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Recent headlines echo a clamor of 40 years ago–as the Russians launched Sputnik. American students fared poorly in tests of mathematics achievement compared to students in the rest of the world. Four decades later, American youth continue to test poorly and this leads inevitably to discussions of how best to teach mathematics.

In fact, major changes are under way in the teaching of mathematics, though not without controversy. The changes are designed to create conditions of success for all students in mathematics. Some object to the new approaches and call instead for a return to basics"–a mistaken exercise in nostalgia.

There are two facts about which there is consensus with regard to the teaching of mathematics to American schoolchildren. The first is the importance of the task. Globalization demands mathematical skill, technical literacy, comfort and ease with computers and other mathematical applications.

The second fact is that rnany Americans are not mathematically literate. Innumeracy, as John Paulos titled his book on the subject, is the current status of the majority of the adult population. They are uncomfortable with mathematics and clumsy in their use of it.

Beyond these two facts, consensus begins to break down. However, the stakes are high and the consequences for a child who is shut out of mathematics at an early age are dire.

Mathematics educators became concerned over a decade ago. That is when the National Council of Teachers of Mathematics outlined achievement standards for all American students. Subsequently teaching and testing standards were detailed and new programs were developed to help students to reach these higher standards. These programs became available in the past few years and two of the best of them are currently in use in the Pittsburgh Public Schools.

Yet the new programs have attracted critics. California, for example, recently adopted watered-down standards for mathematics in a move some hailed as a "return to basics." People long for "good old days" (and ways) and point to the poor achievement of current high school students. But complaints that current high school students are not mathematically literate miss the point

They were not educated using new programs but were taught by the old methods. Concern about how and what to teach is justified. Fuzzy thinking about the subject is not. Older methods of instruction got us into our current situation. They are part of the problem, not part of the solution.

What are some of the characteristics of these new programs and why will they improve learning? The first thing to be said about them is that they are rigorous, demand hard work and teach mathematics better than previous ones. Children are taught to perform mathematics operations with precision. just as they were in older forms of mathematics teaching. But they are taught for more. Students become versatile users of mathematics knowledge in addition to performing rote operations or engaging in mathematical applications.

There are several other ideas that these programs share. Perhaps the most important of these is that achievement in mathematics is a function of hard work and not innate ability. Traditionally, people have believed that only some young minds were capable of doing well with mathematics. The new programs also assume that mathematics is not an isolated set of ideas but rather a set of tools to be used in real world settings. A great deal of problemsolving is asked of students. That is how most people will use what they know during their lifetimes.

When the methods are employed, students work sometimes alone and sometimes in groups, as is the case with adult work. There is an emphasis on understanding over rote memorization. What is understood is known; what is memorized can be forgotten. Teachers do expect their students to master and memorize basic facts. These alone are not enough and so much more is expected

The new programs embrace high standards and rely on tests specially designed to measure whether students are meeting them. It is commonplace in education that what is tested is "taught." Some critics have alleged that these programs and accompanying tests fail to correct student errors and allow mistakes to go unchecked. On the contrary, student errors are now seen more clearly so that teachers-can detect their source and correct the faulty reasoning that led to them.

Mathematics, of course, is not the only important subject for future world-class competence. Foreign languages, writing and reading comprehension are school subjects American students need to know more and better. One route to that heightened achievement is through enhanced student confidence. And a route to that is high achievement in mathematics.

Imagine the student who has long struggled to make sense of number facts with no relationship to the real world. Then she solves a difficult problem and in so doing discovers within herself a mathematical thinker with new confidence in her ability.

There are many theories about how to instill confidence in young people and these are especially discussed with reference to urban and minority young people. In fact, such confidence could come from high mathematics achievement by all students.

Recent test scores may fuel the controversy about how to teach If there is a return to the "old" math–to memorization, rote calculation, assumptions about who can achieve and standardized tests of simple math facts–it will consign yet another generation of children to a life of mathematics incompetence. The goal should be high achievement for all of our children.