The Rote Stuff
|A parent-created regimen of daily math testing reopens the age-old ‘drill and kill’ debate.|
It's late on a rainy Friday in November, and Michelle Mosher's 6th
graders are getting restless. The 33-year-old math teacher at Buena
Vista Middle School in Salinas, California, tries reviewing a homework
problem on the blackboard, but most of the kids are having none of it.
They know what's coming, and they're anxious.
On Mosher's left, a pair of girls double-check their pencil points while intently whispering to each other. Meanwhile, one kid up front tucks his books into a backpack as several boys in the back squirm in their chairs. Mosher peeks at the clock and says, "Get out your MATH*Ability worksheets." Quickly, her students square themselves, face forward, and silently await her next command.
At their teacher's signal, each student will have two minutes and 50 seconds to complete a math test individually matched to his or her skill level. At this point in the school year, most of the 21 kids are focusing on addition and subtraction. A typical test consists of 90 single-digit arithmetic problems, and once it's been mastered, the student will move on to tests for multiplication, division, and fractions.
Since Monday, Mosher's students have been taking practice tests each day of the week. They're about to take one more before wrestling with a "real" exam. The tests constitute the visible half of MATH*Ability, a supplemental curriculum designed to strengthen the computation skills of elementary and middle school students. The other half is conducted behind the scenes, by a computer tucked into a corner of the classroom. With the help of a software program that reads handwriting, the computer will grade the tests, record the results, and then determine the skill level for each student's next exam.
But for now, all eyes are on Mosher. She watches the clock above the blackboard, waiting for the second hand to come around so that it reads 3:17. Normally the students take their tests at the beginning of the period; but today, Mosher has moved the practice test and the exam to the end of the day, just minutes after the final bell. They're so short in duration, her students will still have time to catch their buses home.
Pencils in hand, the students are poised like runners on a track, waiting for the starter's gun to sound. Mosher holds back, watches the clock hands move into place, and..."Go!"
The kids are off, furiously scribbling.
Michael Greene enjoys these kinds of scenes, which he's witnessed hundreds of times. He is not, however, a principal, teacher, or district official. He's a parent who's responsible for creating and implementing MATH*Ability at six elementary and middle schools in Salinas and nearby Monterey. And, at 52, he's about to take the program on the road.
Because of an increase in supplemental services induced by the No Child Left Behind Act, MATH*Ability—begun several years ago, on weekends at Greene's house—is now one of 30 new programs offered to struggling students in both the Los Angeles and Sacramento City unified school districts. According to NCLB, low-performing students are eligible to receive free tutoring paid for by Title I money and provided either by the district or an outside company. To qualify as a supplemental provider, Greene had to win the state board of education's approval, which he did earlier this fall.
So this is clutch time for Greene. Until now, he's been able to handle the demands of roughly 800 elementary and middle school students, thanks in part to parent volunteers who believe in the MATH*Ability program. But taking on a potential influx of hundreds more students is a daunting prospect. And the program has yet to prove itself; while it's won praise from participating teachers, students, and parents, critics see it as yet another "drill and kill" exercise aimed more at developing test-taking skills than at engendering lifelong mathematical knowledge.
Greene, however, is unfazed. He's accustomed to taking risks. In 1987, he started a software company, eventually turning it over to a partner after several successful years of creating programs for Macintosh computers. Seeing the blue-eyed, gray-haired Greene in his leather bomber jacket, it's easy to imagine him as a high-tech whiz behind the wheel of a convertible, cruising the Pacific Coast Highway, the ocean on one side, the rolling hills of Northern California on the other. But Greene drives a silver Honda sedan. As daring as he seems, he's ultimately a pragmatist: With MATH*Ability, he doesn't want to reinvent the wheel; he simply wants to make it more efficient.
On the test sheets, equations are lined up in neat rows, and each one—"9+7," for example—sits atop a small answer box. The idea behind Greene's program is simple: Rather than tell students how to take the tests, a teacher simply adds the brief exams to the existing curriculum, setting aside time to correct wrong answers. The point is not to introduce complicated math problems, but to force kids to learn basic computations by rote, so that, after participating in MATH*Ability as 4th, 5th, and 6th graders, they can begin to calculate equations they'll encounter in the 7th, 8th, and 9th grades.
This idea is not revolutionary, but the trend in many math classrooms these days is to limit the time spent on computation. And, like the phonics-vs.-wholelanguage debate among reading teachers, there's a computation-vs.-conceptual skills debate in mathdepartments. Greene is squarely in the computation camp: Master those skills, and you've built yourself a foundation for dealing with conceptual subjects, such as algebra and calculus.
Because of an increase in supplemental services induced by the No Child Left Behind Act, MATH*Ability is now one of 30 new programs offered to struggling students.
On the other side is Zalman Usiskin, director of the School Mathematics Project at the University of Chicago. Usiskin often derides programs like MATH*Ability for ignoring conceptual elements. "Adults' lack of ability to deal with arithmetic, even when computation was virtually the entire arithmetic curriculum, indicates that rote paper-and-pencil computational practice and facility does not enhance understanding of 'number,'" he writes in Mathematics and Democracy: The Case for Quantitative Literacy, a book to which he and several other professors contributed.
In an interview, he puts it more plainly. "I don't think anybody is against working on skills or getting faster, to an extent," he says, "but not if it's at the expense of realizing '7x8' is related to '7x7,' and not a disjointed fact."
But here's the trouble, according to Mosher and Janet Masuda, a fellow math teacher at Buena Vista: Several years ago, they were teaching 6th and 7th graders who couldn't compute the answer to "7x8," let alone understand its relationship to "7x7." "If they can't do '7x8,'" Mosher says, "how am I going to teach them fractions?"
Prior to using MATH*Ability, Mosher—who wears fashionable outfits and her brown hair in a stylish bob—tried to improve students' computation skills by using similar worksheets in her classroom. But the process was too time-consuming. It's a problem Greene understands firsthand. He began MATH*Ability in the mid-1990s as a weekend tutoring program in his Salinas home. Even though he had the help of fellow parents, by Sunday night, he would have roughly 100 tests to grade. So he put his computer programming skills to work and designed software that can read handwritten numbers and, thus, evaluate each test sheet automatically.
That software allows Mosher to grade the tests between classes or even while her students are taking exams. First, she stacks the sheets on a scanner equipped with a photocopierlike paper feed. Each sheet then passes through the scanner and appears on the computer screen. The computer grades the test, and if there's a question about a written answer—say, a "4" looks like a "9"—a window pops up, asking Mosher for verification. She clicks the mouse once, and the computer moves on. After each test is graded and the student's progress is recorded, the computer creates new exams and sends them to the printer, which, in Mosher's classroom, sits next to the scanner. The whole process takes less than 10 minutes.
The software's speed belies the time it took Greene to develop MATH*Ability. In fact, he's been focused on children's math skills for nearly a decade. The father of two college-age sons, Evan and Jason, he likes to tell the story about his inspiration for the program. "In 1995, my youngest son, Evan, and I were out in the garage working on a project," he recalls. "He had wanted a go-cart. So I showed him a yard-long piece of wood that needed to be 23 inches long. I asked him how many inches we had to saw off to get the desired length. He couldn't tell me. It took me a few minutes to figure out he didn't know how to subtract two-digit numbers—this, despite being told he was at the top of his 6th grade math class."
The incident so troubled Greene that he enrolled Evan in a math enrichment program known as Kumon. More than 40 years ago, Toru Kumon, then a high school math teacher in Japan, developed a repetitive-testing method to help his own son, who was struggling with 2nd grade arithmetic. Kumon is now practiced at "centers" across the United States, and in Northern California, advertisements for the program take up space on billboards and bus shelters. For a year, Greene shelled out $80 a month for his son to practice computation skills twice a week.
Greene didn't just feel that the fee was excessive; he also noticed that Kumon instructors were spending 45 minutes to an hour teaching specifically to each test, which ended up being four to five pages of equations. There had to be a better— meaning, from Greene's point of view, more efficient—way. So he began talking to other parents, including Pam Durkee, a science teacher at a private high school in Monterey, whose son, Andrew, is the same age as Evan. They agreed that quick, short tests could supplement classroom work without disrupting it. Like Greene, Durkee felt that most kids lacked basic computation skills but that those skills need to be put into context.
"There's got to be a balance," she explains. "Having rote material without any conceptual ability isn't going to do the child any good down the road."
Durkee, who's 47, agreed to help Greene assemble the first batch of worksheets for the program that would eventually become MATH*Ability. It began in the kitchen and living room of Greene's house, where, once a week, groups of kids (each paying $50 a month) would arrive to take several three-minute tests. Those tests would be graded by Greene and Durkee, and sessions dedicated to correcting wrong answers would follow. The idea was to provide students with a venue for practicing the computation that had been all but abandoned at their schools.
During those early days, Greene was confident that at least some schools in the area—a swath of farming towns along California's Central Coast— would support his program. They did not, however, have the resources to put each student in front of a computer for the exams. So Greene opted for the paper-and-pencilapproach, knowing that, eventually, he'd develop the appropriate grading software. And, indeed, by early 1998, he and Durkee had so successfully integrated the tests and software that they felt ready to promote the program beyond Greene's living room. So they contacted math teachers in Monterey and Salinas, asking them to give MATH*Ability a try.
At Buena Vista Middle School in Salinas, the timing was right. "We had been looking for a program that dealt with basic skills, and [MATH*Ability] seemed to fit," Mosher recalls. Mickey Tachibana, a 3rd and 4th grade teacher at Monte Vista Elementary in Monterey, also signed on. "What it does is help with their speed and their learning of the basic facts," she says today, after four years of using MATH*Ability. "It also helps them on all the other tests they have to do."
MATH*Ability students agree. Jake Rianda, a blond 8th grader at Buena Vista, says that last year, the program helped him with timed tests in general, "even in other subjects."
Back in Mosher's classroom, the students have finished the practice tests and are now ready for the exam. The material is essentially the same—single-digit addition or subtraction problems—but there's tension in the room. Samantha Stauffer's blond ponytail hangs over her shoulder and touches the desk as she readies herself for Mosher's signal. She grips her pencil tightly, turning the knuckles of her hand white.
|According to NCLB, low-performing students are eligible to receive free tutoring paid for by Title I money and provided either by the district or an outside company.|
Samantha is being tested on subtraction skills, even though this is her second year with MATH*Ability. Like others in the program, she began the school year at the bottom of the scale, to see if the rote skills she'd learned previously were still sharp after the summer break. Evidently, in Samantha's case, they weren't. "Last year, I started on addition and got to high division," she recalls.
At the higher levels, the tests begin to look a little different. A division worksheet, for instance, asks students to determine whether a given number on the left side of the page—say, "48"—is evenly divisible by each smaller number— "2," "9," "15"—on the right side. Students have to mark a box next to each number with a "Y" or "N."
Samantha, like Jake Rianda, says MATH*Ability has helped her become a better test-taker. And to her delight, it's lightened her load outside of school. "I think it helps with homework," she explains. "I don't have to spend an hour on it."
For Durkee, Samantha's and Jake's comments are indications that MATH*Ability has served to boost not only their skills but their confidence as well—an important factor as they move on to more difficult math curricula. "What I have seen in middle school and in high school, teaching first-year algebra, is that kids who struggle with basic skills really have a significant handicap in their confidence," she says. "What ends up happening is that as you introduce simple numbers—if they're not seeing those rote facts instantly—it can take twice as long to complete a test and do homework. They're spending 40 minutes doing a 20- minuteassignment."
Mosher eyes the clock again and gives the signal. The kids begin.
Building better test-takers isn't the primary reason Greene created the program. He realizes, though, that MATH*Ability's success, whether in Monterey or anywhere else, is ultimately going to be measured by standardized test scores.
At Buena Vista, 6th graders have been using MATH*Ability for three years. During that time, the number of students scoring at or above the 50th percentile on the state's Stanford 9 math test has gone from 60 percent in 1999-2000 to 87 percent in 2001-02. Still, Eric Tarallo, the school's principal, is reluctant to tie the improved scores to Greene's program, in part because this is his first year as head administrator. A former history teacher at the school, he was not in charge when Buena Vista decided to spring for the $5,000 it cost to install the software and buy the necessary computer equipment. Tarallo acknowledges, however, that his math teachers really like the program. "The concept is great," he says.
Professor Usiskin, at the University of Chicago, is not as enthusiastic. "Of course you need to have basic skills," he admits, "but math is not memorization. It's thinking....A robot or a calculator can do the arithmetic, but it can't tell you what operation to use."
Usiskin tells a story about how his young daughter, as a 2nd grader, aced the timed math tests repeatedly given at her school in Chicago, completing them faster each time. "They think she's getting better, but she's not getting better; she simply knows the test," he explains. "My wife and I concluded that what she had learned was that this is math—something you should do as fast as you can do it without thinking. This is what kills kids."
What is Greene's response to critics who argue that MATH*Ability is simply a "drill and kill" program? "They don't recognize that it might just be 'drill for skill,'" he quips.
Barbara Dangerfield, who's president of the Monte Vista PTA, concurs. She became a MATH*Ability supporter when her oldest son, Kyle, participated in the pilot program at his school. A 3rd grader at the time, he struggled with math word problems because he has a mild form of attention deficit disorder, she says. But MATH*Ability so improved his computation skills that he was able to focus much more on the conceptual parts of the problems—without distraction.
"One thing a psychologist mentioned after giving Kyle a math test," Dangerfield adds, "was that he'd never seen a kid with ADD whip through a page of math like that."
More than anyone else, parents have helped MATH*Ability expand. At Buena Vista, the school pays for the program so teachers can make use of it in their classrooms. But at other places, it's parent-funded. That means the tests are squeezed in either before or after school or during recess and administered by supportive math teachers, some of whom are retired and volunteering their time. They work in concert with parents, who then deliver the tests to Greene. He handles the computerized grading from his office and sends the test results as well as the next set of exams to the schools.
"I'm at Monte Vista every Friday morning at 7:45, helping the kids get through the test," Dangerfield says. "Then I drop off the tests with Michael."
Greene charges $7 a month per student. At Monte Vista, the PTA picks up a portion of that tab, so parents end up paying $1 a week for the service, which makes it affordable for everyone, according to Dangerfield.
It's perhaps fitting that a program created by a once- frustrated parent would end up being used by hundreds of frustrated parents throughout California.
It's perhaps fitting that a program created by a once- frustrated parent would end up being used by hundreds of frustrated parents throughout California. At this point, however, Greene isn't sure how many parents—or possibly schools—will sign up for the program, as both the Los Angeles and Sacramento districts have been slow to implement NCLB-prompted tutoring services.
While Greene had noble intentions when he created MATH*Ability, he does not operate it as a charity. So far, between the school fees and the $50 a month he and Durkee charge parents who bring their kids to Greene's house in Salinas or the small office he sublets in downtown Monterey, he's been able to "pay the bills." By expanding, he hopes to begin turning a profit.
And regardless of how well MATH*Ability does in other districts, Greene is already sizing up his next challenge: "Algebra," he says with a smile. The risk-taker in him thinks he can create algebra exams for middle and high school students. But developing the appropriate grading software isn't easy. "Add to the stew that we've expanded the character set from 10 digits to several variables, some Greek notation, and the usual operators," he says, "and it all means it's going to be a while before we'll have something comparable to what we're currently doing with whole numbers."
"One minute!" Mosher calls out after the first 60 seconds.
Samantha Stauffer is a picture of concentration: Her nose nearly touches the desk as she works her way down the test sheet, peeking occasionally at her fingers to do a little quick computing.
"Two minutes!" Mosher shouts.
Suddenly, a crisis: Samantha's pencil breaks. She tosses it aside like a shattered sword in a duel and digs furiously into her bag for a replacement. She's back at work but has lost precious seconds. As time ticks away, she scrambles to finish.
"OK. Time's up. Pass them in," Mosher says.
Samantha doesn't make it. "Uuuhhh!" she sighs and slides back her chair. "My pencil broke!" she yells to nobody in particular. Like most of her fellow students, she takes these tests seriously. Mosher posts results at the front at the class, and—possibly for that reason—there's plenty of competitive spirit among the kids. But not finishing an exam won't ruin the rest of Samantha's day. Minutes later, she's happily chatting with the girl next to her and smiling as she exits the classroom.
Mosher can now grade the exams. Sitting in front of the computer, she stacks them in the paper feed, then watches them reappear, one at a time, on the screen. The computer asks for clarification on only three answers out of 21 tests.
After they're all graded, the computer displays the results: 15 of Mosher's 21 students aced the exam today and will move to the next level. "That's not too bad," she says.
Vol. 14, Issue 6, Pages 38-42
- MATH*Ability addresses the question, "Does it really work?" See also its data on standardized test results.
- The School Mathematics Project at the University of Chicago—whose principles "emphasize reading, problem-solving, [and everyday applications ..."—posts curricular resources for the elementary and secondary levels.
- "Adding It Up: Helping Children Learn Mathematics," a 2001 book by the Center for Education, "addresses the concerns expressed by many Americans ... that too few students in our elementary and middle schools are successfully acquiring the mathematical knowledge, the skill, and the confidence they need to use the mathematics they have learned." See also related Web resources.
- The National Council of Teachers of Mathematics has developed math standards that attempt to promote "broader and more meaningful mathematics curriculum that meets the needs of a far greater proportion of the student population than has been true in the past."
- The U.S. Department of Education has launched a "Math and Science Initiative," intended in part to "develop an academic research base to improve our knowledge of what boosts student learning in mathematics and science." Read papers and presentations from a "summit" focusing on the initiative.