[Note: From Thomas Judson, with thanks ...] ********************************************
Portland Oregonian, Monday April 12, 1999;
Big change in math education weighed
Portland's school board will decide tonight whether to switch elementary and middle schools to a newfangled curriculum
By Betsy Hammond of The Oregonian staff
Picture a math class with no textbooks, no problem sets, no formulas and no flashcards. Instead, envision math as a sort of brainstorming exercise, a guided discovery of mathematical thinking arrived at through games, discussions, mind-benders, even essay writing. That would be a big shift -- for teachers, students, parents and potential employers. And it is just what Portland educators are proposing for all the city's elementary and middle schools come fall. The switch is driven by powerful national forces, including the National Science Foundation and the National Council of Teachers of Mathematics.
Portland's school board will decide tonight whether to stick with traditional textbooks or switch to the newfangled math series. That choice foreshadows what the rest of Oregon schools are likely to face when they pick new math programs in three years. Proponents say the new methods will produce a bumper crop of students who are competent in math, important for a nation whose students' math skills rank near the bottom among developed nations. But critics of the new approach, mostly parents and college professors, say asking students to figure out math for themselves will yield a worse muddle.
Committees of teachers, after anguishing over the question for months, decided Portland should forgo math textbooks until high school and opt for the unconventional new approach. Using the new series, which covers fewer topics in greater depth and substitutes student problem-solving for teacher lectures, will require more training, more expertise and more work for teachers. It's also likely to panic some parents. But it's worth all that, selection committee members decided. They are convinced the discovery-laden, no-textbook, no-formulas method is the best way to get far more kids far more skilled at math.
"Connected Math is really difficult to teach," said Karen Moloney, a math teacher at Portland's Fernwood Middle School. "But it is the best program I've ever seen for children." Students understand and retain math skills they discover for themselves but tend to forget formulas and equations they are spoon-fed, said Steve Palumbo, a math teacher at Gregory Heights Middle School. "We really believe the kids are going to come out of this with better skills and better understanding."
For instance, a traditional textbook begins its lesson on equivalent fractions by explaining how to multiply both numerator and denominator by the same number. It then gives an example, showing that one-third becomes two-sixths -- its equivalent -- when multiplied by two over two. Students then work 20 or 30 problems, changing fractions into an equivalent and checking to see whether the fractions meet the equivalency test.
In contrast, Connected Math begins its sixth-grade lesson on equivalent fractions with empty number lines. Students are led to see that one chunk out of three and two chunks out of six are the same size. But their teacher's refrain is not about multiplying numerator and denominator by the same number. Instead, the teacher asks "why?" and again "why?" until students discover the pattern for themselves. Nowhere does the book give students the answer. And homework is typically a single problem.
Connected Math students learn decimals and percents all in the same lesson and must make their case in writing for why ÃÂ½, 0.5 and 50 percent all are equivalent. The traditional textbook lesson on equivalent fractions takes a day or two. Connected Math's lesson intermingling fractions, decimals and percents takes five weeks. The weeks spent on the topic in sixth grade are made up by not having to reteach fraction basics in grades seven and eight, Moloney said. "My experience has been that they hang onto it better," she said.
Even fans of the two proposed programs, Connected Math for middle schools and Investigations in Number, Data and Space for elementary schools, concede the programs will flop if teachers don't get adequate training in how to use them. Superintendent Ben Canada is adamant that the district will provide that training, and the district also plans to provide teachers with supplemental materials so that drill and practice don't get thrown out the window.
Still, some teachers are concerned that the new math programs won't be a good fit for all students. In California, where earlier versions of discovery-based math programs were introduced in the mid-1990s, outraged parents got schools and the state to make an about-face. "The program they are considering for Portland and similar programs render the child basically helpless," said Jamie Clopton, a San Diego psychologist who helped found the pro-traditional math group Mathematically Correct.
"The person they are to turn to is their peer, who is just as baffled as they are," Clopton said, recalling her daughter's experience with a math program similar to what Portland is considering. Then they go to their parents, and the parents say, 'What is this? This is like nothing I have ever seen before.' There is no explanation, there are no examples, there are no models to follow. It's more, 'Let's try it and see if it works.' It's a very frustrating experience, for the child and for the parent."
The National Science Foundation has poured more than $65 million into its eight-year effort to bring Investigations, Connected Math and 11 other math programs to market. The resulting series are regarded as brilliant or catastrophic -- and rarely anything in between.
"You see the dilemma we're faced with," said Andy Clark, Portland's chief of math curriculum. It is ironic that Portland finds itself ahead of the math curve for Oregon. That happened only because Portland is so far behind. The cash-strapped Portland district has not adopted new mathematics textbooks since 1989. Other Oregon districts picked new ones in 1995 and 1996. When Portland set out to have teachers select new series, it ran smack into the programs incubated by the National Science Foundation. With names such as MathScape and Math in Context, packed into colorful boxes or zippered satchels, they don't look like regular math books and certainly do not work like them.
But do they work at all? It seems clear they do not hurt. Test scores for thousands of students in diverse districts that have tested the programs show students do no worse as a result of undergoing the nontraditional teaching.
But studies showing clear advantages from the new programs are sparse so far. Portland's math scores already are strong, besting the average for Oregon and for most large urban districts around the country. Portland needs a program that will improve performance, not merely maintain it, Clark said.
The publishers of Connected Math say their best evidence comes from a 1996 study of about 2,000 middle school students who were taught Connected Math and 1,000 matched students who used regular math books. Both sets of sixth- and seventh-graders performed pretty much the same on a common standardized test. Only in eighth grade did the Connected Math students surge ahead, gaining more than a full year's skills in seven months.
Particularly persuasive to members of the selection committee was the performance of Fernwood, the Portland middle school. Aided by a National Science Foundation grant, the Northeast Portland middle school began using Connected Math two years ago. Last year, its performance on state math tests was turning heads. Fernwood students made about 30 percent more progress than Portland middle-schoolers as a whole. Almost half the school's students performed two years higher than their grade level. Connected Math also seemed to help move students off the lower tiers: Only 25 percent of Fernwood eighth-graders missed the state math benchmark, compared with 37 percent at other Oregon schools with similar socioeconomic levels.
Moloney, the Fernwood teacher, admits Connected Math was tough to take on. "For me, it's really difficult to stand back and allow them to struggle through these very challenging problems, to look at it and work it and work it for themselves," Moloney said. "But I see that what they learn this way sticks with them, rather than flying out of their heads as soon as they walk out of here."
Fernwood sixth-grader Marcy Johnstone said Connected Math can be hard for students, too. "But it's a challenge, so that's better," she said.
Oregon employers such as Intel Corp., which are struggling to find enough mathematically competent workers, applaud Portland's plan. "We very much favor a mathematics curriculum that tries to focus on things in greater depth rather than peanut-buttering all over the world of mathematics," said Wendy Hawkins, Intel's education relations manager.
If the new math series is approved by the board tonight, Portland will be among the first large districts in the nation to adopt it as its sole path for teaching math in every elementary and middle school, said Spud Bradley of the National Science Foundation. And that could be politically risky.
"There are parents who want their children to have the same experience they did when they took mathematics in school," he said. "It's really a political issue and not an educational one, but it can really bite. ------------------------------------------------ Betsy Hammond covers Portland Public Schools. You can reach her at 503-294-7623 or at firstname.lastname@example.org.