Thursday, 19 November 2009

Standards? What standards? [updated]

For reasons explained here several times before, I’m no fan of Ann Tolley’s focus on national “standards” instead of other more important educational issues --  but for reasons that aren’t mine the teachers unions and academics and all the usual suspects are also dead against them.

As you might have noticed.

This story from the States helps to explain why.  It’s not just that teachers don’t want to be found out for their lacklustre teaching – although that’s the motivation for many of them – it’s that today’s fashionable educational theories (which we share with the U.S.) mitigate against any objectivity at all, or even genuine education. Even of mathematics.

    “Assessment experts, technology salesmen, and math educators—the professors, usually with education degrees, who teach prospective teachers of math from K–12—dominate the development of the content of school curricula and determine the pedagogy used, into which they’ve brought theories lacking any evidence of success and that emphasize political and social ends, not mastery of mathematics. . .”
    “The underlying goals of [education]—never made clear to the general public—were social, not academic. Some of the [theorists], for example, sought to make mathematics “accessible” to low-achieving students, yet meant by this not, say, recruiting more talented undergraduates into teaching but instead the employment of trendy, though empirically unsupported, pedagogical and organizational methods that essentially dumb down math content.”

In striving for “social” standards instead of objective academic standards, the professors are still following the pedagogical trajectory mapped out by progressive educator John Dewey, who saw education primarily as “socialisation.” “Education, in its broadest sense,” said Dewey, “is the means of this social continuity of life.” What this means, notes Stephen Hicks, is that “education is not about equipping individuals for life. It does educate individuals, but its purpose is social continuity.”

Think about that, and you’ll understand why teachers, teacher unions, and the academics who teach teachers are dead against the objective standards proposed by Tolley.

    “[These] educational trends . . .  have a long pedigree. During the 1970s and 1980s, educators in reading, English, and history argued that the traditional curriculum needed to be more “engaging” and “relevant” to an increasingly alienated and unmotivated—or so it was claimed—student body. Some influential educators sought to dismiss the traditional curriculum altogether, viewing it as a white, Christian, heterosexual-male product that unjustly valorized rational, abstract, and categorical thinking over the associative, experience-based, and emotion-laden thinking supposedly more congenial to females and certain minorities.
    “Those trying to overthrow the traditional curriculum found mathematics a hard nut to crack, however, because of the sequential nature of its content through the grades and its relationship to high school chemistry and physics. Nevertheless, education faculty eventually figured out how to reimagine the mathematics curriculum, too, so that it could march under the banner of social justice. As Alan Schoenfeld . . . put it, “the traditional curriculum was a vehicle for . . . the perpetuation of privilege.” The new approach would change all that.
    “Two theories lie behind the educators’ new approach to math teaching: “cultural-historical activity theory” and “constructivism.” According to cultural-historical activity theory, schooling as it exists today reinforces an illegitimate social order.
    “Typical of this mindset is Brian Greer. . .  According to Greer, the proper approach to teaching math “now questions whether mathematics as a school subject should continue to be dominated by mathematics as an academic discipline or should reflect more fully the range of mathematical activities in which humans engage.” The primary role of math teachers, constructivists say in turn, shouldn’t be to explain or otherwise try to “transfer” their mathematical knowledge to students; that would be ineffective. Instead, they must help the students construct their own understanding of mathematics and find their own math solutions.”

Yep, sounds like bullshit doesn’t it.  Little Johnny “constructs” his own knowledge; mathematics is about socialisation not education; algebra is more amenable to emotion than to reason; and education is a white, hegemonic, patriarchal practice – at least it is according to alleged educators like Schoenfeld and his colleagues.  No wonder Little Johnny from America came “25th out of 30 countries in mathematics achievement on the 2006 Programme for International Student Assessment (PISA), which claims to assess application of the mathematical knowledge and skills needed in adult life through problem-solving test items.”

That result was a wake-up call for real educators in a way similar results for New Zealand student haven’t been here.

Faced with that clear signal of failure, there were enough alarmed educators still extant to call for the reintroduction of mathematics to American mathematics classrooms – not dumbed down emotionalist mathematics, but the genuine article.  A panel was convened “composed of mathematicians, cognitive psychologists, mathematics educators, and education researchers” which “spelled out the 27 major topics of school algebra that should be taught in every American high school to make us internationally competitive.” Further,

    “The panel found little if any credible evidence supporting the teaching philosophy and practices that math educators have promoted in their ed-school courses and embedded in textbooks for almost two decades.”

Naturally, the “constructivists” and the socialisators revolted. How dare they!  The best response was from Brian Greer (“best” in a way that would be humorous if the entity making the response wasn’t in charge of the indoctrination of new teachers):

    “Greer declared in his [response to the panel that it] offered nothing useful, since it had “restricted” itself to scientific research and ignored the “rich reflections” of educators, who, in his judgment, had produced the “deepest work in the field.”
    “These reflections, which progressive educators call “qualitative” or “practitioner” research, generally consist of educators studying their own classrooms and concluding that, yes, their methods work well.”

And there, right there, is the reason for such stern opposition to the introduction of standards, any standards, to New Zealand classrooms.

Like Greer, New Zealand’s alleged educators would prefer to interview the inside of their own heads (i.e., their “reflections”) than they would confront reality.

Now wonder there’s such snarling hatred about.

* * * * *

I recommend a thorough reading of the article from which I’ve quoted above extensively:
Who Needs Mathematicians for Math, Anyway? (The ed schools' pedagogy adds up to trouble) – Sandra Stotsky, CITY JOURNAL

UPDATE:  I’ve just been sent another splendid article on the same theme by Brad Thompson, from 2002, which uses even plainer language and is even more focussed on the underlying cause, the “whole math” method of teaching.  He calls it Cognitive Child Abuse in Our Math Classrooms:

    “America's children are flunking math. In 1996 American high school seniors finished close to the bottom on an international mathematics test. At the end of last year, American eighth-graders ranked below those of Malaysia, Bulgaria, and Latvia.
    “As educators scramble to explain America's math meltdown--as the Bush administration urges more ‘accountability and a National Research Council study recommends better ‘training’ [the report about which the professors were protesting] --few are willing to look at the fundamental cause: the new, ‘whole-math’ method for teaching.
    “Inspired by a strain of progressive-education theory called ‘constructivism,’ whole-math proponents claim that all knowledge--including mathematical knowledge--is arbitrarily constructed. They reject the idea that there are objectively demonstrable right and wrong answers, and that, consequently, there are basic skills that students must be taught. Instead, the advocates of whole math believe that each student should invent his or her own math ‘strategies’ by using a ‘guess-and-check’ approach. They create an inability to think beyond immediate concretes.”

The results in their respective fields were the same “whole math” as they have been for “whole language”: widespread functional illiteracy and innumeracy.

    “This is cognitive child abuse. Whole-math defenders are shrinking the cognitive capacities of their students to those of infants or even animals.
    “Is it any wonder that most college freshman take remedial math courses, that American universities award more than half of their mathematics Ph.D.s to foreign nationals, that for-profit math remediation companies are booming, and that 200 of the nation's leading mathematicians and scientists signed a public letter denouncing whole math? . . .
    “The controversy surrounding whole math is not simply about how children are taught to deal with numbers. If we undermine the capacity of our children to learn mathematics, we undercut their ability to think. More and more, our schools are turning out students whose capacity to reason has atrophied. . .
    “Now imagine flying on a plane designed by aeronautical engineers who have been trained to concoct their own math schemes and to use a ‘guess-and-check’ method. . . .
   “Today's "math wars," like the controversy over how to teach reading, are at root philosophic battles that will have enormous implications for the future of America. If the advocates of whole math are allowed to win, they will be taking us a huge step away from the values of reason and science that once made America [and the western world since the Enlightenment] great.”

Read Brad Thompson’s Cognitive Child Abuse in Our Math Classrooms.


  1. Why adopt US's approach to mathematics education, when it's failing?
    P.S. I think Hicks has confused Constructivism with Social Constructivism.

  2. @Monsieur, there's a problem with your reading comprehension.

    First of all, I'm suggesting that the opposition to change there is for similar reasons to the opposition here: that we already have here is the failed system.

    Second of all, it's not Hicks who wrote the article, it's Sandra Stotsky.

    Third of all . . . oh I give up. If you can't even get the basic words right, what's the point of discussing the buzzwords.

  3. @PC: I'm sorry for mistaking the authors, you're quotations were not attributed well.

  4. The US has had
    standards-based testing for decades
    Finland's approach seems to work well.

  5. @Monsieur: Let me say it again: "I'm suggesting that the opposition to change there is for similar reasons to the opposition here..."

    Or are you suggesting the same flaccid bullshit doesn't exist in the teachers colleges here?

  6. I'm suggesting that "constructivism" is not how Sandra Stotsky depicts it. You must know this because it is the basis of the Montessori method.

  7. Well, no she hasn't, and no it's not.

    Children in a Montessori classroom do not "construct their own knowledge" -- they do not "theoretically construct knowledge" to explain things they don't understand, and nor do they socially construct knowledge as part of an "artifact" of a group.

    This is just horse shit.

  8. Please read page 10 (Why Poor Models Stick) of 1
    Angeline Lillard - Montessori: The Science behind the Genius
    from the site.

  9. I applaud your research, Monsieur, and while Lilliard is usually very good, she's frankly either out of her depth here philosophically, or is vainly trying to sell Montessori to mainstream educationalists who believe all the horse shit.

    In other words, that looks to me like she's saying, "Look you guys, Montessori is one of you!"

    Why she would want to do that is another question altogether.

  10. Peter, I'm guessing you, like me, studied "New Maths" at school. Remember all those Venn diagrams. I don't know when NZ finally got rid of it.
    In your updated post, I think Brad Thompson is refering to the Mathland program, which was scrapped in 2007.

    So why is everything in the US so "god-darned" political, even teaching maths. The argument raging there at the moment between "traditional" and "modified" maths education seems to be, as usual, between conservative and progressive groups. But it reflects a deeper philosophical divide between logical-positivists (behaviourists) and constructivists.

    Thompson states: "... constructivism whole-math proponents claim that all knowledge -- including mathematical knowledge -- is arbitrarily constructed.". In theory, constructivism does imply that, but in practice it does not.

    Let's take two concepts that derive from a constructivist approach: Problem-solving and Metacognition.
    Here is a link to a big 100 page pdf on why these two concepts are considered integral to Maths education. I'm only asking you to read the first few pages.
    Problem Solving, Metacognition, and Sense-Making in Mathematics, by Alan H. Schoenfeld.
    It sounds very reasonable to me, and now consider the 'guess-and-check' method referred to by Thompson. It is not applicable to flying a plane, but it is valid in other situations where one is trying to solve a problem.
    "Just take a punt... Shhht that's wrong... But close... Hmmmm... What about this? ... ".

    Of course there is the problem of measurability. How can you objectively rate how well a student is doing. The tide is still a bit out on that. But the traditional way of teaching, just feed in information and test the results is hopefully gone for good.