San Francisco Chronicle

Algebra - it's everywhere

Jill Tucker, Chronicle Staff Writer
Monday, August 25, 2008

Algebra.

The very word can twist the stomachs of otherwise well-adjusted adults, dredging up memories of nonsensical X's and Y's and a lifelong loathing of math.

For many, the math course was the educational equivalent of castor oil, forced down the throats of teenagers who questioned when they would ever encounter that train leaving Boston at 60 mph.

In July, the state Board of Education decided every eighth-grader must have a healthy dose of algebra - a decision critics attacked as failing to recognize the lack of qualified math teachers and the high failure rate for the middle school students already taking it.

Supporters, however, argued algebra improves critical thinking, is the gateway to college and puts all kids, regardless of income or ethnicity, on the path to a good career.

Lost in the debate was, well, algebra.

"I doubt if the politicians promoting this have any idea what they're promoting," said Keith Devlin, Stanford University researcher and mathematics professor, as well as the "Math Guy" on National Public Radio. "Few people know what algebra is."

Algebra, says Devlin, is a language, a very precise language written in symbols, and it's everywhere: in nearly all electronic devices, every statistic and each Internet search engine - and, indeed, in every train leaving Boston.

"You can store information using it. You can communicate information using it," Devlin said. "Google has made billions capitalizing on algebra."

Yet our schools don't always do a very good job teaching it, Devlin said. Instead of showing students the possibilities and beauty algebra offers, they ultimately steer frustrated and bored students away from math and the 21st century careers that use it - the opposite of the intended result.

'We're turning kids off'

"Most of us who become mathematicians do so not because of our education but in spite of it," Devlin said. "We're turning kids off a subject that is useful and incredibly interesting and beautiful if taught correctly."

Too often, algebra is taught as a set of rules and procedures - the equivalent of teaching a foreign language through vocabulary lists and repetitive conjugation of verbs, the students never understanding they could use the information to order a meal in Madrid or make a friend in China.

In short, the teacher matters. A lot. Just ask Alameda artist Alana Dill.

"I first took algebra in eighth grade from a bilious, creepy teacher who called all the girls 'hon' and all the boys 'son,' " said Dill, 46, in an e-mail. "He talked like Foghorn Leghorn. I learned nothing."

Devlin would like to see "mathematicians in residence" - in the tradition of artists in residence - at middle schools and high schools. They could visit schools, he suggested, and show students the cool side of math - like how an iPod uses algebra to play music.

"At any age, we will take the drudgery as long as we see a reason to do it," Devlin said.

Algebra, by the dictionary's definition, is essentially abstract arithmetic, letters and symbols representing relationships between groups, sets, matrices or fields. It's a way to find a piece to a puzzle using the pieces you already have in place.

It comes in very handy for engineers, financial analysts and sociologists, not to mention World of Warcraft video game players, some of whom use algebraic formulas to decide which weapon is more effective under certain circumstances - perhaps another hook to lure unsuspecting teens into seeing the useful side of algebra.

"It takes the arithmetic you've learned and lets you answer questions, not just 5 + 4 = what. It lets you (change the unknown) to 5 + what = 20," said Brett Wingeier, a biomedical engineer working on brain implants to treat epilepsy.

While that example is simple enough, algebra requires a mental leap from the solid ground of arithmetic into a shifting world of shapes and symbols.

Among the first folks to use algebraic ideas were the Babylonians, who created math puzzles - a 1600 B.C. sudoku, if you will.

Those ancient civilizations did algebra because it was fun.

Former UC Santa Cruz mathematician Paul Lockhart believes today's schools have killed the fun part.

"In fact, if I had to design a mechanism for the express purpose of destroying a child's natural curiosity and love of pattern-making, I couldn't possibly do as good a job as is currently being done," he wrote in a 2002 essay that traveled the digital world. "I simply wouldn't have the imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education."

In schools, math is something students are supposed to be afraid of, something that's supposed to be hard, Lockhart said in a telephone interview from the East Coast, where he now teaches at a private school in Brooklyn.

From art to artillery

Algebra is actually an art, a beautiful leap of the imagination that schools have turned into a field artillery manual, the mathematician said.

Lockhart favors self-discovery in math, letting students explore the hows and the whys themselves, unraveling problems like a fun puzzle rather than learning and solving equations for no apparent reason.

But his vision doesn't always translate well to the high-stakes realm of standardized testing, which quite literally requires students to solve for X on the eighth-grade exam. That can create a conundrum for time-strapped teachers who must teach the straightforward math skills needed for the state's multiple-choice test.

"I believe everybody can learn algebra," said San Francisco schools Superintendent Carlos Garcia. "I'm just not sure everyone can teach algebra so that the kids understand it and make it fun."

Garcia has some experience with this. While he personally didn't like algebra as a kid, he aggressively enrolled eighth-graders in algebra when he was the superintendent in Clark County, Nevada. He acknowledges that many students failed it, but they were failing basic math anyway.

A local decision

But he disagreed with California's mandate, saying it should be a local decision based on resources, including the number of qualified teachers.

The Santa Cruz-based Center for the Future of Teaching and Learning slapped a strongly worded warning label on the state's new algebra requirement, saying the state doesn't have nearly enough qualified teachers to do the job.

"Scant attention has been paid to this critical issue, and California's approach to math instruction still doesn't add up," according to the center's July report on the issue.

About a third of those teaching Algebra I in state middle schools do not have a credential in math, the center found.

That will get worse with the new requirement, said state Superintendent of Public Instruction Jack O'Connell.

"My fear is it's going to turn kids off and contribute to the dropout rate," warned O'Connell, who recently estimated that it will cost $3.1 billion to train and recruit teachers while boosting student proficiency in pre-algebra and arithmetic before the requirement goes into effect in 2011.

Many teachers say the middle-schoolers won't be ready, either. Understanding algebra requires not only a solid foundation of arithmetic (fractions, division and decimals, for example), but also the maturity to focus on abstract concepts.

"Our plea is, 'Algebra when ready,' " said Hank Kepner president of the National Council of Teachers of Mathematics. "We would not want to put an age level on it."

Recently retired high school algebra teacher David Goldman called the state board's decision "farcical."

"Some kids are not ready for algebra in the eighth grade," said Goldman, who taught at Redwood High School in Larkspur. "We've seen over the years if you try to accelerate that, it just doesn't work. ... At Redwood we saw a lot of kids that came in and then had to repeat it again in the ninth grade."

Teach it over two years

He supports possibly starting algebra in eighth grade, but slowing it down to a two-year course for some.

Last year, 42 percent of the 250,000 eighth-graders - about half the class - who took algebra scored as proficient or above on the state test.

Business leader Jim Lanich, who applauds the state board's decision, said schools should get students up to speed in the academic standards at each grade level.

Algebra is eighth-grade math, said Lanich, president of California Business for Education Excellence. It's the job of teachers and state schools to get them there - without spending $3.1 billion on top of the $50 billion the state already spends on its schools.

"The kids are leaving fourth grade now that will be required systemwide to take the eighth-grade Algebra 1 test," he said. "We have three years to get them to grade level."

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