When Dylan Presman, president of the Rockville High School PTSA, discovered a majority of Montgomery County high school students were failing countywide final math exams, he said, “When you’re talking about half a group failing, there’s something seriously wrong.”

Presman is a thoughtful and enterprising parent, and something may indeed be wrong — but it’s not with the tests. Those big failure rates prove that Montgomery is one of the rare school districts that administers end-of-course tests challenging enough to flunk, thereby exposing poor student preparation and weak state standards. I wish the other districts did that.

We usually think of failure as bad, but most successful people don’t believe that. They know that only when they risk failure are they likely to develop the skills and knowledge that lead to success. This is true everywhere. Manufacturers of tires, aircraft wings and playground swings must push them to their failure points so they can be sure they meet quality and safety specifications. Failure gets to the truth.

More than a decade ago, I interviewed the educators who designed Montgomery’s first countywide exams in math, history and biology. They wanted a consistent, rigorous standard for the whole county to replace the immeasurable mess of different exams written by each teacher.

Their county’s high percentage of affluent, well-educated parents demanded the best, but that was not their only motivation. The Montgomery test designers wanted poor children in Silver Spring to be measured against the same standard as rich children in Potomac. They did not want low-income kids to get an easy test and affluent kids a hard one. That would make it more likely that schools in poverty-stricken areas would teach less and reduce the chance those children would have the reading, writing, math and time-management skills they needed for college or good jobs.

New statewide tests were introduced at the same time in Maryland and the rest of the country under the federal No Child Left Behind law, but they were not much help. State officials knew it was political poison to have many students flunk. They made the tests easier or provided alternatives, particularly if the students had to pass to graduate, as they did in Maryland and Virginia. When too many students were failing Virginia’s Standards of Learning social studies tests, the state school board lowered the passing score.

Experts no longer fear that the new state tests will hurt graduation rates. Last year, 98 percent of 12th-graders met the requirements for graduation in Virginia, and 95 percent met the requirements in Maryland. Graduation barriers are similarly low in most other states, even though in the past 30 years there has been no significant increase in average reading and math achievement for 17-year-old Americans.

Many students fail the Montgomery County tests mostly because they are more difficult than the state tests, which count for graduation. Students can flunk a county test and still pass that course because the exam makes up only 25 percent of the final grade. Teachers tell me the high failure rate on the county math tests comes from overuse of calculators in early grades, failing to train students how to study, accelerating too many students and letting students retake chapter tests they failed the first time.

Montgomery County has an incentive to address those issues because it has tougher district tests that many students fail. The districts without such tests lack that useful goad. Acknowledging failure helps. Covering it up, as most districts do, hurts our schools.

For previous columns, go to washingtonpost.com/class-struggle.com.