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A Clarion Call for Real Mathematics

Posted by: Stephen Wildstrom on March 14, 2008

I have spent more years than I care to remember reading reports of government advisory committees, but I have never encountered anything like “The Final Report of the National Mathematics Advisory Panel” (PDF) released yesterday by the Education Dept. In uncharacteristically blunt language, the report offers an action plan for a radical reconstruction of math education, especially in kindergarten through 8th grade. The overhaul is needed, the panelist argue, because the U.S. is failing produce the technically literate workforce it needs and can no longer count on making up for the shortfall through immigration because “the dramatic success of economies overseas in the age of the Internet cast doubt on the viability of such a strategy in the future.”

It may come as a surprise to anyone who finished their middle school education before the mid-1980s, but [perhaps the [panel's most controversial recommendation is that elementary school students should memorize their addition and multiplications tables and develop proficiency in adding, subtracting, multiplying, and dividing fractions. Educators who felt that calculators had rendered manual calculation obsolete have been denigrating these skills for two decades.

But the National Mathematics Advisory Panel was focused on the readiness of student to learn algebra and found that algebra depends heavily on the computational skills that were being lost. (The panel ended up neutral on the controversial question of whether the use of calculators, particularly in early grades, helps or hurts the development of the ability to do mathematics. The quality of existing research, it found, simply is not good enough to come to a conclusion on the subject.)

The sad thing about the report that despite the unanimity on a panel that represents a broad spectrum of the mathematics and math education communities, it will take a decade or more for its recommendations to be implemented. It simply takes that long for curriculum guidelines to be recast, textbooks to be rewritten, and teachers to be trained or retrained. And in that time, a lot more damage can be done.

Reader Comments

Henry Borenson, Ed.D.

March 17, 2008 10:39 AM

The National Math Panel noted that many students "have difficulty grasping the syntax or structure of algebraic equations and do not understand the procedures for transforming equations or why transformations are done the way they are." It is indeed true that for many students algebra is a foreign language. Many students simply do not understand the meaning of the symbols used in algebra. Some students succeed by memorizing rules or procedures for solving equations.

All students, however, would benefit from instruction in algebra that made the concepts visual and hands-on. Research now shows that such instruction can be provided as early as the 4th and 5th grade, with more than 80% of the students tested experiencing success in solving equation such as 4x+3=3x+9. The students using these methods develop an intuitive and indeed a kinesthetic sense of important algebraic principles, such as the Subtraction Property of Equality, by physically removing three blue pawns, representing the x’s, from both sides of the balance scale.

If students beginning an Algebra 1 course have not been fortunate enough to have had this hands-on experience earlier in their educational career, it is still important for the regular high school algebra teacher to provide this experience to the students. Even a few short lessons can demystify basic algebraic equations and how to solve them.

In the view of this mathematics educator and publisher, however, the proper and ideal place for students to learn to solve the type of equation noted above is in grades 3 to 7. Indeed, solving such an equation, using a hands-on approach which is then transferred to a pictorial notation using only paper and pencil, should be a pre-requisite for a student to enter an Algebra 1 or even a pre-algebra course. The large majority of students, with proper instruction, will meet this prerequisite. If these students also have the strong computational skills being urged by the Panel, then these students can be expected to have a much higher success rate in Algebra 1 than has been the case with students in the past. This is indeed an area of research worth pursuing and Borenson and Associates, Inc. hopes to pursue research in this area over the coming year.

yuhong wang

March 17, 2008 11:33 AM

I hope that somebody could forward my comments to some policy makers.

I was educated in China and immigrated to states in 1992. For the past 10 years, I carefully watched the math education my son(13) and daughter (11) get from public school (Wissahickon, PA). At the same time, I also studied quite a number of education, history and philosophy books.

The fundamental problem in math education is that it violates the child psychology. There are two kinds of math learning: abstract (pure) math and applied math (or word problems). For most people, abstract math is much easier to pick up than word problems when they are very young. The same is true for arts such as music.

In public schools here, teachers spend way too much time teaching and asking kids to solve word problems. In most asian countries including China, schools focus on abstract math first and applied math later.

According to my knowledge, this kind of math education philosophy is not consistent with psychology of child development. We should substantially reduce the time on word problems in elementary school and instead focus more on abstract math.

The "no child left behind" policy also does more harm than good for math education. Different kids have different talents. if a kid excels in language and art, it does not make sense for him or her to be the same good at math.

Yuhong Wang
Ambler, PA

Stephen Baer

March 17, 2008 6:51 PM

As a middle school math teacher I found the survey results from the Algebra teachers to be enlightening. One survey result found that 64% of the teachers surveyed said that there was "too little parent/family support." Most of the students who come to me at or above grade level have parents/gaurdians that take an active role in their education. Yet, most of what I hear about the education system deals with the failure of the teachers. Parents always show pride and take partial credit for their child's successes. When was the last time you saw a parent take responsibility for a child's shortcomings? The problem with making parents assume a more active role in the education system is that it is political suicide. Who would vote for someone who told parents that they need to do a better job raising their children? How about this: tie child tax credits to the child's report card. Your child is failing math? Sorry, no tax deduction! I bet you would see an IMMEDIATE increase in math scores. I know - making parents responsible for their child's education is unconstitutional. It violates their freedom to raise uneducated children.

Steve Wildstrom

March 17, 2008 10:20 PM

@Stephen Baer--Study after study has shown that parent involvement is the single most important determinant of student success. The problem from a public policy perspective is how do you increase parent involvement. When the parents want to be involved, you can’t beat them off with a stick, but getting the unwilling interested is very, very difficult. I don’t think even messing with taxes would do it, even if there were a way to do so.

Mrs. T. Shamim

April 27, 2008 5:59 PM

I have been a teacher from young age of
16 years, adding to that my own education has brought this conclusion that just as a child learn by rote songs and poems and later in life realises the full meaning and sense of the substance, similarily learning or memorising tables and enjoying the full
pontential later is no harm. Only she that it is made happy experience and not
dull and burdensome.

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