Thousands of students in Montgomery County failed final exams in high school math courses last semester, according to data that raise questions about how well students have learned the material and whether there is a disconnect between the test and the course work.

Recently released figures show failure rates of 62 percent for high school students taking the county’s geometry final and 57 percent for those taking the Algebra 2 exam. Among students taking the same courses on the honors level, 30 percent to 36 percent failed the end-of-semester tests in January, according to data from the school system.

The numbers have alarmed parents in the high-performing school system, where nearly 16,000 high school students in seven math courses did not pass their finals — a majority of the roughly 30,000 students taking those tests.

Schools Superintendent Joshua P. Starr said a work group would begin meeting this summer to unravel the reasons behind the poor test results, which he said could involve issues of teaching, student support, or alignment between the curriculum and the exam.

Starr said that he did not know how long the problem has been going on and that he has requested historical data showing exam failure rates for the past five years.

“It’s certainly a concern to me that this many kids failed,” Starr said, adding that “exam failure does not mean course failure.” School officials said they did not have data on course failure but noted that two-thirds of Montgomery’s students earn a C or higher in Algebra 1 by the end of ninth grade.

The underperformance issue comes as the County Council spars with school officials over funding and whether the school system has focused enough on closing the achievement gap.

The new figures also show that 48 percent of students did not pass the pre-calculus final exam, with an additional 14 percent receiving D’s. Most starkly, 86 percent flunked finals for Bridge to Algebra 2, intended for those who need support before moving into the advanced course.

“I think the numbers raise more questions than they do answers,” said Board of Education member Michael A. Durso, a retired high school principal who said one factor may be a recent push by the school system to “super-accelerate” math students. “Obviously, something is not right.”

The failing grades came to light after Dylan Presman, PTSA president at Rockville High School, heard complaints about numerous students not passing exams and obtained data late last month from a school official he declined to name.

Presman said he found the data so “outrageous” that he posted it on his school’s e-mail group list and forwarded it to high school PTSA leaders across the county. The data was confirmed by Montgomery officials as accurate.

Parents were stunned, he added, some saying they thought that only their children had done poorly. “When people saw this data, they said, ‘Holy cow,’ ” he said. “It’s going on all over.”

School officials say the data do not tell the whole story for two of the seven math courses — Algebra 1 and honors geometry — because middle school students are heavily enrolled in them and tend to pass exams in greater numbers. When middle school and high school exam grades are combined, the overall failure rate is 30 percent for Algebra 1 and 25 percent for honors geometry.

Tom Loveless, a senior fellow at the Brookings Institution who researches student achievement, said it is impossible to explain Montgomery’s slump without knowing more about how students have done in past years, how the exam was designed, how the student population may have changed and other factors.

Still, he said, “if this is a test that is supposed to reflect mastery of a course, then these rates of failure are alarming.”

Several experts said multiple forces could underlie the problem.

Kristen Amundson, senior vice president for the think tank Education Sector, said suburban school systems such as Montgomery’s face strong pressures to trumpet their successes, which can obscure problems.

“It’s the ‘We’re great’ syndrome,” she said. “I think you have to take this as a signal that you have to look much more closely and see maybe there are some things kids aren’t learning — maybe as far back as fractions.”

Amundson said math is a cumulative subject, so gaps add up. “Math depends so heavily on what you learned the day before and the week before and the month before and the year before. . . . Eventually there comes a point where the whole edifice comes down.”

Some educators have asked whether students lack the motivation to do well. A final exam counts for 25 percent of a semester course grade, but grades can be fairly settled by day-to-day performance in the classroom over two quarters.

Many parents in Rockville say just the opposite: Students try hard but fail anyway.

They say the problem is a mismatch between curriculum, review packets and tests. Several said their students are high-achievers preparing for the rigors of the International Baccalaureate program — and running aground in finals.

Joyce Gardner, a Rockville High parent, said that when her daughter did poorly on her honors Algebra 2 final exam as a freshman, “I thought she didn’t study enough.” She said she really didn’t believe the teen’s assertion that “everyone” had failed the exam.

“I figured she was just saying that,” she said.

Then her son took the same course, and Gardner watched as he pored over the review packet and other material, formed study groups, and was helped by his father, an engineer.

He had A’s and B’s in the class, but failed the test. His course grade sunk to a C, which will show up on the transcript he submits for college applications.

Her son, she said, was disbelieving. “Something’s wrong,” she recalled him saying.

Gardner said Rockville’s principal, Debra Munk, recently looked into it and reported a disconnect between the exam and the review packet. Munk said in an e-mail that the situation was complex and referred questions to other school officials.

School officials said the countywide math exams were created in 2001, when the curriculum was revised. Many parents contend that the problem is long-standing.

Starr said that although he had not been aware of the failure rate on exams, he recognized early on as superintendent that math is a challenge for many Montgomery students. He said more than 60 percent of high school students who attend Montgomery College after graduation need remedial instruction before taking college-level math.

Starr said Montgomery’s effort to look into the problem will include a school-by-school analysis and an examination of such issues as student placement and professional development. The goal, he said, is to make changes before next January’s finals.

In the meantime, a Rockville father said his daughter dreads the math final that awaits her in June. Last time, she understood everything covered in class and studied hard, he said — only to discover that she had failed.

“It was enormously deflating,” he said. After so many failing grades, “everyone knows you don’t stand a chance.”