Monday, October 13, 2008

This week, staff writer Valerie Strauss concludes The Post's review of math education with a look at college-level work in high schools and what some graduates might be lacking.

It would be hard to find a more advanced math class in public schools than the one Robert Sachs teaches at Thomas Jefferson High School for Science and Technology.

That's because it isn't really high school math.

Complex Variables is usually taught to college juniors and seniors. It is offered at selective Thomas Jefferson in Fairfax County because students demand the challenge.

"This class is pretty difficult," said Bobbie Pelham Webb, 17, a senior. "It is one of the first math classes that is challenging to me. Calculus was easy."

Webb and her classmates inhabit a world of extraordinarily gifted students fluent in the language of mathematics. Sam Rush, 16, a junior, has always loved numbers. In kindergarten, his teacher sent him to learn sixth-grade math. Luke Cheng, 16, a junior, said a great middle-school teacher turned him on to math.

To be sure, Thomas Jefferson draws some of the best students from Northern Virginia. But schools throughout the Washington area are pushing into more advanced math as the high-tech 21st century demands a workforce with a deeper understanding of the subject.

Although educators and employers worry that not enough students have a good grasp of complex math, more kids are taking tough courses. In Fairfax, 12 of 25 high schools teach Multivariable Calculus in the fall and Matrix Algebra (usually called Linear Algebra in college) in the spring.

The College Board reported that thousands of Class of 2007 students in Maryland, Virginia and the District took Advanced Placement tests in Calculus AB, Calculus BC and Statistics.

In 2007, the Education Department reported that the percentage of high school graduates who completed precalculus or calculus rose from 10.7 percent in 1982 to 33 percent in 2004. And although the ceiling was being raised, so was the floor: In 1982, 56 percent of high school graduates finished with Algebra 1 or less as their highest course. That had dropped to 23 percent by 2004 as students began taking more advanced math.

Such advances have been possible, said Thomas Jefferson Math Department Chairman Jennifer Allard, because more students at more schools are being offered algebra in seventh grade. Still, she said, the usual upper-grade math trajectory is Algebra I, Geometry and Algebra II, topping out at Calculus.

At Thomas Jefferson, every student takes Calculus. The entry-level math course is called Advanced Geometry with Discrete Mathematics Topics. About half of all graduating seniors take the most advanced courses. What Sachs teaches is one of the three or four most advanced courses. (Sachs is a math professor at George Mason University.)

Assistant Principal Heather Sondel said the brainpower of the students in Sachs's class intimidates others. "The kid who struggles at the Calculus level, they say, 'I wish I was smarter,' " Sondel said. "It's hard for them to sit next to kids who are so gifted at math."

For the most part, high schools teach applied mathematics. That is, math that is used to solve problems in such other disciplines as physics and engineering. It is distinct from pure mathematics, which is pursued not for its application to other things but entirely for its own sake, for its precision and beauty. To those, of course, who understand it.

That includes Rush and Cheng, who are on the extracurricular math team and who spend at least five hours a week -- beyond classes and homework -- doing work for the team. "I just love math," team captain Brian Hamrick said.

To enroll in Sachs's class, students must first take AP Calculus and another year of advanced math. "This course is really above and beyond," Sachs said.

Sit for a few minutes and listen to the discussion between Sachs and his 16 students. If you are a person for whom math is not music, be prepared to understand almost nothing, save the occasional article and preposition.

Last week, a student asked Sachs what would be on the next quiz in regard to what are called Cauchy-Riemann equations. "I could ask you to prove them," he said. "I could ask you to rewrite them in polar form. I could ask you to use them to show some function is differentiable." They nodded.

What fields do these students go into? Some head into science research, computer science or engineering. Others, Sachs said, might "become the math financial people who aren't getting good press these days."