Virginia schools are at the height of the testing season as students in grades 3-12 take Standards of Learning (SOL) tests in English, mathematics, history and science. The SOLs, which have been a rite of spring since 1998, measure whether students and schools are meeting the commonwealth’s standards for academic achievement.

The mathematics SOL tests students are taking this year are the first to reflect the increased rigor of the 2009 revision of the commonwealth’s mathematics standards. On the online versions of the new math SOLs, test takers have to demonstrate critical-thinking and problem-solving skills in ways not possible on traditional multiple-choice tests. Technology-enhanced items on these tests mirror common classroom tasks, such as ordering information correctly, creating graphs from data, plotting points on a grid and highlighting features on a diagram. There also are open-ended, fill-in-the blank problems.

These innovative items make up about 15 percent of the total on each new math test. On online math tests in grades 3-5, the technology-enhanced problems are field-test items and won’t count toward a student’s score until next year.

The new math tests respond to the desire frequently expressed by teachers for tests that measure critical-thinking and problem-solving skills — as well as content knowledge. Indeed, in many of the newspaper articles and television reports this spring about the new tests, mathematics teachers stand out for their support for more challenging assessments to ensure that students fully understand what they have learned and can apply it in real-life situations.

As with all SOL assessments, Virginia classroom teachers participated in the development of the new mathematics tests, as well as in the determination of pass/fail marks.

Are the new math SOLs more difficult than the tests students are accustomed to taking? The performance of the approximately 24,000 students who took Algebra I, Geometry and Algebra II tests during December and January suggests they are. On average, the statewide pass rates on the three tests were 27 points below those of students who took the old end-of-course math SOLs during the same time period last school year.

For two years, Superintendent of Public Instruction Patricia I. Wright has warned that this year’s math SOL results would represent the start of a new trend line. If pass rates fall, she told state lawmakers in January, it is a sign that the state is expecting more, not that students are learning less.

But the experience of students in 20 of the schools that administered tests in December and January suggests the state Board of Education has not set the bar out of reach. Students found the new tests challenging but still achieved pass rates of 80 percent or higher.

“Having to think a little more and learn a little more and reason a little more is a good thing,” a math teacher at one of these schools said. “And if that is what the standards are asking us to do, I think that’s a good thing for us to be striving for.

Today students require stronger skills to succeed in college and to compete in the increasingly technologically sophisticated work force. Educators, parents and business leaders alike know that we must do better in subjects like math if our graduates are to succeed in the global economy

The case for raising standards also is apparent when achievement of Virginia students on the SOLs and the National Assessment of Educational Progress — also known as the Nation’s Report Card — is compared. For example, during the 2010-2011 school year, 89 percent of fourth graders passed the state test, but only 46 percent met the minimum benchmark on the national math assessment.

My colleagues on the Board of Education and I understand concerns about the potential impact of the new tests on school accreditation ratings. But school divisions have had three years to align instruction with the new standards. Retreating from these higher expectations would send a terrible message to students who are just now taking the tests and the teachers who have worked hard since 2009 to prepare them.

Yes, the new tests are challenging. But Virginia’s accountability system allows multiple opportunities for high school students to retake tests to meet diploma requirements. In the end, they will graduate knowing that they achieved a higher standard.

Virginia has raised the bar before and students — with the help of the commonwealth’s outstanding teachers and instructional leaders — met the challenge and were better prepared for the future because of it. I am confident that with time, support and the multiple opportunities for success provided under the SOL program, they will do so again.

David M. Foster of Arlington is the president of the state Board of Education.