The seventh-graders sat in noisy groups of three and four, tracing triangles on large pieces of paper and then giggling about the creations they called "math monsters." Teacher Sherry Gorrell encouraged their chatter as she prowled around the math class at Fairfax County's Lake Braddock Secondary School one recent day, urging them to consider the way the shapes fit together.
If they understood their "monsters," she promised them, they would begin to learn algebra. Her message seemed to hit its mark among the students, many of whom had feared they would have to endure page after page of textbook problems this year. In Gorrell's class, the algebra textbooks spend most of the time on a shelf, and abstract concepts give way to drawings, blocks and other props that help illustrate algebraic concepts.
"Oh my God, it's so much easier," said Brandy Caldwell, 13, looking up from her pencil drawing. "When you do this, you feel like you're a part of math." That's the aim of many educators across the nation, who are mounting a revolution against the way generations of students have learned algebra, a subject notoriously bewildering to many children but now considered a critical gateway to academic success.
"Algebra is the gatekeeper for higher-level" , said Tom Nuttall, the mathematics for Fairfax schools. 'Without it, they 't even study it, let alone understand it." using hands-on exercises, educators hope to answer the age-old question about algebra: 's the point? They also want to increase interest in algebra among girls, minorities and others who traditionally have been directed to, less types of math. It is unclear whether the approach will work as hoped, but many educators seem convinced it will eliminate much of the baffling drudgery-of algebra.
"If children are given these kinds of experience they view themselves as mathematically capable," Gorrell said during a break from her classroom roving. "All of the kids are exposed to all of ideas. It's not: 'These powerful ideas are reserved for the gifted."
Despite criticism from some parents and educators who say the approach is untested and may students from hard work, several Washington area school systems-including those in and Prince George's counties-are similar methods. The school systems generally follow guidelines by the National Council of Teachers of Mathematics, the group most responsible for encourage the change.
'It sounds so easy, and yet it is a wholesale change in the way we approach mathematics," said Brian Porter, a spokesman for Montgomery schools. "Children take and succeed in a mathematics course that 10 or 20 years ago was seen as an achievement for graduating seniors."
Fairfax has become a leader in using the method and this year for the first time is requiring every seventh-grader to take a course known as pre-algebra, which combines elements of algebra, geometry and other skills. Officials said they hope that eventually all students will take a full algebra course by the time they reach ninth grade.
Until Fairfax began using hands-on math, three of four seventh-grade students took less challenging courses, Nuttall said. Advanced students worked in a traditional format, using textbooks, repetition and rote memorization.
"It was easy for kids to get lost, to not take the most challenging courses. There was a way out,' Nuttall said. "Algebra has been a disaster in this county.... Low numbers of kids get into it, and lower numbers of kids are successful. Critics agree that more children will take classes like Gorrell's, but they worry that the Students will not be prepared to do the hard, abstract calculations required in upper-level math. One of the most ardent opponents is textbook publisher John Saxon, who is leading an effort against hands-on math across the nation, saying he believes it may be an ineffective fad that wastes students' time. 'it sounds like more pie in the sky,' said Saxon, whose own textbooks eschew hands-on work and feature hundreds of pages of problems. 'I want to, know where the proof is."
Some parents have similar questions and worry that their children will be used to test a new program. Evan McNeill, whose daughter, Kristen, is, in Gorrell's class, said he -worries that students might not be able to make the leap from using blocks and drawings to algebra problems. "Do we have to wait for a graduating class to know if we are wasting our time?' McNeill asked.' Mitchell I. Mutnick complained that he could not help his 12-year-old son, Stephen, with the' boy's homework. Lake Braddock, he said, did not prepare parents to work with the small blue and yellow blocks students must use to represent variables and numbers in solving problems. Mutnick and others said they also worry that by requiring all students to take the same class, brighter children will be held back. "If that's the case, are you not hurting the kid?" he asked.
But this past week in Gorrell's class, students expressed resounding support for the new method. After silently beginning their classes with a series of traditional word problems, they beamed when they had a chance to draw and work with the blocks they use for homework. Suzi Gallagher, 12, showed how to mix and match the french fry-sized blue sticks as "X" and the small yellow blocks as numbers as she illustrated the meaning of equations such as (X+5) and (5X). When X equaled 2, she replaced X with two blocks. Her answers were 7 and 10. "It just makes it a lot easier to see what you're doing,' Suzi said.