Calculating Beyond Their Years
For More High School Students, AP Math Just Isn't Sufficient

By Daniel de Vise
Washington Post Staff Writer
Monday, February 6, 2006

Some Washington area high school students are pushing so far ahead in math courses that Advanced Placement, the widely accepted pinnacle of pre-collegiate study, no longer goes far enough.

More than 500 students in the Montgomery and Fairfax school systems, the region's two largest, are taking multivariable calculus, a course traditionally taken by math majors in their second year of college -- at least in the old days. That means the students have a full year of college-level calculus under their belt before they leave high school.

These "post-AP" courses, once taken by a tiny share of elite math students, are riding a growth curve. Montgomery County offers multivariable calculus to 265 students at 12 schools and will add a 13th in the fall. Fairfax County has 242 students enrolled in the course and expects the number to pass 300 in the coming school year. The Anne Arundel County school board approved its own version of the class, called Calculus III, last month to meet rising demand.

Students are pushing the boundaries of math in high school because of a corresponding surge in high school-level math in middle schools. Driving the trend is a conviction that algebra, long the exclusive province of high schools and colleges, is a fundamental pre-collegiate skill that should be taught as soon as students are ready to learn it. Students with a flicker of math talent are taking the high school Algebra I course in eighth grade, if not before. Starting with the Class of 2009, Marylanders must pass an algebra test to exit high school. Virginia requires algebra to graduate; the District does not.

"You have algebra taught in college, and yet we have algebra taught in seventh grade," said Mark Johnston, assistant superintendent of Arlington schools. "The issue there really is, it's a gateway course to more advanced courses in science and math."

Public high schools in the Washington region are witnessing an explosion of college-level study across the curriculum, with students enrolling in record numbers of AP courses and their Euro-inspired counterpart, International Baccalaureate. Many students finish high school with the equivalent of a year's college study completed.

But only in math, administrators say, are students exhausting the supply of available AP and IB courses. This is partly because of the middle school algebra push and partly because of the sequential nature of math study. Each math course is a prerequisite for the next.

Once students complete the AP Calculus BC class, the next logical step is to multivariable calculus, one more step along the branch of mathematics involving the differentiation and integration of mathematical functions. The course takes calculus study into the third dimension.

"All right guys, let's get ready to work," said Tom Moriarty, summoning the attention of 13 seniors in his multivariable calculus course at Quince Orchard High School in Gaithersburg one recent afternoon.

"Look at the contour graph," he said, as students studied a graph filled with wavy, colored lines. "Look to see where the contours are heading toward a max, look to see where they're heading toward a min."

Solving this three-dimensional puzzle required a mix of conjecture and something called the second derivatives test.

When the school tapped Moriarty to teach the new course last year, he had to search his basement to find notes he took on multivariable calculus as a sophomore in college almost 30 years ago.

"So, we're in the learning stages, and I'm learning, as well as the kids," he said.

Two decades ago, high schools offered a greater variety of math courses to students but graduated them with fewer advanced skills, said Cathy Seeley, president of the National Council of Teachers of Mathematics.

Today, math instruction is approaching the opposite extreme, driven by a relentless push toward algebra and calculus.

Some scholars believe educators and parents have enshrined calculus as a status symbol that students feel they must attain before they enter college. Possibly lost along the way: the rich variety of topics in algebra, plane and solid geometry, trigonometry and mathematical applications that once occupied students through much of their journey through high school.

"Kids are missing out on some very important concepts that have been pushed aside to make room for calculus," said Alfred S. Posamentier, dean of the School of Education at the City College of New York and author of numerous math books. Posamentier worries that, apart from a handful of academically gifted students, some teenagers might be "shunted into the calculus course" before they are intellectually mature enough to fully grasp what they are learning.

Seeley said her greatest concern is that schools will run out of math courses to offer their most advanced students, leaving them no math to study in their final year. "Certainly it's better to take math than not to take math," she said.

The College Board has no strong interest in adding yet another calculus course to its AP program, one official said.

Until recent years, students who sought mathematical challenges beyond the first tier of college courses typically traveled to the nearest college to take them. As their numbers grew, school systems began to offer advanced calculus courses.

The Arlington school system introduced multivariable calculus in the late 1990s. Students learn it face-to-face or via real-time broadcasts, with live video and two-way audio hookups.

Anne Arundel is likely to offer a similar program in the fall. At least one student at each school is prepared to take the class. Among them is Paul Wheatley, 16, a junior at Annapolis High School who has a new challenge awaiting when he finishes a combined Calculus I and II course.

"I don't think I could take a year off and still retain the information I've learned," he said.

At Quince Orchard, Moriarty's students are taking things slowly. They are, after all, only the second group to take the high-level calculus course at their school.

"All right, guys, let's see how far you got," Moriarty said, after leaving the class to mull the contour graph.

"We got it," a group of girls boasted from the back of the class. One of them, 17-year-old Alice Chen, smiled and said, "I actually understand this."