By Ian Shapira
Washington Post Staff Writer
Tuesday, February 19, 2008
Greg Barlow, an Air Force officer in the defense secretary's office at the Pentagon, was helping his 8-year-old son, Christian, one recent night with a vexing problem: What is 674 plus 249?
The Prince William County third-grader did not stack the numbers and carry digits from one column to the next, the way generations have learned. Applying lessons from his school's new math textbook, "Investigations in Number, Data, and Space," Christian tried breaking the problem into easier-to-digest numbers.
But after several seconds, he got stumped. He drew lines connecting digits, and his computation amounted to an upside-down pyramid with numbers at the bottom. His father, in a teacherly tone, nudged him toward the old-fashioned method. "How would you do that another way?" Barlow asked.
In Prince William and elsewhere in the country, a math textbook series has fomented upheaval among some parents and teachers who say its methods are convoluted and fail to help children master basic math skills and facts. Educators who favor the series say it helps young students learn math in a deeper way as they prepare for the rigors of algebra.
The debate over "Investigations in Number, Data, and Space," a Pearson School series used in thousands of elementary classrooms, including some in Arlington, Fairfax, Loudoun and Howard counties, is one of the newer fronts in the math wars. Such battles over textbooks and teaching methods are fueled in part by the anxieties of parents who often feel powerless over their children's education, especially in subjects they know.
The curriculum, introduced in the 1990s and updated in a second edition issued last fall, offers one answer to the nation's increasingly urgent quest for stronger elementary math education. The nonprofit organization TERC, based in Cambridge, Mass., developed "Investigations" with support from the National Science Foundation.
Some experts and parents find it wanting. "There's very little substance. I read through all the kindergarten curriculum. It's wishy-washy," said Steve Santee, an engineer whose daughter Olivia is in first grade at Cedar Point Elementary School in Prince William. "My wife and I are very fortunate. She's a former math teacher, and we can teach her all the way up to calculus."Learning Less by Heart
The program de-emphasizes memorization and drills and pushes students to use more creative ways to find answers, such as drawing pictures, playing games and using objects. Prince William officials say "Investigations," which cost the county more than $1 million, teaches students why an answer is correct, prepares them for algebraic concepts on the SAT and increases passing rates on state exams.
Carol Knight, Prince William's math supervisor, said that when children break down numbers into multiples of 10 and 100, their understanding of place value and "number sense" increases.
"Memorization will only carry you so far," Knight said. "With 'Investigations,' kids understand the real values of the numbers and are not doing shortcuts. When they multiply 23 times 5, they'll do five 20s to get 100, and then add five 3s to get 15, and they put that all together and get 115. What they've done is made actual use of the numbers."
Knight said Prince William revamped its elementary math in part to raise "embarrassing" SAT scores that were below national and state averages last year.
Prince William classes use "Investigations" from kindergarten through third grade, and there are plans to introduce it in fourth grade in the next school year and fifth grade after that.
But many parents are lobbying the School Board to kill the program. Opponents have submitted a petition with 1,000 names and started a Web site, http://www.pwcteachmathright.com . They have been checking out a video called "Math Education: An Inconvenient Truth."
"I don't know what happened in Prince William. Have the parents visited the classrooms? This has to be a decision made by everyone that's affected by it," said Cathie Dillender, a senior Pearson executive who handles math issues. "We have a lot of happy customers out there. We're all educators, too, and we certainly wouldn't publish a program that would not work with the kids."In the Classroom
One recent day at Springwoods Elementary School in Woodbridge, third-graders used a mix of methods to solve word problems. Some had difficulty grasping what skill to apply for which problem. For instance: "There are 28 desks in the classroom. The teacher puts them in groups of four. How many groups of desks are in the classroom?"
Ilana Cooper and Audrey Mishler teamed up on the problem. Audrey drew hash marks in groups of four on her paper but stalled. She broke out a set of plastic cubes. Maybe her tactile senses could help.
"How about 4 times 28?" Audrey asked Ilana.
"Yeah, that sounds good," Ilana said.
The teacher, Rhonda Ellington, came over. She put cubes into groups of four. A few minutes later, Audrey and Ilana used their fingers to count the groups of cubes. They arrived at 7, the correct answer.
Jesse Mishler, 33, a financial services manager, said that he and his wife, Priscilla, initially sought to persuade Audrey to memorize flashcards, but she resisted.
"We were trying to teach her to memorize things like 2 times 2 is 4. It created some frustration and anxiety on her part," he said. "We've changed gears. I came to the conclusion that she shouldn't be put in that spot. We felt it was best to partner with the teacher."
Prince William officials cite research from the "Investigations" publisher showing that the percentages of students using the curriculum who are passing state exams have increased in school systems in 20 states. Prince William's data showed that 80 percent of second-graders who used "Investigations" in the past school year were proficient in all 10 skill areas of a Stanford Diagnostic Mathematics Test.
But skeptics say results from the Stanford test show that second-graders ranked average nationally and that first-graders ranked slightly below average, well below parents' expectations.
The critics also point to test scores in the Greece Central School District in Upstate New York. Steven L. Walts, now the Prince William superintendent, presided over the implementation of "Investigations" to schools in the Greece district during his tenure there as superintendent.
Elementary and middle school math test scores rose in 2006 and 2007 in the Greece schools, but results in various grade levels still ranked the district much lower than most of the other 17 districts in its county, according to research by a retired Greece principal, Douglas Skeet.
Debates over math curricula have flared in many parts of the United States. In Ridgewood, N.J., an incoming superintendent who supported math alternatives such as "Investigations" was recently forced to back out of the job after parents complained. In the Alpine City school system in Utah, officials scaled back "Investigations" under pressure from lawmakers and parents, though test scores improved.
In the Washington area, Arlington has been using "Investigations" at all elementary schools for the past two years. Ann Wilson, PTA president at Ashlawn Elementary, said parents initially were apprehensive but have since been positive. In the 2006-07 year, 56 percent of Arlington third-graders scored "advanced" on the state exams, and 90 percent passed.
In Fairfax, most elementary schools use traditional books, but teachers are increasingly using "Investigations" as the main text as they get comfortable with it, said Frank Atchison, math coordinator for the county schools.
As for Greg Barlow in Prince William, the former fighter pilot with college degrees in aeronautics and astronautics, he finds himself in a new role: home-school dad. He has spent about $100 at Sam's Club and Costco on math textbooks.