Understanding Math, and the Zombie Problem

I have been mulling this piece on the evils of explanations for a while. There’s many ways to approach this issue, and I highly recommend the extended discussion at Dan Meyer’s blog, as it captures experience-based teachers (mostly reform biased) with the traditionalists, who are primarily not teachers.

What struck me suddenly, as I was engaged in commenting, was the Atlantic’s clever juxtaposition.

All the buzz, all the sturm und drang about Common Core and overprocessed math has involved elementary school. The cute show your thinking pictures are from 8 year olds and first graders. Louis CK breaks our hearts with his third grader’s pain. The image in the Atlantic article has cute little pudgy second grade arms—with just the suggestion of race, maybe black, maybe Hispanic, probably male—writing a whole paragraph on math. The evocative image evokes protective feelings, outrage over the iniquities of modern math instruction, as a probably male student desperately struggles to obey meaningless demands from a probably female teacher who probably doesn’t understand math beyond an elementary level anyway. Hence another underprivileged child’s potential crushed, early and permanently, by the white matriarchal power structure unwilling to acknowledge its limitations.

And who could disagree? Arithmetic has, as John Derbyshire notes, “the peculiar characteristic that it easy to state problems in it that are ferociously difficult to solve.” Why force children to explain place value or the division algorithm? Let them get fluency first. Garelick and Beals (henceforth referred to as G&B) cite various studies finding that elementary school students gain competence by focusing on procedure first, conceptual understanding at some later point.

There’s just one problem. While the Atlantic’s framing targets elementary school, and the essay’s evidence base is entirely from elementary school, G&B’s focus is on middle school.

Percentages. Proportions. Historically, the bane of middle school math. Exhibit C on high school math teachers list of “things our students should know but don’t” (after negatives and fractions), and an oft-tested topic, both conceptually and procedurally, in college placement.

G&B make no bones about their focus. They aren’t the ones who chose the image. They start off with a middle school example, and speak of middle school students who “just want to do the math”.

But again, there’s that authoritatively cited research (linked in blue here):

Again, all cites to research on elementary school math. The researched students are at most fifth graders; the topics never move above arithmetic facts. G&B even make it clear that the claim of “procedure without understanding is rare” is limited to elementary school math, and in the comments, Garelick discusses the limitations of a child’s brain, acknowledging that explanations become more important in adolescence—aka, middle school, algebra, and beyond.

G&B aren’t arguing for 8 year olds to multiply integers in happy, ignorant fluency, but for 14 year olds to calculate percentages and simply “show their work”. And in the event, which they deem unlikely, that students are just going through the motions, that’s okay because “doing a procedure devoid of any understanding of what is being done is actually hard to accomplish with elementary math.” Oh. Wait.

Once you get past the Atlantic bait and switch and discuss the issue at the appropriate age level, everything about the article seems odd.

First, Beals and Garelick would–or should, at least–be delighted with math instruction in 8th grade and beyond. Reform math doesn’t get very far in high school. Not only do most high school teachers reject reform math, most research shows that the bulk of advanced math teachers have proven impervious to all efforts to move beyond “lecture and assign a problem set”. Most math teachers at the high school level accept a worked problem as evidence of understanding, even when it’s not. I’m not as familiar with middle school algebra and geometry teachers, but since NCLB required middle school teachers to be subject-certified, it’s more likely they profile like high school teachers.

G&B don’t even begin to make the case that “explaining math” dominates at the middle school level. They gave an anecdote suggesting that 10% of the week’s math instruction was spent on 2-3 problems, “explaining thinking”.

This is the basis for an interesting discussion. Is it worth spending 10% of the time that would, presumably, otherwise be spent on procedural fluency on making kids jump through hoops to add meaningless detail to correctly worked problems? And then some people would say well, hang on, how about meaningful detail? Or how about other methods of assessing for understanding? For example, how about asking students why they can’t just increase $160 by 20% to get the original coat price? And if 10% is too much time, how about 5%? How about just a few test questions?

But G&B present the case as utterly beyond question, because research and besides, Aspergers. And you know, ELL. We shouldn’t make sure they understand what’s going on, provided they they know the procedures! Isn’t that enough?

Except, as noted, the research they use is for younger kids. None of their research supports their assertion that procedural fluency leads to conceptual understanding for algebra and beyond. We don’t really know.

However, to the extent we do know, most of the research available in algebra suggests exactly the opposite–that students benefit from “sense-making”, conceptual approaches (which is not the same as discovery) as opposed to entirely procedural based instruction. But researching algebra instruction is far more difficult than evaluating the pedagogy of arithmetic operations—and forget about any research done beyond the algebra level. So G&B didn’t provide adequate basis for making their claims about the relative value of procedural vs conceptual fluency, and it’s doubtful the basis exists.

I’ll get to the rest in a minute, but let’s take a pause there. Imagine how different the article would be if G&B had acknowledged that, while elementary school research supports fact fluency over sense-making (and fact fluency seems to be helpful in advanced math), the research and practice at algebra and beyond is less well established. What if they’d argued for their preferences, as opposed to research-based practices, and made an effort to build a case for procedural fluency over comprehension in advanced math? It would have led to a much richer conversation, with everyone acknowledging the strengths and weaknesses of different strategies and choices.

Someday, I’d like to see that conversation take place. Not with G&B, though, since I’m not even sure they understand the big hole in their case. They aren’t experienced enough.

Then there’s the zombie quote, where Garelick and Beals most tellingly display their inexperience:

Yes, Virginia, there are “math zombies”.

In high school, math zombies are very common, particularly in schools with a diverse range of students and thus abilities. Experienced teachers commenting at Dan Meyer’s blog or the Atlantic article all confirm their existence. This piece is long enough without going into anecdotal proof of zombies. One can infer zombie existence by the ever-growing complaints of college math professors about students with strong math transcripts but limited math knowledge.

I’ve seen zombies in tutoring through calculus, in my own teaching through pre-calc. In lower level classes, I’ve stopped some zombies dead in their tracks, often devastating them and angering their parents. The zombies, obviously, are the younger students in my classes, since I don’t teach honors courses. Most of the zombies in my school don’t go through my courses.

Whether math zombies are a problem rather depends on one’s point of view.

There are many math teachers who agree with G&B, who rip through the material, explaining it both procedurally and conceptually but focus on procedural competence. They assign difficult math problems in class with lots of homework. Their tests are difficult but predictable. They value students who wrote the didactic contract with Dolores Umbridge’s nasty pen, etching it into their skin. They diligently memorize the cues and procedures, and obediently regurgitate the procedures, aping understanding without having a clue. There is no dawning moment of conceptual understanding. The students don’t care in the slightest. They are there for the A and, to varying degrees, play Clever Hans for math teachers interested only in correctly worked procedures and right answers. Left as an open issue is the degree to which zombies are also cheating (and if they cheat are they zombies? is also a question left for another day). For now, assume I’m referring to kids who simply go through the motions, stuffing procedures into episodic memory with nothing making it to semantic, all to be forgotten as soon as the test is over.

Math zombies enable our absurd national math expectations. Twenty or thirty years ago, top tier kids had less incentive to fake it through advanced math. But as AP Calculus or die drove our national policy (thanks, Jay Mathews!) and students were driven to start advanced math earlier each year, zombies were rewarded for rather frightening behavior.

G&B and those who operate from the presumption that math can easily be mastered by memorizing procedures, who believe that teachers who slow down or limit coverage are enablers, don’t see math zombies as a problem. They’re the solution. You can see this in G&B’s devotion and constant appeal to the test scores of China, Singapore, and Korea, the ur-Zombies and still the sublime practitioners of the art, if it is to be called that.

For those of us who disagree, zombies create two related problems. First, their behavior encourages math teachers and policy makers to raise expectations, increase covered material, accelerate instruction pace. They allow schools to pretend that half their students or more are capable of advanced, college level math in high school while simultaneously getting As in many other difficult topics. They lead to BC Calculus pass rates of 50% or more (because yes, the AP Calc tests reward zombie math). Arguably, they have created a distortion in our sense of what “college math” should be, by pretending that “college math” is easily doable by most high school students willing to put in some time.

But the related problem is even more of an issue, because the more math teachers and policies reward zombies, the more smart, intellectually curious non-zombies bow out of the game, decide they’ll go to a state school or community college. Which means zombie kids just aren’t numbered among the “smart” kids, they become the smart kids. They define what smart kids “are capable of”, because no one comes along later to measure what they’ve…well, not forgotten, but never really learned to start with. So people think it really is possible to take 10-12 AP courses and understand the material (as opposed to get a 5 on the AP), and that defines what they expect from all top rank students. Meanwhile, those kids–and I know many–are neither intellectually curious nor even “intelligent” as we’d define it.

The Garelick/Beals piece is just a symptom of this mindset, not a cause. They don’t even know enough to realize that most high school math is taught just the way they like it. They’d understand this better if they were teachers, but neither of them has spent any significant time in the classroom, despite their bio claims. Both have significant academic knowledge in related areas–Garelick in elementary math pedagogy, which he studied as a hobby, Beals as a language expert for Asperger’s—which someone at the Atlantic confused with relevant experience.

Such is the nature of discourse in education policy that some people will think I’m rebutting G&B. No. I don’t even disagree with them on everything. The push for elementary school explanation is misguided and wasteful. Many math teachers reward words, not valid explanations; that’s why I use multiple answer math tests to assess conceptual knowledge. I also would love–yea, love–to see my kids willing to work to acquire greater procedural fluency.

But G&B go far beyond their actual expertise and ultimately, their piece is just a sad reminder of how easy it is to be treated as an “expert” by major publications simply by having the right contacts and backers. Nice work if you can get it.

And the “zombie” allusion, further developed by Brett Gilland, is a keeper.

Math isn’t Aspirin. Neither is Teaching.

First, congrats to Dan Meyer, who finished his doctorate at Stanford and just hired on as CAO for Desmos, a tremendously useful online graphing calculator. He persisted in the face of threatened failure, and didn’t give up even when he had an easy out into a great job. (Presumably Dan and most of the Math Twitter Blogosphere are still annoyed at my jeremiad about the meaning of his meteoric rise, in which Dan played the part of illustration.)

Dan has asked math teachers for ways to create “headaches” for which math can be considered aspirin:

And this interested me because the request completely, perfectly, captures the difference between our two philosophies, which I also wrote about a couple years ago:

The comparison is an instructive one, I think. Both of us find it necessary to build our own curriculum, rejecting the one on offer, and both of us, I think, tremendously enjoy the creation process. Both of us reject the typical didactic contract described by Guy Brouseau, setting expectations very different from those of typical math teachers: explain, work a few examples, assign a set. Both of us largely eschew textbooks for instruction, although I consider them completely unnecessary save as reference books that often provide interesting problems I can steal, while Dan dreams of the perfect digital textbook.

And yet we couldn’t differ more in both teaching philosophy and curriculum approach.

Dan’s still selling curiosity and desire for knowledge, assuming capability will follow. I’m still selling capability because I see confidence follow.

Dan still believes that student engagement captures their curiosity which leads to academic success, that the Holy Grail of academic success in math lies in finding the perfect problems that universally stimulate interest in finding answers, which leads to understanding for all. I hold that student engagement leads to their willingness to attempt what they previously thought was impossible but that the Holy Grail doesn’t exist.

Meyer thinks teachers skeptical of his methods are resistant to change and the best interests of their students. I advise teachers and recommend curriculum; if they find my advice helpful, great. I encourage them to modify or even reject my advice, to continue to see an approach that works for them and their students.

Dan wants to be “less helpful”. I want to teach kids to use their own resources, but given a kid who wants to give up, I’m offering help every time.

Meyer’s methods would probably need tremendous readjustment if he worked in a low-income school with a wide range of abilities. I’d probably be much “less helpful” if I taught at a school with a high-achieving, homogenous population obsessed about grades.

Meyer rose quickly in the rarefied world of rock star teachers. I aspire to the role of and indie with cult status.

Dan’s query: “Why did mathematicians think this skill was worth even a little bit of our time? If the ability to factor that trinomial is aspirin for a mathematician, then how do we create the headache?

My answer: You can’t.

The commenters, mostly teachers, took the question seriously, understanding that it was another way of looking at the students’ demand, “When will we use this?”. Answering this question clearly troubles most of the commenters—or they have an affirmative answer they’re satisfied with.

My answer to the student demand: “Probably never. But the more willing you are to take on challenging tasks you learn from, the more opportunities you’ll have in life, both professional and personal. Call me crazy, but I see this as a good thing.”

Dan Meyer is wrong, I believe, in looking for the Holy Grail that makes math “aspirin”¹. But that’s not the point of my running through the Dan vs. Ed showdown.

Instead, consider the comparison yet another data point in my slowly developing thesis that ed schools need more flexibility and even less prescription. Few people understand the vast scale of values, philosophies, management and curriculum found in the teaching population.

Two teachers developing uncommon curriculum who agree on very little—yet both of us are considered successful teachers. (one has much more success selling his ideas to people with money, I grant you.) Take ten more math teachers likewise who build their own curriculum, have their own takes on philosophy, discipline, and even grading and they’re unlikely to change to suit another model. Take 100 more–ditto. Voila! an expanding population of teachers who have successful teaching approaches and curriculum design that they’ve developed and modified. None of them are going to agree on much. They have come to widely varying conclusions that they will continue to develop and enhance on their timeline as they see fit. No one will have anything approaching a convincing argument that could possibly convince them otherwise.

The point: the current push to “fix” ed schools, a fond delusion of reformers, progressives and union leaders alike. People as diverse as Benjamin Riley, Paul Bruno, Rick Hess and others believe we can find (or already have) a teaching knowledge base that can be passed on to novices.

Teachers are never going to agree.

Agreement or even consensus is impossible. Teachers and students form infinite combinations of interests, values, incentives and unlike reformers, teachers are going to value their experience and unique circumstances over anything ed schools tried to pretend was the only way.

Teaching, like math, isn’t aspirin. It’s not medicine. It’s not a cure. It is an art enhanced by skills appropriate to the situation and medium, that will achieve all outcomes including success and failure based on complex interactions between the teachers and their audience. Treat it as a medicine, mandate a particular course of treatment, and hundreds of thousands of teachers will simply refuse to comply because it won’t cure the challenges and opportunities they face.

So when the status quo has prevailed for the next 30 years, don’t say you weren’t warned.
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¹which isn’t to say I don’t plan on writing up the how and why of my quadratic equations section.

Math Instruction Philosophies: Instructivist and Constructivist

Harry Webb has been on a tear about discovery vs. traditional explanations. The hubbub has pulled the great god Grant Wiggins, originator of backward design, which is a bible of ed schools as a method for developing curriculum.

Now, let us pause, a brief segue, to reflect on those last two words. Developing curriculum. I’m talking about teachers, yes? Teachers, building their own unit lessons, their own tests, their own worksheets. As I’ve written, teachers develop their own curriculum and, to varying degrees, have intellectual property rights (I would argue) to their material. So when reformers, unions, politicians, or whoever stress the importance of curriculum, textbooks, and professional development in implementing Common Core, there’s a whole bunch of teachers nationwide snorfling at them.

So Wiggins and Jay McTighe wrote Understanding by Design, which describes their framework and approach to curriculum. It is, as I said, a bible of ed schools. I have a copy. It’s good, although you have to look past their irritating examples to figure that out.

(Note: See Grant Wiggins’ response below. I’ve reworded this slightly and separated it to respond to his concerns. Also throughout, I changed “direct instruction” to some other term, usually instructivism.)

The book clearly states that there’s no one correct approach for every situation, that arguing between instructivism and constructivism creates a false dichotomy. So I was jokingly sarcastic before, but my point is real: it’s hard to read Grant Wiggins and not think that, so far as K-12 curriculum goes, he leans heavily towards constructivist. As one example, in a text section that discusses the fact that there’s no one right approach, he includes this table on the activities dominant in each approach. When I look at this table, I see a clear preference for constructivist approaches. I also see it in this highly influential essay and much of his writing. But as Wiggins states in the comments, and in the book, he clearly denies this preference. However, Wiggins’ book is the bible of ed schools for a reason, and it’s not for its categoric embrace of all things instructivist. So put it this way: what he says are his preferences and what any instructivist would take away from his preferences are probably not the same thing. I say this as someone who periodically rereads his work because of the value I find in it once I shift my focus away from the trappings and focus in on the substance. I encourage anyone who agrees with my impression of Wiggins’ preference to read him closely, because he’s done a lot over time to inform my approach to curriculum development.

(end major edits–I put the original text at the bottom)

So Wiggins reads all this hooha, and comes out with this outstanding description of lectures and why they are a problem. I agreed with every word of this post (there are two others), so much so that I tweeted on it. (Note: I agree for math. History’s a different issue.) As I did so, I was vaguely disturbed, because look, while I don’t write a lot about ed school per se (and even defend it, slightly), I spent a lot of time in class naysaying. And if they’d been saying reasonable things like this about lectures, what had I been disagreeing about?

And then Harry comes through brilliantly, answering my question and pointing out a huge hole in Wiggins’ 3-part series:

Wiggins writes of a survey of teachers in order to support his view that different pedagogies are required to achieve different aims. Unsurprisingly, the teachers give the right answers; the ones that they probably learnt at Ed School. However, the survey response that is taken to represent lecturing is called, “DIRECT TEACHING Instruction on the knowledge and skills.” Now, although I do not recognise my practice in Wiggins’ definition of lecturing, I do recognise myself in this definition wholeheartedly. And so I think we are being invited here to see all direct teaching – dare I say direct instruction – as non-interactive lecturing that lasts for most of a period.

Hey. Yeah. That’s right! Wiggins naysays the lecture in his essay, but the overall debate is between instructivism, of which lectures are just a part, and it’s , and it’s instructivism that has a bad name in ed school, not solely lectures. Harry says that he explains in classroom discussion, but rarely lectures. Which may sound like someone else.

Harry scoots right by this, because he’s all obsessed about the fuzzy math and constructivist debate, and it occurred to me that this area needs elucidation, because most people—and reporters, I am looking at you—don’t understand this difference.

So here it is: not all explanation is lecture, and not all discovery is constructivist.

In an effort to not turn all my posts into massive tomes (don’t laugh), I’m going to write about this difference later. Here, I’m just going to show you the difference through different teachers.

Before I start: labels are hard. Roughly, the terms reform, student-centered, constructivist, “facilitative” (Grant Wiggins’ term) all refer to the open-ended investigative approach. Instructivist, teacher-centered, traditionalist, direct instruction are all terms used to describe the approach where the teacher either tells you how to do it or wants you to figure out the way (not a way) to do it. (Note: I left “direct instruction” in here, because I believe it’s still an instructivist approach.)

Very few math teachers are pure constructivist. We’re talking degrees. I have no data on usage rates, but I’d be pretty surprised if 80% of all high school math teachers didn’t use traditional instruction-based approach for 90% of their lessons. I speak to a lot of colleagues who dislike pure lecture and would like to teach a more modified instructivist mode, but they aren’t sure how it works. However, most high school math teachers are instructivists who lecture. Full stop.

Constructivist Approach (aka investigation, reform)

Dan Meyer: Dan Meyer’s 3-Act Meatballs
Fawn Nguyen: Barbie Bungee
Fawn Nguyen Vroom Vroom
Michael Pershan: Triangles and Angles (he calls this investigation. I’d personally characterize it as “in between”, but it’s his call.)
Cathy Humphries: Investigation into Quadrilaterals

This is a partial list. Dan’s blog has links to all his various projects, as well as other bloggers committed to the investigative approach.

(By the way, I am dying to do the Vroom Vroom one, but I’m not enough of a mathematician to understand the math behind it. Neither does Fawn, apparently. The math looks quadratic. Is it?)

I’m not a fan of the open-ended reform approach, but I like all sorts of the activities the constructivists come up with. I just modify them to be more instructivist.

Remember that both Meyer and Nguyen use worksheets, practice skills, and many other elements that are pure instructivist. Pershan rarely does open-ended activities. In contrast, Cathy Humphries is very close to pure constructivist math. Total commitment to reform.

Traditional Instructivism (Lectures)

Much MUCH harder to find traditionalists bloggers. I’ve included two of my “lectures” that have relatively little discussion, just to fill out the list:

Me: Geometry: Starting Off
Me: Binomial Multiplication and Factoring with the Rectangle

Dave at MathEquality is traditionalist, a guy who works hard to explain math conceptually, but does so for the most part in lecture form. However, it’s also clear he keeps the lectures fairly short and gives his students lots of in class time for work.

But he’s the only one I can find. Right on the Left Coast appears to be a traditionalist, but he writes more about policy and his disagreement with traditional union views. (Huh, I should have mentioned him in my teacher blogger writeup of a while back.)

In order to give the uninitiated a good idea of what lecture looks like, three google searches are informative:

factoring trinomials power point

holt math power point

McDougall Litell math power point

Many high school teachers build their own power point explanations. Others just take the ones provided by publishers.

Still others use a document camera or, if they’re extremely old-school, transparencies.

What they look like is mostly this:

Khan Academy: Isosceles Right Triangles

Many teachers are really, really irritated at the fuss over Khan Academy because all he does is lecture his explanations—and not very well at that.

The most vigorous voices for traditional direct instruction comes from people who don’t teach high school math. That’s not a dig, it’s just a fact.

Modified instructivist

I’m not sure what to call it. There’s not just one way to depart from instructivist or constructivist. The examples here generally fall into two categories: highly structured instructivist discovery, and classroom discussions with lots of student involvement.

Me:Modeling Linear Equations
Me: Modeling Exponential Growth/Decay
Michael Pershan: Proof with Little Kids
Michael Pershan: Introducing Polar Coordinates
Michael Pershan: The 10K Chart
Ben Orlin: …999…. and the Debate that Repeats Forever.
Ben Orlin: Permutations and combinations

For a complete list of my work, check out the encyclopedia page on teaching. I likewise recommend Pershan and Orlin’s blogs.

A question for Grant Wiggins, and anyone else interested: what differences do you see in these approaches?

A question for reporters: when you write about reform or traditional math, do you have a clear idea of what the fuss is about? And did these examples help?

Question for Harry Webb: You sucked me into this, dammit. Satisfied?

If you have good examples of math instruction that falls into one of these categories, or want to propose it, tweet or add it to the comments. I’m going to write up my own characterizations of this later. Hopefully not much later.

*******

Here’s what I originally said in the changed paragraph:

So Wiggins and Jay McTighe wrote Understanding by Design, which describes their framework and approach to curriculum. It is, as I said, a bible of ed schools. I have a copy. It’s good, although you have to look past their irritating examples to figure that out. The book clearly states that there’s no one right answer, that arguing between direction instruction or constructivism creates a false dichotomy, but then there’s this table on the activities dominant in each approach. Cough. Okay, no one right answer, but a strong preference for facilitative/constructivist.

Traffic

I am not competitive, but I like comparisons. How is my little corner of the blog universe doing? Why am I getting all this traffic? Are people actually reading me? Are all these clicks just random clicks from autobots of some sort? For most of October, I wrote only two posts, but two days before the end of the month it had been my biggest month (click–can’t figure out how to render full-size).

That’s not impossible; my essays are often discovered after the fact. Mine is not a time dependent blog linking in news of the day. Still, I wonder.

So I figured out how to use Alexa, a little (click):

Alexa says that rankings are kind of sketchy until you’re under 100,000. Well. Diane Ravitch’s ranking is something like 161K. Education Excellence–the website, not the blog–is something like 220K. Diane is the only individual education blogger I could find with really high rankings; I didn’t include her on this because the scale eradicated all the other differences.

This is primarily a comparison of my site to those of education policy wonks and reporters, with the exception of Dan Meyer. Most individual teacher bloggers I looked up were well below my ranking; everyone I could think of was in the 2 million range or not ranked at all. I couldn’t look up individual edweek bloggers, so I have no idea how Sawchu, Hess, Gerwitz or Cody do, for example. Alexander Russo’s entire site (scholastic administrator) came in below a million—I didn’t include it because I’m not sure how his blog relates to everything else. Daniel Willingham’s site numbers are for everything, but I’m figuring his blog gets most of the traffic.

I can’t figure the whole thing out—it’s clear I improved a lot from a low point in May, but May was a huge month for me. June and July were big dropoffs. It’s also clear I ended “up”–if I’d done this a few weeks ago, I’d have been slightly below some of the bloggers I’m now above. Larry Cuban has been my own benchmark for a year; I used another site (Quantcast, I think?) and because we are both on wordpress comparisons were pretty easy. He’s usually right above me; it’s a fluke that right now I’m ranked slightly higher than he is.

However, I thought this was a helpful graphic. I’m not imagining things; Alexa thinks I’m doing pretty well in a relative sense. I mean, there’s really major bloggers who are in the same million rankings with me! And I do it for free. Kudos to Joanne Jacobs, who I’ve been reading for years and does it all on her own. Dan Meyer, also doing it all by himself, as a teacher no less, has great numbers, too.

Any ideas? Other sites to check out? Or do your own comparison.

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.

Reform Math: An Isolationist’s View

For my sins, I periodically peruse the Method Math teacher blogs. I call them Method Math teachers because, much like those self-important thespians in the Actors Studio can’t just act, these guys can’t just teach. Not for them the order of a structured curriculum; no, they want “meaningful math”. They don’t want their kids to do well unless it’s the right kind of doing well. Do they love math? Do they have the proper respect and curiosity for math? What’s the student’s motivation?

They are correctly described as reform math teachers. In math, “reform” refers to the “progressive” side of the debate, in which math is not so much a field of study as it is an ideological value system. Discovery and complex instruction are the guiding lights of their lesson planning. However, since they are teachers, and most teachers don’t really care about education policy in any coherent sense, many teachers who embrace the tenets may not be aware of the ideological underpinnings of their chosen Method. They Like or Don’t Like, without much sense of anything beyond their classroom. (and in that, they are like most teachers).

Reform math is all about social justice, enabling blacks, Hispanics, and girls to “feel successful” about learning math. Actually being successful at learning math is a whole different thing; certainly these demographic categories are successful with their teachers, but when it comes to outside assessments, not so much—which is why reformers don’t much care for standardized tests. But in the classroom, constructivists and discovery-based lessons can accept multiple methods, which means no one method is wrong. And explaining! Explaining is vital. “Explaining your process” is the way that the “procedurally competent” kids (only in reform math is this a bad thing) can be flunked or at least marked down for not explaining their work, while other kids can find “other ways to be smart”. Convenient for grading, this value system allows teachers to dream up all sorts of ways for top kids to fail with the right answer, while tolerating all sorts of other ways for low ability kids to succeed with the wrong one.

(Ironically, these same people who focus on the importance of explaining the “why” are always insisting that teachers reduce the literacy demand of word problems, for kids who can’t read. That’s because the explaining aspect is meant to assist white girls weak on math but strong on literacy, whereas literacy reduction is all about making the problem set up easier for blacks and Hispanics to interpret.)

Reform math practitioners enthuse about this “open-ended discourse”, which avoids calculations and algorithms and, you know, answers. At least definitively right answers. Which teachers don’t give. Teacher explanations = failure. Hence Dan Meyer, the Lee Strasberg of the math blogosphere, famous for his Ted talk, has a blog that proudly bears the label “less helpful”.

Open-ended discourse requires curiosity and ability, which some might deem a feature, but the knowledgeable understand is a bug. Inquiry teaching deliberately eschews algorithms or process or anything resembling a structured approach (while allowing that “blind memorization” might occasionally be useful). Few reform teachers understand the underlying rationale for this method, which lies in the hope that open-ended problems will narrow the achievement gap—not by improving achievement of the lower half, but by narrowing all achievement into a much thinner band. Hence the importance of grading down the top students, and slowing (well, they call it deepening) instruction to be sure that no one is pulling too far ahead.

Ed schools ferociously pretend that all but a few racist fuddy-duddies teach using constructivist methods, but out in the real world, reform math is mostly fringe. The greatest penetration is at the suburban elementary school level, which has a teaching population disproportionately comprised of cheery young women who care more about their students’ interpersonal skills than intellectual development (a feature, not a bug). Complex instruction requires students to “share ideas and knowledge” and the strongest students are responsible for the weakest students’ learning, entrancing elementary school teachers with the delusion that math lessons can enhance social justice. Besides, elementary school teachers aren’t terribly strong at math to begin with, so a method that de-emphasizes algorithms reinforces their own preferences.

Since elementary school teachers rarely have the math chops to develop their own lessons, most reform curriculum development is found in middle school, where kids don’t stay long enough for the parents to complain and the teachers are knowledgeable—and teaching the subjects most attended to by reformers (pre-algebra, algebra, and geometry). So there’s a big support group and lots of material to build on.

Few high school math teachers embrace reform; those who are committed to the Method don’t have a long shelf-life. Most give it up after a few years, the rest show up at grad school where they can pretend that constructivism and complex instruction are valid, proven methods. They get a Phd and demand conformity from prospective teachers in ed school, successfully selling their dogma to a few eager apostles. These converts, alas, ultimately abandon the method or return to grad school where the cycle begins again. Thus Dan Meyer is no longer teaching math but getting his PhD at Stanford with Jo Boaler, Queen Mother of Reform Math. (Understand, however, that reformers do not practice what they preach in ed school. There aren’t multiple ways and many right answers when training new teachers. Heavens, no.)

To the extent reform math survives for any length of time, it does so in white, suburban elementary schools, although not without a struggle. Elementary teachers’ support is counterbalanced by well-educated parents who generally despise it. Parental protests have killed reform math programs at all levels for decades throughout the country. Districts have to balance happy teachers with howlingly angry parents. The high school battles ended over a decade ago, but elementary school parents have to deal with teachers who actually like the program.

But reform math wars are mostly a tale of suburban woes, as parents push back on well-meaning districts hoping to close the achievement gap of their bottom 10-20% by depressing their top performers. It stresses the parents out, but the kids will catch up. For all that reform math propagandists want to change the world for black and Hispanic kids, the techniques are abandoned quickly in high poverty, low ability schools, particularly at the high school level. The story goes like this: a complex instruction curriculum is introduced with great fanfare, math teachers complain, the complainers that can’t be fired are transferred, cue the fawning news coverage with much noise about “equity” and “access”, a few beaming parents who barely speak English talking about their children’s newfound love of math, clips of young black teens and Hispanic girls talking about how they like this math sooooo much better than “just being told what to do”…..and then the dismal state test scores come rolling in and all the canny zealots who once exhorted the grunts to be guides standing to the side are now publicly championing sage on the stage. Back comes explicit direct instruction and the cycle begins again.

The Jo Boaler brouhaha contains one such example, as James Milgram points out:

Indeed, a high official in the district where Railside is located called and updated me on the situation there in May, 2010. One of that person’s remarks is especially relevant. It was stated that as bad as [our work] indicated the situation was at Railside, the school district’s internal data actually showed it was even worse. Consequently, they had to step in and change the math curriculum at Railside to a more traditional approach. Changing the curriculum seems to have had some effect. This year (2012) there was a very large (27 point) increase in Railside’s API score and an even larger (28 point) increase for socioeconomically disadvantaged students, where the target had been 7 points in each case.

Railside High is San Lorenzo High School, in California. As Milgram says, its 2010 scores are dismal, while 2012 scores are improved. Not substantially—ain’t no getting around basic cognitive ability coupled with absurdly unrealistic expectations. But improved.

So I began this post to explain the tiny twitter tempest I began last week, and I’m not there yet. And to get there would take the post into specifics when thus far it’s been general. Sigh. For some reason, I’m writing very slowly this summer. But I didn’t have any clear description of reform math that I could link to in order to explain reform math as I see it, which is not quite as most critics see it.

If the Method teachers out there in the blogosphere do read this, they may confuse me for a traditionalist and, uh, no. My ed school is committed to complex instruction and inquiry-based learning, and I am very fond of my ed school. It’s not fond of me, of course, but then who is?

At that ed school, my all-discovery, all-inquiry, all-complex-instruction master teacher provided me with the best learning experience of my life, adopting effortlessly to my strengths and skepticisms to give me fantastic advice that I hark back to this day. I am, to put it mildly, Not Easy to Teach. That I got six months of valuable education counts for a lot. Thanks to that teacher’s willingness to focus on goals, not methods, I learned to do the same. I can find a lot of good in reform objectives, and steal interesting concepts in their lessons. I might think reform methods are awful but, like progressive educators in general, reformers are thinking about how to teach math, which as it happens is a subject much on my mind.

I am not and never will be a member of the Method group. I am Switzerland, or the US between world wars. Ignore the fact that my first year out I put my students in rows for three weeks until I couldn’t stand it anymore and put them in groups. Second year out I lasted 10 days. Third year out and beyond, I gave into the inevitable and just put the kids in groups from the start. I use manipulatives, introduce units not with facts but with activities that illustrate facts, minimize my use of algorithms, and always remind students that I’ll take a good estimate in lieu of a calculation (and give most of the credit). Anyone evaluating my teaching practice would conclude I have much more in common with the Method crew than I have with traditionalists.

Still, they are profoundly wrong, and their nonsense grates on me much more than the many ways in which the traditionalists err. That’s what led to my tweet, which yes, I still haven’t explained. But I’m ready to start explaining now, so that’s a step up.

Edited later to add:

A couple points. First, I welcome comments on this much because it will help me determine whether I’m getting the right ideas across. I know I can be tough on commenters who misinterpret me, much as I try not to, but I will really try not to if you want to complain about something you’ve misinterpreted on this particular post.

Second, I paint in broad brushes. Keep that in mind!

I’m going to try hard to get the second part of this up faster than normal, for me. I’m hoping for a couple days, but if I fail, know that I tried.