Bruce Ramsey / Times editorial columnist
New-age math doesn't add up
New-age math First way: 26+100=126. 90 is 10 less than 100, so take 10 away from 126 = 116. Second way:
2 + 9 = 11, so 20 + 90 = 110. Add 6 to 110 to get 116.
Traditional math: 30 cm. (Perimeter = 2 x (length + area/length)
It's called reform math, discovery math, constructivist math, fuzzy math. I think of it as new-age math, and believe it is one reason why last year nearly half the 10th-graders in Washington public schools failed the mathematics portion of the high-school graduation test. It is also one reason American kids do so poorly when measured against kids from Europe and East Asia.
New-age math, which is used in most schools today (including many private schools), came packaged with a garden basket of fragrant thoughts. "It was hands-on," recalls Seattle math teacher Martha McLaren. "Make math fun. Small groups. Kids learning to work together, to 'appreciate the differences.' It was all going to be somehow more democratic." It was better for girls and immigrants, who maybe didn't learn in such a "linear" way.
Linear it is not. One of the leading new-age series, TERC's "Investigations," leads the sixth-grade student to scissor out parts of a disk and paste them over other parts. The book tells the student, he has discovered the number pi. The lesson does not require the student to solve any problems with pi. It does not list the formula c=2 pi r. Instead, it prances on to a lesson about how to estimate the area of a baby's hand by counting squares on graph paper.
A middle-school math teacher I've known for years recalls the new-age "Integrated Mathematics" books adopted by the Lake Washington School District in 1995: "They wandered all over hell and gone. I tried teaching out of them for one year, and then I spent the next August writing an entirely new curriculum."
Lately, this teacher has been given a new Algebra 1 book. Lesson one introduces chaos theory, recursive relationships and fractals — not comprehensively, because that wouldn't be possible with eighth-graders, but in a look-how-smart-I-am way. "The book is a nightmare," he says, noting that it was "written by a committee."
The new-age math has several attributes. It tends to introduce topics in a roundabout way that aims for a eureka moment. That is the "discovery" part. It introduces many subjects early, focusing on concepts rather than calculation. That is the "constructivist" part. It sometimes wants the student to estimate an answer rather than find the right one. That is the "fuzzy" part. It demands written explanations of how an answer was arrived at, often in "math journals." That is the part parents find most baffling.
New-age math uses games, colored blocks, dice, poker chips and other manipulatives. It requires working in groups. "The idea is that if you let them struggle and come up with their own solutions, they'll learn it better," McLaren says.
None of these things is necessarily bad. A good teacher may use a game or lead the students to a eureka moment. But there are drawbacks. With group work, McLaren says, there is a tendency for "the majority to struggle and other students to show them the answers."
The new-age math takes time. "They'll give you one problem and ask you to find five ways to solve it," says Seattle math teacher Linh-co Nguyen. "And that takes up a whole hour of class time." The idea is that the student who works through five ways will have it down solid. Maybe, but it might be better to learn one good way.
Always, the new crowds out the old. What's getting crowded out with new-age math is solving problems with paper and pencil. Kids are taught to use calculators. The result, says McLaren, who substitutes across the Seattle district: "In the seventh grade, you can ask students what's 38 take away 3, and a lot of them have to use a calculator for that — probably 30 percent in the average class. Kids don't know basic addition and subtraction. They haven't been taught long division."
Nguyen, who substitutes, has been in eighth-grade math classes in Seattle where not one student would volunteer the equation for the area of a rectangle. [Area=length X width]
Ted Nutting, who teaches calculus at Ballard High, says, "Supposedly, reform math is heavier in concepts but weaker in skills. But in my experience, kids are weaker in both." He says the weakness is most noticeable in "B" and "C" students.
The official measure of math skills is the Washington Assessment of Student Learning. The WASL is a new-age test, with many questions being as much about explanations as answers. Some are more of logic than math — making the WASL a better test for the college-bound than the high-school grad expected to know basic algebra and fractions. At the same time, Washington, D.C., consultant Michael Cohen, who has reviewed the WASL, says the actual math in it is seventh-grade level.
Consider that. To graduate from high school, our state was going to require kids to demonstrate knowledge of seventh-grade math — and because of the way we teach them, and the way we test them, half of them can't do it.
And after high school? At community colleges, half the students take remedial math. At the University of Washington, atmospheric-sciences professor Cliff Mass says, "I saw a profound drop in math skills starting in the mid-'90s." New-age math, he says, has created "a whole generation of students who can't do fractions."
"I have students who want to do meteorology," he says. "They can't do the math — and they have to give up their careers."
Some of the teachers quoted here — Mass, Nutting, Nguyen, McLaren — are involved in Where's the Math? (www.wheresthemath.com), a group that promotes international-standard math or, as math teacher Marta Gray calls it, "Real math. We want real math."
The group found a sympathetic legislator, Rep. Glenn Anderson, R-Sammamish. He and Rep. Ross Hunter, D-Medina, introduced House Bill 1906 to replace the state's fuzzy math standards. It has passed the Legislature and is now on the governor's desk.
In 2005, the Fordham Institute graded Washington's math standards "F" for fuzziness, reliance on calculators and focusing on "talking about solving problems rather than actually solving them." In math standards, it ranked Washington 46th among the states.
The math teachers hope Washington will follow "A"-rated California, which began to ditch new-age math in 1999. William Hook of the University of Victoria is co-author of a peer-reviewed study of seven California districts, published in the Jan. 3 issue of "Educational Studies in Mathematics." In four years of Saxon Math, he reports, the Sacramento schools moved up from the 30th to the 64th percentiles in the nationally normed SAT-9 test. The four other districts he studied that used Saxon also made big gains, and two control districts that kept new-age math, Los Angeles and San Diego, did not.
Saxon Math is unfashionable in the educational bureaucracy. It is structured — even a bit rigid. One lesson leads to the next. Each ends with a list of problems, and all of them demand the right answer. It's so ... linear.
"That's what math is," says retired principal Niki Hayes. "It's linear. It's structured."
Hayes is one of the heroes of the math rebels. She discovered Saxon Math being taught successfully to kids on the Spokane Indian Reservation and brought it to North Beach Elementary. It is the only Seattle public school that has it.
With Saxon Math, from 2001-04 North Beach's pass rate on the fourth-grade math WASL jumped from 68 percent to 91 percent. It has since fallen back 10 points, which Saxon supporters say was because students were not drilled on the need to explain answers on the WASL. They are worried that the district will take their program away. Using a phrase from "The Godfather," Principal Ed James says parents and teachers are "willing to go to the mattresses" for it.
In Seattle, associate academic officer Michelle Corker-Curry says Saxon is not in line with state standards — and she is right. It isn't. She notes that Saxon was written by one person, whereas the approved (new-age) text, "Connected Math," is written by a team. A final decision on elementary math will be made this summer, and Corker-Curry said the district "will be looking at a citywide curriculum for all our students."
For Seattle, that might leave home-schooling or private school as the ways to get more traditional curricula such as Saxon Math or Singapore Math. For example, the K-8 Holy Rosary School in West Seattle chose Saxon two years ago for grades four through eight. "Our kids' scores are improving," says principal Kris Brown.
In Vancouver, Clark County, Marta Gray is teaching her kids from the Singapore Math books — a curriculum directly from the nation with the world's highest test scores.
Tacoma Public Schools introduced the Saxon books districtwide in September. New Superintendent Charles Milligan was faced with the problem of what to do about Tacoma's catastrophic 32 percent pass rate on the 10th-grade math WASL. Milligan, an ex-Marine with a Ph.D. in quantitative analysis, decided that the new-age texts didn't have enough real math in them.
He says Tacoma has been pushing hard on math. It tested students in November and January, and scores are up. But what counts is the WASL, and the scores on that won't come out until September.
Milligan expects big things. "You'll see," he says.
Bruce Ramsey's column appears regularly on editorial pages of The Times. His e-mail address is firstname.lastname@example.org
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