Alexa Williams knew her academic experience would be different when she transferred into Episcopal High School in 10th grade.

The teenager grew up in the Mount Vernon area and attended Fairfax County Public Schools her whole life. Attending Episcopal, a boarding school in the City of Alexandria, would be nothing like her ninth grade year at West Potomac High School.

But Alexa, who had always been a straight-A student, was unprepared for how much more challenging Episcopal’s curriculum was.

"I got straight A’s without trying to hard and I took four honors classes at West Potomac, which is the most you can take as a freshman," said Alexa, who had also gone through the honors program at Carl Sandberg Middle School and taken some pull-out "gifted and talented" classes at Fort Hunt Elementary School.

Alexa assumed that, even if she had to try a little bit harder in school, she would be able to earn all A’s at Episcopal as well. She was wrong.

Even though she was giving it her all, Alexa’s grades still dropped sophomore year as she adapted to Episcopal’s tougher academic standards.

"I had to take a grammar test at Episcopal and I completely failed it. I didn’t even know what a gerund was," said Alexa, who had always considered English her best subject. At West Potomac, she had earned a numerical average of 100 percent in her ninth grade honors English class.

"I didn’t really know how to study before Episcopal," she added.

Now headed into her senior year, Alexa’s grades have gone back up and she has adjusted to Episcopal’s higher academic standards. She is planning to take five Advanced Placement classes this fall, though she said most of her general education classes will also be challenging.

"I think the regular classes at Episcopal are equal to the honors classes at West Potomac," said Alexa.

FAIRFAX AND MONTGOMERY counties have robust and well-regarded public education programs for students who are motivated and academically advanced.

Both offer a range of educational options for students who are working above-grade level, including honors, Advanced Placement and International Baccalaureate courses. But the academic programs in the two suburban school systems that are considered the most elite tend to be the "gifted and talented" centers, where qualified students have their own teachers and only take classes with each other.

In Fairfax, about 13 percent of the elementary and middle school students are enrolled in one of these special gifted centers at the elementary and middle school level. Out of the county’s 12,900 ninth grade students, just 480 — including a handful from outside Fairfax County — were admitted to attend Thomas Jefferson High School for Science and Technology, Fairfax’s only magnet program for the upper grades.

Montgomery County’s gifted and talented centers are even more exclusive. The Maryland school system identified nearly 34 percent of its student population as "gifted" last year but just four percent of elementary school students, three percent of middle school students, and two percent of high school students attend the most exclusive programs.

With few slots available, both Fairfax and Montgomery counties adhere to relatively rigid admissions standards when it comes to centers and schools for students identified as "gifted."

The two public school systems rely heavily on standardized test scores to determine who is initially "center eligible." Students who do not achieve a very high score on an aptitude test are usually not even considered for gifted center admission, though they can enroll honors and advanced placement courses at the middle and high school level.

LOCAL PRIVATE SCHOOLS take a very different approach to the education of academically advanced students and could offer an alternative to parents of high-performing students who are able to cover the tuition costs, which are typically well over $20,000 per year.

"We don’t label kids. We are opposed to the whole idea of children thinking of themselves as gifted and talented," said Robert Kosasky, head of school at St. Andrew’s Episcopal School in Potomac.

Kosasky said St. Andrew’s likes to emphasize persistence as over natural ability. They want students to know that if a person works hard enough, they can perform at a very high academic level, regardless of their innate aptitude.

Several other administrators made similar remarks about their school’s philosophy and said that is why the standards for their advanced academic standards tend to be more flexible than the public school system.

For example, several private schools are more likely to let a child take an honors or accelerated course if the student is enthusiastic about the subject but even if he or she hasn’t been identified as advanced in that area.

MANY INDEPENDENT SCHOOLS said they did not have a "cut off" score students must achieve on a standardized test to be accepted either to the school in general or into an honors class, like the public school systems do.

At The Potomac School in McLean, math is the only subject for which students are separated out into different classrooms by ability, and that separation does not happen until students reach the seventh grade.

But at Potomac, until ninth grade, there are no honors or advanced sections for courses like science, social studies or language arts, though students in one class section may be "grouped together" based on ability level, said Bill Cook, Potomac’s assistant head of school for academics.

Cook would not answer whether Potomac considers all of it students gifted and talented.

"That is the kind of question I would rather not answer but we are blessed with an able constituency of families. That doesn’t mean they are all brilliant though," said Cook.

MANY INDEPENDENT SCHOOLS also offer more opportunity for students who might be considered gifted in certain subjects areas but are not academically advanced across the board.

In both counties, elementary school gifted and talented centers take an "all or nothing" approach to education. Students are unable to enroll in gifted and talented center classes for just one class, like math, while working at or below grade level in another course, like language arts.

Those who are "center eligible" are assumed to be intellectually advanced in all core subject areas. In Fairfax, this is even true at the middle and high school level. For example, all English classes at Thomas Jefferson are considered to be "honors" courses, even though the school focuses on science and technology.

Most private school administrators interviewed said it rare for any one student to be one of the highest achievers across all subject areas.

"We do not have a gifted and talented track. … We find that students’ performance in math and reading is not aligned at all. A child that is advanced in reading may not be advanced in math. In fact, they may need extra support in math," said Mimi Mulligan, admissions director and former teacher at Norwood School in Bethesda.

Even at Nysmith School for the Gifted, which uses I.Q. tests to help determine who is admitted, faculty do not find that students are working on a superior level in all academic courses.

"That is the exception. There are very, very few students who excel in all subject areas," said Ken Nysmith, who has been working at the Herndon school for about 25 years.

"Some of the children here are working on grade level in certain subjects," he said.

NYSMITH’S MOTHER, who taught in Fairfax County’s gifted and talented program, originally started the school in the 1980s for kindergarten through second grade students, who were expected to feed into the local gifted and talented center at Sunrise Valley Elementary School at third grade.

The school ended up expanding up to eighth grade at the suggestion of parents and families, Ken Nysmith said. Approximately 30 to 40 percent of the students who graduate from Nysmith end up attending Thomas Jefferson in high school, he said.

Like proponents of the gifted and talented centers in public schools, Nysmith said it is important for advanced students to be in a learning environment with their intellectual peers for social reasons.

In a program or school filled with gifted children, children who are exceptionally smart are not as likely to be picked on or isolated. They tend to feel more confident.

"The biggest benefit is that the children don’t feel different," he said.

But even in a school focused on gifted children, Nysmith does not organize its class sections for most courses by ability level. Math is the only subject for which they separate out the more advanced students.

Instead, Nysmith faculty will teach children operating on several different grade levels in one classroom. For example, children in one science class could be working on three or four different lessons at the same time, said Nysmith.

One of the reasons private schools like Nysmith do not have to group students in classes by ability level is because of smaller class sizes with lower teacher-to-student ratios.

For example, at Nysmith, there is one teacher for every nine students and the faculty have time to give each child one-on-one attention.

At Norwood, individual classes for math and reading have no more than 12 students in them, compared to approximately 25 to 30 children that are grouped together in Fairfax County, regardless of whether it is a gifted or general education program.

"We have very small groupings so we can meet every child’s educational needs," said Mulligan of Norwood.

BUT A CRITICAL MASS of students, particularly for those operating well beyond their other "gifted" peers, can make a difference.

For example, at 480 students, Thomas Jefferson’s freshman class is likely to be larger than the entire high school program at most independent schools. With that many academically advanced students, the school is more likely to be able to offer an extremely advanced class, like Real Analysis, an upper level college course that a handful of students from Fairfax are ready for in high school.

Still, many administrators said their private schools can accommodate students who have moved beyond the school’s standard curriculum. At Potomac, Cook taught a student advanced Latin one-on-one.

St. Andrew’s has joined with other local private high schools in and around Potomac to offer one niche course, like Advanced Placement Economics, on each campus which only a few students from each individual school would be qualified to take. These classes are scheduled at 7:15 a.m., before the private high schools begin their traditional school day, and students go to the nearby campus where their course is offered prior to coming to St. Andrew’s for the rest of their classes.