Math teacher urges explanations over plugging in formulas

By Michael Alison Chandler
Monday, October 19, 2009

The teenagers in Stephanie Nichols's algebra class have nothing on her blank stare. And they can't even come close to her best confused expression: eyebrows furrowed, mouth frowning, a flash of ditziness framed by a blond bob.

"Sorry if I'm the slow kid," she said, slowly, during a lesson on slope. "I don't get it." As students calculated problems on the board, she interrupted, "I'm really lost. . . . How did you do that?" Occasionally, she was more blunt: "Huh?"

Nichols's vacant looks and incessant questions put the students at Arlington County's Washington-Lee High School in the uncomfortable position of being the math teacher, explaining how the numbers on the white board relate to each other, how algebra actually works.

Like encouraging men to elaborate about their feelings or getting couples to come clean about their money habits, engaging teenagers in open-ended conversations about math is an uncomfortable challenge. How does that work? Dunno. Just does.

But getting students to better understand how math works -- and what it's good for -- are fundamental goals for the nation's corps of high school math teachers. So says the National Council of Teachers of Mathematics, which represents about 100,000 of them.

The Reston-based council released new guiding principles for high school mathematics this month emphasizing that "reasoning" and "sense-making" should be at the center of all lessons. The document, which includes specific tips for teachers, administrators and parents, will probably influence how textbooks are written, teachers are trained and lessons are crafted in coming years. It arrives three years after the group promoted more tightly focused curricula for elementary and middle school math.

Many math teachers say that stimulating higher order thinking has long been considered good practice. But the council says a fresh emphasis on the goal is necessary after a half-decade of high-stakes testing has taken spontaneity from many math discussions. Multiple choice tests leave little room for expansive thought.

Textbooks, too, often have a "here's-the-rule-and-here-are-some-examples format," with word problems buried in Section C, said W. Gary Martin, a professor of mathematics education at Auburn University in Alabama. He chaired the committee that wrote the document.

That approach won't help students understand how math works in their daily lives. "Nobody has ever given me a worksheet with eight quadratic equations to solve, except in math class," he said.

The council is hoping that rethinking instruction will catapult more students into math-related careers and get teens out of their collective math funk. The National Assessment of Educational Progress, known as the Nation's Report Card, has charted steady improvement in math performance among 9-year-olds for 30 years. But scores for 17-year-olds have been stagnant.

One reason for the rut could be that teenagers are more autonomous thinkers, Martin said. Younger students are more willing to work at something because they are told to; teens need a reason to care. They need to be engaged.

Talking about math is a good start.

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