Students in the U.S. Could Use New Formulas

By Tanya Caldwell
LA Times Staff Writer
February 3, 2006

The nation's children aren't the best and brightest in the world when it comes to math, according to the 2003 Trends in International Mathematics and Science Study. Even among industrialized countries, the United States ranked ninth out of 12.

As the Los Angeles Times' Monday installment of "The Vanishing Class" series described, 35% of future elementary school instructors who studied at Cal State Northridge, the largest supplier of new teachers to the Los Angeles Unified School District, got Ds or Fs in their first college-level math class last year.

Los Angeles schools Supt. Roy Romer has cited the "cumulative failure of our ability to teach math adequately in the public school system."

William Schmidt, a professor at Michigan State University and executive director of its Third International Math and Science Study Research Center, was asked by The Times whether other countries have as much trouble finding adequately trained math teachers as the United States.

Question: Why are many other countries so far ahead of the United States in math achievement?

Answer: These other nations have a much higher level of expectation for their students. The teachers who then teach these courses - at least in the highest-achieving countries - have a much greater preparation in the subject matter of mathematics, so that they're able to teach those more challenging levels of mathematics.

Put simply, from the data we have, we know that by the end of eighth grade, U.S. students are probably some two years behind their counterparts in most of the rest of the world.... Middle school in the rest of the world is about algebra, geometry, chemistry, physics. In this country it's still about a lot of arithmetic and what I call "rocks and body parts."

Q: It seems that the quick solution would be to just set higher expectations.

A: That's really what the whole thing surrounding No Child Left Behind is about. States have begun to raise their standards and, as a result ... there has been a movement to greatly increase the rigor and the demand of the state standards. Here in Michigan we have new standards, and they are much more demanding than were the standards that preceded them. So I think that there has been a response to this and it's beginning to change.

Q: How is it that students aren't excelling as well in high school math classes - presumably because they haven't learned the basics - when they seem to have done better in previous years when those basics were first applied?

A: Studies show that middle school is where we lose a great deal of ground, at least internationally. The middle school in these other countries in mathematics is much more demanding. And it's much more of a transition into what we in this country first do in high school. So when our kids come into high school, they're a couple of years behind already. And our high schools just can't make it up.

Basically, the middle school is not preparing kids adequately. But it actually goes all the way back even into primary school, where, again, the kids are not being prepared well, don't understand and aren't able to do the computations associated with simple arithmetic.

Q: So it starts in elementary school?

A: We need to really start a much more serious, clearly defined, coherent curriculum all the way back there, and then we'd have a better shot at doing better with our kids.

A lot of mathematics in this country is not designed very coherently. It doesn't progress from the simple to the more complex in ways that are reflective of the mathematics discipline. There's a sequence of things that make the most sense. And very typically in American schools, these sequences are not very clearly laid out.

Q: What do you mean?

A: Fractions, for example, are very difficult for students. Instead of introducing the concept clearly enough so that they understand fractions as numbers on the number line, we oftentimes try to move too quickly to other parts of fractions, such as the operations, before they really have a clear understanding of what fractions are and how they fit into the broader number system.

So kids are trying to learn how to operate on these things, and at the same time they really don't understand what they are, so things get very muddled in their minds.

Q: What will it take to get U.S. students to perform better than their overseas peers?

A: We need a more coherent, challenging curriculum. And we need a set of teachers who have a strong background in mathematics and who know how to teach mathematics to kids and can then bring those high expectations to these kids. It's fairly simple. You look across the world, and that's what the difference is.

Q: Are the nations throughout the world using a different curriculum? Do they have different teaching methods?

A: That's actually a point I want to make very clearly. There doesn't seem to be one perfect method for doing this across the world. Different countries have different methods, just like we do here in the United States.

The real issue is the what. What it is that they're studying, in what grade levels in what sequence and at what level of rigor. Those are the issues that become important, not the how. It's more the what.

Q: We're just not being hard enough.

A: Yes. That's it, in a certain sense. As we move through the grades, we keep repeating topics year after year. We try to do too many topics at each grade level. We coined the phrase the "mile-wide, inch-deep curriculum" as a characteristic of the U.S., which means they just keep repeating these topics and as a result they have so much every year that it's too much for the kids to try to learn.

In these other countries it's a more focused attention on a smaller number of topics that progress across the grades in a logical fashion, leading to higher levels of expectation as you get up in the grades, like in the middle grades. And that's what we need.

Q: In Los Angeles, some educators say they have a hard time finding qualified teachers. Is that a problem for other nations?

A: For some. In the elementary grades, everybody struggles with this, because elementary teachers have to teach all the subjects. But once you get into about middle school, this is more of a problem in the United States, where our teachers are not as well prepared as the teachers in these other countries.

We are doing a study right now across six countries in which we very clearly find that U.S. teachers - U.S. teachers from middle school - are not being ... required to take the same level of mathematics that is true in other countries. Teachers that are going to teach middle school mathematics have to have a stronger background.

Q: What can be done to ensure that the future math teachers who are still in school will be better than the teachers who taught them?

A: The simple answer is that they have to have a more rigorous training while at the university level. Many of our teachers carry with them that inadequate preparation and carry it right back and teach much the same way. It is a vicious cycle.

We need to raise the level of expectation for the students that are in our K-12 system so that they are more competitive. But we also have to raise the level of preparation of our teachers so that they can come in and actually teach those more challenging and more demanding curricula. It really demands both of those things in order to make the difference and catch up with the rest of the world.

By the numbers
A 2003 study found that U.S. 15-year-olds scored low among industrialized nations on the PISA* mathematics test.

Rank Country Score
1. Hong Kong (region)
3. Japan 534
4. Belgium 529
5. Australia 524
6. New Zealand
7. Norway 495
8. Hungary 490
9. Latvia
483 (tie)
10. United States
483 (tie)
11. Russia 468
12. Italy

* Program for International Student Assessment
Source: American Institutes for Research

Copyright 2006 Los Angeles Times