Math Changes Reflect Broader Schools Debate
Such is the raging debate over math in America that when California dares to ask students to memorize multiplication tables and to “know” rather than simply “identify” a formula, it is lauded--or condemned--as a sharp swing back to the basics.
Those were two of the 78 changes, many just a couple of words, the Board of Education made this week to a set of standards for math lessons in kindergarten through seventh grade.
To those new to the infighting within educational bureaucracies, such editing may seem like no big deal, merely an effort to make the goal of the lessons more precise. After all, this is math.
But the shouting must be seen as part of a broader debate over educational philosophy these days. It lurks behind fights over how to teach science (how much like play should it be?), reading (through stories or phonics?) or even spelling (will correcting mistakes hurt youngsters’ creativity?).
At issue are two views of children and how they learn best.
Are they like flowers that will bloom naturally if exposed to the sunlight of experiences--in the form of compelling literature or fun math games? Or, are they more like puzzles that, to become whole, need to be assembled piece by piece--through teacher-directed lessons in essential skills such as learning the sounds of letters or those multiplication tables?
To be sure, common sense--and research--suggest there should be a blend. No one really believes that phonics alone is enough. Students also need to read good stories and do lots of writing.
But when is it not enough that they simply show enthusiasm for, say, geometric shapes? When do we stop calling it success merely because they worked well with others grappling with the Pythagorean theorem?
Monday’s 10-0 board vote was a clear victory for the crowd that believes it’s important, at some point, to get the right answer.
The standards, though, go far beyond simply asking elementary school students to spit out 9 x 6 = 54 without a calculator. Step by step, they take 12-year-olds to a level of math sophistication that few Americans can muster, having them work on spreadsheets, calculate the volume of a cylinder and analyze statistics.
To Mike McKeown, that’s long overdue in a state that embraced math lessons such as “Fantasy Lunch.” Three years ago, McKeown, a molecular biologist from San Diego, went to his son’s school to complain that a math class was leaving out essentials. He said he was told that the old-time skills were outdated.
“I was thinking, ‘Some of this math I still use in solving problems in my work and you’re saying it isn’t important?’ ” recalled McKeown, a researcher at the renowned Salk Institute.
That experience spurred him to reach out to other parents. Communicating via the Internet, they formed an online group called Mathematically Correct and became a national force.
But McKeown celebrated only briefly this week. For a decree from Sacramento, he knew, will not change overnight how math is taught in the classrooms of California’s 1,000 public school districts.
For starters, the standards are nonbinding. And there is much momentum--along with money and legions of true believers--headed in another direction.
The Los Angeles Unified School District, the state’s largest, is midway through a five-year overhaul of math and science education that stresses hands-on activities while downplaying memorization. Similar programs, funded by the National Science Foundation, are underway nationally.
Under the program used in half the L.A. district’s schools, third-graders, for example, will learn to multiply by drawing fruit in packing crates so they can visualize that two layers of 12 yields 24--a method most educators agree can complement memorization, but not replace it.
As part of a $1.4-million project in four school districts in eastern Los Angeles County, 80,000 students are eventually to be taught math customized for minority and low-income students--often by taking out the numbers.
Across the state, more than 80% of the school districts use a curriculum in which elementary students keep “math journals” to record their feelings.
And next March, 400 Bay Area teachers are to attend a symposium where they will learn to “empower” their fourth-graders mathematically at sessions with such titles as “Let the Games Begin.”
Also on the agenda is how to teach math through making popcorn, building castles and sewing quilts. All are devices that can enrich understanding of sophisticated concepts in the classrooms of accomplished teachers. But in the hands of the untrained--a category that includes too many California math teachers--they can be meaningless time-fillers that invite parody.
Paul Giganti, who heads the Bay Area Math Project, the conference sponsor, has felt the political winds that led to the board’s vote. So there is more attention to “basics” in his programs for teachers.
But he sees no need to reverse his overall course.
“The state board members may set policy, but they probably won’t set up a design for implementing that policy,” Giganti said. “That will be left to other people, the teachers down the hall.”
Indeed, the math standards do not specify one right way to teach. They will, however, generate a new curriculum guide and tests for grades four, five, eight and 10. It will be apparent then if students taught math through games have learned what the board wanted.
The two camps are labeled traditionalists and reformers, though neither term is wholly accurate.
The reformers, such as Giganti, gained ascendancy a decade ago by arguing that the age-old sequence of math lessons had been unfair to all but a gifted elite.
Most of us, it was said, never really got the abstractions of math--we needed to visualize concepts. And was there really one right way to do a problem, the one imposed by the teacher? Shouldn’t kids be encouraged to come up with their own ways--perhaps drawing pictures to understand fractions--just as they might someday be encouraged, as workers in a rapidly changing age, to think on their feet?
What’s more, the reformers said, some students simply can’t learn long division or fractions. Should that automatically brand them as failures or keep them from going on in math? Perhaps they have a gift for geometry.
“Math is broad, and it’s quite possible for somebody to be atrocious at basic skills, absolutely horrible, but be an incredible problem-solver or have a special spatial sense,” Giganti said.
This was, then, a philosophy of self-actualization, multiculturalism and--in contrast to what was seen as the old elitism--democracy.
It also was an easy target for traditionalists. And parents.
Education professors could fill journals justifying handing calculators to 9-year-olds, but the court of public opinion found it hard to believe that was a wise substitute for memorizing 6 x 5 = 30.
It didn’t help that while California’s educators led the reform crusade, its students remained near the bottom, its fourth-graders ranking 41st in a 1996 comparison of 43 states.
So over the past three years, state officials up to Gov. Pete Wilson have ordered up smaller classes, more tests and the first-ever statewide standards.
On Monday, board members insisted that this was not a blind return to the past. While saying students should “make precise calculations,” they also wanted the kids to “understand” mathematical concepts such as constants--for example pi, the key to calculating the circumference of a circle--and use them in the real world.
Still, given the years of rancor, it was not surprising that the reformers were dubious. Their supremacy was being threatened.
What was surprising was their rhetoric. Suddenly, they were the defenders of academic “rigor.” It was the traditionalist board, they charged, that wanted to go easy on kids. Speaker after speaker said the standards “dumbed down” math: Children would do so much number-crunching there wouldn’t be time for anything else.
Joining the attack, state Supt. of Public Instruction Delaine Eastin went so far as to charge that the return to basics would especially shortchange California’s poorer communities, whose students would never escape low-level math--as if those students could do much worse than they are doing now.
To traditionalists like McKeown, all the noise was a transparent attempt to hijack the very arguments long used against the reformers’ own methods. The San Diego activist said it was ludicrous to suggest that his group--scientists, engineers and statisticians--was out to dumb down anything.
UC Berkeley math professor Hung-Hsi Wu also was appalled.
Wu is respected by both sides in the math wars. He sees nothing wrong with fun and games. That’s what motivates kids. But once motivated, he says, youngsters have to understand that, like anything else, learning math takes hard work and practice. Denying that, he said, is “to cheat children.”
As he sees it, the board’s point was obvious: There is no substitute for arithmetic as a foundation for more challenging math.
Underscoring how the debate goes beyond math, he turned to literature to explain.
“Suppose you are the greatest writer in the English language and you have the most wonderful ideas and great emotion,” he said, “but you can’t spell and can’t say things grammatically. We’re saying, ‘Get your act together. Learn to spell and get your grammar straight.’ ”
*
Times staff writer Duke Helfand contributed to this story.
