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She explains, appropriately enough, through an equation. If Tammy has three baskets and seven balls in each basket, how many balls does she have? While adults tend to do a quick mental multiplication, kindergartners tackle such a question literally. They may draw the baskets and count. They may use pennies to represent balls. Or they may come up with a novel method that makes math majors stop in their tracks.

"A child as young as first grade, or even kindergarten, might say, 'I know 7 + 7 is 14, so you add 6 and you get 20. So I added one more to get 21,' " says Franke. "What's surprising is that kids so young can follow a grouping problem, something we would never expect them to do."

But adults rarely ask children to solve the problems themselves. They wait until children can multiply, then coach them to think in multiplication terms. Very soon, kids abandon the creative learning strategies they've devised on their own.

Franke first became fascinated by how children's mathematical thoughts unfold while studying for her advanced degrees at the University of Wisconsin, Madison. By the time she joined UCLA in 1992, she was determined to teach teachers to learn from their students.

"What's really powerful is how excited teachers get," says the 1997 distinguished faculty award winner. "All of a sudden, they start thinking in terms of what children can do and not what they can't do. The school learns not to infringe on children's learning strategies, but to cultivate them."

These days, Franke, who just completed a book, Teaching and Teacher Education, which will be accompanied by a CD-ROM featuring teachers learning from children, has taken her theories to the chalkboard: She's heading a two-year program for 35 teachers and their students at Los Angeles-Moffat Elementary School. In addition, she codirects Center X, a departmental effort to enhance the intersection of teacher education and practice.

Oh yes, and she still teaches, too.

-- Betsy Bates

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