The Math Wars

by
KenG

There is a war raging all around us.  It is a global war.  It is a war that the United States cannot afford to lose.  No one has died in this war, and no one is likely to.  But there are casualties.  Their injuries are not physical; they are mental.  And the suffering is life-long.  I’m not referring to the Global War on Terror or the War on Drugs.  I’m talking about the Math War.

While the United States is, militarily, the world’s only superpower, we are, mathematically, merely a second-rate power, and losing ground every year.  In the Math War, the superpowers are Singapore, Korea, Japan, Taiwan, Hong Kong, Belgium.  In assessment after assessment, those countries prove that their weapons – in this case, mathematically-competent 4th, 8th, 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 War” but it is really a generally civil, though passionate,  disagreement.  Passionate for good reason:  The outcome may well determine whether America can remain the world’s leading economic power.  

There are two distinct sides in the debate which for simplicities sake I’ll label as the “Reformists” and the “Traditionalists.”  Because I subscribe to the “BLUF” principle – Bottom Line Up Front – I’ll tell you now that I side with the Traditionalists.  Call me a neo-Traditionalist. 

I can’t possibly present in this forum all the relevant information necessary for you to make an informed decision on this issue.  Instead, my goal is to pique your interest in the subject so that you will want to become better informed, will want to take a stand.  Why?  Because good jobs will be created in those countries that take seriously advanced mathematics education and student ability.  And right now, America is falling behind.  As in World Cup Soccer, our math team is not a contender.  And math whizzes in other countries are not going to grow up to become tax-paying supporters of the American baby-boomer’s 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 Reformists, representing the education establishment, believe that “process” is more important than memorizing core knowledge, and self-discovery more important than getting the right answer.   For them it’s the journey, not the destination.   

“Traditionalists,” consisting of parent groups and mathematicians, insist on 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.

Two examples will help to make the difference clear. 

  •   One of the broad standards in an actual Reformist curriculum states that students should "use computational tools and strategies fluently and estimate appropriately."  A similar statement in a Traditional standards document states “The student will add and subtract with decimals through thousandths.”  The standard is fuzzy on the one side, clear and concise on the other. 
  • One of the math projects in a reformist math program  – the program used in my school district – is called My Special Number.  Sixth graders are told that “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, the teacher is directed to ask students to find an interesting way to report to the class about their 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, then put them in context.  Reformists provide context, then attempt to guide the 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.  To quote again from a Reformist math standard:

"By talking about problems in context, students can develop meaningful computational algorithms."

The problem is that this is not true. If by "meaningful computational algorithms" we mean “simple, accurate, repeatable” – things like the traditional addition algorithm, or long division, the fact is that the average student will never develop such an algorithm.  Universal mathematical algorithms were developed by the likes of Archimedes, Euclid, Descartes, and Pascal.  There are not many budding Pascals in our local school districts.  

I said that I was a “neo-Traditionalist,” which simply means that I believe that the traditional methods of teaching mathematics have proved their worth, and while they could be tweaked, they s
hould not be discarded.  Reformist curricula might make for an interesting PhD dissertation, but they don’t hold up well when ivory tower meets brick-and-mortar.  In math education, our children used to compete quite well against their foreign peers.  But today our students’ mathematical performance earns them a place in the bottom quartile of industrialized countries, and middle of the pack status when less-developed nations are added to the mix. 

What has changed over the past couple of decades?  The teaching philosophy has changed.  The Reformists of the education establishment – Big Ed – have taken over.  Billions have been spent to achieve this outcome, which should spark outrage among parents and taxpayers.  It should, as well, be cause for concern for anyone counting on today’s students to create or get good jobs and pay taxes to support our social safety net.         

In my opinion, students should be taught, and made to master, the traditional algorithms.  The best way to advance students’ conceptual thinking about mathematics is to have them learn and take advantage of the existing core body of mathematical knowledge.  This is the traditional approach.  With such tools, and with the guidance of good teachers, a student can grasp and integrate in twelve years a body of mathematics that took hundreds of geniuses thousands of years to devise.

Now cross posted over at www.GilfordGrok.com!

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