By Karin Chenoweth

Thursday, December 25, 2003; Page GZ06

I have been involved in a running argument for the last couple of years about Maryland's algebra and data analysis assessment. This is one of the four tests the state requires every student to take before graduation -- and starting with the Class of 2009, every student will have to pass it before earning a state diploma.

Jerome Dancis, an associate professor of mathematics at the University of Maryland, calls it a "pretend algebra" test and predicts that it will undermine mathematics instruction throughout the state. He has made this argument to the state Board of Education and to anyone else who will listen.

I have told him he has unreasonable expectations. To me, the algebra/data analysis High School Assessment exam represents a reasonable view of what every adult needs to be able to do mathematically, and thus it is a reasonable requirement for graduation.

In thinking about this, I was trying to keep in mind the student who is an artist or a history buff and who really has trouble with math. That student still needs to know some math, and it seemed to me that the algebra assessment represented a fair sample of such knowledge, including some real -- if not terribly difficult -- algebra.

Dancis and I have been peppering each other with e-mails every few months, neither of us convincing the other, until I finally got the bright idea that if he and I worked our way through an exam together, he would see the error of his ways.

So last month we got on the phone and went through the algebra/data analysis test that was given to students who completed Algebra I classes in 2002. It took a couple of hours, at the end of which my ear hurt from resting against the phone. If you want to see what we were looking at, go to mdk12.org/mspp/high_school/look_like/2002/algebra/intro.html. The Web site has three years' worth of tests.

It's easy to see where this is headed, isn't it? I now call the test a "pretend algebra" exam and fear that it will undermine mathematics instruction throughout the state.

Take, for example, question No. 3:

Mary graphed the system of equations below.

y = 3/2 x + 7/2

y = -2/3 x + 7/3

Which of these best describes the relationship between the two lines?

A. They have no point in common.

B. They have one point in common.

C. They have two points in common.

D. They have infinite points in common.

This is one of the questions I thought I could use to sway Dancis. It is real algebra -- not horribly difficult, but that doesn't concern me.

To answer the question correctly, you have to understand that each equation represents a line and be able to plot it on a graph. You have to understand that two intersecting straight lines have only one point in common. It represents, in other words, a fair amount of algebraic knowledge.

Except for one thing, which I didn't realize until Dancis pointed it out to me. If you have your trusty graphing calculator -- which all kids taking the exam have -- all you have to do is punch in the two equations and see what pops up on the screen. You don't have to know anything except how to use the calculator. A lot of grown-ups won't know what I'm talking about, unless they have kids in middle and high school, but graphing calculators have little screens that can display algebraic functions and all kinds of other things.

Dancis agreed with me that the above question is a real algebra problem. But by allowing graphing calculators to be used on the test, he said, "They've found out how to trivialize it. This is why I call it pretend algebra." And, he argued, if instruction focuses not on the math required to solve the problem but on calculator tricks, that could seriously undermine math instruction in the state.

Calculators allow kids -- and adults -- to do a lot more math than they would without them. But calculators should supplement, not supplant, basic mathematical knowledge. And I would like to know that kids can graph a simple line without a graphing calculator before they graduate from high school.

The head of math instruction for the state, Donna Watts, disagreed. "The technology is there. It's not going to go away," she said. "There is a limited population who can do math symbolically, the way mathematicians do. If this is an exam for all students, we want to make it comfortable for however students learn."

She made the analogy to cooking. "All students should be able to cook to survive. Does that mean that all students should be able to cook like a chef, or be able to follow a simple recipe?"

I would agree with her that the simple recipe standard is appropriate as a requirement for all students. But we shouldn't then say that a simple recipe means: "Remove from container and place in microwave for three minutes." That is what we call "dumbing down" the standards.

Behind this argument is another, deeper one about what a high school diploma should represent: Should it certify that high school graduates have some real knowledge and skills they can be proud of, and that colleges, trade schools and employers can be sure the graduates' knowledge represents mastery of enough material that they don't have to start teaching it from scratch? Or is graduation akin to a property right? That is, if you're 18 and have shown up at school for the requisite days, do you have a right to a diploma?

When Maryland embarked on its reform efforts more than a decade ago, state officials promised that when they were done, a high school diploma would no longer simply be a certificate of attendance. Rather, it would demonstrate that the person holding it would be fully prepared for the next step in life, whether it be a four-year college, trade school or whatever. To that end, the state planned for students to take 10 high-level assessments to demonstrate that they had learned enough to earn a diploma.

But Maryland officials have been spooked by thousands of students in Florida and Massachusetts not passing their state exams and not receiving high school diplomas in the last couple of years.

So now Maryland has just four high school assessments -- in algebra/data analysis, biology, English and government -- and has set the passing scores in such a way that students have to correctly answer only about half the questions to pass. Even so, about half the students who took the tests last year failed them.

Ron Peiffer, deputy superintendent of Maryland schools, puts it this way: "The whole notion of pushing for higher standards has been lost, with people afraid of the failures."

This is one reason for the somewhat confusing proposal that state Superintendent Nancy S. Grasmick made a couple of weeks ago: to have five levels of high school diploma. The state diploma would represent that a student had passed all four of the required exams. Grasmick said perhaps there should be one new level of diploma for students who don't pass the four exams but have disabilities documented in an Individualized Education Plan, and another type of diploma for students who pass three of the high school exams but not four.

Then there would be a certificate for students who have such severe cognitive disabilities that they really can't be expected to take those exams, but who have demonstrated mastery of other skills and knowledge as represented by what is called the IMAP exam, for Independence Mastery Assessment Program. This diploma, already in place, would probably apply to a very small group of students -- less than 5 percent.

A fifth credential is also already in place, for students who have dropped out of high school and then passed the GED, or high school equivalency exam.

"If we have the three-out-of-four option, that would probably just be for two or three years -- it would be a temporary cushion," Peiffer said, referring to the diploma for students who pass three of four state exams.

"I believe kids are going to pass these tests at a much higher rate than is feared," he added. "I think far more special-ed students will end up with four-out-of-four than we give them credit for."

But for kids and parents, the real message is that these exams -- and the diplomas -- will not represent what they need in order to avoid remedial classes at community college. These are very low-level, base-line markers of knowledge and skills, not at all what is needed to prepare for the next 50 years of life. For that you need to aim higher.

Homeroom appears every week in Montgomery Extra. Send questions, opinions and issues that you would like discussed to Homeroom, The Washington Post, 51 Monroe St., Suite 500, Rockville, Md. 20850. The fax number is 301-279-5665. Or e-mail homeroom@washpost.com.