In the years leading up to the introduction of tougher standardized tests in Virginia, the number of students who earned perfect scores soared. In Arlington County, nearly half — 45 percent — of fifth-graders who took the Standards of Learning math tests in the spring of 2011 got every single question right.

Across the river in Maryland, perfection has been more elusive. In 2011, there were only 25 perfect scores on the fifth-grade math test in the whole state, according to data from the Maryland Education Department.

Smarter kids in Virginia? Not likely.

Variations in the tests’ rigor is typically the reason for such difference. States historically have determined their own standards for what students should know from grade to grade.They write their own tests and set their own cut scores for who should pass.

This variability has been identified as a major weakness in the American system. It’s also why states across the country are moving toward common standards and common tests.

One way to compare the relative rigor of individual state tests is to look at their results compared with the results of a national standardized test, known as the Nation’s report card, which is administered in the fourth and eighth grades every year.

The 2011 National Assessment of Educational Progress showed that eighth-graders in Virginia and Maryland performed about the same in math, scoring 289 and 288 respectively, both above the national average score of 283. The portion of students who scored advanced on the test was also similar -- 11 percent in Virginia and 12 percent in Maryland.

But on Virginia’s own math tests that year, 47 percent of eighth-grade students earned an advanced score, with an 82 percent pass rate overall. And in Maryland, 32 percent earned an advanced score, with a 66 percent pass rate over all.

In Virginia, such high success rates are already slipping. It’s one of a few states that did not sign on to new standards known as the Common Core, but it is updating its standards and tests. Math tests administered in the spring of 2012 were more difficult, and the results showed a major drop in scores. Perfect pass rates also plummeted.

Maryland is updating its learning standards so they align with the Common Core, and it plans to introduce new tests in 2015.