Stumped by the X Factor

Factoring polynomials. Graphing inequalities. Solving for x.

The very language of algebra makes sweat pop out on the palms of the Mathis family of Woodland Hills.

“I can’t even begin to get near it,” said Lynette Mathis, talking of her 13-year-old son’s homework. Her husband’s math skills, though more robust, also fall short.

The Mathises are far from alone. Anxiety about algebra is on the rise, reflecting the higher stakes attached to this sorest of subjects.

California is in the early stages of a dramatic shift in the teaching of algebra--the branch of mathematics that uses abstract variables in equations to express mathematical relationships.

Long a course only for the college-bound, Algebra 1 is now a graduation requirement for all California public high school students.

Algebraic concepts also figure in more than a third of the questions on the state’s new high school graduation exam. The new academic standards indicate that the subject should be taught in the eighth grade--a year or two earlier than in the past. Some educators reckon that is at least a year too soon.

All this is multiplying the stress on parents, teachers and students. “Algebra anxiety always has been rampant but more so now,” said Carol Hatsell, who heads the math department at Glendale High School.

California’s race to ramp up algebra has schools scouring the landscape for trained teachers, and instructors puzzling over how best to get the subject across. Parents, meanwhile, are scrambling to ensure that their offspring aren’t left behind.

Objective: Graphing equations with two variables. Problem: Graph the equation y-x=1. (Solution: See graphic on Page 28.)

On a warm spring afternoon tailor-made for ollieing into a nose-slide on a skateboard, Lucas Mathis instead is huddled with his tutor in the bustling Barnes & Noble cafe at the Calabasas Commons. She is quickly but firmly walking him through a gaggle of graphing problems in preparation for an exam.

An honors student accustomed to A’s and Bs, Lucas in January brought home a C in Algebra 1. Turning to his parents was no use.

A helpful administrator at Hale Middle School in Woodland Hills, where Lucas attends eighth grade, provided a list of potential tutors. Enter Sanaz Adhami, 17, a junior at Calabasas High School. For $15 an hour, Adhami meets weekly with Lucas, tempering good-natured digs with heartening words.

“Be careful with your negatives, Lucas. You always make that mistake. . . . Where do you have a problem, Lucas? To me, you’re getting it.”

Getting math has never been a problem for Adhami, who came to California from Iran eight years ago and hopes to go to medical school. For her, algebra is easy as pi (to inject a little geometry).

“Math is just my thing,” she said.

Thanks to Adhami, Lucas is bringing his grade up to a B. But, he sighs, “I wish it were easier.”

Objective: Solving a linear equation. Problem: One rental car company charges $21.95 per day plus 41 cents a mile. Another charges a flat rate of $39.95 per day with unlimited mileage. For what driving distances should you pick the second company over the first? (Solution: See graphic on Page 28.)

Is it wise or necessary to require algebra? Who needs it, anyway?

For decades, algebra has been a gatekeeper course, determining which students go on to college and which are more likely to be doomed to low-paying, menial jobs.

But it’s more than that, said Judy Sowder, a professor emeritus in the math department at San Diego State University. “Algebra gives people a way to deal with problems in real life,” she said.

Algebra teaches people how to think logically and can even make them wiser consumers. A facility with formulas can help a customer decide between two cellular-phone plans or two competing video-membership deals.

Algebra also sets the foundation for higher-level math and science, vital skills in a world increasingly driven by technology. In recent international tests, U.S. middle schoolers have underperformed those of nations such as Canada, England, Australia, the Czech Republic, Japan and South Korea.

But are eighth-graders ready for the rigors of this ancient subject, the earliest record of which dates to a scroll of papyrus from 1650 BC?

“They’ll be ready for it in eighth if they have had good preparation in the seven grades before,” Sowder said. “Without that, it’s a lot to ask of them.”

Some youngsters are cognitively and emotionally ready for concepts like functions and powers and variables--and the hours of homework that usually accompany them. Others flinch at the sight of x’s and y’s in place of numbers. Something as basic as a+b=b+a, the “commutative property” of addition, can throw the uninitiated for a loop.

“If students don’t have the mathematical maturity, there are going to be many failures,” said Desiree McNeal, who teaches algebra at Dorsey High School in Los Angeles.

In the Los Angeles Unified School in Algebra 1 during the 1999-2000 school year failed the first semester; 26% flunked the second semester of the course. In Glendale Unified School District, which has students take algebra over three semesters, 23% of students failed Algebra 1 last fall.

Many students struggle to keep their brains above water. “If you don’t pay attention or don’t do your homework, you get lost,” said Debra Gallet, an eighth-grader from the magnet school for gifted students at Palms Middle School in Los Angeles. “Most of my friends agree that Algebra 1 is their hardest subject.”

Objective: Graphing a line using a slope-intercept equation. Problem: -2x=-4y+16. (Solution: See graphic on this page.)

The new statewide algebra mandate, which puts California into a vanguard of just 10 states requiring the subject for graduation, also collides with a nationwide shortage of math teachers. Gov. Gray Davis has set aside millions of dollars for teacher training. Much of it will be used to lift the skills--and confidence--of many middle-school instructors who did not sign on for algebra but suddenly find themselves required to teach the subject.

California will need to add about 1,300 qualified algebra teachers over the next three years to instruct 160,000 additional students enrolled in algebra in grades seven through 12, according to Davis.

In her Dorsey High classroom, McNeal, who has taught the subject for many years, uses props to help students comprehend slope and y-intercept. One recent morning, hulking football players joined forces with girls in ponytails to run toy cars down wooden ramps in a hallway outside their classroom. The object was to create an equation for the relationship between the length of the ramp that the car traveled and the distance the car rolled once off the ramp.

At Lakeside Middle School in Norwalk, all eighth-graders are required to take Algebra 1. The school uses College Preparatory Mathematics, a program created by math teachers that emphasizes conceptual understanding.

California’s education policymakers, who back strong math fundamentals and lots of problem practice, disdain the program. But at Lakeside, where most students are Latino and many come from low-income homes, teachers say it works. “We’re not failing 50% as is common [in some communities]. We have 70% at C or better,” said math teacher Craig Harvey.

“You open a regular Algebra 1 textbook, and it’s forbidding, with 50 to 60 problems on a page,” Harvey added. “We are trying to dispel the anxiety that’s there.”

Although failure rates remain formidable, the situation statewide is improving, many educators say. One reason is that California pupils at ever-younger ages are exposed to algebraic concepts. The state’s new math standards require that variables and other algebraic ideas be introduced in the earliest grades.

“Algebra is a strand that starts in kindergarten,” said Susan Hudson Hull, mathematics director at the Charles A. Dana Center, a research unit at the University of Texas. “By high school, students should have the foundation.”

The idea, math teachers say, is to present arithmetic in ways that make algebra seem familiar.

Consider the notion of equality as it is traditionally taught in simple arithmetic problems, as in 8+5=13.

“Students learn the answer comes next”--right after the equals sign, said Thomas P. Carpenter, who directs the National Center for Improving Student Learning and Achievement in Mathematics at the University of Wisconsin. As a result, when those students later in their studies see a problem like 8+4=?+5, huge proportions of them will put 8+4=12+5 because they have been trained in early grades to put “the answer” after the equals sign, Carpenter said.

To avoid that, teachers need to explain early on that the equals sign indicates a relationship, he said.

“One of the things we’ve found is that young kids don’t have any anxiety about algebra,” Carpenter said. “They love the notion they’re dealing with algebra.”

Objective: Understanding the Pythagorean theorem. Problem: For Katja’s party, her friends are going to hang a pinata halfway between two poles with a rope over the top of each pole. Both poles are 20 feet high, and they are 30 feet apart. The pinata must hang four feet above the ground. How much rope is needed to hang the pinata? (Solution: See graphic on this page.)

Another promising approach involves reaching kids by teaching their parents.

Maria Becerra, an immigrant from Mexico, successfully helped her two oldest children navigate middle and high school and get into college. Lately, though, she found herself stymied when it came to advising her two middle-schoolers on their math homework.

Late last year, at Becerra’s urging, Sergio Flores, the principal at Sparks Middle School in La Puente, launched Algebra for Parents.

Randy Beasley, the sixth-grade instructor who teaches the class in a fractured mix of English and Spanish, spent many weeks reviewing basic arithmetic and pre-algebra concepts with his adult pupils. But lately, the group has handled a bit of actual algebra.

“They’re tackling their own demons,” Beasley said.

Becerra is happy with the results. “When families work together,” she said, “kids do better.”

Whether all California students will be able to conquer algebra remains to be seen.

But most educators agree with Hatsell of Glendale High that it will be a grand thing for Golden State students if the state can pull it off.

“I went into this [algebra requirement] kicking and screaming,” she said. “But I realize it’s a positive thing. . . . When you reach, you are left standing in a better place.”

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Times researcher Maloy Moore contributed to this story.

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Algebra Sampler

Objective: Graphing equations with two variables.

Problem: Graph the equation y -- x = 1.

Solution: First isolate y by adding x to both sides. (Cardinal rule in algebra: What you do to one side, you must do to the other.) That yields y = x + 1. If x = 0, then y = 1. Those two numbers represent your first set of coordinates. If x = 2, then y = 3. With those, you have two points and may proceed to draw your line.

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Objective: Solving a linear equation.

Problem: One rental car company charges $21.95 per day plus 41 cents a mile. Another charges a flat rate of $39.95 per day with unlimited mileage. For what driving distances should you pick the second company over the first?

Solution: If you plan to travel m miles, the first rental company charge would be 21.95 + 0.41m (where m equals the number of miles). To know when the second company’s rental will cost less than the first company’s, solve 39.95 < 21.95 + 0.41m. Subtract 21.95 from both sides to obtain 18 < 0.41m. Then divide both sides by 0.41 to obtain 43.9 < m. Thus you would pick the second company if you expect to drive 44 miles or more.

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Objective: Graphing a line using a slope-intercept equation.

Problem: --2x = --4y + 16.

Solution: The equation y = mx + b is called the slope-intercept equation of a line. The slope is m and the y--intercept is b.

Slope indicates how steep a line is. It is the ratio of the “rise” of the line (the y axis) to the “run” of the line (the x axis) or the ratio of the change in y to the change in x.

To solve this problem, you must first isolate y on one side. First, subtract 16 from both sides. That would leave you with an equation that says --2x + (--16) = --4y. Then divide both sides by --4. That will yield y = 1/2x + 4. So 4 is the y-intercept, or the point on the y axis where the line will cross. And 1/2 is the slope of the line. To plot the next point on your graph, go up 1 point and over 2 points.

Since you need just two points to plot your line, you may now draw it.

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Objective: Understanding the Pythagorean theorem.

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Problem: For Katja’s party, her friends are going to hang a pinata halfway between two poles with a rope over the top of each pole. Both poles are 20 feet high, and they are 30 feet apart. The pinata must hang four feet above the ground. How much rope is needed to hang the pinata?

Solution: The key is visualizing the two right triangles (as above). Once you know the two legs of a right triangle, you can find the length of the hypotenuse.

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Pythagorean theorem: (leg 1)2 + (leg 2)2 = (hypotenuse)2

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Sources: Britannica.com; “Algebra 1,” published by Prentice Hall, and Joe Brumfield, math teacher and consultant; Zalman Usiskin, director of the University of Chicago School Mathematics Project; “Algebra, Vol. 2,” published by College Preparatory Mathematics, and Craig Harvey, teacher at Lakeside Middle School, Norwalk; Los Angeles Times researcher Maloy Moore