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 absenceThat'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.
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.
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.