Category Archives: engagement

The Release and “Dumbing it Down”

I’ve said before I’m an isolationist whose methods are more reform than traditional. I try to teach real math, not some distorted form of discovery math, but I also try to avoid straight lecture. I want to make real math accessible to the students by creating meaningful tasks, whether practice or illustration, that they feel ready to tackle.

I can’t tell you that students remember more math if they are actively working the problems I give them. Research is not hopeful on this point (Larry Cuban does a masterful job breaking down the assumptions that chain from engagement to higher achievement.) Will my students, who are often actively engaged in modeling and working problems on their own, retain more of the material than the students who stare vacantly through a lecture and then doodle through the problems? Or six months from now, are they all back to the same level of math knowledge? I fear, I suspect, it’s the latter. I think we could do better on this point if we gave students less. Not Common Core “less”, in which they just shovel the work at the students earlier. But a lot less math, depending on their ability and interest, over the four year period of high school.

Four plus years of teaching has given me a lot more respect for the sheer value of engagement, though. I believe, even if I can’t prove, that the kid who works through class, feeling successful and capable of tackling problems that have been (god save me for using this word) scaffolded for his ability, has learned more than the kid who sits and does nothing. Even if it’s not math.

Anyway. There comes a moment when the teacher says to the students, “go”. Best described as release of responsibility, whether or not a teacher follows any particular method, it’s when the teacher finishes the lecture, the class discussion, or simply handing out the task the students are supposed to take on without any other instruction.

It’s the moment when novices often feel like Mork. Done poorly, it’s the lost second half of a lesson. Done well, it’s the kind of moment that any observer of any philosophy would unhesitatingly describe as “good teaching”.

I started off being pretty good at release, and got better. That is, as a novice using straightforward explanation/discussion (I rarely lecture per se) or an illustrating activity, I could usually get 30% of the class going right away, another 40% doing a problem or two before asking for reassurance, and convince most of the remaining 30% to try it with explicitly hand-crafted persuasion. And for a new teacher, that’s nothing to sneeze at. Sure, every so often I let them go to utter silence, or a forest of raised hands, but only rarely. (And every teacher gets that sometimes.)

I remember pointing out to my teacher instructor, however, that I spent a lot of time re-explaining to kids. He said “Yeah, that’s how it works. You’re going to get some of them during the first explanation, some of them while helping them through the first task….” and basically validated the stats I just described in the previous paragraph. I still think he’s right about the fundamental fact: teachers can’t get everyone right away.

But all that re-explaining is a lot of work, and it leads to kids sitting around waiting for their personal explanation—and no small number of kids who then decide why bother listening to the lecture anyway, since they won’t get it until I explain it to them again, with of course the stragglers, the last 30%, screwing around until I show up to convince them to try. Of course, I went through (and still go through) the exhortation process, telling them to ask questions, “checking for understanding”, and so on.

And it absolutely does help to make the “release” visible to the kids, “Okay, let’s be clear–we are wrapping up the explanation portion, it’s time for work, and I WILL NOT BE HAPPY if you shoot your hand up right after I say ‘go’ and whine about how you don’t get it.”

This works. No, really. Kids say “Could you go through it one more time?” before I release them, particularly after I’ve put them “on blast mode” for saying “I don’t get it” when I show up at their desk to see where they are.

But I focused on release almost immediately as an area for my own improvement. As I did so, I began to understand why release is so hard for teachers, particularly new ones.

We overestimate. We think, “I explain it, they do it.” We think, “I gave them instructions they can follow.” We think, “This is the easy part” and are already mapping out how we’ll explain the hard part.

And then we say “Fly, be free!” and the class drops with a splat. Burial at sea. Wash away the evidence.

We aren’t explaining enough. Or they aren’t listening. We aren’t giving clear instructions. They don’t read the instructions. “Too many words.”

What I have discovered, over time, is that I must halve or even quarter what I think students can do, and then deliver it at half the pace. With this adjustment, I can release them to work that they will find challenging, but doable. This is the big news, the news that I pass on to all new teachers, the news they invariably scoff at first and then, reluctantly, acknowledge to be true.

But what I have begun to realize, again over time, is that by first “dumbing it down”, I have slowly increased the difficulty and breadth of coverage I can deliver. Not a lot. But some. For example, I now teach the modeling of inequalities, modeling of absolute values, and function operations, in addition to modeling linear equations, exponentials, probability, and binomial multiplication. I don’t think my test scores have increased as a result, but it makes me feel better about what my course is called, anyway.

In mulling this development, I have concluded, tentatively, that I’ve become a better teacher. Or at least a better curriculum developer. That is, I don’t think “dumbing down” itself has led to my increased coverage or my students’ ability to handle the topic. But I’ve gotten better at the “release”, at developing explanations and tasks that allow the students to engage in the material.

It’s possible I’ve been unwittingly participating in a positive feedback loop. As I get better at the release, at correctly matching their ability to my tasks and explanations, the students are more likely to listen, to try to learn, to dig in to a new task and give it a shot. So I get bolder and come up with ideas for more complex subjects.

I dunno. Here’s what I do know: effective release requires willing students. The able students are willing by default. The rest of them need something else.

Put it another way: the able students have trust in their own abilities. The kids who don’t trust in their own abilities need to trust me.

No news there, that trust is an essential part of teaching. But I’m only now considering that my lesson sequencing and content might be an essential element in building the trust the students need to take on challenges.

Eighteen months ago, I wrote an essay that captured the moment when teachers realize that their students don’t retain learning. They demonstrate understanding, they pass tests demonstrating some ability, and then two weeks, three weeks, a couple months later, it’s gone. (Every SINGLE time I introduce completing the square, it’s a day.)

The “myth” essay describes what happens after release. That is, after the teacher realizes that students didn’t understand the lecture, didn’t understand the worksheet, are goofing off until the teacher comes around to give one on one tutoring, after the teacher does the additional work to get the instruction out, the kids seem to get it. And then forget it all completely, or remember it imperfectly, or rush at problems like stampeding cattle and write down anything just to have an answer.

So consider this the companion piece: the front end of classroom teaching to the myth’s back end.

But in fact, it’s all part of the same problem. And, as I said in the first essay, teachers tend to react in one of two ways: Blame or Accept. Many accepters just skedaddle to higher ability students. I’m teaching precalc this year and have some interesting observations on that point. But leave that for another essay.

I’m an accepter:

Acceptance: Here, I do not refer to teachers who show movies all day, but teachers who realize that Whack-a-Mole is what it’s going to be. They adjust. Many, but not all, accept that cognitive ability is the root cause of this learning and forgetting (some blame poverty, still others can’t figure it out and don’t try). They try to find a path from the kids’ current knowledge to the demands of the course at hand, and the best ones try to find a way to craft the teaching so that the kids remember a few core ideas.

On the other hand, these teachers are clearly “lowering expectations” for their students.

And that’s me. I lower expectations. I do my best to come up with intellectually challenging math that my students will tackle. I don’t lecture because the kids will zone out; instead, I have a classroom discussion in which the kids live in some terror that I might call on them to answer a question, because they know I won’t ask for raised hands. So they should maybe pay attention. I have no problem with students taking notes, but for the most part I know they don’t, and I don’t require it. I give them a graphic organizer with key formulas or ideas (or they add them). I periodically restate the critical documents they should save, tell them I designed the documents to be useful to them in subsequent math classes, double check them periodically to see if they have the key material.

Dan Meyer sees himself as a math salesman. I see myself as selling….competence? Ability? A sense of achievement?

Whatever. When you read of those studies showing that math courses don’t match the titles, you’re reading about courses I teach. I teach the standards, sure, but I teach them slowly, and under no circumstances are the kids in my algebra II class getting anything close to all of second year algebra, or the geometry students getting anywhere near all the geometry coverage. That’s because they don’t know much first year algebra, and if you’re about to say that the Next New Thing will fix that problem, then you haven’t been paying attention to me for the past two years.

But at some point, maybe we’ll all realize that the issue isn’t how much we teach, but how much they remember.

Or not.

Be clear on this point: I do not consider myself a hero, the one with all the answers. I am well aware that many math teachers see teachers like me as the problem. Many, if not most, math teachers believe that kids can learn if they are taught correctly, that the failings they see are caused by previous teachers. And I constantly wonder if they are right, and I’m letting my students down. While I sound confident, I want to be wrong. Until I can convince myself of that, though, onwards.

I began this essay intending to describe a glorious lesson I taught on Monday, one in which I released the kids and by god, they flew. But I figured I’d explain why it matters first.


Dan Meyer and the Gatekeepers

I have at least one more post on reform math, but I got distracted while looking for examples of Dan Meyer’s teaching (as an example of his math in action) then realizing that many of my regular readers wouldn’t know Dan Meyer, and so started to construct a brief bio. In doing so, I got distracted again in considering Meyer’s quick-yeast rise and what it says about the gatekeepers in the education racket and access to microphones.

This may seem like insider baseball, but I hope to illustrate that Dan Meyer is an unobjectionable guy with a good idea, whose unhesitating adoption by the elites represents a real problem with educational discourse in this country. I will probably overstate and paint a picture that suggests plan and intent by those causing the trouble, when in fact it’s fuzzy and reactive with only big picture general directions, but probably not to the extent that Diane Ravitch (or, indeed, Dan Meyer) commit that particular sin.

Dan Meyer, 31, is in the process of becoming a celebrity math teacher (hey, it’s a small group). Much of his rapid trajectory upward can be explained by his message, which involves a digital curriculum that will (he says) instantly engage and perplex kids and thus resolve all classroom management issues (more on this later), a message tailor-made to appeal to both techies, since it implicitly attacks all teachers, and progressive educators, since it is inherently constructivist.

Most of the rest of his said trajectory can be explained by his excellent luck in his early audience—not only were they progressives and techies, but they were influential progressives and techies–Chris Lehmann, O’Reilly Publishing folk like Kathy Sierra, Nat Torkington and Tim O’Reilly himself, Brian Fitzpatrik of Google, and Maggie Johnson of Google and Stanford.

A teeny-tiny bit–ok, maybe more–of that trajectory can be explained by the Great White Hope factor. As I’ve written many times, every corner of education is desperate for young teachers, particularly young male teachers, most especially young white male teachers. Smart young white male pushes technology-based teaching, implicitly or explicitly declaring that all those old teachers (mostly white female grandmas) are doing it wrong. Hard to resist. So attractive message, demographic felicity, and luck. Not bad.

I’m going to summarize what I see as the relevant points of Meyer’s career thus far, but go straight to the source: Meyer describes his teaching career in this excellent video, which I recommend watching to instantly “get” his appeal. Go watch. I’ll wait.

He taught his first year at a Title I school in Sacramento, CA and, as he says above, was both miserable and ineffective, which he blames on his failure to create a “classroom ethos”. The improvement in classroom ethos began during his second year at San Lorenzo Valley High. It apparently never occurred to him to wonder whether the “classroom ethos” improvement at his second school, was helped along by a student demographic that was 87% white. Meyer actually noted the novelty of a non-English speaking Hispanic student which is the only time he ever mentions a minority student on his blog, best I can see.

While he made numerous videos that ended with the tagline, “I like to teach”, he in fact wasn’t all that attached to teaching. At the beginning of his third year, he was already predicting he’d be in school for either an administrative credential or doctorate by the end of the next year (he was off by two), because “I’m just keenly aware how much of my strength as a teacher derives from my ability to relate to student culture, to talk like they talk and dress like they dress” and his awareness that he feels “obliged to entertain”. He often implied that he’d mastered the technical aspects My personal favorite::

I am at a place, for example, where classroom management no longer challenges me. Not that every day is all smiles and hard work, just that I have identified the mix of engaging instruction, mutual respect, and tough love that eluded me for years.

Four ENTIRE years, this eluded him! This meme runs throughout his blog and is, in fact, the seed of his image-based curriculum. Meyer states time and again that he worked hours on end to keep from boring his students, thinks student approval as essential to improved learning outcomes and thus presents his curriculum as a better way to entertain kids, to perplex them in a way they will value, and once entertained and perplexed, they will learn.

Then, at the end of five years, he declared he was quitting teaching because he’d been transformed from “miserable to happy, incompetent to competent” (astonishing, really, how few of the commenters openly laughed at his hubris). He originally planned to attend UC Santa Cruz’s PhD program but his aforementioned contacts got him a year as curriculum fellow at Google, and he taught part-time for one more year. While at Google, he made his first TV appearance on Good Morning America (probably via Google) to discuss his theory as to whether regular or express grocery lanes were faster.

At some point after that, he pulled a TEDx invitation—very nice work if you can get it—which got him onto CNN and good lord, how could Stanford let him get his doctorate at Santa Cruz, after all that publicity? So now he’s at Stanford in year 3 of his doctoral program.

A star was born.

Like most teachers, Meyer’s a good talker; unlike many teachers, he’s good with any audience. He’s a bright guy and his videos are genuinely entertaining (go to the end to catch his early work), and I say that as someone who disagrees with very close to all of his primary assertions. As a young white male teacher he could demand nearly anything, and he nonetheless stayed in algebra and geometry, rather than push for advanced classes that his principal, eager to keep him, would easily grant. I suspect that some of his willingness to stay in low status classes was caused by his short-timer’s attitude, while another part of it was caused by his 70-hour work week. Anyone working that hard and long on classes he’s been teaching for years is unlikely to embrace new subjects. But those stated priorities nonetheless reveal a guy who is well beyond committed and flat out obsessed with doing a good job.

He’s hard to pin down ideologically not because he’s an original thinker but because he was, and is, profoundly uninterested in education policy. So no coherent philosophy, but Me Like, Me No Like. He would disavow the charge that he is on the “reform” side of the math wars, although less vehemently than a few years ago—Jo Boaler, High Priestess of Reform Math, is his adviser, after all. But even now, a few years after starting a Stanford PhD program, he’s very foggy about the specifics of major debates in math education. So he’s been trying to consolidate his positions, but he’s not always sure what the right ones are. In his earlier iterations, for example, before he became well-known, he often adopted strong education (not math) reform positions—he had an “educrush” on Michelle Rhee. In the early years of the blog, he dripped contempt on most teachers, particularly older ones, including coworkers. Early on he harped often on the need for professionalism, and asserting we’d be better off without teachers that do it just for love. But once Stanford put him on the doctoral payroll, he’s become more typically math reform, which means he’s disavowing education reform positions and doing his best to walk all that talk back. Well, not all of it–here he is on a forum last year talking about the need to train teachers on Common Core:

I think if you’ve taught for thirty years under a particular style of teaching, it has to distort what your perception is of math and how it should be taught. It’s unavoidable, to be steeped in that for so long. So to realign yourself, I imagine, is a very difficult thing. So PD that involves problem solving, involves reasoning, argumentation, that’ll be essential going forward.

So the nastiness to older teachers, still there. I don’t blame anyone who wonders if promoters consider that a bug or a feature.

Meyer’s writings never describe his “classroom action” in detail relative to other math bloggers (e.g., Fawn Nguyen, Sam Shah, Michael Pershan, Kate Nowak and, okay, me). He rarely describes the success or failure of a particular lesson, or gives any kind of walkthrough. He never describes a lesson in full detail, down to the worksheets and responses. He often went to the data collection well, and just as often failed, as in his two-month long “Feltron” project in which half the class dropped out early during data collection and had to be given other tasks, or this similar project

Meyer and metrics aren’t a natural fit. A few years ago, he was, comically, shocked by news of California’s Hispanic achievement gap. Dude, didn’t you get the memo? He never blogs about it, never discusses it, then out of the blue: Damn! We’ve got an achievement gap! And then he rarely mentions it again, save for this recap of Uri Treisman’s speech. He almost never discusses his student’s test scores and when he does, they are usually not great, although he mentions once in passing that his algebra students beat the department (no data, though). He cheerfully talked about standards-based grading for a year or two and blew off the commenters who wondered if the students were retaining the skills they’d “mastered” twice in a week. When he did finally get around to looking for that data, the answer was no, and it’s quite clear that he’d never before wondered about this essential element of success. So while I suspect that Meyer was a popular teacher who convinced a lot of kids–mostly white boys–to work hard at math, there’s little evidence of that in his written history of his years teaching.

I can find little evidence of intellectual achievement in education once he left teaching, either. At Google, he and three other curriculum fellows worked for a year on computational thinking projects. When his project shipped he wrote, somewhat obscurely, “Near as I can tell, of the sixty-or-so modules listed, only one of them ….is mine. I always admired Google’s lack of sentiment in deciding when to invest itself and when to divest itself. Still it’s strange to see a year of work reduced to a single entry in a long list.” (emphasis mine)

At Stanford, his qualifying paper was not hailed as an instant masterpiece:

The criticism I remember most vividly: a) my weak review of the literature, b) the sense that I wasn’t really taking myself anywhere new with the study, and c) a claim about equity that had me reaching beyond my data.

In short, he didn’t set the curriculum world on fire at Google, and the critiques of his qualifying paper suggest an analytical lightweight—which is pretty typical for salesfolk. So thus far Meyer has established himself as a stupendous salesman, but not much of an intellectual—at least, not of the sort that Google and Stanford like to pretend they invest in. He was even wrong in the GMA segment. Unsurprisingly, he was unflustered.

Realize that I know all of this because of Dan Meyer’s blog, so he’s not hiding anything. Hell, he doesn’t need to.

But he was brought to Google and then to Stanford and then Apple gets involved, and now we’re talking three of the most elite institutions in the country are pushing him not because they have any evidence of his ability to close the achievement gap, or even whether his digital curriculum works, but simply because he’s Dale Carnegie, and boy oh boy, is that a depressing insight into their motivations, just as his success is indicative of the desires of the larger educational world. It’s not “go develop your ideas and expand and prove them” but “here’s a bunch of elite credentials that will make your sales job easier”. So they dub Dan an “expert” and give him a microphone—which makes it a whole lot easier for a largely ignorant general media to hear him.

No, I’m not jealous. My karmic destiny demands that I enter new communities with neither warning nor fanfare and utterly polarize them within a month, usually without any intention of causing trouble. Lather, rinse, repeat. I gave up fighting that fate fifteen years ago. I have attended two elite institutions in recent memory; one of them ignored me desperately, the other did its best to hork me up like a furball. I don’t want to go back. Academia isn’t for me. And if a corporation handed me money to sell my message, they’d be facing a boycott. My blog has fifty times the readership and influence that I ever imagined, and I love teaching. I am content.

Previous paragraph notwithstanding, this essay will be interpreted by some as an attack on Dan Meyer, who is largely unfamiliar with anything short of worshipful plaudits from eager acolytes (he occasionally heeds polite dissenters, but only occasionally) since he began his blog. But while he’s a dilettante as a teacher, I think his simplistic curriculum ideas have interesting potential in teaching certain demographics, and I wish him all success in developing a coherent educational philosophy. Oh crap, that was snarky. I wish him all success in his academic and business career.

Dan Meyer’s rapid rise isn’t the problem. Dan Meyer himself isn’t the problem. The problem lies with the Gatekeepers: with Stanford, who knows that Dan’s not the solution, with Google, Apple, and publishing companies like Shell Centre (well, they’re in England) and Pearson. That intersection between academia and business, the group that picks the educational platitudes and pushes them hard, while ignoring or banishing dissent. They’re the ones granting Meyer the credentials that cloak him in the illusion of expertise. And I believe that, at least in part, they grant those credentials with a clear eye to the attributes that are diametrically opposed to the attributes they pretend to focus on. It’s no coincidence that Dan Meyer is a young white male. It’s the point. It’s not a fluke that he primarily taught white kids, many of whom were obviously sent to him with strong skills by teachers who valued homework above ability. It’s the only way he could have come up with his curriculum. Yet his message is adopted and embraced by elites who castigate education, particularly teachers, for failing black and Hispanic kids. I don’t know if they do this consciously or if they genuinely believe that all teachers are just meanspirited morons who don’t know math and deliberately deprive certain kids of meaningful math experiences. Ultimately, it doesn’t matter.

I suspect Meyer and others will ignore this essay (Meyer snarked obscurely at my reform piece, assuming this tweet means what I think it does), but whether that’s because he doesn’t like dissent or, more probably, because he subscribes to the Voldemort View, I couldn’t tell you. But maybe this piece will make reporters and educational wonks a bit more wary about the backgrounds of the “experts” they quote, and the gatekeepers who create them.


Who I Am as a Teacher

As I thought about writing specific disagreements I have with reformers, I realized that time and again I’d be having to break off and explain how my values and priorities differed. So I thought I’d do that first.

At my last school’s Christmas party (Year 1 at that school, Year 2 of teaching), the popular, widely respected “teacher at large” showed up an hour late. A PE teacher whose credential had been disallowed by NCLB-wrought changes, he was at that point responsible for coming up with plans to help “at-risk” kids.

“Yeah, I was having all sorts of fun reviewing the Lists.”

“The Lists?” asked another teacher.

“Top 25 Discipline Problems, Top 25 Kids On Probation for Felonies, Top 25 Absentee/Truancy Students, Lowest 25 GPAs, you name it. I look for the kids who aren’t on more than one or two lists and try to reach them before they qualify for more lists.”

“I think I have a few of those kids.” groused a teacher.

“A few? Pity Ed here.” He nodded at me. “Half the kids on each list are in one of your classes.”

I think he made up the felonies list. I hope.

Fall of year two was about as tough a time as I’ve ever had as a teacher.

Getting quiet for teaching was job one. I’d separate inveterate chatters, then I’d move the worst offenders to the front groups, and then, if one of them still didn’t shut up, I’d pull the desk forward all the way to a wall (with the kid in it). The rest of the class would snicker at the talker—at, not with.

“It’s not like I’m going to pay attention to you up here. I’ll just go to sleep,” one of them said, defiantly.

“You say that as if it were a bad thing.”

He or she often did go to sleep, which gave me some quiet from that corner, anyway. Otherwise, I wrote a referral. I also wrote referrals when they called me a f***ing [noun of your choice, profane or not], a sh**ty f**ing boring teacher (boring! I ask you), when they threw things, when they got up and wandered around the room refusing to sit, when they texted in open view and refused to give over the phone, when they left the room without permission, when they howled I HAVE TO PISS at the top of their voices (usually one at a time), and so on—all during the time that I was trying to teach the lesson “up front”. Once I released them for work it got easier, as I wasn’t trying to maintain order and some notion of what I’d been doing before the last interruption, but rather walking around the room helping students and telling others to shut up.

As bad as I make it sound, every senior teacher I worked with was astonished at how well I did, given the pressure; all the previous teachers stuck with all algebra all the time had routinely lost control of the classes and had supervisors posted. Administrators didn’t approve of my approach, alas; since my kids were mostly Hispanic, my referrals were, too. So I was caught between an administration who would really rather I’d have flailed ineffectually than kick kids out for order, and the bulk of my students, who opined frequently that I should boot students more often and earlier.

The beginning of the way back up that year began in second period when I’d thrown out the third kid of the day, and Kiley said “Could you toss out Elijah, while you’re at it?” and much of the class laughed. Elijah stood up and said “Yeah, send me, too! I don’t want to be here! Let me go!”

I tend to stay pretty focused on teaching; rarely do I give A Talk. Today, I have no idea why I made an exception.

“Why don’t you want to be here, again?”

“Because I hate math? F***ing duh.”

“What is it you think I want?”

“You want me to shut up.”

“Well, yeah. But why?”

“So you can teach!”

“Why?”

“Because it’s your job!”

Because I want everyone to pass this class.” And to this day, I thank all that’s holy that I caught the class’s sudden silence and realized that my remark had an impact.

“Maybe I need to make that clearer. I want every single person in here to pass algebra and move onto geometry. Remind me again, how many people have taken algebra more than once?” Almost everyone in the class raised a hand, including Elijah.

“Yeah. Don’t raise your hand, but I know at least ten students in here are taking it for the third time, including some people who get tossed out of class regularly. I don’t kick kids out for fun. I kick them out because I need to teach everyone. I have kids who want to excel in algebra. I have kids who would like to get better at algebra. I have kids who simply would like to survive algebra, although many days they think that’s a pipe dream. And I have kids who don’t want to be here at all. I figure, I kick kids out from the last group, I’m meeting everyone’s goals but mine.” I actually get a couple laughs; they’re listening.

“But make no mistake, that’s my goal. I want everyone in here to pass.” I looked at Elijah, who’d slipped back into his chair, his eyes fixed on me.

“You could tell me about your troubles, and I’ll give you an ear, but here’s a basic truth: there’s not a single situation in your life that gets worse if you pass algebra. And there’s a whole bunch of things that improve.”

“I could get a work permit, for one thing,” Eduardo muttered.

“Get back on the football team,” said DeWayne.

“And now I know some of you are thinking sure, there’s a catch. No. I didn’t say I want you to like algebra. I didn’t even say I want you to understand algebra, although I guarantee that trying will improve your understanding. I’m making a simple commitment: show up and try. You will get a passing grade. No catch.”

The rest of second period, the toughest class, went so well that I decided to repeat that little speech for every class, and in every class, I got utter quiet. I don’t say that all the problems were solved that day, but from that point on far more of the kids “had my back”. Psychologically, their support made it much easier for me to develop a strategy to teach algebra in the face of these challenges.

Here’s how I taught it, and here’s how they did. I only failed 10 kids out of the final 90, or 11%. (Elijah had left. Eduardo got his permit, and DeWayne made it back onto the football team.) That’s the highest failure rate I’ve ever had, but then it’s the last time I taught algebra I. It’s easier to work with kids in geometry and algebra II—they’ve got skin in the game, and graduation becomes a real objective as opposed to the remote possibility it presents to a sophomore taking algebra I for the third time.

The wise reader can infer much about my students and a great deal, although certainly not all, about my values and priorities as a teacher from that tale.

First, I mostly teach kids from the lower third to the middle of the cognitive ability spectrum, with a few outliers on each end. That’s who takes algebra in high school. No more than 10% of my students in any year are capable of genuinely comprehending an actual formal math course in geometry or algebra (I or II). Another 30-50% of the rest are perfectly capable of understanding geometry, algebra and even more advanced topics in applied math, even if they couldn’t really master a formal math course, but they’d have to try a lot harder and want it much more. About a quarter of my students each year are barely capable of learning basic algebra and geometry well enough to apply it in simple, rote situations. A much smaller number can’t even manage that much.

For other teachers, the percentages are skewed heavily to the first and second categories; some of them don’t even know there’s a third and fourth category. A teacher covering precalc and honors algebra II/trig in high-income or Asian suburb, teaching mostly freshmen and sophomores, would have a much higher percentage of students who could master a formal course; their notion of “struggling kids” would be those who aren’t working hard enough. But that’s not my universe—and it’s not the universe I signed up for, although I wouldn’t mind visiting occasionally.

Until this year, my assignments weren’t deliberate. I was just an unimportant teacher who schools didn’t care about losing. In fact, the following year at that same school the administration assigned Algebra II/Trig classes to a teacher who was not qualified to teach the subject while I, who was qualified, was given the lower level Algebra II classes. The administration knew full well about the distinction, which necessitated a “your teacher is not highly qualified” letter to some 90 kids, but that teacher was more valuable than than I was, and so it goes. I’m not bitter, and I’m not marking time until I get “better” kids. I’m doing exactly what I want to do. But every teaching decision I make must be considered in light of my students’ cognitive abilities and, related to that ability, their motivation.

Second, I am a teacher who doesn’t overvalue any individual student at the expense of the class, which means I have no compunction about kicking kids out for the day. You run into these teachers philosophically opposed to removing kids from class; how can these students learn if they aren’t in class, they bleat. These teachers never seem to worry about how all the other kids learn with a disruptive hellion wreaking havoc because, they strongly hint (or outright assert), the right curriculum and caring teachers would eliminate the need to disrupt.

I ask these teachers, politely, do you have kids with tracking bracelets and/or probation officers? Do you have students who have fathered two kids while wearing that tracking bracelet, or gave birth to one? Do you have students who have been suspended or expelled for putting other students in the hospital, or for having a knife in their backpack? Do you have students who routinely tell you to f*** off and don’t bother me? Do you have all of these students plus twelve more who have just enough motivation that, given no distractions, would be able to learn some math but with a distraction will readily jump over to the side telling you to f*** off? And with all that, are you math teachers trying to help students with a four-year range in skills figure out second year algebra? Because otherwise, you can go sing your smug little songs of no student left behind to someone with kids who really shouldn’t be kicked out of the classroom. Okay, maybe not politely.

Come back the next day or even the same day, hat in hand, and no harm, no foul. I don’t only act like it didn’t happen, I have completely forgotten it happened. But get out of my class if you won’t shut up or can’t consider the day a success unless you’ve sucked in three other kids with your distractions.

The biggest pressure on teachers like me these days is the huge pushback they get from administration, district, and state/federal education agencies when they try to maintain an orderly classroom. And charter schools’ ability to a) have none of these kids to start with and b) kick moderately ill-behaved kids back to public school when they act out can’t be overstated as factor in their “success”.

That’s a shame. Because invariably, the bulk of my unmotivated rabble-rousers realize that I really mean it about that whole “passing” thing, if they would just shut up and give the class a shot. And so they do.

Next, I am a teacher who explains. I don’t mean lecture; my explanations always take the form of a semi-Socratic discussion, leading the kids through a process. But when I start to talk, the conversation has a direction and that directed conversation, to me, is the heart of teaching. One of my favorite memories of an ed school classmate came about as we were driving to our placement school.

“I’m really enjoying working on aspects of my teaching that I don’t like. For example, explanations. I hate doing that.”

“Um, what? You hate explanations?”

“Yeah. I’d rather never explain anything.”

Pause.

“What is teaching, if it’s not explaining things?”

I thought it was a rhetorical question. I was wrong. He went on and on about other aspects of teaching: curriculum, motivation, role modeling, assessing students, and so on. Huh. Interesting. Eye-opening. It’s not that I disagreed, but how can you be a teacher if you don’t like to explain things?

And as I began to develop, I realized that teaching is not synonymous with explaining. Still. It’s my go-to skill, it’s what I do best, it’s a big part of my success with low ability students, and it’s why I prioritize getting my students to shut up while I’m teaching up front.

Next, the story reveals that I adopt my students’ values and goals, rather than insist they adopt mine. The kids were shocked into silence when they realize that my most heartfelt goal was to pass everyone in the class.

I learned a key lesson I still use every time I meet a new class, and make it clear I want to help them achieve their goals, which usually involve surviving the class. I do not understand why so many teachers set out objectives based on the assumption that they will successfully re-align their students’ value systems.

And in a related revelation, you can see how I frame my task. In his TED talk, Dan Meyer asks the audience to imagine:

“you really loved something…and you recommended it wholeheartedly to someone you really liked…and the person hated it. By way of introduction, that is the exact same state in which I spent every working day of the last six years. I teach high school math. I sell a product to a market that doesn’t want it but is forced by law to buy it.”

All math teachers can relate to this statement; it’s clever, funny, and does a good job of introducing the fundamental dilemma of high school math teachers: most kids hate math and are required to take it. Many dedicated math teachers would not only relate, but agree with Dan’s framing of his task as a sales job, regardless of their teaching ideology. When I say I disagree, it’s not because Meyer is wrong but because we approach our jobs in fundamentally different ways. I don’t love math, and I’m not selling a product.

Victoria: I’m terrible. I know I’m terrible. I look at the mirror and I’m ashamed. Maybe I should quit. I just can’t seem to do anything right.

Joe Gideon: Listen. I can’t make you a great dancer. I don’t even know if I can make you a good dancer. But, if you keep trying and don’t quit, I know I can make you a better dancer. I’d like very much to do that. Stay?

Were it not for the unfortunate plot point about Joe Gideon’s motives for hiring Victoria for the show (he was a hounddog who had her in bed an hour after they first met), I suspect more math teachers would reveal that they can quote this scene from All That Jazz verbatim.

And those math teachers mostly would agree with me. Teaching math, for us, isn’t about creating mathematicians. It’s only occasionally about working with kids who want to be engineers, doctors, or architects. Mostly, it’s about giving kids enough math skills to pass a college placement test so they won’t end up spending a fortune on remedial math classes and never get any further—or at least enough skills so they’ll pass a remedial math class and move on. Or giving kids enough math so they look at a trade school placement test and think, “Hey, I can do this.” Or just giving kids the will to pass the class and keep them out of mindless credit recovery in alternative institutions, letting them feel part of the educational system, not a failure who couldn’t cut it at normal high school.

We don’t promise miracles. We do promise “better”.

Finally, though, the story indicates that I am acutely aware of all my students’ motivations, that not all my students just want to pass. I have bright kids in almost every class, I have highly motivated kids, I have kids with specific objectives, most of whom want to learn as much as they can. I never forget them, and if I can’t dedicate my entire teaching agenda to meeting their goals, it’s only because I owe allegiance to all my students. I never stop looking for better ways to give these kids what they need while still ensuring I meet my overall responsibility. Many other teachers say these kids should come first. I always worry they might be right. But as I said above, I do not overvalue any individual kid over the needs of the entire class.

This tale doesn’t tell much about how I teach, but that particular topic gets plenty of coverage in other essays.

Anyone who is familiar with reform math can probably infer not only my teaching values and priorities, but also a lot of reasons why I’m not crazy about reform math. But I’ll go into details in the next post.


Modeling Linear Equations, Part 3

See Part I and Part II.

The success of my linear modeling unit has completely transformed the way I teach algebra.

From Part II, which I wrote at the beginning of the second semester at my last school:

In Modeling Linear Equations, I described the first weeks of my effort to give my Algebra II students a more (lord save me) organic understanding of linear equations. These students have been through algebra I twice (8th and 9th grade), and then I taught them linear equations for the better part of a month last semester. Yet before this month, none of them could quickly generate a table of values for a linear equation in any form (slope intercept, standard form, or a verbal model). They did know how to read a slope from a graph, for the most part, but weren’t able to find an equation from a table. They didn’t understand how a graph of a line was related to a verbal model—what would the slope be, a starting price or a monthly rate? What sort of situations would have a meaningful x-intercept?

This approach was instantly successful, as I relate. Last year, I taught the entire first semester content again in two months before moving on, and still got in about 60% of the Algebra II standards (pretty normal for a low ability class).

So when I began intermediate algebra in the fall, I decided to start right off with modeling. I just toss up some problems on the board–Well, actually, I start with a stick figure cartoon based on this lesson plan:

modelingsketch

I put it on the board, and ask a student who did middling poorly on my assessment test, “So, what could Stan buy?”

Shrug. “I don’t know.”

“Oh, come on. You’re telling me you never had $45 bucks and a spending decision? Assume no sales tax.”

Tentatively. “He could just buy 9 burritos?”

“Yes, he could! See? Told you you could do it. How many tacos could he buy?”

“None.”

At this point, another student figures it out, “So if he doesn’t buy any burritos, he could buy, like,…”

“Fifteen tacos. Why is it 15?”

“Because that’s how much you can buy for $45.”

“Anyone have another possibility? You? Guy in grey?”

Long pause, as guy in grey hopes desperately I’ll move on. I wait him out.

“I don’t know.”

“Really? Not at all? Oh, come on. Pretend it’s you. It’s your money. You bought 3 burritos. How many tacos can you get?”

This is the great part, really, because whoever I call on, and it’s always a kid who doesn’t want to be in the room, his brain starts working.

“He has $30 left, right? So he can buy ten tacos.”

“Hey, now, look at that. You did know. How’d you come up with ten?”

“It costs $15 to get three burritos, and he has $30 left.”

So I start a table, with Taco and Burrito headers, entering the first three values.

“And you know it’s $15 because….”

He’s worried it’s a trick question. “…it’s five dollars for each burrito?”

I force a couple other unwilling suckers to give me the last two integer entries

“Yeah. So see how you’re doing this in your head. You are automatically figuring the total cost of the burritos how?”

“Multiplying the burritos by five dollars.”

“And, girl over there, in pink, how do you know how much money to spend on tacos?”

“It’s $3 a taco, and you see how much left you have of the $45.”

“And again with the math in your head. You are multiplying the number of tacos by 3, and the number of burritos by….”

“Five.”

“Right. So we could write it out and have an actual equation.” And so I write out the equation, first with tacos and burritos, and then substituting x and y.

“This equation describes a line. We call it the standard form: Ax + By = C. Standard form is an extremely useful way to describe lines that model purchasing decisions.”

Then I graph the table and by golly, it’s dots in the shape of a line.

datamodelmockup

“Okay, who remembers anything about lines and slopes? Is this a positive or a negative slope?”

Silence. Of course. Which is better than someone shouting out “Positive!”

“So, guy over there. Yeah, you.”

“I wasn’t paying attention.”

“I know. Now you are. So tell me what happens to tacos when you buy more burritos.”

Silence. I wait it out.

“Um. I can’t buy as many tacos?”

“Nice. So what does that mean about tacos and burritos?”

At this point, I usually get some raised hands. “Blue jersey?”

“If you buy more tacos, you can’t buy as many burritos, either.”

“So as the number of tacos goes up, the number of burritos…”

“Goes down.”

“So. This dotted line is reflecting the fact that as tacos go up, burritos go down. I ask again: is this slope a positive slope or a negative slope?” and now I get a good spattering of “Negative” responses.

From there, I remind them of how to calculate a slope, which is always great because now, instead of it just being the 8 thousandth time they’ve been given the formula, they see that it has direct relevance to a spending decision they make daily. The slope is the reduction in burritos they can buy for every increased taco. I remind them how to find the equation of a slope from both the line and the table itself.

“So I just showed you guys the standard form of a line, but does anyone remember the equation form you learned back in algebra one?”

By now they’re warming up as they realize that they do remember information from algebra one and earlier, information that they thought had no relevance to their lives but, apparently, does. Someone usually comes up with the slope-intercept form. I put y=mx+b on the board and talk the students through identifying the parameters. Then, using the taco-burrito model, we plug in the slope and y-intercept and the kids see that the buying decision, one they are extremely familiar with, can be described in math equations that they now understand.

So then, I put a bunch of situations on the board and set them to work, for the rest of that day and the next.

DataModelingstart

I’ve now kicked off three intermediate algebra classes cold with this approach, and in every case the kids start modeling the problems with no hesitation.

Remember, all but maybe ten of the students in each class are kids who scored below basic or lower in Algebra I. Many of them have already failed intermediate algebra (aka Algebra II, no trig) once. And in day one, they are modeling linear equations and genuinely getting it. Even the ones who are unhappy (more on that in a minute) are getting it.

So from this point on, when a kid sees something like 5x + 7y = 35, they are thinking “something costs $5, something costs $7, and they have $35 to spend” which helps them make concrete sense of an abstract expression. Or y = 3x-7 means that Joe has seven fewer than 3 times as many graphic novels as Tio does (and, class, who has fewer graphic novels? Yes, Tio. Trust me, it’s much easier to make the smaller value x.)

Here’s an early student sample, from my current class, done just two days in. This is a boy who traditionally struggles with math—and this is homework, which he did on his own—definitely not his usual approach.

StudentSampleModeling

Notice that he’s still having trouble figuring out the equation, which is normal. But three of the four tables are correct (he struggles with perimeter, also common), and two of the four graphs are perfect—even though he hasn’t yet figured out how to use the graph to find the equation.

So he’s doing the part he’s learned in class with purpose and accuracy, clearly demonstrating ability to pull out solutions from a word model and then graph them. Time to improve his skills at building equations from graphs and tables.

After two days of this, I break the skills up into parts, reminding the weakest students how to find the slope from a graph, and then mixing and matching equations with models, like this:

MixandMatch2

So now, I’m emphasizing stuff they’ve learned before, but never been able to integrate because it’s been too abstract. The strongest kids in the class are moving through it all much faster, and are often into linear inequalities after a couple weeks.

Then I bring in one of my favorite handouts, built the first time I did this all a year ago: ModelingDatawithPoints. Back to word models, but instead of the model describing the math, the model gives them two points. Their task is to find the equation from the points. And glory be, the kids get it every time. I’m not sure who’s happier, them or me.

At some point in the first week, I give them a quiz, in which they have to turn two different models into tables, equations, and graphs (one from points), identify an equation from a line, identify an equation from a table, and graph two points to find the equation. The last question is, “How’s it going?”

This has been consistent through three classes (two this semester, one last). Most of the kids like it a lot and specifically tell me they are learning more. The top kids often say it’s very interesting to think of linear equations in this fashion. And about 10-20% of the students this first week are very, very nervous. They want specific methods and explicit instructions.

The day after the quiz, I address these concerns by pointing out that everyone in the room has been given these procedures countless times, and fewer than 30% of them remember how to apply them. The purpose of my method, I tell them, is to give them countless ways of thinking about linear equations, come up with their own preferred methods, and increase their ability to move from one form to another all at once, rather than focusing in on one method and moving to another, and so on. I also point out that almost all the students who said they didn’t like my method did pretty well on the quiz. The weakest kids almost always like the approach, even with initially weak results.

After a week or more of this, I move onto systems. First, solving them graphically—and I use this as a reason to explitly instruct them on sketching lines quickly, using one of three methods:

SketchingLines

Then I move on to models, two at a time. Last semester, my kids struggled with this and I didn’t pick up on it until a month later. This last week, I was alert to the problems they were having creating two separate models within a problem, so I spent an extra day focusing on the methods. The kids approved, and I could see a much better understanding. We’ll see how it goes on the test.

Here’s the boardwork for a systems models.
systemsboard

So I start by having them generate solutions to each model and matching them up, as well as finding the equations. Then they graph the equations and see that the intersection, the graphing solution, is identical to the values that match up in the tables.

Which sets the stage for the two algebraic methods: substitution and combination (aka elimination, addition).

Phew.

Last semester, I taught modeling to my math support class, and they really enjoyed it:

SlopeWorkMathsupportdatamodel1Mathsupportdatamodel2MathSupportdatamodel3

Some sample work–the one on the far right is done by a Hispanic sophomore who speaks no English.

Okay, back at 2000 words. Time to wrap it up. I’ll discuss where I’m taking it next in a second post.

Some tidbits: modeling quadratics is tough to do organically, because there are so few real-life models. The velocity problems are helpful, but since they’re the only type they are a bit too canned. I usually use area questions, but they aren’t nearly as realistic. Exponentials, on the other hand, are easy to model with real-life examples. I’m adding in absolute value modeling this semester for the first time, to see how it goes.

Anyway. This works a treat. If I were going to teach algebra I again (nooooooo!) I would start with this, rather than go through integer operations and fractions for the nineteenth time.


Push the Right Buttons

Since my school only has four block periods, teachers often sub for each other during their prep periods. Cheaper than hiring an outside sub, and with an experienced classroom manager running things, there’s an outside chance that the class won’t be a complete waste of time, which is normally the case for all but honors and AP courses when teacher’s not around.

Today I subbed for an economics teacher during fourth block, last class of the day. She told me to go to the library, that she’d put a note on her classroom door telling the students where to go. Ten minutes after the late bell, no students. I wander over to her classroom, where about half the students are milling around trying to get the nerve to leave. No note on the door. (I suspect someone pulled it down.)

“Are you Ms. L’s Econ class?

“Class was cancelled.”

“Yeah. What is this, college? Go to the library and work on your business project.”

“Who are you?”

“I’m the person telling you to go to the library and work on your business project. Come on, move. You’re late.”

(Note to new teachers, particularly you little twenty-somethings bleating about relating to students: it goes much smoother if you expect obedience. Better yet if you demand compliance. And like John Travolta says in Get Shorty, what you’re not doing is feeling about it one way or the other.)

They all trudge to the library and get to work on their project with little fuss; most of the remaining third trickle in over the next 25 minutes.

Last in, half an hour late, are two African American young men who clearly took the opportunity to pick up a second lunch at Wendys, and tried to get out of a tardy by telling me that they’d been waiting by the door “the whole time!” I laugh at them and tell them to get to work.

“We don’t know what to do.”

“Here.” I produce the assignment handout.

“Oh, yeah, the sports project. But there aren’t any computers open, they’re all full.”

“You two?” I speak to two kids on the end row of computers. “You’re not in this class?” They try to ignore me. “Are you in this class?” They still ignore me. “Let me find your name on the class list.”

“Okay, we’re not in this class. But we have homework.”

“Good for you. Do it later. Bye.” They are not happy, but they leave. (The computers are booked for the class, in case you just think I’m mean.)

“Look, guys! Two computers! Put the food away, and get to work.”

It’s a trip watching these two. They try. I watch them page through the assignment, puzzling over it, telling each other man, this is f**** up, she doesn’t tell us what to do. “It’s just a list of things we need to have done! But what do we do, man?”

After five minutes, I see them both paging through search lists, getting “Site blocked” messages. I wander over.

“Please tell me you aren’t googling porn sites in open view of a teacher and librarian.”

“Naw, I’m just finding shoe prices.”

“Shoe shopping?”

“For the team.”

“Oh, so you’re pricing shoes for your business. How much are you spending on personnel?”

“We don’t know how to do that. She doesn’t say how.”

“What are you staffing?”

“We have to staff a professional high school basketball team for $100,000.”

I look at them expectantly.

“What?”

“Nothing comes to mind?”

“She didn’t tell us what to do.”

“But you’re pricing shoes.”

“Yeah.”

I wait, to see if enlightenment will dawn. But it is still well before midnight.

“Okay. Who will be wearing the shoes?”

“The players. Oh.”

“Indeed. So maybe start with people instead of shoes. How many players on a professional basketball team?”

“Twelve. And we’ll need a manager, and at least three coaches….”

“and what about a guy to manage endorsements at the team level?”

And now they are cooking with gas, telling me what they need to staff the team, what prices seem reasonable for a “basketball farm team, these are high school players, they’ll be chill with maybe $500 a season”. I walk away, and ten minutes later they come back to me asking if I know how they can put this “in a file or we’ll lose this paper with our notes.” I bring up Excel, they carefully enter all their data.

A bit later, one of them comes over to me and says “I took this class on Excel when I was a freshman and you could, like, add things up?” So I look at what they have, and suggest that they create one column for count and one for price, so they could then change values and automatically change the sums and they caught on and by god if they didn’t have a damn spreadsheet with personnel variables and starting costs entered, ready for tweaking. They were brainstorming equipment and facility costs by the end of class.

Do not imagine, dear reader, that these two boys will come on time to class tomorrow, ready to jump in and pick up where they left off. More likely, they will cut class one day, get pulled out for some activity on another, and by the time they get back to it will have forgotten the file name and where they emailed it. Still, for 45 minutes, these kids did productive work, thinking about what they’d need to create a small business. Count it in the win column, once I pushed the right buttons.

There’s a larger point in this story somewhere, about the degree of scaffolding low ability, low incentive kids need to do any sort of project based work. The teacher had put together a good lesson, too: achievable, relevant, and interesting. But many of the kids would need far more support—leading questions and a project broken down into key milestones, Excel templates for business plans and budgets, and so on. And as always, I am boggled by the gap between the idiots calling for project based learning which is, to their thinking, essential to modern education, and the actual students who simply don’t have the ability or motivation to meaningfully engage in the learning required for the projects as they are currently envisioned.

But it’s late and I’m pleased with the win, so I’ll stop here.


Boaler’s Bias (or BS)

I began this piece a week ago intending to opine on the Boaler letter. However, I realized I have to confess a strong bias: I read Boaler in ed school and nearly vomited all over my reader. And that will take a whole post.

Experiencing School Mathematics: Traditional and Reform Approaches to Teaching and Their Impact on Student Learning

Boaler, a Brit who has held math education academic positions in England as well as at Stanford, performed a three-year study of two English schools, matched up in demographics and test scores. Phoenix Park believed in progressive, student-centered instruction, whereas Amber Hill taught a traditionalist method—more than traditionalist, they taught math by rote and drill, which is by no means required for teacher-centered instruction.

Boaler was ostensibly investigating the two instruction methods, but the fix was clearly in. Despite Boaler’s constant assurances that the Amber Hill teachers were dedicated and caring, the school presents as an Orwellian fantasy:

One of the first things I noticed when I began my research was the apparent respectability of the school. Walking into the reception area on my arrival, I was struck by the tranquility of the arena. The reception was separated from the rest of the school by a set of heavy double doors. The floors were carpeted in a somber gray; a number of easy chairs had been placed by the secretary’s window and a small tray of flowers sat above them. …Amber Hill was unusually orderly and controlled. Students generally did as they were told, their behavior governed by numerous enforced rules and a general school ethos that induced obedience and conformity. All students were required to wear a school uniform, which the vast majority of students wore exactly as the regulations required. The annual school report that teachers sent home to parents required the teachers to give the students a grade on their “co-operation” and their “wearing of school uniform.” The head clearly wanted to present the school as academic and respectable, and he was successful in this aim at least in terms of the general facade. Visitors walking around the corridors would see unusually quiet and calm classrooms, with students sitting in rows or small groups usually watching the board. When students were unhappy in lessons, they tended to withdraw instead of being disruptive. The corridors were mainly quiet, and at break times the students walked in an orderly fashion between lessons. The students’ lives at Amber Hill were, in many ways, structured, disciplined, and controlled

(page 13)

Phoenix Park, on the other hand:

…had an attractive campus feel. The atmosphere was unusually calm—described in a newspaper article on the school as peaceful. Students walked slowly around the school, and there was a noticeable absence of students running, screaming, or shouting. This was not because of school rules; it seemed to be a product of the school’s overall ambiance. I mentioned this to one of the mathematics teachers one day and she agreed, saying that she did not think she had ever heard anybody shout—teacher or student. She added that this was particularly evident at break times in the hall: “The students are all so orderly, but no-one ever tells them to be.”…. Students were taught all subjects in mixed-ability groups. Phoenix Park students did not wear school uniforms. Most students wore fashionable but inexpensive clothes such as jeans, with trainers or boots, and shirts or t-shirts worn loosely outside. A central part of the school’s approach involved the development of independence among students. The students were encouraged to act responsibly—not because of school rules, but because they could see a reason to act in this way.

(emphasis mine) (page 18)

And yet, while the Amber Hill students were well-behaved little automatons, the Phoenix Park kids–the ones who simply behave well by choice and idealism, not some lower-class aspiration to respectability–ran amok:

In the 100 or so lessons I observed at Phoenix Park, I would typically see approximately one third of students wandering around the room chatting about non-work issues and generally not attending to the project they had been given. In some lessons, and for some parts of lessons, the numbers off task would be greater than this. Some students remained off task for long periods of time, sometimes all of the lessons; other students drifted on and off task at various points in the lessons. In a small quantitative assessment of time on task, I stood at the back of lessons and counted the number of students who appeared to be working 10 minutes into the lesson, halfway through the lesson, and 10 minutes before the end of the lesson. Over 11 lessons, with approximately 28 students in each , 69%, 64%, and 58% of students were on task, respectively [the corresponding numbers at Amber Hill were in the 90%s].
….
More important than either of these factors, however, is that the freedom the students experienced seemed to relate directly to the relaxed and non-disciplinarian nature of the three teachers and the school as a whole. Most of the time, the teachers did not seem to notice when students stopped working unless they became very disruptive. All three teachers seemed concerned to help and support students and, consequently, spent almost all of their time helping students who wanted help, leaving the others to their own devices.

(page 64, 65)

But far from criticizing the school for abysmal classroom management, Boaler blames the students.

However, this freedom was also the reason the third group of students hated the approach. Approximately one fifth of the cohort thought that mathematics was too open, and they did not want to be left to make their own decisions about their work. They complained that they were often left on their own not knowing what to do, and they wanted more help and structure from their teachers. The students felt that the school’s approach placed too great a demand on them—they did not want to use their own ideas or structure their own work, and they said that they would have preferred to work from books. What for some students meant freedom and opportunity, for others meant insecurity and hard work. There were approximately five students in each class who disliked and resisted the open nature of their work. These students were mainly boys and were often disruptive— not only in mathematics, but across the school. (page 68)

In every mathematics lesson I observed at Phoenix Park, between three and six students would do little work and spend much of their time disrupting others. I now try to describe the motivation of these 20 or so students, who represented a small but interesting group. The students who did little work in class were mainly boys, and they related their lack of motivation to the openness of the mathematical approach and, more specifically, the fact that they were often left to work out what they had to do on their own. …..Many of the Phoenix Park students talked about the difficulty they experienced when they firststarted at the school working on open projects that required them to think for themselves. But most of the students gradually adapted to this demand, whereas the disruptive students continued to resist it.

In Years 9 and 10, I interviewed six of the most disruptive and badly behaved students in the year group: five boys and one girl. They explained their misbehavior during lessons in terms of the lack of structure or direction they were given and, related to this, the need for more teacher help. These students had been given the same starting points as every-body else, but for some reason seemed unwilling to think of ways to work on the activities without the teacher telling them what to do. This was a necessary requirement with the Phoenix Park approach because it was impossible for all of the students to be supported by the teacher when they needed to make decisions. The students who did not work in lessons were no less able than other students; they did not come from the same middle school and they were socioeconomically diverse. In questionnaires, the students did not respond differently from other students, even on questions designed to assess learning style preferences. The only aspect that seemed to unite the students was their behavior and the fact that most of them were boys. The reasons that some students acted in this way and others did not were obviously complex and due to a number of interrelated factors. Martin Collins [one of the Phoenix Park teachers] believed that more of the boys experienced difficulty with the approach because they were less mature and less willing to take responsibility for their own learning than the girls. The idea that the boys were badly behaved because of immaturity was also partly validated by the improvement in the boys’ behavior as they got older .

(page 73) (emphasis mine)

Meanwhile, the Amber Hill girls were miserable:

All of the Amber Hill girls interviewed in Years 9 and 10 expressed a strong preference for their coursework lessons and the individualized booklet approach, which they followed in Years 6 and 7, as against their textbook work. The girls gave clear reasons why these two approaches were more appropriate ways of learning mathematics for them; all of these reasons were linked to their desire to understand mathematics. In conversations and interviews, students expressed a concern for their lack of understanding of the mathematics they encountered in class. This was particularly acute for the girls not because they understood less than the boys, but because they appeared to be less willing to relinquish their desire for understanding…..Just as frequently, I observed girls looking lost and confused, struggling to understand their work or giving up all together. On the whole, the boys were content if they attained correct answers. The girls would also attain correct answers, but they wanted more. The different responses of the girls and boys to group work related to the opportunity it gave them to think about topics in depth and increase their understanding through discussion. This was not perceived as a great advantage to the boys probably because their aim was not to understand, but to get through work quickly. These different responses were also evident in response to the students’ preferences for working at their own pace. In chapter 6, I showed that an overwhelming desire for both girls and boys at Amber Hill was to work at their own pace. This desire united the sexes, but the reasons boys and girls gave for their preferences were generally different. The boys said they enjoyed individualized work that could be completed at their own pace because it allowed them to tear ahead and complete as many books as possible….The girls again explained their preference for working at their own pace in terms of an increased access to understanding. The girls at Amber Hill consistently demonstrated that they believed in the importance of an open, reflective style of learning, and that they did not value a competitive approach or one in which there was one teacher-determined answer. Unfortunately for them ,the approach they thought would enhance their understanding was not attainable in their mathematics classrooms except for 3 weeks of each year .

(page 139)

(all emphasis mine)

So in each school, there were students who really hated the teaching method used. But Boaler blames the complex-instruction haters at Phoenix Park (of course, it’s just a coincidence they are mostly male), for their immaturity and disruption, because they didn’t like the open-ended discovery method she so vehemently approves of. Meanwhile, she not only sympathizes with the Amber Hill girls, poor dears, who didn’t like the procedure-oriented teaching method at their school, but continually slams the Amber Hill boys who do enjoy it because those competitive, goal-driven little twerps aren’t interested in learning math but just doing more problems than their pals.

It was at this point I threw my reader across the room.

Moreover, reading between the lines of Boaler’s screed shows clearly that both schools are doing what I would consider an utterly crap job of teaching math. Boaler also mentions Phoenix Park is the low achiever in its affluent school district, and both schools have dismal test scores (which, let me be clear, could be true even if both schools were doing an outstanding job in math instruction).

Indeed, Boaler’s entire thesis—that the “reform” approach leads to better test scores—is poorly supported by her own data. Boaler received special permission to evaluate the students’ individual GCSE scores. She coded problems as either “procedural” or “conceptual”.

Amber Hill, of the dull, grey school and the dreary uniforms, actually outscored Phoenix Park, the progressive’s paradise, on procedural questions. While Phoenix Park outscores Amber Hill on conceptual problems, it wasn’t by all that much.

Like any dedicated ideologue, Boaler misses the monster lede apparent in these representations: Phoenix Park’s score range is nearly double that of Amber Hill’s, suggesting that discovery-based math helps high ability kids, while procedural math helps low ability students. Low ability students lost out at Phoenix Park, because they couldn’t cope with the open-ended, unstructured approach. Boaler didn’t give a damn about those kids, because they were boys. Meanwhile, high ability kids do better with an open-ended approach, gaining a better understanding of math concepts.

This finding has been well-documented in subsequent research—at least, the research done by academics who aren’t hacks bent on turning math education into a group project. I wrote about this earlier.

Here, too, is a takedown of some of the specifics in her research. You can read the whole thing, but here are the primary points in direct quotes:

  • “Also these scores are very similar. A notable difference is that rather a lot of students at Amber Hill fail, whereas more students at Phoenix Park get the very low grades E,F,G. Boaler sees this as a positive thing about Phoenix Park. A possible explanation (which Boaler does not give) has to do with the fact that the GCSE is actually not one exam, but three exams….. it is perfectly conceivable that at Amber Hill many students aimed higher than they could achieve and failed. Note that it is essential for further education to receive at least a C, so that participating in the basic exam is virtually useless. The figures show that nonetheless at Phoenix Park at least 43.5 percent of the students (the Fs and Gs) participated in this exam and by doing this gave up their chance at higher education without even trying.”
  • “This indicates that, compared to the nation, the students at Phoenix Park did worse on the GCSE than they did on the NFER. So Phoenix Park seems not to have done its students a lot of good. The same is of course true for Amber Hill, which performed very similarly to Phoenix Park. I also took a look on the internet at typical average scores of schools on the GCSE. It seems that Phoenix Park and Amber Hill are just about the schools with the worst GCSE scores in the UK. I cannot help but think that Amber Hill was specifically chosen for this fact.”
  • “Boaler doesn’t say anything about the GCSE scores of Amber Hill at the moment that she decided to include this school in her study, but there is not reason to believe that it was markedly different from the above mentioned scores for Amber Hill. If that is the case, then Boaler seems to have been stacking the deck in favor of Phoenix Park and its discovery learning approach to mathematics teaching.”
  • “Boaler also doesn’t mention that the grades for the GCSE at both schools are lower than one would expect given the NFER scores. She seems determined to interpret everything in favor of Phoenix Park. ”

If you’ve read anything about the Boaler/Milgram/Bishop debate, some of these Boaler critiques may sound a tad familiar. But don’t get them confused. This is a different study. Which means Boaler has pulled this nonsense twice.

It was reading horror shows like Boaler that made me loathe progressive educators. It took me a while to acknowledge that they weren’t all dishonest hacks bent on distorting reality. Not all progressives are determined to create an ideological force field that repels all sane discussion of the genuine advantages and disadvantages of different educational approaches, and an honest acknowledgement that student cognitive ability—which appears unevenly distributed by both race *and* gender, at least as we measure it—is a factor in determining the best approach for a given student population. And ultimately, I find myself slightly more sympathetic to progressives than reformers because at least progressives (and here I include Boaler) actually know about teaching, even if they often do it with blinders on.

So getting all this out of my system means I’m not writing—yet—about Boaler/Milgram/Bishop. But then, I imagine my opinion’s pretty clear, isn’t it?

Ironically, I know people who know Boaler, and assure me she’s quite nice. But then, she’s British. It’s probably the accent.


Best Movie About Teaching. Ever.

Cheery news: Won’t Back Down had a hideous opening. Here’s a hint, folks: teachers are a big piece of the audience for simplistic, feel-good teacher movies, so it’s a terrible idea to make a simplistic feel-good teacher movie suggesting that most of them suck.

I, however, am not a fan of simplistic, feel-good teacher movies: Dangerous Minds, Lean on Me, Mr. Holland’s Opus, or Freedom Writers, are tripe. (But the best of that group by far is Holland.)

I occasionally enjoy movies about flamboyant teachers for whom students function primarily as an audience (Prime of Miss Jean Brodie, Dead Poets Society)—and in my enrichment classes, I fear I am that sort of teacher—but they send the wrong signal and thus, I deny them official status as teacher films. They are “idiosyncratic adult who happens to be a teacher opens the eyes of his appreciative audience” movies.

Stand and Deliver is overrated, but Lou Diamond Phillip’s performance covers up a lot of sins. The story’s a big lie alas, and the students did cheat.

Up the Down Staircase, written by Bel Kaufman—still enjoying life at 101, Holla!—is far superior to To Sir with Love, which had the bigger star and English accents, so the first film has been mostly forgotten. It’s worth a look for its honesty and refusal to portray simplistic success. Staircase, like Kindergarten Cop, a guilty pleasure, and the delightful Goodbye Mr. Chips, does a nice job of focusing on classroom management, so essential to teaching inner city kids, wild suburban kindergartners, or British boarding school brats.

Searching for Bobby Fischer is a beautiful film about parenting and teaching; both Vinnie and Mr. Pandolfini are exemplars of their individual approaches. School of Rock is sublimely silly, but at its heart is a similar film; specialist teachers (the arts, chess, what have you) have all the fun, sometimes.

There has been much in the news lately about the importance of teaching writing, which reminded me of an odd, lesser, film for both Doris Day (another Holla!) and Clark Gable, Teacher’s Pet. Day is quite gorgeous as a journalism professor who thinks rough, tough (and far too old) newspaper editor Clark is actually a journalism student with great talent. Gig Young has a great role as the intellectual boyfriend (no holla for Gig, alas). It’s no great shakes, but has two or three excellent scenes about the “how” of writing, particularly towards the end, when Clark tells a young Nick Adams how much time he had to spend learning to write.

Best Movie about Teaching Ever: The Browning Version

But the most perfect movie ever made about teaching focuses, paradoxically, on a failed teacher. Written by Terrence Rattigan, The Browning Version explores the last days of classics teacher Andrew Crocker-Harris, who is leaving a mid-tier “public school” post from which he has been prematurely retired. It’s the kind of play with a few parts, the type about which one says “the TV version has Ian Holm as the Crock, Judy Dench as the wife, and Michael Kitchen as the lover” and anyone familiar with the play goes oh, great cast! Albert Finney played the Crock in the 1992 remake, but Michael Redgrave offers the definitive version in Anthony Asquith’s 1951 film.

To describe the plot is to unnecessarily depress the unprepared. One must witness four or five scenes of brutal psychological cruelty and then blink away tears at moments of extraordinary kindness. Rattigan was gay when homosexual activity was a crime, and that may be why that in the pantheon of Brit Lit, Crocker-Harris’ wife is ranked second only to Lady Macbeth as the Ultimate Evil Female, from whose clutches Crocker-Harris must be rescued by a sympathetic male friend if only to view the wreckage of his failed life from a safe distance.

The Browning Version examines that failed life through the prism of the Crock’s status as a failed teacher. His failure lies not in his ability or knowledge, but in his failure to teach with joy and passion and, most importantly, in his failure to show his students that he cared for them (although it’s clear that privately, he did). Faced with students who didn’t care about his subject, he gave up. Eduformers talk about such teachers with cheap abandon and no understanding; Redgrave, a theater legend in the best of his few film roles, does nothing on the cheap, and his pain, which rarely cracks his stiff British reserve, is ever present. If you’re up for it, watch the Himmler scene, and see what eduformers miss about these failing teachers.

But if we must bear witness to the Crock’s failure, we also are given the relief of his redemption in the film’s great insight: students bear a responsibility to their teachers, too. Thanks to the glorious accident of a young man who normally loves science but thinks the classics a bit of a bore, Crocker-Lewis learns that he is, still, a teacher who can find and inspire passion for his subject, given a willing student. Of course, if one teaches Greek and Latin—or algebra II and math support— willing, engaged students are about as thick on the ground as dodos. In the early scenes, we see Crocker’s class paralleled with the science teacher’s (who is also Crocker’s wife’s lover). The science teacher, who has an easy, informal rapport with his students, also has a way cooler subject and offers up a whiz bang experiment. Crock has nothing but old plays and conjugations. How much of a teacher’s ability to hold on to enthusiasm is dependent on the subject he teaches? How much easier is it to hold onto your own motivation when most of your students are actually interested in your subject?

I’ve been at three schools now, all of them with a high percentage of low ability students, and the math teachers are always on the outside looking in. They aren’t the ones the principals thank profusely at the end of the year for inspiring the students. When math classes have a 40-60% failure rate, math teachers don’t make “favorite” or “best” lists. They are the ones who are on the hook for test scores, the ones who are simultaneously expected to keep standards high but not fail too many students, the ones most likely to see students two years in a row in the same class. I became a teacher knowing full well this was in my future, knowing that most of my students, at best, would think of me as someone who makes a horrible hour and hated subject marginally bearable. Yet even with that hardnosed realism, I still often end the day feeling a tad beat down. I cope with the knowledge by continuing my work in private instruction and tutoring, where my kids think I’m the bomb. Many teachers don’t have this out, and leave for schools with higher ability kids–or leave teaching altogether—unable to stand the dreary hatred reflected back at them class after class.

The Browning Version assigns all blame to the teacher for his failure, but at the same time shows how little it takes to put the Crock back on his game. All the man needed was one student who cared; he responded tentatively and then more openly, as the teaching relationship gelled. We are left with the impression that Crocker-Lewis, reminded of what teaching feels like when students care, will go to his new post with a determination to at least show his kids he cares, and search for the very few who might be engaged. That is, we trust and believe he’ll do his job.

The Browning Version is neither easy nor feel-good. It will thus add nothing to the current educational policy debate. But every teacher should watch it, if only to remind themselves that giving up damages souls, their own even more than those of their students.


The false god of elementary school test scores

Rocketship Academy wants to go national. Rocket Academy is a hybrid charter school chain that focuses solely on getting low income Hispanic elementary school students to proficiency. (Note: Larry Cuban has some excellent observations from his visit to a Rocketship Academy.)

First things first: I’ve checked the numbers every way I can think of, and Rocketship’s numbers are solid. They don’t have huge attrition problems that I can see. They are, in fact, getting 60% or higher proficiency in most test categories, and the bulk of their students are Hispanic, many of them not proficient in English. Of course, that brings up an interesting question–if they are proficient on the ELA tests, why aren’t they considered proficient in English? But I digress.

The larger point is this: getting high test scores on California’s elementary school math tests ain’t all that much to get worked up about. Here’s some data from the 2011 California Standards test in math:

I used two standards, because the NCLB obsession with “Proficient and higher” is, to me, moronic. I prefer Basic or higher. The blue line is the percentage of all California in grades 2-9 scoring Basic or higher in General Math, the red is the percentage of same scoring Proficient or higher.

So it gets a bit tricky here, because after 6th grade, the entry to algebra varies. In order to simplify it slightly, I’m ignoring the seventh grade algebra track (call it “accelerated advanced” path), which is about 40,000 students this year, fewer in previous years.

I combined 8th and 9th grade students in General Math and attached that result to the red and blue lines.

Then I separated two groups–the ones who took algebra in 8th grade, and the ones who took algebra later than that. The first group are those who entered algebra in 8th grade, passed it, and continued on the “average advanced” course path, culminating with Calculus senior year. The second group are those who took algebra for the first, second, or third time in high school and then continued on. For each group, I calculated percentages for Basic + and Proficient +.

Notes:

  1. Through grade 6, the scores represent all students. In grade 7 and 8/9, general math scores reflect only those students who haven’t moved onto algebra. That’s probably why the proficiency levels drop to 50% and lower for the last two groups.In other words, the green and purple lines represent the advanced track students–most, but not all of the the strong algebra and higher math students. The turquoise and orange lines represent the weaker students taking algebra and higher.
  2. Roughly 80% of all students test at Basic or higher from second through sixth grade.
  3. Over 70% of the strong studentws test at Basic or higher from algebra through “summative math” (taken for all subjects after Algebra 2).
  4. The percentage of students testing proficient from second through sixth grade starts at 65%, rises slightly, and then drops steadily.
  5. In no course do more than 50% of the strong students in algebra and higher achieve a score of Proficient or higher.
  6. In no course do more than 50% of the weaker students in algebra or higher achieve a score of Basic or higher.

So the chart reveals that all California second through sixth graders, high and low ability, averaged higher scores on their tested subject than the strongest high school students did.

I used 2011 scores, and I may have made a minor error here or there, but the fall off has been in the scores for several years now, and it’s easy enough to check.

What could cause this? Why are California’s elementary school students doing so phenomenally well, and then fall apart when they get to high school? Let’s go through the usual culprits.

California’s high school math teachers suck.–Well, in that case, there’s not much point in demanding higher standards for math teachers, because California’s high school math teachers have had to pass a rigorous content knowledge test for over 20 years. California’s elementary school teachers have to pass a much easier test–which is much harder than anything they had to pass before 2001. In other words, try again.

The teachers aren’t covering the fundamentals! So when the students get to algebra, they aren’t prepared.–But hang on. Elementary school kids, the ones being taught the fundamentals, are getting good test scores. What evidence do you have that they aren’t being taught properly?

Well, they’re only getting good test scores because the tests are too easy!—dingdingding! This is a distinct possibility. Perhaps the elementary tests aren’t challenging enough. Having looked at the tests, I’m a big believer in this one. I think California’s elementary math tests, through seventh grade, are far less challenging to the tested elementary school population than are the general math and specific subject tests are to the older kids. (On the other hand, the NAEP scores show this same dropoff.)

However, while that might explain the disparity between the slower track math student achievement and elementary school, it doesn’t adequately address why the students in the “average advanced” track aren’t achieving more than 50% proficiency, does it?

Trigonometry is harder than memorizing math facts–We should take to heart the Wise Words of Barbie. Math achievement will fall off as the courses get more challenging. Students who excelled at their times tables and easily grasped fractions might still struggle with complex numbers or combinatorics.

So if you ask me—and no one does. Hell, no one has even really noticed the fall-off—it’s a combination of test design and subject difficulty.

Whatever the reason, the test score falloff has enormous implications for those who are banking on Rocketship Academy, KIPP, and all those other “proven” charters that focus exclusively on elementary school children.

Elementary school test scores are false gods. We have no evidence that kids who had to work longer school days simply to achieve proficiency in fifth grade reading and math will be, er, “shovel ready” for algebra and Hamlet. KIPP’s College Completion Report made no mention of its college students SAT scores, or indeed made any mention of demonstrated ability (e.g., AP tests), and color me a cynic, but I’m thinking they’d have mentioned both if the numbers were anything other than dismal.

So let’s assume that those Rocketship scores are solid (and I do). So what? How will they do in high school? Where’s the follow through? Everyone is banking on the belief that we can “catch them early”. Get kids competent and engaged while they are young, and it all falls into place.

Fine. Just let me know when the test scores back up that lovely vision.

Added in January 2014: Well, hey now. Growing Pains for Rocketship’s Blended-Learning Juggernaut.

Alas, it seems that Rocketship’s scores are declining, their model doesn’t scale, they are making decisions based on cost rather than learning outcomes and, my FAVORITE part:

Lynn Liao, Rocketship’s chief programs officer, said the organization has also received troubling feedback on how students educated under the original blended learning model fare in middle school.

“Anecdotal reports were coming in that our students were strongly proficient, knew the basics, and they were good rule-followers,” Ms. Liao said. “But getting more independence and discretion over time, they struggled with that a lot more.”

That graven image gets you every time, doesn’t it?


I am very Barbie about math*

Why are High School Teachers Convinced that White Girls Can’t Do Math?: apparently, high school teachers rate white girls lower than boys when they are matched in grades and test scores. Therefore, sez the Forbes article and the study it reports on, high school math teachers are biased against white girls.

Okay, so first off, the headline and the study are absurdly biased, which is a tad ironic in an article about bias.

Using the Forbes article as a guide to the study, the study didn’t establish bias. What it established was that high school teachers consistently rate white girls a tad lower in ability than boys with the same grades and test scores. That’s not the same thing.

First off, throw out grades. I’ve written on this before, but it bears repeating: if a teacher counts homework as a significant part of the grade, the grade simply isn’t accurate. Moreover, grades skew dramatically based on population. Suburban schools with lots of high-achieving kids have a tougher grading standard than Title I schools.

I am hoping that this study focuses primarily on test scores. Let’s assume that teachers rate boys higher in ability than girls, even though they have the same test scores. Is that necessarily a sign of bias?

Hell, no. Girls do more homework than boys. Girls are, as a group, more worried about grades than boys. Girls, as a group, work harder than boys.

So suppose you have two students. One of them turns in every bit of homework, asks questions purely about methodology and algorithsm, works very hard to “get it”. The other student doesn’t do homework, asks questions about process and concept, and always grasps everything without any particular effort involved. They both get the same test scores.

Who will the teacher say is “better” at math?

That’s not bias. That’s a totally rational inference about the ease of understanding, grasp of concept, and underlying aptitude.

I have a good number of students who are entirely obsessed with grades and utterly uninterested in math. Most, but not all, of these students are girls. I have a large number of students who are fascinated by how math works, often praise an “interesting” question, ask all sorts of conceptual questions because they want to know how things work. Most, but not all, of these students are boys.

Spare me the sturm und drang. It’s not bias. Teachers are longing to find female students who are strong at math. They aren’t ignoring white female students with math talent. They are just less likely to confuse “slog” with “talent” than, say, your average researcher.

*I used to say that all the time, until I became a math teacher. I hate it when my cultural references start to date. (They should stay single for life. Hyuk.)


Discovery Doesn’t Work

I had trouble in ed school because (well, at least in my view of it) I openly disdained the primary tenets of progressive education. I am pro-tracking, anti-constructivist, and pro-testing, all of which put me at odds with progressives. Here is the irony: I mention often that I am a squishy teacher (squishy=touchy feely). I am not just squishy for a math teacher, I’m the squishiest damn math teacher from my cohort at the elite, relatively progressive ed school that made my life very difficult. My supervisor, who knew me first as a student in a curriculum class, was genuinely shocked to learn that I didn’t talk at my kids in lecture form for 45 minutes or more, given my oft-expressed disagreement with discovery. Even my lectures are more classroom back and forth than me yammering for minutes on end. (In fact, my teaching style did much to save me at ed school, but that’s a different story.)

Here is what I mean by squishy: My kids sit in groups, not rows. When I set them to practicing, which is usually 20-35 minutes of class, they are allowed to work independently, in pairs, or as a group of four. I often use manipulatives to demonstrate important math facts. My explanations are, god help me, “accessible”. I don’t just identify the opposite, adjacent, and hypotenuse and then lay out the ratios. No, I’ve been mentioning opposite, adjacent and hypotenuse for weeks, whenever I talked about special rights. I introduce trig by drawing a line with a rise of 4, a run of 3, and demonstrate how every right triangle made in which one leg is 3 and the other 4 (that is, have a “slope” of .75) must have the same angle forming it. I spend a great deal of time trying to think of a way to help kids file away knowledge under images, concepts, pictures, anything that will help them access the right method for the problem or subject at hand. (For more info, see How I Teach and The Virtues of Last Minute Planning.)

However, I am not in any sense a constructivist as progressive educators use it. I use discovery as illustration, not learning method. I don’t let kids puzzle over a situation and see if they can “construct” meaning. I explain, give specific instructions, and by god, my classroom is teacher centered. I am the sage on stage, baby. And that’s why I got in trouble in ed school, despite my highly accessible, extremely concept-oriented teaching style; I routinely argued against constructivist philosophy, and emphasized the importance of telling kids what to do.

Anyway. I was incredibly excited to read an article that openly states the obvious: Putting Students on the Path to Learning: The Case for Guided Instruction. This article is just so dead on right. To pick one of many great excerpts–click to enlarge, but why can’t I copy text from pdf files any more?:

Yes. Low ability kids like discovery; it is less work for them, yet they feel they are doing something important—but in fact, they aren’t learning very much. High ability kids tend to be “for chrissake, give me the algorithm”, when they would be better off puzzling through the math for themselves.

The article talks about the importance of worked-out examples. I read the article this morning and had a worked out example on the board the same day—step by step factoring of a quadratic. Here’s the weird thing: the kids who need the help with factoring had to be prompted to use the example, but the kids who got factoring were clamoring for worked examples in the area they had trouble with.

This would be a great thing for notebooks. But how do you get the kids who need help to keep the notebooks?

Great article, that changed my teaching immediately. How often does that happen?


Follow

Get every new post delivered to your Inbox.

Join 843 other followers