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September 12, 2006
Flash: "Progressives" Decree That Multiplication Tables Have Value After All
There's great news (with a hitch) from the battle for sensible and effective education. From today's Wall Street Journal comes the news that the National Council of Teachers of Mathematics has reversed its endorsement of "discovery" methods of teaching math:
In a report to be released today, the National Council of Teachers of Mathematics, which represents 100,000 educators from prekindergarten through college, will give ammunition to traditionalists who believe schools should focus heavily and early on teaching such fundamentals as multiplication tables and long division.The council's advice is striking because in 1989 it touched off the so-called math wars by promoting open-ended problem solving over drilling. Back then, it recommended that students as young as those in kindergarten use calculators in class.
Those recommendations horrified many educators, especially college math professors alarmed by a rising tide of freshmen needing remediation. The council's 1989 report influenced textbooks and led to what are commonly called "reform math" programs, which are used in school systems across the country.
The new approach puzzled many parents. For example, to solve a basic division problem, 120 divided by 40, students might cross off groups of circles to "discover" that the answer was three.
Infuriated parents dubbed it "fuzzy math" and launched a countermovement. The council says its earlier views had been widely misunderstood and were never intended to excuse students from learning multiplication tables and other fundamentals.
All emphases are mine.
I'm both pleased and infuriated at this announcement--we can't return soon enough to teaching math with an emphasis on learning the proper algorithm necessary to arrive at a definite answer. But the NCTM's disingenuous protest that "we never intended to excuse students from learning ... fundamentals" is feeble bullshit. Google up the NCTM and you'll find plenty of evidence of the influence of their organization; they are in the business of writing standards for math education, and they knew very well that their ideas would have widespread influence. Ideas such as "discovering" the answer to 25 divided by 5, instead of simply memorizing the answer and moving on to more advanced topics.
Unlike many countries, the U.S. has no nationally mandated curriculum, so the math council's guidance has significant influence. In recent years, states have developed their own standards, in part because of the federal No Child Left Behind law, which requires that schools make progress in raising students' scores on state achievement tests. Another math group, the National Mathematics Advisory Panel, created by President Bush, is preparing its own guidance for how best to teach the subject. It meets in Cambridge, Mass., this week.A recent study by the Thomas B. Fordham Foundation, a Washington nonprofit group, found that only two dozen states specified that students needed to know the multiplication tables. Many allowed calculators in early grades.
Whatever their stated ass-covering intentions after the fact, this is the real-world result of the NCTM's "discovery learning" adventure. The grim reality of US kids' performance versus the rest of the world may have something to do with this sea change:
Francis Fennell, the council's president, says the latest guidelines move closer to the curriculum of Asian countries such as Singapore, whose students tend to perform better on international tests. There, children focus intensely on a relative handful of topics, such as multiplication, division and algebra, then practice by solving increasingly difficult word and other problems. That contrasts sharply with the U.S. approach, which the report noted has long been described as "a mile wide and an inch deep."
So it's taken 17 years for the NCTM to find its nose hanging in front of its face. Meanwhile a whole generation of kids have been saddled with a ludicrous progressive/psychologically motivated math curriculum that satisfies the educators' misguided sense of social responsibility at the expense of their students' skills.
Life-long learning indeed. How about a life-long need to keep a calculator in your pocket. Pah!
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Comments
Testify! And pah!, indeed.
The faster kids learn the tables, the faster they'll be able to get to the real stuff. By which I mean social justice math, of course. </snark>
Posted by: jpe at September 13, 2006 08:50 AM
As I've said before ad nauseum, the politicization of education is just as damaging to the Left as it is to the Right. I bet all the academics who are touting critical pedagogy went to private high schools and took philosophy and logic in the tenth grade.
And of course (again, as I've said before) the real injustice falls on those who don't have a strong support system at home, i.e., the inner city kids.
Posted by: Jeff at September 13, 2006 10:58 AM
"Ideas such as "discovering" the answer to 25 divided by 5, instead of simply memorizing the answer and moving on to more advanced topics."
It's all well and good that students have their multiplication and division tables memorized. But I'm curious, when students move on to more advanced topics--say algebra and calculus--should they simply memorize how to solve for x and how to differentiate/integrate? Where does the understanding begin?
Posted by: Daniel Scher at September 13, 2006 04:03 PM
Well, the understanding begins at the same time they're learning their math facts. It's a very effective tactic of the "progressives" to denigrate memorization as "rote learning" and concurrently imply that there's nothing else being taught. My son in second grade is being thoroughly drilled on his facts, but he's also using that knowledge to solve word problems, interpret graphs, etc.
Mastery of arthmetic gives a sound foundation for algebra, and mastery of algebra is the key to all advanced mathematics.
Posted by: Jeff at September 13, 2006 11:46 PM
To elaborate on Jeff's reply, from someone who's been through a long educational cycle as an applied physicist, your "understanding" pops up always one level behind what you're currently studying, and a good helping of drill and rote is needed at the cutting edge of your knowledge, wherever you are.
This was told to me by others and I found it true with myself: You understand multiplication and division when you learn algebra; you understand algebra when you learn trig; you finally understand trig when you do calculus; you understand calculus when you learn vector calculus and/or complex analysis; etc.
I'm just not quite sure where linear algebra, matrices, and tensors fit in that scheme yet... :-)
Posted by: RDS at September 14, 2006 09:42 PM
What's a division table? Progressive indeed!
Posted by: Floyd at September 26, 2006 11:48 AM
Well, I think he just means division "facts". ;-)
Posted by: Jeff at September 26, 2006 01:18 PM
