Inside Scoop
Math Wars

A new report tells how to keep your students from becoming casualties.

Should children memorize how to do "long division," or investigate what division is and when to use it? Is it better to assign a multiplication worksheet, or to have students figure out what home improvements they could afford on a limited budget?

Educators have debated such questions for decades. The National Council of Teachers of Mathematics (NCTM) has campaigned for teaching that helps children understand math and relate it to their daily lives. But NCTM has run into strong opposition from those who favor a more traditional approach.

Now the National Research Council (NRC), an arm of the National Academy of Science, has weighed in with a strongly worded report called Adding It Up: Helping Children Learn Mathematics.

Why fight? Are American students bad at math?
In the Third International Math and Science Study (TIMSS), American fourth grade children did better than the world average. Our eighth graders were average. Our twelfth graders scored low.

Just as important, many Americans are afraid of mathematics, and convinced they can't do it. The National Research Council report says students must be comfortable enough with math to size up real-world problems and figure out what calculations they need to do.

When they are adults, the report points out, they won't be handed worksheets.

To develop confidence, the NRC says, students must feel that math is something they can make sense of, not just a long list of rules to be memorized.

What are some battles going on today?
One is over "algorithms"--procedures used to come up with correct answers.

When you "borrow" from the tens column to do 73 minus 55, the borrowing is part of our traditional algorithm. There are other valid algorithms, some of which are taught in other countries.

Some "progressive" math educators believe students should work out their own algorithms in order to understand better what the math operations are all about. Traditionalists say that's a waste of time, and students should learn our established algorithms.

The NRC report recommends teaching algorithms, but in a way that helps children understand why they work.

The NRC says people often think an inevitable competition for classroom time exists between helping children understand mathematics and teaching them skill with algorithms, but the authors deny this.

"Understanding makes learning skills easier, less susceptible to common errors, and less prone to forgetting," the report says. With better understanding, there's less need for repetitive, time-consuming practice.

How about calculators?
According to a 1996 survey of teachers, more than half of eighth graders were using calculators in class almost every day.

They were not so common in lower grades--less than one-third of fourth graders were using calculators at least once a week.

The NRC report cites studies showing that calculators can be used to help children learn to understand math and do not hurt their ability to do paper-and-pencil calculations.

How does math teaching here compare with other countries?
TIMSS classroom observers found that American teachers focus heavily on memorizing.

Teaching in high-scoring Japan and Germany is aimed more at helping students understand math.

The mediocre American scores are sometimes used as an argument for more emphasis on multiplication tables and rules for procedures such as long division. However, the international classroom observation study suggests the opposite.

The TIMSS observers also found that many American teachers thought they were teaching for understanding, but actually were teaching the way they themselves were taught: Learn the rules and practice, practice, practice.

The NRC report presents classroom vignettes that show the differences in approach.

What math training do teachers need?
The report says you don't have to learn calculus to do a good job with third graders. What's critical is that teachers have a thorough understanding of the math they teach--for example, what it means to divide by a fraction.

Second, it says teachers should study how children think about math, because you can't help students learn if you don't understand their mistakes.

The report urges teachers colleges to beef up courses in these two areas, rather than simply piling on more math requirements.

It says classroom teachers need professional development programs in which they collaborate to examine their own lessons and how students respond.

Achieving math proficiency for all students, the NRC concludes, will take time and money. But in today's world, mathematics can no longer be restricted to a select few.

For more: The NRC report is at www.nap.edu/books/0309069955/html. The NCTM Web site is www.nctm.org. For an opposing view, see www.mathematicallycorrect.com.