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Four Big Ideas of Algebra Given Top Billing In Randomized Study

By Scott J. Cech — August 28, 2007 6 min read
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If you heard just the name, you might think it was something for sale at Radio Shack, or maybe Home Depot—a generator, perhaps, or a high-tech battery. About the last thing “Powersource” would conjure up is a conceptual rethinking of how to teach algebra.

But that’s exactly what’s been developed by a team of education researchers at the National Center for Research on Evaluation, Standards, and Student Testing, or CRESST, at the University of California, Los Angeles. Powersource, to be piloted with about 70 randomly selected 6th and 7th grade teachers this fall at 25 middle schools in four school districts in the Southwest, is designed to get students learning algebra like experts, so they can quickly connect new concepts to those they’ve already learned.

“How do experts look at knowledge versus people who don’t know?” said Noelle Griffin, an assistant director for research and evaluation at CRESST. “The difference is that experts are able to group information around big ideas. Those big ideas help organize all the pieces of information.”

It’s no idle experiment. Amid concern that the United States is falling behind other countries in the so-called STEM fields—science, technology, engineering, and mathematics—math and science education are under heightened scrutiny from federal and other policymakers. And because algebra introduces many concepts central to higher math and science, the subject is seen as a make-or-break milestone for students.

“We know that algebra is the single most obvious barrier for low-performing kids to leap across to be able to get into either technical jobs or postsecondary schooling,” said CRESST director and UCLA professor Eva L. Baker, who came up with the idea for Powersource. “We want to make sure that kids can actually do this stuff.”

Ms. Griffin, who has worked with Ms. Baker, CRESST assistant director David Niemi, and other researchers on the project, which is financed by a grant from the U.S. Department of Education, said the associations Powersource evokes aren’t accidental.

“Being able to look at the big picture is the source of power and knowledge,” she said.

Before spraying students with algebraic problems, goes the theory behind Powersource, first make sure they’ve mastered four core mathematical concepts all those problems are supposed to exemplify: rational number equivalence; the distributive property of arithmetic; principles for solving linear equations; and application of core principles in those domains to other critical areas of math, such as geometry and probability.

In Sync

While Powersource’s name and pedagogy might be unusual, the president of the National Council of Teachers of Mathematics, Francis “Skip” Fennell, says its four core concepts are widely viewed as pillars of the subject, and are in line with the standards his Reston, Va.-based association promulgates.

Mixed Media

Scholars hope that comic-book-format assessments (excerpted here) will help students better learn algebraic principles.

STORY AND ILLUSTRATIONS BY SIMON MASKELL AND ANDREA DIETRICH. COURTESY OF NATIONAL CENTER FOR RESEARCH ON EVALUATION, STANDARDS, AND STUDENT TESTING.

BRIC ARCHIVE

“There’s some real resonance with what we think are foundational mathematics,” said Mr. Fennell, who also serves on President Bush’s National Mathematics Advisory Panel. The panel is crafting recommendations on the best use of scientifically based research in the teaching and learning of math.

Ms. Baker said Powersource is “not intended to confront or replace an existing curriculum,” despite its differences from the conventional approach to teaching algebra. “We’re trying to get in over the transom and under the door—trying to get these ideas infused into practice,” she added.

That jibes with teacher Laura Vinyard’s experience. She’s going into her twelfth year of teaching 6th grade math, and her second year of using Powersource. (CRESST’s confidentiality agreement with the four districts taking part in the randomized experiment using Powersource prohibits releasing the names of participating schools.)

Ms. Vinyard said the CRESST-provided Powersource lessons—each focused on one of the four core concepts—accounted for only a total of eight days of instructional time, spread out over the year, and mirrored the topics she would have covered in class anyway.

Presenting unifying principles first, she reported, seemed to help her students integrate new information with what they’d already learned. She compared the idea to the course outline a typical social studies class starts with.

“You say, ‘We’re going to learn about the Civil War,’ ” said Ms. Vinyard, a past county-level teacher of the year. “You give them an outline, and everything goes together. In math, we tend to treat each lesson as discrete.”

Assess This

But the concept-first idea is just half the equation. Powersource also sprinkles in a dozen pinpoint formative assessments throughout the year—each lasting a maximum of 15 minutes—that reflect the project’s concept-first orientation. Among the assessments requiring students to complete partially worked problems and explain why a certain equation works the way it does is a comic-book-style assessment page that illustrates the distributive property.

“The hypothesis is that using the [comic-book] design will increase student engagement and reduce student anxiety,” Ms. Griffin said. “We’ll see if we’re right.” Whatever the medium, said Stephen Dunbar, a professor of education at the University of Iowa and the director of the Iowa City-based Iowa Testing Programs, which develops the widely used Iowa Tests of Basic Skills, it makes sense to introduce key math concepts explicitly, rather than always relying on students to connect the dots.

“But in real teaching and learning situations, there’s an interplay of both types of learning,” he said, drawing an analogy to differences between the whole-language and phonics methods of teaching reading.

“I think the real wisdom is, you have to do both,” said Mr. Dunbar. While he said he was only slightly acquainted with Powersource, he was familiar with the potential pitfalls of its general type.

“I think a downside of something like Powersource could be that, in the wrong hands, it could possibly promote a more mechanistic approach to learning: ‘Here’s the general principle—learn it. Here are a bunch of instances—learn them.’ ”

Into the Future

This fall, Powersource will start the third of its five planned years as a pilot, and the first year of its expansion into 7th grade classrooms. By 2009-10, the final year of funding for the project, Powersource will be running in grades 6, 7, and 8.

“The plan is to set up the systems within the districts,” said Julia C. Phelan, a senior research associate at CRESST. With math teachers and math coaches serving as on-site coordinators, she said, “the goal is for this to become a self-running machine.”

Although the results of last year’s field test of students in Powersource classes vs. control-group classrooms are not yet available, “our preliminary results have been very positive,” said Ms. Griffin. “The classrooms using Powersource have performed significantly better on our measures than kids who haven’t.”

Ultimately, she said, the goal is to measure the project’s effectiveness by comparing Powersource students’ standardized-test scores with their peers’. Plans are also afoot to make much of Powersource deliverable online.

“You want to give projects like this the time the prove themselves,” said the NCTM’s Mr. Fennell of Powersource and its drive to put fundamental math principles first. “When we push kids into algebra without these foundational experiences, we notice that kids have trouble because of the gaps [in their knowledge], which we have to fix.”

“It’s early,” he added, “but it sounds like that’s what this program is trying to do.”

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Coverage of mathematics, science, and technology education is supported by a grant from the Ewing Marion Kauffman Foundation, at www.kauffman.org.

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