Cover Story : Strength in Numbers : Why Did Fourth-Graders at One School Do So Well in Math on the State Test? The Answer May Lie in Creative Teaching and Controversial Grouping Based on Ability

Take the numbers 523 and 651. Which one is divisible by 3? Easy. Add up the digits. Five plus 2 plus 3 equals 10. Does 3 go into 10? No way. Six plus 5 plus 1? 12.

Yes! Yes! Yes! The fourth-graders at Horace Mann School in Beverly Hills hiss their satisfaction.

Teacher Ellen Morehead does not let up, filling their math hour and much of the school day with mind-stretching exercises designed to help them get beyond just finding the right answer.

“We’re trying to make sure your brain doesn’t get lazy on us over vacation,” she told the class the day before they left for spring break last week.

This is the sort of teaching that helped last year’s fourth-graders at Horace Mann score among the highest in their age group in Los Angeles County on the new statewide California Learning Assessment System, a comprehensive test known as CLAS.

Although state authorities decline to cite any one indicator for ranking schools by their CLAS results, the figures show that of all the schools in the county, Horace Mann had the highest percentage of students in the top three scores and the lowest percentage in the bottom three scores.

The scores were announced last month to the dismay of almost everyone in the county except Horace Mann, which serves a neighborhood of modest homes and apartments in the southeast corner of Beverly Hills, where about a third of the residents do not speak English at home, according to census data.

This year’s 84 fourth-graders will face the CLAS challenge next month, but Morehead and her two fourth-grade colleagues said they do not believe the results of the test, which was given for the first time in 1993, were a fluke.

The school’s performance, they and others maintain, is due to the approach Horace Mann takes to teaching math, a strategy that emphasizes analytical thinking and, despite some controversy, groups students by ability. It is an approach that had other districts calling the school for tips after the test results were announced.

“As long as I’ve taught, I’ve taught this way,” said Morehead, who has been at Horace Mann for her entire career. Now that state experts who wrote the test are looking for evidence of the skills that she has been teaching for 25 years, “we’re ahead of the game,” she said.

The CLAS test replaced multiple-choice exams that did not take into account how students arrived at their answers. Students now must explain some of their answers, with points assigned not just for correct responses but also for evidence of understanding basic principles and being able to explain how they arrived at the solutions. Students in grades four, eight and 10 were tested in reading, writing and math.

Students were given scores of 1 to 6, with 1 meaning little or no grasp of mathematical ideas and 6--a score experts say is virtually impossible to attain--showing deep understanding of the subject.

Morehead said she and her colleagues, who have been working as a team for five years, were most proud of the low number of 1s reported for Horace Mann. Only 2% of their fourth-graders tested scored that low, compared to totals ranging from 12% to 26% at the three other elementary schools in the Beverly Hills district, 44% countywide, and 38% statewide. On the higher end, 49% of Horace Mann students received scores of 4 and up, compared to a district average of 25% and a county average of 6%.

How did they do so well? At Horace Mann, Morehead said, instruction goes beyond the basics to probe the why behind mathematical ideas.

“Our philosophy is instilling the basics. That’s crucial,” said Morehead, who starts by working with colleagues Rachael Zanka and Lynn Koff and lower-grade teachers to drum the standard arithmetic curriculum into their kids.

“Once they understand that, it’s our goal for them to be able to explain the why of any problem we present to them, whether it’s how many triangles I can get out of a hexagon, or how many different ways there are to make change for a dollar,” she said.

The teachers had to overcome the objections of some parents who did not want their children sorted into groups by ability for the one-hour daily math session.

The teachers say that pupils also tackle math at other times during the day, when they work together, regardless of skill level.

But parents of about a dozen students, some of whom have since opted for private schools, do not buy that.

“The math tracking was a very big reason why I left. Many brilliant children were put into the low group and made to feel very stupid,” said Rosanna Grabel, whose son was put in the low group.

“The kids in the low group think they’re bad in math, and it’s a stigma that sticks with them all their lives,” added Deborah Mehrez, whose son was put in the middle group despite scoring high on another statewide math test. She has since placed her son in private school.

The parents were also upset at the blow to self-esteem caused by a field trip that the high group took to the Pacific Stock Exchange. The others stayed at school to watch a movie.

“The way people feel about themselves, not just the top of the barrel, is the most important thing,” said Mehrez, a former PTA president.

Although Morehead acknowledges that the field trip was “a big mistake,” she, Koff and Zanka defended grouping. They said it brings them as close as they can get to having one teacher per student.

Pam Kraushaar, president of the Horace Mann PTA and the mother of a fourth-grader, agreed.

“Whoever did disapprove of it, they have to see now that it works,” she said. “By putting kids in different levels, you can still have kids achieving high in lower levels.”

Although her daughter is in the high group, she said, “I see it working for her friends too, so we’re very happy with it.”

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During class, students may work on problems at their desks, sit in small groups on the floor, talk among themselves about such things as place value, integers and quotients, or play a strategy game on a graph projected on the wall.

Homework often includes puzzlers such as this one: A waiter divides a round pizza pie into eight equal slices with only three straight cuts of a knife. How did he do it?

Think about it. Now let’s talk to some fourth-graders.

Ernie Klein, 10, came to Horace Mann in January, transferring from another Beverly Hills school where pupils were not grouped by math ability.

“There, they were always teaching out of a book,” he said. “The smarter people were really bored because they had to wait for the not really fast people.”

Micah Amado, 9, said, “The people that are really strong go to a math class that’s really hot. It’s better, ‘cause the math book is really dull.”

Danny Abraham, 10, added, “If we need help, then all of us (on the same ability level) need help at the same time.”

And Sogol Simino, 10, said, “They don’t just want answers. They want you to explain the whole thing.”

OK, who’s ready for pizza? Here’s the answer: The waiter makes one cut across the diameter, creating two equal halves, and another at right angles, yielding four pieces. He then stacks them up in a pile and slashes down the middle.

This puzzle came from a logic book designed for fifth- to eighth-graders, something that the teachers scrambled to find, along with problem sheets and educational toys, since most arithmetic texts do not reflect their approach to teaching.

Although Supt. Sol Levine was careful to note that other Beverly Hills schools did well in the reading and writing portions of the CLAS test, he said Horace Mann’s success in the math exam will be held up as a model.

“In large measure, (Mann’s success) is due to the work of the teachers, and to the fact that the exam does test thinking skills, the ability to explain why certain things are done in math, and the teachers involved use those approaches along with teaching the basics,” he said.

“It’s not inflexible. It’s a process where they try to identify where the children are, and to work with the children at that particular point,” he said.

The teachers, too, stress the flexibility of their approach, which allows students to change levels easily as they improve skills.

It also allows children to ask questions without fear of setting off scornful laughter from their peers.

“They’re not afraid to ask questions, because it’s probably on the minds of several kids in that group,” Koff said.

It also makes it easier for teachers to pay attention to the children at the top and bottom of their classes, extremes that are often neglected when teaching everybody at once. At Horace Mann, the middle and top groups are a little larger, so there is more time per pupil in the lower section.

“Frankly, teachers like to teach the brighter kids,” said school board President Lillian Raffel. “If we did that all the time, it would be a disaster politically, and demoralizing to the other kids.”

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There were a few complaints from parents two years ago, she said, but they have since dropped off.

“Maybe (the teachers) explained it to the parents better,” she said. “There’s always some pressure to jam the high group, and it’s unfair to kids to be pushed like that.”

Board member A. J. Willmer, whose daughter is in the fifth grade at Horace Mann, said the impact of the CLAS results will be immediate districtwide.

“The point is to look at all those 3s, 2s and 1s and move them all up,” he said. “We don’t want to compare ourselves to the rest of the L.A. County but to ourselves, and to get better.”

Though parents and administrators credit the cadre of veteran teachers at Horace Mann, the teachers themselves pointed to the arithmetic basics that their children got in earlier grades, and to the support of Principal Arthur E. Fields.

“I’ve gotten a lot of calls from different school districts asking what we did,” Fields said. “My answer is that it depends on your teachers, how good they are and how much time they’re willing to put in to develop these materials.”

Will Horace Mann repeat its math success on this year’s CLAS?

“It’s a lot of pressure,” said one of the three teachers. “Don’t you dare quote me (by name), but I lie awake at night wondering if it was a fluke. I don’t think it was.”

Head of the Class

Horace Mann Elementary outpaced other Beverly Hills schools in the fourth grade math portion of the California Learning Assessment System test. Results are expressed in terms of the percentage of students who ranked in the top or bottom scoring range.

ELEMENTARY SCHOOL 4-6 (TOP) 1-3 (BOTTOM) Horace Mann 50% 51% Beverly Vista 5% 94% El Rodeo 18% 83% Hawthorne 28% 73% Districtwide 25% 75% Countywide 6% 93% Statewide 7% 91%

Note: Scores may not add up to 100% because of rounding and statistical variations.