It's math time at the Sherman Oaks Dixie Canyon Avenue Elementary School. But instead of pulling out paper and pencils, the mixed class of kindergartners and first-graders snuggles up on the reading rug as teacher Marlene McLemore props up a large book called "Tom Fox and the Apple Pie."
As she narrates Tom's pursuit of the pie, Ms. McLemore throws out an occasional question. "Tom has 13 brothers and sisters. Why would he need 16 pieces of pie?" An attentive kindergartner pipes up, "because he has a mom and dad!"
Afterward, the children break into small groups to construct and share an apple pie made up of small tiles.
Welcome to what's been dubbed California's "new-new" math curriculum. Literature-based, hands on, with emphasis on "real world" applications, the curriculum is a reflection of the latest thinking in math education. And it's as controversial today as was the new math of the 1960s and '70s. In California, as well as many other states where math curricula are being revised, concerned parents are facing off with state boards of education over the new textbooks.
Spurred by sinking test scores and new teaching standards issued by the National Council of Teachers of Mathematics (NCTM) in 1989, schools around the country have been updating the way they teach math. The Golden State issued a new math "framework" in 1992, which led to new textbooks in 1994. The refurbished curriculum, designed to give students greater skills in conceptual thinking and problem solving, began appearing in classrooms last September.
But its arrival has sparked a battle over the proper balance between teaching strong critical-thinking skills and adequate preparation in basic computation. And the outcome, given California's clout in the textbook market, has national implications for how the next generation will learn its numbers.
"Every child can and should learn math," says Jack Price of the NCTM, acknowledging the importance of computational skills. But, he emphasizes, such ability must go hand-in-hand with higher-level math skills, like thinking and reasoning, because "these kids are going to live in a different world than their parents."
Bob Hamada, mathematics coordinator for the Los Angeles Unified School District also touts the virtues of the new approach. "[It] is not menu-driven, with the teachers telling students what to do," he explains. "It has lots of student thinking and investigation, lots of participation."
But many districts, gun-shy after the bitter battles over whole-language versus phonics that erupted nearly a decade ago when the state revised its language curriculum, have been slow to adopt the curriculum. Relatively few of California's nearly 1,000 school districts have implemented it entirely. Those that have often have found their efforts rewarded with controversy.
In San Diego, for example, one of the few cities that has adopted the math texts district-wide, a vocal and well-organized group of parents is actively fighting the new method.
Michael McKeown, a San Diego parent and scientist at the world-renowned Salk Institute in La Jolla, says the curriculum has serious flaws. "It's critically weak in basic skills training," he says, adding that the textbooks cover less material in less depth than either traditional or other alternative math approaches.
The consequences of such gaps can be serious. "Students who are not well-prepared in the basics can't succeed in math later on," Mr. McKeown asserts.
McKeown is co-founder of "Mathematically Correct," a loose coalition of some 200 parents concerned about the new-new math finding its way into schools nationwide. The group has a Web page on the Internet and has communicated with concerned parents as far away as England and Australia. "Many of us are scientists and engineers," McKeown points out. "We know what kind of math you need in the real world. This isn't it."
But Vance Mills, math supervisor with the San Diego Unified School District says the new approach is exactly what students need. "When I taught math, it was all isolated skills. Students didn't have any idea how to apply them."
Mr. Mills thinks arguments against the new books are more emotional than logical, adding in frustration that "parents want a date that this will all work out, but we won't know until we use it."
This experimental attitude is precisely what concerns McKeown's group. "Our children should not be guinea pigs," he says.
At Dixie Canyon elementary, principal Melanie Deutsch has not backed away from the new texts. But she sees flaws as well, saying they don't go far enough, thus putting even more strain on her overworked teachers.
"Every one of the recommended texts we looked at was lacking in something," notes Ms. Deutsch, thus forcing individual teachers to create additional materials to fill in the gaps. "Classrooms are full of xeroxes and handouts created and paid for by our teachers," she adds.
But NCTM's Price says teachers always have filled in the gaps left in curriculum texts with their own materials. "It's much easier for teachers to add a page or two of basic skills drills than it is to create a page of higher math reasoning," he observes.
Price is concerned about the polarization of parents and educators, saying that the new guidelines were meant to enhance, not replace, the teaching of basic skills. "We have zealots on both sides of this issue," he laments. "The answer to a good math program is somewhere in the middle."
But, says University of New Hampshire mathematics professor Joan Ferrini-Munday, "controversy is important."
With the nation's largest textbook market, she says, California can play a crucial role in helping the country shape the kind of the math education that the next generation of children is going to need.
"Everyone is concerned about education," she points out. A national debate, spurred by California's battles, will help everyone figure out the right balance between basic and higher math skills, she says.
Going Fishing for Frogs and Bugs in Math Class
With the emphasis on thinking and creating rather than doing drills, children are as likely to learn math armed with scissors and crayons as with pencils and erasers. The following are two games designed for children in kindergarten through second grade.
The first is called "The Impossible Game." Children are given blank spinner patterns, paper clips, and pencils, as well as blue, green, red, and yellow crayons. Each child also receives one yellow, two red, three blue, and four green pattern blocks. They all receive a game board.
First, the teacher discusses the concept of impossible versus possible. Could something happen, even though it is not certain? Or is it out of the question?
Next, the players start spinning for the blocks. The child spins for a color and covers that color block on the board with his blocks. If he spins a color for which he has no block, he loses a turn. Players who use all their blocks, win.
After a while, the teacher asks if anyone is close to winning. Then they discuss why, and the children are invited to offer suggestions for changing the game.
The real task of the game only starts after this initial play. The goal is to change the game so it is possible for a player to win.
At this point, the children are challenged to design both an impossible and a possible game of their own using the blank spinner and the crayons.
Children tackle the concept of prediction with a game called "Going Fishing."
Players receive crayons, and bags with colored tiles: one blue, one red, and 10 yellow. The teacher produces a big book showing frogs diving for bugs. Then, mimicking the frogs, the children "fish" the tiles (bugs) out of the bag, taking 10 turns and recording what they got on each turn. (A multicultural note in the text teaches kids that that frog's legs are a delicacy in some countries.)
The real task starts at this point. It is to predict what color tile you will pull out on your next turn and discuss which colors you are more or less likely to pull out.