The Pasadena Unified School District's decision to buy supplemental, back-to-basics math books was just one of many recent developments throughout Los Angeles and the country in a long-standing battle over the effectiveness of math reforms often called the "new-new math." But while that move acknowledges that these unconventional math programs alone do not always provide students with the needed skills, many Los Angeles school administrators continue to favor them.

The new-new math debate has prompted a nearly unprecedented outcry in mathematics circles throughout the country.

New-new math advocates, for example, reject conventional "drill and kill" rote memorization exercises that they believe tend to alienate students, particularly girls and minorities. But critics say that such basic skills as learning multiplication tables provide math students--regardless of their gender or ethnic or racial background--with critical grounding.

ERICA ZEITLIN spoke with two experts on the front lines of the new-new math wars.

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GUILLERMO MENDIETA

Teacher and director of math education at the Los Angeles-based nonprofit Achievement Council

Mathematicians are notorious for their poor teaching practices. What to them seems obvious is often perceived as difficult by the average student. Sadly, educational policy in California has been held hostage to the views of a narrow group of university mathematicians with little understanding of how children best learn.

Attempts to make the teaching of mathematics more meaningful and engaging often are criticized and ridiculed by these mathematicians as efforts to water down the curriculum.

Advocates of the back-to-basics movement have misrepresented the choices for curriculum as being either for or against the emphasis on basic skills. The real issue is about whether we teach the basics through meaningful and engaging practices or through rote memorization that leaves the learner with no conceptual understanding.

Once students understand the ideas behind the concept of multiplication of fractions, the teacher will help them make sense of the traditional procedure for multiplying fractions. The textbooks we use are but one among many factors impacting student achievement. Student motivation, appropriate assessments, parental involvement and teacher placement and training are some of the other factors we must address.

If we are serious about improving student learning in mathematics, we must listen to mathematics educators--the experts in the area of how children learn mathematics best--and support teachers' efforts and textbook selections to teach mathematics basics in the context of meaningful and engaging teaching practices.

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BARRY SIMON

Chair, Caltech's math department; served on the LAUSD Committee on Mathematics Curriculum and Textbooks

There is no dichotomy between emphasizing basic skills and stressing the big concepts. There is no way that you can understand math without learning the basic skills, such as being able to add fractions or do division or multiply numbers. That's not to say that learning the skills is easy. It's hard. But it's necessary.

One of the basic problems has nothing to do with this fight but rather with a serious defect in teachers: Many teachers, especially those teaching in the lower grades, are math-phobic and convey that fear to their students. Many of them are very well-meaning, but not trained properly. The bottom line is that if you had teachers who were all spectacular, it wouldn't matter as much which math books were being used.

We have to begin to address that problem and one way is by using skills-based texts that are very scripted, so that weaker teachers can follow them closely. There are really superb textbooks that mix this skills-based curricula with a lively presentation. Mathematics does not have to be dull. It can be a lot of fun and really exciting.

Mathland, a new-new math textbook widely used in Los Angeles Unified elementary classrooms, is just awful. I have also seen geometry books that have numerous mathematical errors in them. I have no doubt that high school geometry books can be dull and dry, but a good teacher knows how to liven his or her lessons up. I would rather have books that are boring than books in which the content is incorrect.

I think it is a crime that we are not being better served by the book publishing companies.

Often the argument is made that algebra is the gatekeeper to higher science and higher math and, yes, that is true. But if you try to solve this by changing what algebra is, you not only close the gate on these students, you've never even given them a chance. Pushing this fuzzy approach denies people the skills they need to succeed in college and the work market.

I am not a teacher of K-12, but for five years I taught the main first-year calculus course required for the majority of Caltech students; I was aghast at some of the gaps in their education.

I believe that the California state math standards and state math frameworks are really superb. From data I had on the LAUSD committee I served on, I know that only about 2% to 3% of the books being used in the LAUSD elementary grades are aligned to these standards, while over 40% use Mathland. Only in "Alice in Wonderland" or the LAUSD can they talk about aligning books to the standards and then continue to use these books.