber” as a low-skilled proxy when in fact the occupation is one of the more cognitively complex of blue collar jobs. But I think his focus on the job is also a tactical choice. “Plumber” sounds good, like a meaningful career. You can be self-employed or build a business.

Imagine telling a kid his best option is “janitor”. Now imagine telling a poor black kid his best option is “janitor”. Then imagine telling about 1 in 4 black kids that yeah, “janitors” where it’s at for them.

If you can’t imagine doing that, then don’t write a book arguing that Americans get too much education.

When people talk about the “bad old days” of American education, they are referring to the era when people did exactly what Caplan advises. School counselors looked at the students’ test scores and gave them a list of possible careers. White kids had higher scores and were advised to go to college. Black kids had lower scores and were advised to go to factories or custodial work. For a guy who spent several pages on the likelihood of Griggs lawsuits, Caplan doesn’t seem to have spent a single second looking at the case history of school district consent decrees.

But then again the kicker: Caplan wants open borders. So in Caplan’s ideal future, all those  teenagers of all races that have been kicked out of school because they aren’t worth educating  will be  competing for jobs and housing with millions or more adults from third world countries.

Earlier, I wrote:

I’ve been struggling with the best way to take on Bryan Caplan’s woefully simplistic argument about the uselessness of education. What do you do when someone with a much bigger megaphone takes up a position similar to one you hold–but does it with lousy data and specious reasoning, promoting the utterly wrong approach in seeming ignorance about the consequences?

Nowhere is this dilemma clearer than in Caplan’s utter refusal to engage with the racial implications of his proposals. I, too, want fewer people in college. The best way to keep unqualified people from investing in college is to make work worthwhile. But Caplan wants to devalue work to the point of worthlessness through open borders, all the while denying even the possibility of education to those who can’t afford it.

Caplan complains that no proponents of public education have seriously engaged with his book. That’s because no one has observed, in so many words,  “Bryan Caplan thinks most blacks shouldn’t go to college because they’ll fail. He thinks state funded education is a waste of time. Kids whose parents can’t afford education should have to be smart enough to get a scholarship.”

That’ll get him some engagement. But then, he knows that.

Caplan is often rather smug about his media popularity. “Steve Sailer’s policy views are much closer to the typical American’s than mine.  Compared to me, he’s virtually normal.  But the mainstream media is very sweet to me, and treats Steve like a pariah.  I have to admit, it’s bizarre.”

It’s not bizarre at all. Honesty usually goes unrewarded.

 

 

 

 


International Students in America: Fewer, Please. A Lot Fewer.

I just noticed Noah Smith’s recent thread on importing students. He’s quite wrong (which wouldn’t be the first time).

Noah is upset that international students are choosing Canada rather than America.

I couldn’t be more pleased.

The best argument for reducing the flow of international students: America should not be draining the brains of the world.  If indeed we are taking China and India’s brightest people, then we are robbing those countries of the intellects needed to lead and educate their next generations–all so that they can drive down labor costs for Facebook and Google.

Noah doesn’t care about other countries, though–well, that’s probably not true. But in this case, he thinks more international students is good for America.

His case: we shouldn’t worry about foreign STEM students, because the US is graduating more STEM students than any country but India or China.

stemgradsforbes.PNG

But as anyone following education trends in the US can tell you, a substantial number of those US STEM graduates are from China and India. Many STEM graduate programs are overwhelmingly dominated by international students.

and at least

33,000 of Science and Engineering undergraduate degrees go to international students. This is six year old Pew data, but it’s a good look at how big a slice of our undergraduate STEM degrees are taken up by international students.

While Smith is correct that educational attainment has consistently risen in US, I’ve written before that much of this is driven by a relentless push for US colleges to lower standards and give college credit and diplomas to students with limited reading skills and middle school math ability.  We can debate the value of this increase, but it’s certainly not evidence that international students aren’t hurting American college education.

We can import international students AND lower standards. Neither is related to the other, and neither is anything to brag about.

Smith then proceeds to argue that 1)  foreign students aren’t taking slots from citizens and 2) rather, they are PAYING for the education of American students!

The first is simply false. From 2008 to today, the undergraduate student population at Stanford has increased by 8.5%. The undergraduate international student population increased over that same time by nearly 47%.  At the University of Michigan Ann Arbor over the same time period, campus population grew by 14%, while the international students increased by half.  In this long-form article on University of Illinois at Champaign-Urbana, the university admits that admission of out of state American students had dropped since the massive increase in international students–and the number of African American students has fallen hard from an already low rate.  And none of these schools mentioned are among the campuses, most of them top 50 schools, with the most international students.

International students are taking spots from Americans at selective college campuses.  Full stop. Noah is wrong.

The second part is more complex. Unquestionably, public research universities with limited domestic-out-of-state enrollment began turning to  international students when states cut funding.  Moreover, some schools, like  Ohio State , seem perfectly willing to keep students in Intensive English hell for eternity, or as long as they’re willing to pay tuition, whichever comes first. So some of the appeal of unqualified foreign students does seem to be their money.

But is that all? I see several reasons to wonder.

First, the choice to turn to international students is, by definition, a choice against instate students.  The universities could choose to charge more tuition and focus on providing services for the in-state students who can pay. They choose otherwise.  Why? Next, it appears that international students get about 8%  of their funding from US sources (7.9% from state, a bit from US government, according to link above).

While their additional tuition is attractive, it’s also obvious that international students cost a great deal to support. Despite the protestations of many a university admissions officer, many if not most international students are completely incapable of functioning in an American university. Some schools have started charging more for those services, but, as the story acknowledges, before that point the international students were costing a great deal more. And if international students are valuable for their out of state tuition, why are some universities abandoning the international student premium, or giving it back in scholarships? .

So the argument that international students are increasing purely to subsidize in-state low income recipients  at public universities is….shaky.  Besides, a quick look again at all these private schools with the most international students. State funding wasn’t behind those increases.

Having watched this most recent push for international students going on for a decade now, I’m deeply skeptical that public universities are increasing their take of international students for the sake of their in-state applicants. These aren’t short-term moves. Prestige and money for niceties seem to be much more the focus than the in-state students.

Pish tosh, sez Noah, the advantage of international students  is not about educating local undergrads”.  We are thus instructed to ignore all his arguments in favor of American students that I carefully spent half a page deconstructing and rebutting.

It’s about RESEARCH. Research is what boosts the local economy, by drawing in talent and capital and money. The goal should be to UPGRADE scattered second-tier universities into good research universities.

And, from a different tweet thread:

International students are an important part of the university-centered regional development strategy that is pulling towns and regions all across America out of the hole dug by the Rust Belt and the Great Recession…But that’s not all that international students do for America. Their presence improves and increases research labs at American universities. That generates business activity in small cities across America. Want to revive the Midwest? You’re going to need second-tier universities to become first-tier universities, and create local innovation. International students are very important to that strategy.

He develops his thoughts on the value of a university to a community in an op-ed:

smithcollegeadvantages

I’m sorry, I can’t resist: You boys know what makes this bird go up? 

So, mid-tier universities should import international students to fuel a Midwestern Enlightenment, create intellectual capital that will draw in others to benefit from the bounty. A western Renaissance of smart educated people wading through the rich flow of generated ideas.

Of course if the ideas were generated by international students, the ideas are probably copied. Or maybe the research was just faked.

Take look at the names on his list of top international countries turning out STEM students, or just the countries sending the most students.  China, India, Russia, Iran, Indonesia, and Japan.  Toss in Saudi Arabia.

These are all countries that excuse and encourage tremendous educational and academic fraud.

The students who have the means and desire to come to America to study come from fantastically corrupt countries. They generally show up for college  woefully unprepared, which is unsurprising, given that their test scores and transcripts are generally a work of fiction created by the very companies the colleges hire to find, er, “qualified” students.

Before and during their college experience,  many international students cheat every way they can–from lying on their applications, to  paying ringers to take college admissions or TOEFL tests, to cheating in class, to not even being students at all and just getting work visas–and when they are caught, they routinely wail that their cheating is totally okay in their own cultures, so how could they possible know?

Numerous reporters will hunt down academics to bleat reassuringly that oh, dear, it’s terrible, but not all international students cheat, but far fewer will mention the numerous studies demonstrating that it’s quite a lot of them, and always in greater percentages than domestic students.  The research that exists is far less interested in quantifying the impact of the cheaters on the rest of the university, and far more interested in explaining why they cheat and how they can be educated and encouraged to stop.

These often unqualified students with no understanding of American academic standards are just the seeds of Noah Smith’s grand plan to revitalize the Midwest. He wants many, many more of the same.  He wants American colleges to import millions more rich students from countries with a strong culture of student cheating and academic fraud. We’ll get them to plagiarize grant applications and produce a stream of federal funding that will run Potemkin research labs from Pocatello to Wheeling, the better to pull in start up companies to lie to venture capitalists about the great new product that some kid lied about to get an A in a senior seminar.

I’m not entirely kidding, either.  The degree to which universities are actively encouraging fraud in admissions and overlooking dishonesty and plagiarism to avoid upsetting international communities is shocking. Increasing the population would make a bad situation far worse.

Colleges have brought in far too many international students as it is. We should bring in less. I’m pleased the wave appears to be receding, although it has receded–and come back–before. I might not agree with Stephen Miller’s reasons for ending Chinese student visas, but bring it on. Ending Saudi Arabian student visas would be an inadequate, but painful, penalty for Saudi Arabia’s murder of Jamal Khashoggi.

One thing is certain: the mid-western townsfolk wouldn’t object to fewer middle-easterners. Or easterners, for that matter.

What should public universities do if states reduce their funding? They should reduce the number of students or reduce the number of services. Perhaps they could consider accepting only college ready students, insisting on students who could read at a tenth grade level and demonstrate mastery of second year algebra.  They might limit first year curriculum to a sequence of humanities and advanced math–put everyone in the same courses, leave variety to the following years. I feel sure there are ways to teach capable students more cost-effectively.

That approach may not revive moribund towns. But it wouldn’t flood them with international students who view the locals with contempt, either. Or turn them into mini-Vancouvers.

Rather than flooding the zone with federal dollars for research projects staffed by rich Chinese kids, we could use those same dollars to start vocational training centers. Maybe give grants to unemployed or unemployable to relocate and spend some money being trained in construction, in digital technology, auto mechanics and body work, and other skilled labor. That would stimulate the local economy. And if those trained left the area, well, there’d be more coming. Just like with college.

America has to start making do with its own people. It might not be easy.  It might not be better, at first. But it will certainly be fairer.

 

 

 

 

 

 

 


Memorization or Learning?

I originally started to write a post on a memorization technique I’m using for the unit circle, and went looking for representative jeremiads both pro and con. Instead, I found Ben Orlin’s piece When Memorization Gets in the Way of Learning (from five years back):

memoryorlin

…which is the opposite of a standard, boring piece and serves as a good counterpoint to explain some recent shifts in my pedagogy.

It’s a good piece. In many ways, the debate about memorization runs parallel to the zombie problem–students regurgitate facts without understanding. Ben’s against that. Me, too. Ben says that testing requirements create tensions between authentic learning and manageable tests; I have various means of ensuring my students understand the math rather than just hork it up like furballs of unknown origin, so am less concerned on that point.

But I don’t agree with this sentiment as much as I probably did a decade ago: Memorizing a list of prepositions isn’t half as useful as knowing what role a preposition plays in the language. 

Not in math, anyway.

 

A couple years ago, after I’d taught trigonometry two or three times, I suddenly noticed that at the end of the year, my students were very fuzzy on their unit circle knowledge. (It’s no coincidence that Ben’s article and my observations are both focused on trigonometry, a branch of math with a significant fact base.) When working trig equations, they’d factor something like the equation above, use the Zero Product Property, solve for sin(x)…and then stop.

“You’re not done,” I’d point out. You’ve only solved for sin(x). What is the value of x?”

Shrug. No recognition. My tests are cumulative. Many students showed significant recall of concepts. They were using ratios to solve complex applications; they were sketching angles on the coordinate plane–both concepts we hadn’t revisited in months. They could sketch the unit circle from memory and eventually figure out the answer. But they had no automatic memories of the unit circle working backwards and forwards, even though I had emphasized the importance of memorizing it.

Upsetting, particularly at the end of the year. The name of the class is Trigonometry, after all. Solving for sin(x) requires not one tiny bit of trig. It’s all algebra. Trigonometry enters the picture when you ask yourself what angle, in radians or degrees, has a y to r ratio of 1 to 2.

The sine of π/2 is not among [the important things to memorize]. It’s a fact that matters only insofar as it connects to other ideas. To learn it in isolation is like learning the sentence “Hamlet kills Claudius” without the faintest idea of who either gentleman is–or, for what matter, of what “kill” means.

Well, okay, but….if a student in a Trig class can’t work a basic equation without a cheat sheet, what exactly has he learned? He already knew the algebra. Does the same standard hold for SOHCAHTOA, or can I still assume the student has successfully learned something if he needs a memory aid to remember what triangle sides constitute the sine ratio? What else can be on the cheat sheet: the Pythagorean Theorem? The ratios of the special rights?

Ben describes memorization as learning an isolated fact through deliberate effort, either through raw rehearsal or mnemonics, both of which he believes are mere substitutions for authentic learning. He argues for building knowledge through repeated use.

Sure. But that road is a hard one. And as Ben knows much better than I, the more advanced math gets, the more complex and numerous the steps get. Most students won’t even bother. Those who care about their grades but not the learning will take the easier, if meaningless route of raw rehearsal.

So how do you stop students from either checking out or taking the wrong road to zombiedom?

I’ve never told my students that memorization was irrelevant, but rather that I had a pretty small list of essential facts. Like Ben, I think useful memorization comes with repeated use and understanding. But what if repeated use isn’t happening in part because of the pause that occurs when memory should kick in?

So I’ve started to focus in on essential facts and encouraged them to memorize with understanding. Not rote memorization. But some math topics do have a fact base, or even just a long procedural sequence, that represent a significant cognitive load, and what is memorization but a way of relieving that load?

The trick lies in making the memorization mean something. So, for example, when I teach the structure of a parabolas, I first give the kids a chance to understand the structure through brief discovery. Then we go through the steps to graph a parabola in standard form. Then I repeat. And repeat. And repeat. And repeat. So by the time of the first quiz, any student who blanks out, I say “Rate of Change?” and they reflexively look for the b parameter and divide by 2. Most of them have already written the sequence on their page. The memorization of the sequence allows them repeated practice.

But it’s not mindless memorization, either. Ask them what I mean by “Rate of Change”, they’d say “the slope between the y-intercept and the vertex”. They don’t know all the details of the proof, but they understand the basics.

I take the same approach in parent function transformations, after realizing that a third of any class had drawn parent functions for days without ever bothering to associate one graph’s shape with an equation. So I trained them to create “stick figures” of each graph:stickfigures

I drew this freehand in Powerpoint, but it’s about the same degree of sloppiness that I encourage for stick figures. They aren’t meant to be perfect. They’re just memory spurs. Since I began using them a year ago, all my students can produce the stick figures and remind themselves what graph to draw. They know that each of the functions is committed on a line (to various degrees). Most of them understand, (some only vaguely), why a reciprocal function has asymptotes and why square root functions go in only one direction.

So did they learn, or did they memorize?

I haven’t changed my views on conceptual learning. I believe “why” is essential. I’m not power pointing my way through procedures. I am just realizing, with more experience, that many of my students won’t be able to use facts and procedures without being forced to memorize, and it is through that memorization that they become fluid enough to become capable of repeated use.

Like Ben, I think a zombie student with no idea that cosine is a ratio, but knows that cos(0) = 1, has failed to learn math. I just don’t think that student is any worse than one who looks at you blankly and has no answer at all. And addressing the needs of both these students may, in fact, be more memorization. Both types of students are avoiding authentic understanding. It’s our job to help them find it.

So I’ll give an example of that in my next post.