Re: the June 2005 District of Columbia Math Curriculum Adoption

Email to Ms. Peggy Cooper Cafritz
President of the DCPS Board of Education
and Dr. Clifford B. Janey
Superintendent of the DCPS

Cc to other members of the Board
and to members of the press

By Barry Garelick
June 15, 2005

Dear Dr. Clifford and Ms Cafritz:

My name is Barry Garelick. I am employed by the U.S. Environmental Protection Agency. I am writing as a private citizen and not as an employee of US EPA. I am writing on behalf of parents who are concerned that their children receive an effective math education. In my spare time I tutor students in mathematics. I majored in mathematics and am greatly concerned with how math is taught. I recently wrote an article on mathematics education which appeared in the Spring 2005 edition of Education Next. The article focuses on some of the serious problems in math education in K-12 in the U.S. In my opinion as well as those of many mathematicians I consulted when writing the article, some of the educational theories informing how math is currently taught are seriously flawed. I have attached a copy of the article for your information.

Two years ago I had the opportunity to tutor students at the Macfarland Middle School in DC in mathematics. I enjoyed working with these students. I was also impressed with the math program that Macfarland had at that time. What impressed me was the students' knowledge of the standard algorithms needed in math: long division, multiplying and dividing fractions, dividing decimals. They knew the rules.

They may not have understood why the rules are the way they are. So I explained as best I could and made some headway. They also had difficulties with story problems. So we worked on those. The point is, they had the basic foundation upon which I could build, and where needed, to retrofit with additional explanation.

And that is why I am extremely sorry to hear about the possibility of adopting the series "Everyday Mathematics" in the DC public schools. I am familiar with this series and have talked with many parents who are extremely dismayed with the program.

Everyday Mathematics does not systematically teach the standard algorithms that students need to know to build the mathematical foundations that will get them through algebra and beyond. Rather, the developers of EM hold standard algorithms in disdain, and believe that students should be exposed to a variety of approaches to the four basic mathematical operations: addition, subtraction, multiplication and division. They believe that this choice benefits students because the children will pick the method that makes the most sense to them.

Students do not know from one day to the next what is going on. There is one method explained one day, and another method the next. Then an entirely new unrelated topic. This is known as the "spiral process", and is touted by EM as a great benefit in learning. If students don't get it now, they'll get it eventually, so the philosophy goes. Imagine if that philosophy prevailed in medical schools, or in teaching people how to fly planes.

EM claims that students are drilled on the number facts, but the drills are not often from what I've seen. The course load in one year covers so much ground in an ever-looping spiral of mathematics topics that is an inch deep and a mile wide; teachers can't possibly have the time to drill as often as they would like if they follow EM's program. Parents tell me: "My kid doesn't know the basic facts; we have to make sure they drill them at night."

Everyday Mathematics embraces the philosophy of having students learn "strategies" for learning the number facts. One favorite strategy for learning addition facts is the "Add by tens" technique, so that 8 + 7 is broken up into partial sums, one of which equals ten, enabling (so the theory goes) quicker addition, via "friendly numbers". To do this, the student has to figure out what to add to 8 to make 10, and so he writes 8 + 2; then he has to figure out what the difference between 7 and 2 is, so he is left with the "much simpler" problem of 10 + 5. This approach is not new and has been used effectively in other math programs, but as a supplement to help, rather than a "main event". Students are forced to work through these "friendly number" problems, essentially memorizing (yes, by rote) a series of steps that may or may not make much sense.

Coaching children in "originality" of this kind is time-wasting except perhaps to check results by trying another way of doing something, or to illuminate what is going on. But the standard method should be the main event. All the other ideas should be sidebars. In the world of Everyday Mathematics, all are given equal weight. Correction: All but the standard method, which is the most efficient. The result is confused students. In the words of one student I know: "I'm not very good at math. I don't know what method to use to solve a problem"

EM holds to the present education-school derived philosophy that drills and routine prevent understanding. This is a false dichotomy. Many mathematicians and teaching professionals agree that children need routine and practice in order to gain the understanding that math reformers think will come about by having students memorize (yes memorize) the many different ways to solve a problem.

One result of the imposition of the EM program in the various school districts is that many teachers opt to use the older math texts that they relied on in the past to teach their students math. It is not uncommon to find students taking home photocopied sheets from these textbooks, and working problems from them. It is also not unusual to see parents hiring tutors, or enrolling their children in learning centers, which by the way are becoming a growth industry. Unfortunately, low income families do not have the luxury of paying for such services.

My advice to the teachers in DC is as follows: If EM is adopted in DC, hold on to your old math texts. You and your students are going to need them.

Thank you for your interest and consideration.

Barry Garelick

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