Teacher Jennifer Dial Santoro asked her eighth-grade geometry class to throw the formula out the window and instead try to reason out the area of shapes drawn on a large grid.
Didma Valenzuela, a girl in the front with her head down, struggled with a parallelogram. Then the class was given a shape that looked like an Egyptian sphinx. Didma figured that she could fill up the space inside the shape with triangles and rectangles and use them to find the area.
"Yes!" she said, slapping Santoro's hand. "And I did it all by myself."
The class in Anne Arundel County's Marley Middle School represents to Santoro the best kind of teaching: students learning to understand the abstract thinking behind math rules and formulas. Too much of the time, Santoro believes, math teachers are flying over material, never giving students a deep grasp of the subject.
It is a complaint that has echoed across the nation. But what is taught in math classrooms in Maryland could be on the verge of changing. In the next several months, math educators here will decide whether they want to slim down the curriculum, focusing on a deeper understanding of a few basic tenets and excluding some of the extraneous material that teachers such as Santoro feel is hindering instruction.
Maryland's soul-searching, and that of more than a dozen states across the country, is the result of a report by a well-regarded group of math educators, the National Council of Teachers of Math. The council released a grade-by-grade list of three essential concepts - just three per year - that each student should learn in kindergarten through eighth grade.
Council President Francis "Skip" Fennell said the organization wanted to address the long-held criticism that America's math curriculum is a mile wide and an inch deep. He hopes that states will change their standards to be more in line with the council's Focal Points report.
"The report is driving those kind of discussions. Already we have spoken to about 12 to 15 states that are doing that," Fennell said.
The discussion is part of a decade-long debate over whether the country has gone too far from the basics toward reform math, a more creative approach that came to be known as "fuzzy" math by detractors. Those who believe in the basics are celebrating, saying they hope the new report will force a 180-degree turn in math instruction.
Most educators agree on the need to improve math education in the United States. Not only has the country lagged behind Asian countries in the number of science and math graduates, more college students are needing remediation. According to state statistics, 30 percent of students in the state's public colleges and universities need math remediation. While most of those students are at community colleges, 17 percent are at the state's four-year institutions.
And most students never catch up. "A child who doesn't learn certain math content in elementary school has little chance of becoming a doctor, engineer or scientist," said W. Stephen Wilson, a Johns Hopkins University math professor.
Fennell said the question that must be asked is "What must every kid do and do well?" Often math teachers are not trained mathematicians, he said, and they enter a classroom each August faced with a laundry list of dozens of standards the state says they must teach.
Maryland, for instance, has between 50 and 60 objectives for each grade. The math council would narrow that to three. For instance, for fourth grade, the council says students should learn quick recall of multiplication and division facts, have an understanding of decimals and fractions and an understanding of area, including how to find the area of two-dimensional shapes.
Another criticism leveled against the Maryland standards is that teachers quickly cover the same concepts many years in a row using more complex equations and bigger numbers each year. Instead, Joy Donlin, coordinator of secondary mathematics in Anne Arundel County, said she would like students to learn one concept, such as fractions, well at one grade level.
"If we did it well, then we wouldn't need to do it again," she said. She said students wouldn't forget those skills because they continue to be used as the student goes up the ladder, through algebra and geometry.
The State Department of Education is now meeting with math supervisors in each jurisdiction around the state to get a consensus on whether they should follow the Focal Points. If changes are suggested, they would not take effect for at least 18 months, said Donna Watts, coordinator for the department's Office of Mathematics.
In the 1960s, students didn't have to understand why a formula worked. It was enough to memorize the facts and do the problems. Then in 1989, a report by the math council helped swing the country toward an approach that encouraged teachers to have students discover the theory behind the formulas. They called the new approach reform math.