MICHELE NORRIS, host:

If you have children in school, chances are they've carried home fuzzy math assignments. Fuzzy math encourages kids to find their own ways to solve problems. It doesn't give them a single strategy for getting an answer. It also turns out fuzzy math not only drives parents crazy, it also confounds mathematicians.

So for the past two years, a group of experts has been working to put an end to all the fuzziness. The National Mathematics Advisory Panel was appointed by President Bush to decide the match skills students need to compete in the 21st century. The panel's final report is due out tomorrow. But if you want a glimpse of how a top-notch math curriculum is working right now, the place to go is Massachusetts.

NPR's Claudio Sanchez has the story.

CLAUDIO SANCHEZ: Making sure every high school graduate has learned advanced math skills is one thing, but immersing 3 and 4 year olds in the world of numbers and algorithms…

Ms. MEG MAKITA JOHNSON (Teacher, West Zone Early Learning Center, Jamaica Plain): Simon(ph), you can (unintelligible). Look at my face when you're talking to me.

SIMON: Look at his braces.

SANCHEZ: Welcome to Meg Makita-Johnson's preschool class in Boston's West Zone Early Learning Center in Jamaica Plain.

Ms. JOHNSON: You want to try to do that? If we had four and we counted on three more, how many do you think we would have?

Unidentified Child: Three and four makes seven.

Ms. JOHNSON: You're right. Exactly.

SANCHEZ: Johnson has seen many education trends come and go, but she thinks teaching little kids math is here to stay.

Ms. JOHNSON: This is the first solid, you know, research-based curriculum that we've had and I've been teaching 21 years, young children. So these kids have these, you know, very solid foundations.

Ms. JOHNSON: I bet today we have. Let's count. We know that's four, let's count on.

SANCHEZ: It's not thrilling(ph) kill. There are lots of games, like Mr. Mix-up, a hand puppet that children love to correct because he never gets anything right. Then there's dinosaur shop, where kids buy little plastic dinosaurs from a glass bowl with Monopoly money.

Ms. JOHNSON: You want to know how to buy and sell dinosaurs.

And that's adding and subtracting, and they're doing it by playing and they think that they're geniuses and they are, right? And the geometry thing, they know if they put their little finger like this and it makes and L in the corner, this shape has a right angle.

SANCHEZ: This is real-world math says Johnson, and it's catapulting these kids' understanding of mathematics way beyond everybody's expectations.

Ms. JOHNSON: I'm completely blown away by the progress these kids have made.

Unidentified Group: A chameleon.

Ms. JOHNSON: A chameleon. Using your fingers - like when we do a snapshot…

SANCHEZ: Ms. Johnson's classroom may be a window into the future of math education but Wilfried Schmid, mathematics professor at Harvard University says that, as a country, the United States today is playing catch up.

Professor WILFRIED SCHMID (Mathematics, Harvard University): Very much so. I mean, that will certainly be our message.

SANCHEZ: Schmid is one of 25 members on the National Math Advisory Panel that has just wrapped up a two-year study of mathematics education in the United States. The panel's task was to recommend the best way to improve mathematics instruction and identify the problems that stand in the way.

For example, the panel found that, overall, math instruction in the U.S. is weak and incoherent because it's based on a hodgepodge of state standards which are often watered down. There's also little or now continuity to what kids learn grade to grade. Schmid says it's been this way ever since well intentioned reformers introduced a radical idea.

Prof. SCHMID: That somehow we can teach mathematical thinking without the children being able to actually calculate, that is just funny.

SANCHEZ: Schmid says students need both. Just as importantly, schools need to reduce their number of math topics they cover every year and focus longer, more deeply on a few. That's what schools in the top achieving countries do, says Schmid. It's one reason students in some European and Asian countries do so much better in math than students in the U.S.

Prof. SCHMID: The contrast is absolutely striking. I mean, in Singapore there is no argument that kids should remember multiplication tables. There is no argument that they should be able to do long addition. There's no resemblance to what is being done in these high-achieving countries.

SANCHEZ: The Bush administration's interest in match education was driven by the drumbeat about how China and India, for example, are producing more mathematicians, scientists, and engineers. To keep up with these countries, the National Math Advisory Panel says, the U.S. must create a bigger talent pool of mathematicians in its public schools. And to do that, says Schmid, schools must absolutely focus on two things: algebra, the gateway to higher lever mathematics, and fractions, the gateway to algebra.

Prof. SCHMID: So in middle school, children need to be very comfortable adding fractions, multiplying fractions, and also knowing what these operations mean. That is the best preparation for algebra.

SANCHEZ: And yet by middle school, no more than 25 percent of students are taking real algebra. And worse, says Schmid…

Prof. SCHMID: The teaching of fractions is, as far as we can see, sort of the biggest problem, the biggest obstacle.

SANCHEZ: But not at Boston's Washington's Early Middle School.

Ms. SHELLY PICK(ph) (Teacher, Washington's Early Middle School) : What do we call all of those expressions - if they don't look the same but they equal the same thing? Jeffrey(ph).

JEFFREY: Equivalent.

Ms. PICKS: Equal fractions. Very good. Okay.

SANCHEZ: This is Shelly Pick's 8th-grade algebra class. Not only are her students well grounded in fractions, they're zooming right along in algebra.

Ms. PICK: Talking about the number 12, that was easy. Everyone should have no problem doing that. We have no problem. Easy. Piece of cake.

Mr. SANCHEZ: Today, Pick is using an overhead projector to show the dimensions of a swimming pool. The problem she's posed requires that students come up with three different ways of mathematically expressing the number 12 using division, multiplication or subtraction. These 13 and 14 year olds are hooked.

Ms. PICK: What did you do to put it into expanded form? Gerard(ph).

GERARD: Distribute it.

Ms. PICK: What do you mean you distributed it?

GERARD: When you multiply three times X, times two, times four.

Ms. PICK: There you go.

SANCHEZ: Ms. Pick has only been teaching three years, and by all accounts, she's turned out to be a terrific match teacher. So does is matter that she doesn't have a math degree? The National Panel couldn't answer that question. It's not exactly clear what should go into preparing a good math teacher. What is clear is that student's interest in math absolutely depends on engaging creating teachers who really know their math. Otherwise, says Pick, kids get bored and frustrated.

Ms. PICK: They say, you know what, math is hard for me, I didn't get it that way, I'm done. I don't like math. I'm bad at math. That's the kind of attitude you see.

SANCHEZ: That attitude may be the biggest obstacle of all, because unless it changes, the push for a more coherent, rigorous math curriculum may not be enough for U.S. students to catch up to their peers abroad.

Claudio Sanchez, NPR News.

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