At the Environmental Protection Agency, a doctoral chemist frets that his junior high school age daughter - steeped in the theories of "New Math" in grade school - has become part of a mathematical lost generation, unable to add, subtract, multiply or divide properly.
In Prince George's County, the seventh grade math curriculum has been in the process of voerhaul in recent years, essentially to stress computational skills that students should have learned in grade school.
"Usually, we started junior high school with a unit on geometry," said mathematics supervisor Conrad Seeboth. "But we've found we have to go back and do the basic computation."
At Arlington Thomas Jefferson Junior High School a seventh grader entatively pushed a test paper across the table to his teacher. "Seven times seven is 42," he said. "Right?"
"No, I don't think I can agree with that," said the teacher, Elmer McNeil.
In varying degree, each incident reflects what many educators believe to be the legacy of new math or modern math - a sweeping reform of elementary school mathematics teaching that occurred over the last two decades.
Each incident also reflects a growing disenchantment with new math and a push at local schools to re-emphasize basic computational skills.
Essentially, the idea of new math grounded in mathematical theories and concepts - the figure 537 represents five hundreds, three tens and seven ones, for example. This, it was argued, would help them better understand the reasoning behind computation.
"Plain old fashioned third grade arithmetic. The kids are coming out of high school not being to do it in their heads."
Four years ago Shackelford attracted nationwide attention when he complained to the Arlington School Board that the exercises in his then fourth-grade daughter's math book were so theoretical and so conceptual that many of his EPA colleagues - most of whom had advanced degrees - could not do them.
Many would argue that the term mathematical lost generation is overstating the seriousness of the new math problem, but there's no disputing the fact that computational skills did go down substantially. Beginning in 1963, scores on the math section of the Scholastic Aptitude Tests, taken by one million college bound high school seniors, began a steady 12-year decline, falling 30 points on a scale of 200 to 800.
Additionally, the National Assessment of Educational Progress reported in 1975 that many teenagers and young adults lacked the basic math skills to shop intelligently, drive a car or balance a checkbook.
Only 39 per cent of the persons in the age 26 to 35 category could figure which of these packages of rice offered the lowest price per ounce: 12 ounces for 40 cents, 14 ounces for 45 cents, 1 pound 12 ounces for 85 cents or 2 pounds for 99 cents. (1 pound 12 ounces is correct.)
"At the elementary level, the new math has been a disaster," declares George Weber, associate director of the watchdog Council for Basic Education.
Weber, Shackleford and hundreds of others have been complaining about new math for some time. In the last few years, there is evidence that their voices are being heard. School systems throughout the Washington area are stressing basic addition, subraction, multiplication and division more and more, and many are taking a hard second look at new math and making appropriate revisions.
"There definitely has been a swing away from some of the new math terminology to a more traditional type program with more emphasis on computational skills," says Frank Miller, mathematics curriculum specialist for the Arlington public shools.
Thus, exerises like the games in mental computation that occur whenever there is a few minutes free time in the sixth grade class Anne Nystrom teaches at Arlington's Oakridge Elementary School have become common-place.
There, the other day, a towheaded youngster stood in the middle of a circle surrounded by a score of classmates and asked them to figure in their heads the answer to:
"Seven times six, divided by 21, times 82, divided by 82, times six, divided by three, times seven."
A dozen hands shot into the air almost immediately and one boy proudly announced the correct answer, "28."
"Rapid retention of the facts is some of the facts is something we stress now more than ever before. You've got to memorize the facts," says curriculum specialist Miller.
Miller is quick to add that Arlington is in no way scrapping new math.
It is simply supplementing some of the theories and concepts stressed in new math with heavy doses of multiplication tables, drills and problem solving exercises.
For while it's generally acknowledged that computational skills did go down during the new math heyday, not everyone agrees that new math was responsible.
Some argue that reading skills also decreased in the same period, suggesting that the drop in math scores may be part of an overall academic decline.
In any event, most mathematicians say they welcome the new emphasis on computational skills, but they are also voicing some strong reservations.
"We are deeply distressed," said the National Council of Teachers of Mathematics in a recent position statement, "by the danger that the back to basics' movement might eliminate teaching for mathematical understanding. It will do citizens no good to have the ability to compute if they do not know what computations to perform when they meet a problem.
"I'm concerned about what I see is a basic misconception about new math," says Dr. Robert Harvey, a former math professor and now dean of Knoxville College in Tennessee.
"The problem was in poor teaching. New mathematics poorly taught is bad mathematics. But if you don't lay the foundation, the computational skills will deteriorate. I believe, if you lay the appropriate foundations, you could attend to all the computational skills in a year's time."
By 1975, the conflict over new math had so polarized the mathematics community that one group urged the dispute be resolved simply by declaring that new math no longer exists.
In a "strong recommendation," the National Advisory Committee on Mathematical Education asked that "all who are interested in what is going on in school mathematics today, whether as supporters or critics . . . from this point in time use the term 'new math' only as an historical label for the vague phenomenon or the very diversified series of developments that took place in school mathematics between 1955 and 1975."
Math education going on in schools today, the committee suggested, should be called something like contemporary mathematics or current mathematics.
"It was the terminology that caused a lot of parents a lot of grief because they didn't understand it," said math supervisor Conrad Seeboth of Prince George's County.
Like the computative law of addition.
"What that means," Seeboth said, "is that four plus three is the same three plus four. That's a nice thing to know, but now let's get the answer."