Math comes with its own problems
Seattle Times staff reporter
DEAN RUTZ / THE SEATTLE TIMES
STEVE RINGMAN / THE SEATTLE TIMES
DEAN RUTZ / THE SEATTLE TIMES
Jeremiah Pilkington knows the drill: First the butterflies in the stomach. Then the frustration.
"I sometimes would feel some people are smarter than me," said Pilkington, an eighth-grader at Bellevue's Tillicum Middle School.
But Pilkington, who until recently was behind in math, pulled a near-perfect score on his most recent test. His secret? Breaking problems into pieces to see what was really going on behind the numbers.
"Then I understand," Pilkington said. "It's actually a really cool feeling, because then you know what you are actually doing."
His is the kind of turnaround Washington educators hope to see in classrooms all over the state.
A lot depends on it: No barrier to high-school graduation looms larger right now for Washington students than math.
Year to year, more students flunk the math segment of the Washington Assessment of Student Learning than reading or writing. Last year, more than half the state's 10th-graders failed math. And it's even worse for low-income and minority students; in 2005, only about 28 percent of low-income sophomores passed, and only about a quarter or fewer of black, Indian or Hispanic 10th-graders.
The class of 2008 is the first for which passing the WASL, or an alternative assessment, is required for graduation. The math segment of the test will be administered this week. So will science, but it won't count toward graduation until 2010.
Experts predict we'll have to change the way math is taught, and even the way we think about it, or math will continue to be a stumbling block.
What's the problem with math?
Research shows kids learn math best when they begin with a thorough grounding in mathematics fundamentals and progress in an orderly sequence, with the help of similar instructional approaches, from class to class and grade to grade.
But in Washington, many kids face bamboozling instruction that can be a mile wide and an inch deep. They endure competing approaches and instructional materials. And many textbooks aren't even in sync with the material kids will be expected to know on the WASL.
And by high school, kids have spent years marinating in a culture that disses math. Few people in this country boast about being illiterate. But it's long been a laugh line to declare "I'm not a math person." Not so in countries such as Japan and Singapore, where students are expected to conquer math — and keep trying until they do.
And in America, where are the math bees, the volunteer math tutorial corps, the math-is-fundamental public-service campaigns? As a society, we root for reading. But we expect success in math to just happen ... or not.
Ilana Horn, associate professor of mathematics education at the University of Washington, says that makes a big difference. "We have a belief in innate ability. It perpetuates this idea that you either have it or you don't, instead of that you aren't trying hard enough.
"It allows teachers to not question student failure in the same way, and it allows parents to excuse the kids' poor performance, and kids to excuse their own poor performance."
Math plays catchup
Both nationally and at the state level, math has taken a back seat to reading.
Mary Alice Heuschel, deputy superintendent for learning and teaching at the state Office of Superintendent of Public Instruction, said reading has received the lion's share of national research, funding and attention. "We haven't seen that in math at all."
The feds will pour about $15.6 million into targeted reading grants in Washington state this year alone, and about $2.6 million in math and science grants combined.
In last year's WASL testing, 73 percent of sophomores passed the reading portion.
At the state level, math has been among the last content areas for districts to bring curriculum into alignment with state standards. Math is also where teachers say they feel they have the least expertise. And the state spent nearly five times as much on special help on curriculum and instruction for reading as for math from 1994-2005.
The state is ramping up its attention to math. A review of curriculum is under way to help districts make choices aligned with state standards. A small cadre of math specialists is helping teachers with instruction and curriculum. And 10th-graders who fail the math segment of the WASL this week will be eligible for extra help, at state expense, before retaking the test.
Math matters. Mastering math means learning problem solving, abstract thinking and the ability to make connections between ideas. Math trains the mind. It also pays the bills.
It's a simple formula: The higher the math a kid can master, the higher the wage he or she is likely to earn later on. More than 80 percent of workers in professional jobs, including managers, engineers, doctors and lawyers, got at least as far as algebra II, and more than half of them completed at least some trigonometry, according to a 2003 study by the Educational Testing Service, which creates and scores standardized tests.
Implementing state standards for graduation was intended, in part, to make sure every kid mastered at least a basic level of math. But some fear failing the WASL will only add injury to the insult of a school system that is not working for their kids.
To close the achievement gap between whites and ethnic minorities, teachers also have to bring mathematical concepts to students from other cultures in a way that engages them. That can require not only mastery of the material, but a creative approach.
Yakama tribal elder Levina Wilkins, a former teacher for the Mount Adams School District, used beadwork projects to teach her kids they not only had to answer problems, but know how to deconstruct them, just like creating and taking apart pieces of beadwork.
She also demanded performance from her students.
"They would say, 'This is stupid, why do we have to do this,' and I would tell them, 'Excuse me? We never had a word in our language that said 'stupid.' "
In theory, if teachers are teaching according to grade-level expectations set by the state, the mathematical knowledge kids need will be delivered when they are developmentally ready for it, and within the scope and sequence that will make sense to them. The WASL should be a breeze.
But Mike Riley, superintendent of the Bellevue School District, says it took a consultation with a national expert, and an overhaul of the way the district teaches math, beginning in 1996, to get scores headed in the right direction.
"What you teach is important and when you teach it is important," Riley said. "The biggest problem we have with mathematics in the U.S. is there isn't a clear mathematics program. If it is not clearly organized, and you don't have agreement on what kids need to learn in second grade so the third-grade teacher can count on it, you get what we have: weak performance in mathematics."
Washington, like most states, hasn't standardized curriculum or instruction in any subject.
But today in Bellevue, teachers must use the same curriculum districtwide. "And the teachers must teach it. If they feel like it or not, that is the job," Riley said. The approach has been controversial with some teachers, who prefer to use their own favorite units and lesson plans. But it seems to be working.
About 72 percent of the 10th-graders in the district passed the math portion of the WASL in 2005, up from 58 percent in 1999.
At the state level, only 47.5 percent of 10th-graders passed math.
William Schmidt, a math expert at Michigan State University who helped assess Bellevue's math curriculum, says it's no coincidence the district's scores are going up.
The secret, Schmidt said, is coherence. Instruction should progress in a sequence of topics over the grades that is consistent with the inherent structure and logic of mathematics. Kids have to master the basics, such as ratios, decimals, percents and fractions before they are ready to tackle algebra and geometry.
Otherwise, kids get confused and don't see the connections between topics. Clutter — teaching kids topics before they are ready for them — and holes in the logical sequence are traps kids may never dig their way out of.
Just as important is focus: Kids must reach deep understanding of the principles behind mathematical operations — how and why they work — before moving on to the next subject, or they will never catch up. "The idea is to build ideas on each other in an increasingly complex way," Schmidt said.
That's also the kind of deep understanding kids need to pass the WASL, which demands kids show more than an ability to compute. On some questions, getting the right numerical answer on a WASL math problem isn't enough.
Students must also demonstrate they understand what they are doing. They have to explain the steps they used to solve the problem. Answers won't get full credit if students don't show their work.
Too much talk?
The same thing that helped Jeremiah Pilkington finally get algebra — a level of deep conceptual understanding — requires a different approach by teachers.
It's not enough for some students to say one-eighth is smaller than one-sixth. Some need to understand more deeply what a fraction is, by drawing a picture perhaps, before they truly get it.
But many teachers didn't learn math that way themselves. And neither did many parents. For some of them, the emphasis on processes and explanation, in addition to traditional computation skills and problem-solving techniques, is "too talky," or "fuzzy."
"Why do you have to explain it, or draw a picture of how you figured it out?" said Bob Brandt of Bellevue, a former software engineer who is part of a group of advocates pushing for a more traditional approach to teaching math in the public schools.
"How do you know three times two equals six? Any idiot knows that."
Sandy Cooper, an associate professor of mathematics at Washington State University, sees kids and teachers caught in a change of huge proportions.
"We are moving from math taught in a cut-and-dried, calculation-based fashion to more explanation. Teachers weren't trained that way, and it's hard for them to teach it that way in the classroom. It's a huge expectation, it's moving in the right direction, it's just that the students and teachers are caught in the middle."
Lynda V. Mapes: 206-464-2736 or email@example.com
Information in this story, originally published April 16, 2006, was corrected April 22, 2006. In an earlier version of a photo caption with this story, the last name of Amanda Gadian was misspelled. We regret the error in her last name.
Copyright © 2006 The Seattle Times Company