Leighton Smith has been talking about this on his show, this morning:
New Zealand's foremost mathematician has spoken out against the way maths is taught in schools, saying children need to know basic arithmetic before they try to start problem solving.
Sir Vaughan Jones, winner of the Fields Medal - the maths equivalent of the Nobel Prize - told the Weekend Herald that children had to do "lots and lots of exercises" to build up familiarity and confidence before they moved on to more advanced concepts.
His comments follow those of Education Minister Hekia Parata, who said last weekend that she was "extremely concerned" by results from an international survey of Year 5 children in December, which showed half could not add 218 and 191.
This might be the first education minister to be concerned by basic educational failure.
"People are trying to teach kids broad concepts too early [says Jones] when, in fact, the best way to learn is the complete opposite.
"It is really important that kids learn how to multiply and add, to the point where they are certain they will get the right answer if they do the steps right. Then, and not before, they start to see more aspects of the structure. It is a slow process built on understanding each step…
He said that since the 1980s New Zealand had slavishly followed California in abandoning perfectly functional maths methods built up over thousands of years.
And so we have. As Sandra Stotsky explains in an article it’s worth reading thoroughly, what's been abandoned, both here and in the States, is any objectivity at all, or even genuine education. Even of mathematics. Because what’s become more important in the factory schools both here and there is not education of children, but their socialisation:
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 undisturbed by a widespread failure to add 218 and 191.
[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, Greer 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.”
Brad Thompson calls this whole approach 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 … 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 for “whole math” as they have been for “whole language”: whole generations of children emerging from school functionally illiterate and almost wholly innumerate.
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.