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Math project helps solve old problem of poor skills

Sunday, August 23, 1998

Jane Blotzer, Associate Editor, Post-Gazette

That children have an innate enthusiasm for math might seem foreign to most mathphobic adults. But that truth might hardly be missed in Barbara Cooper's first-grade class at the Tenth Street School in Oakmont.

When she announces plans for a math exploration, the room erupts in whoops and applause.

A few minutes earlier, during their daily calendar exercise, the class came up with 19 equations that equal 26 - the day's date. And before the class is over, they will compare high and low temperatures in the state, nation and world.

"Oh, oh, guys, this is bad," says one young mathematician, shaking her head and poring over the temperature readings in the morning newspaper. "I can't figure out the coldest temperature." But working together with her three deskmates, she eventually makes an accurate meteorological reading.

The room is a buzz of activity, all of it very much focused on math. "It's noisy," Cooper explains to visitors. "That's how kids learn today. It's not just sitting in your seat anymore, listening to the teacher."

And what comes out of this new approach amazes the longtime teacher. "They're learning so much, it boggles your mind sometimes. They're doing things I didn't know they could do."

Cooper's first-graders, who know their way around a fraction and a polygon, are experiencing Everyday Math, a curriculum that the University of Chicago School Math Project designed in 1983. It - and the dozen other new math approaches that have followed - are the latest salvo in a half-century struggle in the United States to improve math education.

The most recent round of reform began when international surveys showed that American pupils lagged in math achievement. It was given added impetus when the Third International Math and Science Study, the most comprehensive international comparison ever, not only found American pupils at the back of the pack but also showed that the most advanced 12th-grade U.S. math students were well behind their international peers. The survey was done in 1995, but the results were released last year and this year.

Everyday Math is offered to about 10 percent of elementary pupils nationwide, making it the most widely used of the new approaches. Numerous districts locally, including the city of Pittsburgh, Quaker Valley, Greensburg Salem and Beaver Area, have made it a grade school staple.

The impact of the new programs is not limited to the classrooms in which they are used. The concepts that distinguish the courses - an emphasis on problem solving and mathematical experiences over pencil and paper drills and rote learning - have been incorporated into many of the newer texts that mainstream publishers put out.

Share their results

Most elementary math classes in the region look different than they would have 20 years ago. Traditional practices are routinely supplemented with hands-on, real-world activity and fun.

Schools that choose the new offerings think their path represents the best possible combination of drill and problem-solving, of teacher lecture and student exploration.

Max Bell, one of the designers of Everyday Math, said he and his colleagues began by interviewing pupils to see what they knew.

"We saw they were all willing to give math concepts a try, a lot with some success. Kids entering kindergarten can count well beyond 10, and they recognized numerals. Ask for half, and they give you half. Ask them to divide these up between the three of us, and they got it done. They had the essential ideas of operations. Kids were way ahead of what was being asked of them."

But instead of allowing them to develop these basic understandings, most schools were asking them to "push a pencil." Much of the natural excitement and enthusiasm that youngsters brought to the subject were systematically drained away.

Everyday Math introduces concepts of multiplication and division, fractions and geometry, early in the child's school experience, laying the groundwork for mastering the operations and processes down the line.

Despite the fears of anti-reformers, pupils taking Everyday Math are expected to know their number facts. But they are also prepared for the higher-order thinking needed to tackle algebra, geometry and more advanced problem solving in middle school, where, most agree, reform is most desperately needed.

Such deep understandings start early.

Joyce Liptak, a second-grade teacher in the Greensburg Salem District,

introduces the concept of squaring a number by having her pupils work with coins or blocks to create square "arrays" - figures that have as many objects across as they do up and down.

As in Cooper's room, the pupils get quickly to their task, and a half-dozen quiet conversations begin. Some children decide what the length of the sides of their array will be and go from there. Lauren Waugaman, Emily Etling and John Syner go a more adventurous route: They pick out a number of blocks and see if that will make a square array. Thirty-eight won't work. But it doesn't take long to see that 36 will. While one pupil is creating the array, another is writing down the factors (6 times 6) and the product (36). A third is reproducing the array by marking X's on graph paper.

From one desk comes a mock anguished cry from a pupil working with the graph paper. "She's trying to kill me!" he says of his group's array designer. "She's doing 10 times 10 in pennies. She's going to use up a whole dollar!"

After about 20 minutes, the pupils gather to share their results. They discover that when you square numbers, the values rise rapidly. The groups have done up to 12 times 12 for 144, but young Zach Wise isn't satisfied. He asks Liptak what 24 times 24 would be. "Zach, you're interested in more challenging problems. Why don't you try to figure it out?"

After thinking for a few moments, Zach says, "24 times 20 would be . . . 480." Liptak writes it on the board. "And 24 times 4 would be . . . 96. And 480 plus 90 is 570 and 570 plus 6 is 576."

While the visitors quickly take pencil to paper to double-check the answer, the class recognizes Zach's efforts with a round of applause.

Liptak acknowledges later that Zach is a very good math pupil, but she says he would never have had an opportunity to stretch himself like this so early in his schooling had it not been for Everyday Math. "We never would have gotten to this multiplication in the old program," Liptak says.

Transitions are hard

Everyday Math, the elementary component of the kindergarten through 12th grade University of Chicago School Mathematics Project curriculum, has been used for almost a decade in the Greensburg Salem district. The district was a pilot for the program, and now offers the full curriculum. But it still generates controversy - it was targeted by three candidates for school board positions last year.

"I get the impression that 20 percent grasp Chicago math and 80 percent have problems," said school board candidate Lee Kunkle.

The statistics suggest otherwise. The district's math scores on the Pennsylvania System of School Assessment were on the high end for comparable schools; on the Iowa Tests of Basic Skills they were above grade level - particularly in problem-solving and concepts - and were generally higher than the reading scores; and on the SATs, they were above the state and national averages.

National assessments of the program have shown that pupils in Everyday Math do as well or better than their peers in traditional classrooms in computation and far better in problem solving.

All three of the candidates won, though how much the math curriculum played into the result is not clear. Now in office, Kunkle says the vote was not a referendum on the math program and that he has no intention of just going in and removing it, although he is still not sold on the concept.

The resistance doesn't surprise the University of Chicago's Bell. In his project update submitted last year to the National Science Foundation, which helps fund the project, he wrote that "responding to anti-reform backlash" is one of the major issues facing the project.

He quips that parents have painful memories of their own math experience and want to be sure their children kids go through the same thing. "For many parents, 7 times 6 equals 42 is the last mathematical concept they were completely comfortable with," he said, and they want their children's school to put enough emphasis on such basic facts.

Bell says the emphasis is there, but it doesn't look like the drill work earlier generations went through.

No matter how good a program, however, transitions are difficult.

In the Riverview district, Everyday Math just completed its second year.

And despite the excitement in Cooper's classroom, it has not been an easy adjustment.

Unlike many districts, including the city of Pittsburgh's, which phased in Everyday Math, Riverview decided to implement the program in all grade levels at the same time.

The program was a shock for pupils students who were used to an entirely different approach to math, and teacher did not it was not universally accepted it. by the teachers. That combination made for a very difficult year.

Laura Duff, whose son is in Cooper's first-grade class, has been won over to the program. She says her son is thriving and that math has been the highlight of first grade. But last year was a different story. Her fourth-grade daughter spent much of the year frustrated and scared, and her experience was far from unique. Making matters worse, Duff and her husband didn't know how to help her.

Last year also was difficult for her daughter but less so, thanks in part to the fifth-grade teacher's willingness to go to extra lengths to help the pupils students - before and after school and during study halls.

"I really think this is a good program. It's just the way it was implemented."

For all the early introduction of sophisticated concepts in Everyday Math, the focus for elementary pupils students remains what it has always been: to master basic arithmetic.

The challenge for the middle schools, according to the reformers, is much greater. They must change not only how math is taught, but what is taught. That will require new programs and approaches and, most importantly, a new mind-set.

CAPTION: PHOTO: Joyce Mendelsohn/Post-Gazette: Carrie Visk and Joey Killian work on a math problem in Barbara Cooper's class.

PHOTO: Joyce Mendelsohn/Post-Gazette: Molly Farmer, 6, holds up her answer to a math problem in Barbara Cooper's first-grade class at the Tenth Street School in Oakmont.

PHOTO: Joyce Mendelsohn/Post-Gazette: Alyssa Richard and Jordan Moser use calculators in the class to figure the difference between temperature highs and lows.


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