COLLEGE PARK - Ashleigh Knox thought she was good at math. She got A's and B's in the subject at a good Howard County high school, and she did well enough on the SATs to get into the University of Maryland in its most competitive year ever.
But when she arrived on campus this month, she was told otherwise.
After taking a math placement test given to freshmen, Knox was assigned to the lowest level of remedial math. Her only consolation is that there are hundreds more like her.
That's because the university - like many others around the country - is confronting a puzzling phenomenon: While the academic credentials of incoming students are on the rise, their math abilities are declining.
"There's a certain paradoxical nature to it. Our students are coming in with considerably higher SATs and GPAs [grade point averages]," said Patrick M. Fitzpatrick, chairman of Maryland's math department, "but quite a number of our professors who teach first-year calculus say the algebra skills of students are not as good as they used to be."
In response, the university has created an elaborate developmental math program that now enrolls more than 800 students. About 13 percent of all freshmen and transfers participate. Only after passing one of the remedial courses can students take the college-level math course required to graduate.
University math faculty say the high demand for math remediation is not a reflection on the students' intelligence. This year's freshman class arrived with a medium range of SATs (the scores for the middle 50 percent of students) between 1200 and 1350 - 20 points higher than last year's freshmen. More than a third had high school grade point averages of 4.0 or higher.
Rather, the faculty say, the need for remediation is a reflection of a growing national trend: As high schools ease math requirements, abandon traditional math curricula and integrate calculators into the classroom, more students are arriving at top colleges with surprising gaps in their abilities.
Although community colleges and less selective four-year schools have long contended with students' poor math preparation, the challenge is catching many more selective colleges off guard.
'A pernicious effect'
"These are issues we're finding nationwide, not just here," said Denny Gulick, a Maryland math professor and member of a group that oversees state math standards. "One of the problems we've had is that algebra has been downgraded in many high schools."
But faculty at Maryland and elsewhere say colleges and universities must accept some of the responsibility. By encouraging high school students to take Advanced Placement math, they say, colleges may have pressured schools to rush students through algebra to get them to calculus.
"There's a pernicious effect - schools concentrate only on those precalculus things useful for passing [the AP exam]. What happens is you're expert in that but lacking the foundations to go on," said Dennis DeTurck, last year's math department chairman at the University of Pennsylvania. "Fundamentally, it's the universities' fault. We dropped the ball and let the market dictate the curriculum."
Universities have found widely differing ways to deal with the problem. At the most aggressive end are schools such as Maryland, which last fall replaced its old developmental math offerings with a two-tiered system that showed promise in its first year.
Students who score the lowest on the math placement exam given to all freshmen are assigned to a computer lab, where they work six hours a week with a self-paced computer program geared toward their weaknesses. Instructors are available for extra help.
Students with slightly stronger skills take rigorous courses that meet daily and are designed to improve their skills in just five weeks, after which they are given another exam. If they pass, they spend the rest of the semester in an accelerated version of the college's for-credit precalculus course. If they fail, they go into the not-for-credit computer lab.
The success of the computer lab has not been evaluated, but the accelerated courses seem to be working - about 80 percent of the 550 students who enrolled in them last fall passed and received credit for precalculus.
To support the 30 sections offered under the new developmental math program, Maryland charges remedial students a $250 fee on top of tuition.
At some colleges, such as Towson University, there is a separate developmental education department. Towson, with about 3,000 freshmen and transfers, has approximately 350 students enrolled in two different levels of developmental math, the lower of which is described as a "preparatory course designed to develop basic competence in arithmetic." There is no extra fee.
Remedial math offerings are much slimmer at many private universities that, unlike Maryland's public colleges, don't require students to take math. Officials at elite colleges acknowledge that some of their incoming students are weak in math, but they say those students typically fulfill their math/science requirement by taking basic science courses.
As a result, remedial enrollments are a tiny fraction of the student body at such schools. About 120 students are enrolled this fall in entry-level Math 103 at the University of Pennsylvania. The Johns Hopkins University has 34 students this fall in its lowest-level math class, and Georgetown University has about 25 students each year in its Math 001.
The high demand for remedial math at College Park has fueled the debate among some non-math faculty about whether the university should keep the math requirement, but most favor it.
Instead, the university is trying to reduce remediation by adding a line in its application catalog that "strongly recommends" four years of high school math. Many good students, the university finds, take their state-required three years of math and then take none their senior year - a gap that comes back to haunt them in college.
That's what happened to Luis Oliva, a transfer student from Prince George's Community College. He went a year and a half without math, and he now finds himself in Maryland's computer lab - even though he scored a respectable 580 of 800 on his math SATs, which test basic algebra and geometry.
'Figured I'd start over'
"I fulfilled my [high school] requirement and felt I didn't have enough math to go into calculus, so I just figured I'd start over when I got to college," said Oliva, of Hyattsville.
Knox took four years of math at Atholton High School in Howard County. Like many high schools, Atholton has departed from the traditional sequence of algebra, geometry, advanced algebra, trigonometry and calculus. Instead, Knox spent her first two years in "integrated" courses that mixed algebra and geometry.
"When I studied in high school, I studied for a test, not for the long term," she said. "I looked at the formulas before the test because I have a good short-term memory, but I forgot them afterward."
'You are not alone'
Many of Maryland's math faculty blame the dominance of the calculator for such forgetfulness, pointing out that students can use calculators to do intricate algebraic functions they once had to do on their own.
"Students aren't asked to own mathematics; they don't memorize the concepts they need to use," Gulick said. "You can't do math unless you know the rules, and the calculator doesn't tell you the rules."
There were no calculators in Maryland lecturer Debbie Franklin's accelerated precalculus course last week, where she rapidly reviewed homework problems such as -2x/3 = 2/5. It was algebra of the sort taught in eighth grade, but several students had wrong answers. (The correct answer is x = -3/5.)
"I was able to get that part, but I was totally stumped after that," a student said of one problem.
"You are not alone," Franklin said, unfazed. "Many students make the same mistake."