I want to wish everyone a Happy New Year, and I hope you all emerged from the holidays rested, relaxed and ready to grapple with the problems of the world.

Dear Homeroom:

Regarding your Dec. 12 column ["Numbers on Remedial Education Provide Sobering High School Lesson"], I think that it is important to understand that telling students to "make sure you take Algebra II" in high school is not the answer. The reason that students are not taking Algebra II in high school is because many of them barely got through Algebra I. You can see this in the state's new High School Assessment (HSA) in algebra.

The number one reason for low math achievement is Montgomery County public schools' poor math curriculum and teaching methods in the lower grades.

Children in the elementary grades are not expected to learn multiplication tables by writing them. The teaching of multiplication facts is delegated to parents, many of whom are incapable of teaching this material.

Teachers could easily assign students to write a few facts each night just as they write spelling words, but this is not done. Students could have flashcards in their desks so that they could quiz one another each day, but this is not done. Drill software could be used in the computer lab, but this is not done. As a result, year after year children are passed on without mastering this essential math skill.

Another problem is the new MCPS math curriculum. I have a daughter in fourth grade, and the new curriculum seems to cover too many topics too quickly. Right now there are still children in my daughter's class who do not understand long division, but the curriculum is out of time for that topic and must move on to fractions.

There will undoubtedly be children who will not learn to do long division in fourth grade or in any grade because of the time misallocation in this curriculum. The old math curriculum was very shallow and addressed too many nonessential topics, but the new math curriculum actually seems to have exacerbated this tendency.

Those parents who can work hard to compensate for the deficiencies of the MCPS curriculum and teaching methods. We buy textbooks, software and flashcards, send our children to private math tutors, and spend many hours remediating in our homes.

I contend that the achievement gap that you see in Algebra I HSA scores is the gap between children whose parents have the means and ability to make up for the deficiencies in MCPS math. So, telling low-achieving high school students to take Algebra II in high school is like closing the barn door after the cow has left. These children are already damaged mathematically long before they walk through the high school doors.

Isadora Paymer

Rockville

I never know if it is encouraging or discouraging to say that this is a national problem. But it is a fact. We have a national crisis in math education, and Montgomery County is part of it.

In general, our elementary school mathematics curriculum lacks focus and depth, our math books and materials lack clarity, and our teachers lack the knowledge and skill to overcome the deficiencies in the curriculum and the materials they are given.

The whole thing's a mess.

To compound the general national problems, Montgomery County seems to have focused its reform efforts on accelerating elementary and middle school children through its dizzying curriculum rather than on making sure every elementary school child completely masters fundamental mathematics. Many Montgomery County parents have been baffled by letters home from teachers telling them to make sure their children master the multiplication tables.

Now, I should note here that the county's math supervisor, Leah Quinn, states absolutely that parents "are not expected to teach multiplication." But I think what happens is that some teachers -- not all, by any means -- become so overwhelmed with the sheer number of topics they are expected to teach that they understandably try to offload what seems to them to be a manageable task to the parents.

The point made in the letter above is absolutely correct: The students who emerge from all this unscathed tend to be those whose families have the resources to notice and make up for deficiencies in the curriculum.

I should also note that old-style arithmetic is not the only math kids should be learning in elementary school. But the patterns and relationships among numbers that are established by a solid grounding in arithmetic form a foundation for algebra and all higher mathematics. Imagine trying to solve equations without being able to divide, and you'll see what I mean.

One of the ways this lack of systematic teaching affects students is that more and more of them are failing the Maryland Functional Math Test (MFMT). Passing the MFMT has been required for high school graduation since 1993, but it is a very low-level instrument, testing arithmetic skills at about the fifth-grade level.

Maryland has supplanted the test with harder math tests at the high school level, but schools still give the MFMT, beginning in seventh grade, to figure out who needs extra help. Our neighbor, Howard County, doesn't allow anyone who hasn't passed it to enter high school, which makes sense to me.

But in Montgomery County, more than 10 percent of our students still haven't passed the MFMT at the end of ninth grade, much less at the end of middle school -- and that percentage has been going up every year since 1997 (see accompanying chart). Some of those kids are new to Montgomery County, some ven to the country -- but by no means all of them. And this is not a problem that is evenly spread out. A little less than 5 percent of white and Asian ninth-graders failed the MFMT last year (up from about 2 percent in 1997), but almost one-quarter of the African American and Latino ninth-graders students failed it (up from about 13 percent in 1997).

Having large numbers of kids who can't pass the MFMT is a real problem at the high school level for both them and their teachers. The kids keep hearing from people like myself that they need to take and master math at least up through Algebra II -- and preferably through calculus -- which must be very frustrating to them when they still have trouble adding, subtracting, multiplying and dividing.

And high school teachers really are not prepared to teach kids at such a basic level. They aren't trained to teach arithmetic, and they often resent being expected to do the job of elementary and middle school teachers while still being held responsible for a high-level math curriculum.

Elementary and middle school teachers, for their part, often don't have nearly enough knowledge to teach the math curriculum. This is not necessarily their fault. To become certified as teachers, most of them were required to take only one university math class, and often they took only a math-for-teachers class rather than real college math. This means they often lack what mathematician Liping Ma has called a "profound understanding of fundamental mathematics."

In a really wonderful book I would recommend to anyone interested in this topic, "Knowing and Teaching Elementary Mathematics," Ma documents the misunderstanding of mathematics among many American elementary school teachers. For example, when she asked American elementary school teachers to make up a story that could be represented by the problem, "1 3/4 {divide} 1/2," very few teachers gave a correct response. Most of them made up a story that would be represented by "1 3/4 {times} 1/2" instead. This contrasted with their Chinese counterparts, almost all of whom could make up a story problem that would require dividing the fractions.

Montgomery County, with its relatively high pay (by national standards) and fairly stringent hiring requirements (again, by national standards) should be immune from these problems, but it is not, in part because the colleges and universities that train teachers have done such a woeful job. The county tries to provide math training to elementary school teachers to make up for the deficiencies of their education, but much more is needed.

We need a coherent curriculum, clear materials and highly expert teachers who understand a lot more math than they are expected to teach and are given time to deepen their understanding. I do think Montgomery County is working on those issues. But in the meantime, parents might want to show their kids how to make multiplication flashcards.

And parents should be asking whatever happened to Singapore math. Remember the program based on the materials used in Singapore, the country whose students have the highest math achievement in the world? Superintendent Jerry D. Weast introduced it at four elementary schools a few years ago with some fanfare. At least one of them, College Gardens, which has provided solid training and support for its teachers, has shown substantial improvement in math achievement. So why aren't we expanding the use of Singapore math?

Homeroom appears every week in Montgomery Extra. Send questions, opinions and issues that you would like to see discussed to Homeroom, The Washington Post, 51 Monroe St., Suite 500, Rockville, Md. 20850. The fax number is 301-279-5665. Or e-mail homeroom@washpost.com. To see previous columns, go to www.washingtonpost.com, click on the Education page and look for Homeroom under Education Columnists.