University of Massachusetts > STEM > U.S. math woes add up to big trouble

U.S. Math Woes Add Up to Big Trouble

By Ken Gorrell
Apr 8, 2007

There is a war raging all around us, a war the United States cannot afford to lose. No one has died in this war, and no one is likely to. But there are casualties. The injuries are mental rather than physical, but the suffering is lifelong. I'm not referring to the global war on terror or the war on drugs. I'm talking about the mathematics war.
 
While the United States is the world's only superpower militarily, mathematically we are a second-rate power, and losing ground every year. In the math war, the superpowers are Singapore, Korea, Japan, Taiwan, Hong Kong and Belgium. In assessment after assessment, those countries prove that their weapons - fourth, eighth and 12th graders - are more accurate and advanced than our own. Their strategies are more focused. Their national resolve is stronger.

The debate in this country about mathematics education and curricula has been termed the math wars, but it is in reality a generally civil disagreement. There are two distinct sides in the debate, which for simplicity's sake I'll label "reformers" and "traditionalists." Because I subscribe to the BLUF principle - Bottom Line Up Front - I'll tell you now that I side with the traditionalists.
In this forum, I can't possibly present all the relevant information necessary for you to make an informed decision on this issue. My goal is to pique your interest so that you will want to become better informed, will want to take a stand.
Why? Because the issue is critical to our nation's ability to remain an economically advanced world power.
 
Let's face it: Math whizzes in Taiwan or Belgium will get good jobs in the global economy, but they are not going to grow up to become taxpaying supporters of the American baby-boomers' social safety net. Only American math whizzes can be counted on to do that. We need to grow our own. A bit of context is important. The reformers, representing the education establishment, believe learning "process" is more important than memorizing core knowledge. They see self-discovery as more important than getting the right answer. For them it's the journey, not the destination. Traditionalists, consisting mainly of parent groups and mathematicians, advocate teaching the traditional algorithms. They advocate clear, concrete standards based on actually solving math problems. The destination - getting the right answer - is important to traditionalists.

Fuzzy vs. clear

Two examples will help to make the difference clear.
One broad standard in an actual reformers' curriculum states that students should "use computational tools and strategies fluently and estimate appropriately." A similar statement in a traditional standards curriculum says: "The student will add and subtract with decimals through thousandths." Fuzzy standard on one side, clear and concise on the other.

One math project in a reformers' program - the program used in many New Hampshire school districts - is called "My Special Number." Sixth graders are told:
"Many people have a number they find interesting. Choose a whole number between 10 and 100 that you especially like. In your journal: "Record your number. "Explain why you chose that number. "List three or four mathematical things about your number. "List three or four connections you can make between your number and your world. "At the end of the unit, your teacher will ask you to find an interesting way to report to the class about your special number." Sixth graders are given a month to complete this project. To traditionalists, tools and context are important - in that order. Master the tools, put them in context. Reformers provide context, then attempt to guide students to discover the tools. This is cart-before-the-horse thinking. The reformers' approach is to have students devise their own methods for achieving a mathematical goal rather than have them learn the traditional algorithms. "By talking about problems in context, students can develop meaningful computational algorithms," a reform standard states. This is not true. If by "meaningful computational algorithms," we mean simple, accurate and repeatable - things like the traditional addition algorithm, or long division, then the average student will never develop such an algorithm and should not have to try. Universal mathematical algorithms were developed ages ago by Archimedes, Euclid, Descartes and Pascal. There are not many budding Pascals in our school districts, but there are plenty of children capable of learning from the methods discovered by the great mathematicians in history.

Return to tradition

Traditional methods of teaching mathematics have proved their worth. While they could be tweaked, they should not be discarded.
Reformist curricula might make for an interesting doctoral dissertation, but they don't hold up well when ivory tower meets bricks and mortar. In math education, America's children once competed well with their foreign peers. But today our students' mathematical performance earns them a place in the bottom quartile of industrialized countries. They are in the middle of the pack when less-developed nations are added.

What has changed during recent decades? The teaching philosophy. The reformers of the education establishment - Big Ed - took over. Billions of tax dollars have been spent on a social experiment in which the tried-and-true was discarded and the intellectually fashionable was foisted on schoolchildren. This should spark outrage among both parents and taxpayers. It should trouble anyone counting on today's students to get good jobs and pay taxes.

The best way to advance students' conceptual thinking about mathematics is to have them learn and take advantage of the existing core of mathematical knowledge. This is the traditional approach: Students are taught, and made to master, the traditional algorithms.  With such tools, and with the guidance of good teachers, a student can, after 12 years of school, understand and apply mathematical principles that took scores of geniuses thousands of years to devise.

I urge you to learn more about the math wars, about how your school is teaching math, and to take a stand in favor of the traditional, proven methods.

Ken Gorrell of Northfield works for a New Hampshire-based defense contractor.

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