GFBrandenburg's Blog

GFBrandenburg's Blog

Regrets & clarification…after signing one of Michelle Rhee’s petitions « Parents Across America

Regrets & clarification…after signing one of Michelle Rhee’s petitions « Parents Across America

Another "Load" From A Familiar Source: Sweller and Friends Try To Deceive Again

John Sweller

Paul Kirschner

Richard E. "Dick" Clark

The trio pictured above are Australian educational psychologist John Sweller (known particularly for "cognitive load theory," Paul Kirschner, a professor of educational psychology based in Holland, and Richard E. Clark, an educational psychologist and clinical research professor of surgery at USC. These gentlemen have written several articles that intend to show that progressive, discovery-oriented, student-centered approaches to mathematics education are not viable. The first such article that caught my attention is their 2006 EDUCATIONAL PSYCHOLOGIST piece, "Why minimal guidance during instruction does not work: An analysis of the failure of constructivist discovery, problem-based, experiential, and inquiry-based teaching." 

Note, please, the subtle, intellectually modest language of that title. It isn't that such instruction may be in some ways flawed, in need of refinement, or in any way worth employing. No, in the view of these good professors, it DOES NOT WORK and is a FAILURE. And what do they propose we should use in place of this list of approaches? Not to keep you on tenterhooks, it is, of course, direct instruction. In the words of Hamlet to Polonius, "My lord, I have news to tell you. When Roscius was an actor in Rome. . . "

Apparently, however, the 2006 article did not suffice to remove the scales from everyone's eyes. So in 2010, this stalwart band of clear-eyed thinkers saw fit to address their ideas directly to the American Mathematical Society, one of the two organizations of professional mathematicians in the United States. While their previous piece was twelve pages long, "Teaching General Problem-Solving Skills Is Not a Substitute for, or a Viable Addition to,Teaching Mathematics," last year's opus took but two.

Again, the authors make no pretense of intellectual modesty: not only is teaching problem-solving methods not a replacement for teaching mathematics (who would disagree?), but there's no benefit from teaching problem-solving methods at all! Polya be damned, it turns out that these ed psych guys know WAY more about how mathematicians do mathematics than did the world-class mathematician known for having dedicated a sizable amount of work to how to solve mathematical problems and develop heuristic methods for improving students' problem solving.

 In this recent article, we are treated to the following:

Recent “reform” curricula both ignore the absence
of supporting data and completely misunderstand
the role of problem solving in cognition.
If, the argument goes, we are not really teaching
people mathematics but rather are teaching them
some form of general problem solving, then mathematical
content can be reduced in importance.
According to this argument, we can teach students
how to solve problems in general, and that will
make them good mathematicians able to discover
novel solutions irrespective of the content.

That's some heady, alarming stuff indeed. The only problem is that it has no foundation in reality. And that is likely why our heroes are able to offer not a single citation to tell us who, exactly, is making the argument with which they wish to further bash any approach to mathematics teaching that isn't business as usual.

Now, if I were not a veteran of the history of the Math Wars and someone told me that there were folks who believed that we could improve mathematics education by reducing the importance of mathematical content, I'd be alarmed. And I suspect that a majority of readers of AMS Notes are generally ignorant of the specifics of the two-decade-long fight between a small number of educationally conservative mathematicians and the leadership of the mathematics education research community (though, of course, there are more than two sides and there are many more players on the two main sides than those subgroups I've mentioned). Like previous conservative efforts in various mathematics publications to scare the bejeezus out of the community of working mathematicians, this one is intended to convince people that there are some really crazy folks who want to take the mathematics out of mathematics education. It's got all the appeal of the usual efforts to win a political, ideological war through sound-bites rather than facts. And like the vast majority of such efforts, it just ain't so.

Given that fully 1/4th of the 12 pages offered in 2006 were references, it's noteworthy that there isn't a single citation to let us know who it is that's making the "argument" we're supposed to be so contemptuous of: downplay mathematical content because we can teach problem-solving methods absent actual mathematics! Well, not to put too fine a point on it, but were anyone making that argument, I'd be in the forefront of those pointing out its absurdity. The reason I'm not leading the parade, however, is because in more than twenty years of work in mathematics education, I've never seen evidence that anyone believes anything of the kind. To suggest that our ed. psych. friends are using the straw man technique is to underrate the outrageousness chutzpah that goes into writing something founded completely on myth (no little irony in the fact that one of the authors, Professor Kirschner, puts himself forth as a debunker of "intellectual urban legends." Apparently, that gives him license to sign on to promulgating an egregious whopper of his own).

It's not that these academics are supporters of direct instruction uber alles that makes them so dangerous. It's that they appear willing to simply make things up in order to try to rid the world of all competition to their favorite pedagogy. While repeatedly claiming that educators and learning theorists who take issue with direct instruction or, to the dismay of our heroes, dare to advocate for other sorts of instruction have NO evidence to support their views, Sweller, Kirschner, and Clark are hardly above making unsubstantiated claims about ghostly demons who believe things one only reads in the writings of. . . well, people like Sweller, Kirschner, and Clark. Further, they ground their own work in the usual "gold standard" sorts of laboratory research that generally seem to have nothing to do with what goes on in actual classrooms, while complaining that their adversaries aren't doing the same thing.

Without wanting to once again go over all the reasons that educational research in the field differs dramatically from educational  and psychological research in the laboratory, I'll simply point out that the kinds of things these fellows tend to base their arguments upon are either disconnected from what is feasible in schools and classrooms, or are at least as questionable as the ideas and practices of which they are so contemptuous (see, for example, the chess analogy in their 2010 piece).

Why is it that critics of progressive ideas in education (particularly those grounded in respect for students' interests, their need for ownership of their own learning, and their desire to be listened to and taken seriously, as well as those designed to promote democratic values and build skills necessary for actively participating in democratic societies) are so quick to load the dice when they "critique" those ideas? Why, too, do so many of them seem to operate with the same sorts of rhetorical tricks and propensity for utterly dismissing everything connected with educational methods at odds with their own? Is it really necessary, I wonder, to claim that progressive ideas in education are UTTERLY without merit or application in order to question and view them skeptically? 


I am increasingly convinced that absolutism is a common thread amongst anti-progressives whether regarding education or just about anything. The lack of intellectual modesty and humility is to be expected from poltical pundits these days, but academics are supposed to show a little more restraint than Glenn Beck or Rush Limbaugh. The more I read from Messrs Sweller, Kirschner, and Clark, however, the more I expect to see them getting a weekly show on Fox News.

No matter how cynical you become, it's never enough to keep up:

Ordinarily, I try to keep the focus here directly on mathematics education issues, but it's impossible to view what's going on in this country right now without seeing how a host of threads come together through almost any lens one chooses to look.

The situation in Wisconsin and the rhetoric being deployed by the anti-worker governor and his supporters would be funny if the stakes weren't so high and the incredible hypocrisy and cynicism so deep and real. However, there are times when it seems that the only source that completely captures just how unprincipled and transparently dishonest such influential sources as Faux Snooze are is THE DAILY SHOW. After viewing one of Jon Stewart's most recent broadcasts, I feel that there's really nothing more that I need say than to urge you to watch. If you have any doubts as to which side is lying through its teeth every time it says anything, just watch this Thursday, March 3, 2011 excerpt:

Daily Show: Crisis in Dairyland - For Richer and Poorer - Teachers and Wall Street

A Must-Read Book on mathematics education

Derek Stolp

I am nearly finished reading a truly remarkable book about mathematics education in the US, what we can do about it to make it more effective and meaningful, and a call for a return to democratic core values in our entire approach to schooling (okay, I'm not sure the author goes quite that far explicitly, but let me do so for him if he doesn't). The author is Derek Stolp, pictured above, and the book is MATHEMATICS MISEDUCATION: The Case Against A Tired Tradition. 

It's a definite must-read if you are concerned about just how off-base both traditional and many reform efforts are in US mathematics education. For example, Stolp makes a very telling point about NCTM's commitment to real-world mathematics in his examination of the article content in THE MATHEMATICS TEACHER from 2002, the year he was writing his book. Unsurprisingly, to me at least, he found a rather dramatic mismatch between NCTM's public commitment in, say, PSSM to real-world connections and the focus of the vast majority of articles that appeared two years later in MT. I suspect that a similar study regarding the productive, creative use of technology in mathematics teaching would show even greater disconnections between NCTM's talk and walk. But they are hardly alone in this regard. 

Stolp has a lovely website with a lot of curricular ideas that jibe with his philosophy of mathematics education. It looks like it could prove to be an excellent resource for teachers who want to create a similar sort of mathematics teaching and opportunity for students in their classrooms.

I have only one quibble thus far with Mr. Stolp: at several points in his book, he mentions as an example of the difference between conceptual and procedural understanding the importance that students "get" that multiplication is repeated addition. Regular readers of my blog will recognize that those are (nearly) fighting words to my ears. But, hey, I don't expect perfection from anyone, not even myself. ;^) So even if Stolp is at least temporarily in the MIRA camp, I hope he will come to see the limitations of that viewpoint, and even if he doesn't, he's got way too much of value in his writing for me not to promote it here. 

Finally, I'd love to see what Derek Stolp and Dan Meyer would make of each other's work and viewpoints. I see the potential for a very productive exchange and potential collaboration between them. But then, I always tend to think synergistically when it comes to math and math teaching: probably comes from knowing how little I'd know in this domain if it weren't for the brilliance and inspired work of a host of other people.

It Ain't Just Claptrap: Can We Meaningfully Critique Our Schools?

On an education discussion list I follow, Jonathan Groves made that I will not reproduce here, in which he was critical of many aspects of US math and literacy education, based on what he sees in his own teaching at the college level. One reader of the list replied to Jonathan's post, "This is just a repetition of all the claptrap, generalizing, and stereotyping [this list] is supposed to combat."


I think the situation, particularly from the perspective of mathematics educators, is a bit more complex than would allow the dismissal of Jonathan's post as "claptrap."

The fact is that if you spend time in classrooms where things are not going well (for a host of reasons, not merely the short list that the deformers cite, if those apply at all), you can't help but be frustrated at how poorly we are presenting mathematics to a vast majority of students there. In that context, I speak of places like Detroit, but that list includes many other poverty-stricken places, large and small, in this country.

Next, looking at many classrooms in less economically depressed districts, one sees teachers who don't know the mathematics they're expected to teach (particularly, but not exclusively, at the K-5 level); those who 'know' the math, but don't know nearly enough about how to teach it well and effectively to any but a small number of so-called "mathy" kids - generally those who already like math, particularly when math is reduced to quick, accurate calculation; and then the lovely but all-too-rare cases of inspired teachers allowed to do their jobs without absurd shackles placed on them by national, state, or district tests and other idiocy that has little or nothing to do with mathematics or education.

We also know that this overall inadequacy doesn't result in an under-supply of mathematically competent folks. There's no shortage of mathematicians, economists, engineers, physicists, etc. That was made crystal-clear in THE MANUFACTURED CRISIS, but those numbers are ignored by the deformers, the anti-progressives in the Math Wars, by Obama and his "Sputnik moment," and many others.

So the question becomes much more an ethical one about whether to teach mathematics better to more kids for its own sake (the pleasure, power, and beauty of mathematics), for the sake of equity (everyone has a right to become mathematically competent and rise to whatever heights she desires and is capable of reaching), and for reasons of core democratic values (an innumerate citizenry is one easily deceived by politicians, demagogues, advertisers, and other scam artists). It is NOT a question of "saving" the economy with a new wave of math and science folks. So many jobs in the predictable future will NOT require all that much math or, for that matter, what's typically viewed as a college education, though competition and raising the bar may make folks have to have college degrees to get jobs that don't really require much of what colleges generally teach and students generally study there (in other words, even if employers choose to make a college degree a basic requirement for a service job, that doesn't mean the course of study will better prepare anyone to DO that job).

What this all boils down to, for me, is the issue of criticism from the right versus criticism from the left - to use a crappy metaphor - when it comes to public education. Not being of the educational deform mindset, my back goes up every time I read or hear an attack on our public schools that comes from Duncan, Klein, Rhee, the usual think tanks and foundations, the typical education reporter, ad nauseum. At the same time, I don't think our current public educational model is sound, I don't think it's been sound for a long time, and I think we can and must do better.

The problem becomes how to level correct, meaningful, constructive criticism at the system that leads to real change without throwing in with the deformers or inadvertently winding up supporting their causes (it's rather unlikely that they will help ours, no matter what their rhetoric about choice, accountability, raising the bar, and a host of other catch phrases and buzz words).

It becomes exhausting to have to keep repeating that I don't want to see our public schools dismantled or privatized, that I don't want to see teachers sacrificed on the altar of real or phony economic shortages (and misplaced priorities), that I "get" why we have teachers' unions, that teaching is a very difficult job, etc., etc., and that I STILL know that there are many crappy schools, crappy teachers, crappy administrators, crappy tests, crappy politicians with their fingers in the education mess making it worse, and a bunch of greedy asshats trying to suck away billions from kids into their own pockets, all the while singing psalms about global competition, accountability, 21st century skills, and so on.

Your mileage, of course, may vary.

A MUST read: "PISA: It's Poverty Not Stupid"

"PISA: It's Poverty Not Stupid" by Mel Riddile http://tinyurl.com/povertyandPISA My comments: The sky isn't falling in US public schools, folks. Some readers likely already knew that, particularly those who are followers of the late Gerald Bracey's work, amongst other debunkers of educational disinformation. The results of the recent PISA exams highlight this fact, but you wouldn't know it from US Sec. of Education, Arne Duncan or any other doom-sayer, bloviator, pundit, or deformer. And with good reason. Because what the numbers say is disturbing, but not because our schools are failing us. The facts are that our schools are amongst the best in the world, but to see it you have to compare apples to apples. And what's being done with the PISA scores for the most part is what's been done with so much other data: the wrong things are compared and the apparent results make our public schools look like they're at best doing a mediocre job. What is being missed or hidden by the 'experts' who want to convince us to fire teachers, bust unions, turn public education over to Wall Street, promote charters, hand out vouchers to parents (particularly rich and upper-middle class ones), and generally dismantle our public schools in order to turn them over to drooling private market entrepreneurs and (many) charlatans? The fact that the US has an enormous disparity between rich and poor compared with other industrialized nations, and the impact of poverty on the average scores. But disambiguate scores so that we compare similar economic strata across nations and suddenly we're just where one might guess: Number One. But please, don't take my word for it. Read a detailed analysis. Then consider why Duncan, Rhee, Klein, and so many others are SO invested in convincing you that it's our ENTIRE nation's schools that are in crisis, at risk, failing, collapsing, corrupt, incompetent, bleeding money, and all the rest of it. Why they look at the public schools alone as having failed to solve the effects of severe poverty in rural and urban settings alike. Or in other words, why they don't want you to realize that poverty and greed at the top of our economic system, not teachers' unions, is what's keeping the folks at the bottom from lifting themselves by their non-existent bootstraps. http://tinyurl.com/povertyandPISA