The statistics on U.S. math performance are grim. American eighth-graders ranked 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. We do better on the Trends in International Mathematics and Science Study (TIMSS), whose test items are related to the content of school mathematics curricula. (Differences in participating countries aren’t significant.) But according to Mark Schneider, a former commissioner of education statistics at the Department of Education, the United States lags behind too many countries in “overall mathematics performance and in the performance of our best students.” And achievement gaps between different student groups within the United States, Schneider says, are “about the same size or even bigger than the gap between the United States and the top-performing countries in TIMSS.”
As part of his education-reform plan, President Obama wants to “make math and science education a top priority” and ensure that children have access to strong math and science curricula “at all grade levels.” But the president’s worthy aims won’t be reached so long as 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.
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The educational trends that led to the NCTM’s approach to math 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, the lead author of the high school standards in the 1989 NCTM report, 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, a mathematics educator at Portland State University, who argues “against the goal of ‘algebra for all’ on the grounds that . . . most individuals in our society do not need to have studied algebra.” 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.
Classroom practices follow logically from these theories. Teacher-directed learning goes out the window, despite its demonstrated benefits for students with learning problems; instead, schools should embrace “student-centered” math classrooms. High-math-achievement countries teach arithmetic in the elementary grades in a coherent curriculum leading, step by step, to formal algebra and geometry in middle school. The progressive educators, by contrast, support “integrated” approaches to teaching math—that is, teaching topics from all areas of mathematics every year, regardless of logical sequence and student mastery of each step—and they downplay basic arithmetic skills and practice, encouraging kids to use calculators from kindergarten on. The educators also neglect the teaching of standard algorithms (mathematical procedures commonly taught everywhere, with only minor variations, because of their general applicability), insisting instead on the value of student-developed algorithms—this despite research by cognitive psychologists strongly supporting a curriculum that simultaneously develops conceptual understanding, computational fluency with standard algorithms, and problem-solving skills as the best way to prepare students for algebra. [emphasis added]...
Read the whole thing here. Yet another reason to homeschool your kids if you can. When high school and college graduates can't do basic algebra, heck, basic arithmetic, you've got a problem:
More city kids are graduating from high school, but that doesn't mean they can do college math.
Basic algebra involving fractions and decimals stumped a group of City University of New York freshmen - suggesting city schools aren't preparing them, a CUNY report shows.
"These results are shocking," said City College Prof. Stanley Ocken, who co-wrote the report on CUNY kids' skills. "They show that a disturbing proportion of New York City high school graduates lack basic skills."
During their first math class at one of CUNY's four-year colleges, 90% of 200 students tested couldn't solve a simple algebra problem, the report by the CUNY Council of Math Chairs found. Only a third could convert a fraction into a decimal. [emphasis added] ...
Horrifying, no? Math is the cornerstone of our technological society. In addition, a good mathematics education develops critical thinking, reasoning and analytical skills essential for, among other things, intelligently exercising your responsibilities as a citizen. Perhaps that's exactly why the Leftist education cabal wishes to water down math education -- to pervert the very critical thinking abilities needed to intelligently question authority and see through their superficially nice-sounding but fundamentally flawed ideology.
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The educators also neglect the teaching of standard algorithms (mathematical procedures commonly taught everywhere, with only minor variations, because of their general applicability), insisting instead on the value of student-developed algorithms
This is an absolutely ridiculous concept.
All human progress springs from building on the progress that has gone before.
Einstein would have never been able to expand our knowledge of physics had he not known the basics of physics to begin with...he would have had to have started at the beginning. His big discoveries, versus the theory of relativity and mass to energy relationships...would have necessarily been, for example, duplication of Newtonian laws...because he would have had no idea that those laws had already been discovered, nor would he have had them available to build upon.
To presume that every person has to start at the beginning and learn each and every basic thing in their own way and under their own terms is to hamstring them from building further upon basic knowledge that's been around for thousands of years.
Ridiculous.
The thing is, these people aren't stupid. There's no way that they don't well understand these concepts.
Which leaves only one possibility. This is an intentional, concerted effort to undermine the educational system in this country.
And I think you nailed the goal right on the head:
to pervert the very critical thinking abilities needed to intelligently question authority and see through their superficially nice-sounding but fundamentally flawed ideology.
Which is also why they hate homeschooling so much. Even if a small percentage of Americans receive a REAL education, they will go on to become the leaders and critical thinkers and undermine the goals of the leftists that have commandeered our educational system.
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