To the Editor:
As an increasing number of high schools strive to offer more Advanced Placement classes (“Advanced Placement Courses Cast Wider Net,” Nov. 3, 2004), a 2002 study by the National Research Council shows that the nation’s honors programs for high school students fail to offer an enriched learning experience to mathematically gifted and high-achieving students. The study’s findings remind us that secondary schools must develop new alternatives to provide mathematically talented students the opportunity to do challenging work well beyond their traditional grade level with students of their own age.
For too long, mathematics at the secondary level has been viewed as a fixed progression of topics, often not going beyond Advanced Placement Calculus. But there are a large number of very able students who naturally “see” math (as opposed to students who work hard and are considered good, or even excellent, at math by traditional standards) and who are not well served by this approach. These are students who naturally think algebraically, long before they are actually taught algebraic manipulations, and who express an interest in mathematical topics, such as fractals or non-Euclidean geometries, that are not usually included in the high school curriculum.
Identification of these talented math students can and should begin in middle school, and a program addressing their needs should be implemented. At my school, mathematically talented students identified in the 6th grade study advanced topics by solving complex problems in grades 7-9. Often, as many as a third of our graduating class—in some years, as many as a third of them females—will graduate having taken multivariable calculus. And a number of them will have studied nonlinear dynamics, linear algebra, and beyond.
At the high school level, these students should be identified by the school and invited to participate in the alternative math track. Schools that endeavor to attract students with these special abilities enjoy the benefits of developing a well-populated program, rather than designing independent-study arrangements that cause students to feel isolated, or simply placing students in classes with significantly older peers, which can lead to social difficulties. We have found that many of these talented students are strong across all academic subjects and enhance not only the profile of the class, but also the performance of their classmates.
By devoting resources to developing a math curriculum for mathematically talented students, schools will attract and keep new students who will enhance the institution as a whole. And they will give these students the opportunity to be challenged and to learn at a pace commensurate with their abilities and interests, without experiencing boredom and feelings of isolation.
Ralph Sloan
Headmaster
Dwight-Englewood School
Englewood, N.J.
