• elaborate  make-work homework assignments,
• cutting and pasting extravaganzas,
• overly  complex and roundabout procedures to add or multiply numbers,
• estimation  exercises that won't quit, and
• the use of calculators in place of  traditional  arithmetic methods.

You  thought: "Of course, the educational professionals must know what they are  doing. Once my children catch on to these clever techniques, they will develop into mathematics geniuses!" Unfortunately, what you discover is that they never learn the core facts and methods, their confusion grows, they lose their self-confidence, they decide they just can't do math, and you are stuck paying  for tutoring. Even worse, children who might have become exceptional mathematicians, engineers, or scientists are denied their rightful future.

What went  wrong? Years ago the educational establishment decided that teaching mathematics had to either consist of rote memorization (without real understanding) or students had to discover mathematics through trial and error, because it was assumed that only 'if they discovered it themselves'  would they truly understand  it. While this view presented a false choice (there are much better  alternatives), the educational community was sold on the second alternative, because it had an intellectual cache that was lacking in "rote memorization." 

What resulted are the various "modern" math curricula for our children that  under-emphasize learning math facts, that bend over backward to avoid teaching standard methods for addition, subtraction, multiplication, and division, and that refuse to teach traditional processes for manipulating fractions.

Almost all  our public schools today use one of the "modern" math curricula and millions of  promising math-based technology careers are being ruined every year.

Permit me a short excursion. I have a technical/engineering background (Ph.D. MIT, '74) that  rests largely on advanced mathematics. One reason I followed this path is that, as a student, I always had poor memorization skills and, therefore, subjects such as biology, chemistry, and foreign languages were very difficult for me. I loved math and physics because there was very little memorization; I could derive any formula I needed during a test. "Understanding" was a much more  powerful asset for me than memorization.

If anyone would be inclined to favor understanding over memorization, it would be me. But the modern math is a disaster. I'm convinced that if I had been "taught" math with it 50 years ago, I would probably have become a poet (my English teacher is rolling over in her grave).

So do I favor just rote memorization? Of course not. Successful math education requires that students learn the techniques that true geniuses have developed over the last 3000 years. You may think the standard technique used to add numbers is trivial (place value concepts, carrying, etc.), but it was not obvious to the ancient Greek philosophers. Multiplication, long division, and fractions are even more complex. Teaching the techniques first, and then exploring the underlying concepts and why these techniques work is the most efficient way to achieve true understanding. If Socrates and Aristotle couldn't invent our modern arithmetic system, why do we think the typical third or fourth grader can?

The impact  of "modern" math on students in the US has been devastating. Just look at how the US stands up against other countries.

Place an  equal emphasis on method mastery AND conceptual understanding, and you have the makings of a powerful elementary math curriculum -- a curriculum that leads to real learning, that builds self-esteem and, rarest of all, a child that comes home and says, "Hey mom, I really love math!"

This  approach to math education is not new. It is what a well-taught, traditional mathematics course always emphasized. In some cases, poor teaching may have led to over-emphasis on rote memorization drills, but that is no reason to stop teaching the critically important mathematical methods.

How are we  doing with early mathematics education in this area? As the table shows, not very well. While the differences in scores between towns/cities may be accounted for by socio-economic factors, the percent of students who are not proficient (meaning they scored as "Needs Improvement" or "Warning/Failing") in fourth grade (90 percent in Lawrence, 60 percent in Methuen, 50 percent in North  Andover, and 34 percent in Andover) cannot be excused. Even worse is the lack of  progress after four more years of what passes for math "education".

2003  MCAS SCORES       (Percent ADVANCED OR PROFICIENT)
Town/City -     4th Gr -        6th Gr -        8th Gr

• Andover --  66% - 76% - 66%
• Lawrence -  10% - 9% - 9%
• Methuen --  40% - 41% - 34%
• No  Andover - 50% - 51% - 60%