So, your kid is getting A's in high school algebra class, and you're feeling pretty good about it. It has been a long time since you were in high school, and basically you've given up trying to help your child with math homework. But you figure that if your kid is getting A's, he or she is learning a lot and all is well.

Maybe. Maybe not.

A school system analysis of how Prince George's students did on the High School Assessment tests reveals a profound disconnect between grades and performance. County students in high school algebra last year who received A's earned a median score on the state test of only 50. That's also the median score for all Maryland students. The median is the middle number in a sequence.

A students should be up in the 80s or so. In other words, some Prince George's kids are receiving A's, but the tests show they don't know enough A-level algebra.

Furthermore, this isn't true of algebra alone, it is true, to varying degrees, for all the subjects on which Prince George's students were tested for the High School Assessment. And what this means, said Leroy J. Tompkins, chief accountability officer for the county's public school system, who prepared these analyses, is that "for our district, we have to raise the rigor and standards of performance of our courses as well as the expectations we have of our children." Parents, he said, should question an A as much as they do an E.

The issue of grading and expectations will be one of the biggest facing Prince George's County schools in the next few years.

To understand why, a little background is in order. Time was when all students had to do was show up for 12 or 13 years and not be a major pain in the neck, and they could get a high school diploma. In fact, sometimes students who were pains in the neck would get pushed even faster toward a diploma just so the school could get rid of them.

It didn't matter if they couldn't read or write or do simple calculations -- they still got diplomas. This was not just a Prince George's problem or just a Maryland problem, but a national one, laid out in the now-famous 1983 "Nation at Risk" report by the Department of Education.

In response, states began establishing minimum competency tests that students had to pass before graduating. Though these were pretty low-level tests of reading, writing and calculating, they at least ensured that students achieved functional literacy before they received high school diplomas.

In Maryland, the tests are the MFMT (Maryland Functional Math Test), the MFRT (Maryland Functional Reading Test) and MFWT (Maryland Functional Writing Test).

In the first few years the tests were given, large numbers of kids failed, and lots of people who opposed the tests had dire things to say about how requiring kids to meet even those low standards would cause them to become discouraged and drop out of school.

The exact opposite happened in Maryland and the other states that instituted competency tests. Not only did failure rates drop fairly quickly, but dropout rates declined as well. It seemed that requiring kids to know something, even if it wasn't much, made high school a more meaningful experience and made kids more willing to stay.

But Maryland, along with some other states, has decided to up the ante. It's not enough, Maryland officials have decided, to be able to read, write and compute at low levels to earn a high school diploma and thus go forth as a responsible citizen.

It is necessary to know something about history and American government, science, literature and mathematics. And so Maryland has put into place five High School Assessment tests -- in English, biology, algebra, geometry and government -- with promises of more in the future.

(To see the tests for the past three years, go to www.mdk12.org and click on "Public Release of the High School Assessments" at lower right.)

Last year, students who were taking those five courses had to take the exams, but the state hadn't decided what a passing score would be, so the results were reported only as percentile rankings -- that is, the state simply arrayed all the students in a scale from top to bottom, then reported where students were on that continuum. Although quite a few Prince George's students performed at top levels for the state, county students as a whole were toward the bottom quarter or third, depending on the test, which has caused great consternation and a renewal of interest in high schools on the part of Prince George's school officials. In fact, it has prompted Prince George's chief executive officer Iris T. Metts to begin visiting every high school in the county.

Now the ante is about to be upped again. Sometime this summer, the state school board will probably decide to make passing the exams a requirement for a high school diploma. The big question will be what the passing score is.

If the state school board requires students to correctly answer 90 percent of the questions on the tests, most students in Maryland will fail. If, more realistically, it requires students to correctly answer 50 percent of the questions, many students still will fail. In fact, no matter how the state school board defines passing, some students will fail the first time they take the exam and will not be able to receive their diplomas until they pass.

The idea is that they should have additional opportunities to learn the material and then to take and pass the exam and earn a high school diploma. The idea is not to deny kids a diploma but to make sure it means something. In other words, once these tests are required for graduation, kids and high schools will have to focus very closely on the kinds of information they are expected to know and teach.

That's when this mismatch between grades and performance that Tompkins has documented will become quite painful. Kids who have received A's for showing up and not being a major pain in the neck are going to be in for a rude awakening -- as will teachers who have given A's to kids for being reasonably well behaved and turning in work sheets on time.

That's the message Metts has been taking in her whirlwind, two-high-schools-a-day tour of the county. She has been showing high school officials how their A students performed on the assessments, how their B students performed and so on, and asking them to think deeply about what they expect for their students.

Of course, different high schools have different test results. Some have higher expectations for their students than others, which shows in the fact that their A students score at higher levels than A students in other schools.

There are interesting anomalies, however. Some Prince George's students who received E's on their report cards scored at the top of the state in some exams. Not many, mind you, but some. I imagine some are students who are pains in the neck and don't act in ways that grown-ups want them to, yet they have mastered a fair amount of material. Perhaps they don't show up to class because they think its a waste of their time -- and, in fact, they may have a point.

I hope every high school with one of those E students scoring at the top of the state figures out what is going on with those kids. Maybe they need to be in more challenging high school classes. Maybe they need to be taking college classes. Maybe they need someone to notice that they are smart and on the ball, despite appearances to the contrary.

In any case, the data shown in the table below should prompt schoolwide, countywide and even statewide discussions about how much our children know, how much they should know, and how those expectations and standards are expressed every day in classrooms and quarterly on report cards.

Homeroom, which appears every other week, is a forum for you. Send questions, opinions and issues that you would like to see discussed to Homeroom, The Washington Post, Prince George's Extra, 14402 Old Mill Rd., Suite 201, Upper Marlboro, Md. 20072. The fax number is 301-952-1397; the e-mail address is homeroom@washpost.com. To see previous columns, go to www.washingtonpost.com, click on the Education page and look for Homeroom under Education Columnists.