My colleague Bill Turque's energetic coverage of suspicious erasures on D.C. school standardized tests in 2008 reminds me of my attempt many years ago to delve into the only classroom cheating scandal ever to become a major motion picture.

This happened at Garfield High in East Los Angeles in 1982. Fourteen students at that impoverished neighborhood school were suspected of cheating on an Advanced Placement calculus exam. Twelve of them took the test again and passed. Six years later, the film "Stand and Deliver," with Garfield math teacher Jaime Escalante played by Edward James Olmos, turned the incident into a legend and boosted a national effort to bring challenging courses to low-income schools.

The film left the cheating question up in the air. But a book I wrote about Escalante showed that at least nine students were involved in copying an answer for one question on the first test and then proved in the retest that they knew their subject and that our academic expectations for inner-city children were much too low.

Despite Turque's good work, I fear we will never have the same certainty about the irregularities on the D.C. Comprehensive Assessment System (DC-CAS) tests. Thirty-four students in a class at Bowen Elementary School in Southwest Washington averaged more than 10 wrong-to-right erasures on the exam, five times the citywide average. Similarly questionable results turned up in some other schools. But the CTB/McGraw-Hill expert who reported this recommended that we "not draw conclusions about cheating."

We are left with unresolved doubts and disagreements, poisoning attitudes toward school improvement without answering the key question: Did our kids learn the subject matter, or not?

There has always been cheating in schools, as well as in businesses, government agencies and even churches. We are a clever, devious primate species, always looking for an edge. Whatever school achievement assessments we use -- tests, portfolios, inspections -- somebody will seek an advantage.

Often we shrug at this. Several years ago one of The Washington Post's best reporters, Justin Blum, developed evidence of exam-fixing by an elementary school principal. Blum reported as much of this as he could, but no one confessed and the school district took little action.

At Garfield, it took me five years to get to the truth of that one incident. Ten students agreed to sign waivers so the College Board could show me their exam papers. The calculus test was a distant memory, their lives were going well and I think they assumed that since their old teacher blessed my book project, I would reveal nothing that put them in a bad light. I thought my inspection of the exams would clear them.

Instead, I found that nine of the 10 had made identical silly mistakes on free-response question number 6. That could only mean at least eight had copied from the same source, perhaps the ninth person. I got two of them to admit that in a moment of panic near the end of the exam, somebody had passed around a piece of paper with that flawed solution.

Yet they knew their stuff, and would have done no worse if they hadn't cheated. The counselor who proctored the exam apparently missed the note-passing. When the nine students whom I knew had cheated, plus three more, retook the exam in August -- with little time to review and two proctors watching their every move -- they once again did very well, mostly 4s and 5s on the 5-point exam. The answer to the important question was obvious: They learned a lot.

Retesting is a standard option for AP exams when results are questioned. What would have happened if the Garfield students had not followed Escalante's suggestion to give it another try? Many people would have assumed that the school's success was bogus, that the children of seamstresses and day laborers were incapable of mastering something as difficult as calculus.

Teachers at other schools would not have been inspired to give low-income students extra time and encouragement to learn. I would not have one of my favorite statistics: In 1987, 27 percent of all Mexican Americans who scored 3 or higher on the calculus AP exam were students at Garfield High.

What can we do about the tainted test results in the District? The doubts encourage those who want to get rid of standardized tests but have demonstrated no practical, affordable alternatives. Many educators who have found such testing useful, to guide their teaching and win credibility for their schools, will have their good work questioned.

Why not do what Garfield did? In D.C. classrooms that had the most dubious results, let's get the students back together and give them another test, this time carefully proctored. I realize that they are now more than a year older. I hope we address these issues more promptly in the future. But I still think the retest will tell us something.

Perhaps they erased bad answers the first time because they conscientiously went back and checked their work. Or someone coached them during the exam or changed wrong answers for them afterward.

Having them take another test won't solve those mysteries, but providing D.C. kids the educations they deserve is too important to leave this in limbo. Let's check, as they did in East L.A., and make sure we know how much our children have learned.

E-mail: mathewsj@washpost.com