This summer, at Arlington's Oakridge Elementary School, Elizabeth Iacoponi's students learned decimals, geometry and fractions without textbooks, homework or tests.

As participants in a five-week experiment at three elementary schools that ends today, Iacoponi's students, most of whom will enter the sixth and seventh grades next month, worked to solve math problems with their hands, eyes and ears. Students used toys, puzzles and games with mathematical applications to master basic math concepts.

"It will never replace the textbook," said Lorraine Groff, county mathematics specialist. "All I'm saying is that during the regular school year, when {these students} look at the pictures in the math book, they'll know they've physically manipulated them."

Groff initiated the experiment with the hope that the fresh, hands-on approach to math would help the students to grasp the computations they are required, but often fail, to memorize or work out on paper during the regular school year.

Groff said she also plans to ask teachers to include mathematical toys and games more often in math classes during the regular school year.

"If anything, the students have had a break from a textbook" and from "a mindset," Groff said.

During the summer session, about 115 first- through sixth-grade math students solved math problems by manipulating wood blocks and other teaching tools typically used only briefly by teachers to demonstrate math concepts to a class.

Teachers involved in the experimental classes reported that by handling the toys themselves, students took a greater interest in the lessons and challenged themselves in ways the teachers could not.

"Kids are so used to the computations that they don't understand the concepts. {But} they need that first, developmentally, to move from concrete to paper," said Kathleen Moore, who taught rising second- and third-graders.

"There's no sense learning a math problem if you don't learn how to manipulate what you're doing," Iacaponi said. 'With the quick kids, you can show them shortcuts" to solve a problem, and "with the slower kids, you can break it down a little further."

For three hours one morning last week, Iacaponi's students learned how to add and subtract fractions with unlike denominators with the help of wood pieces of various sizes and shapes that combined in different ways to form hexagons. Each student was asked to solve math problems by manipulating the blocks and then translating the computations onto paper.

Students were encouraged to cooperate on difficult problems, breaking a math class tradition of students keeping their eyes on their own work.

Admittedly, Iacaponi's students showed more enthusiasm for recess than for sitting in a classroom on a warm summer morning to solve problems, despite a curriculum that included toys and games. Still, many students said they like learning math hands-on. "It's easier" than textbook learning, said Pedro Hernandez, 12. "It's the same thing, but it's fun too."

The problem with textbooks is that "you can't understand them," said April Rowe, 12, who is entering the seventh grade. "Sometimes they write the directions, but you can't go by them. It's complicated when you read {math} in the book."

Younger students agreed.

"Just like exploring in the jungle, you can learn anything by doing," said Julia Oritz, 7, a student in Moore's class who said she had feared timed addition tests during the previous school year and regretted not being recognized on the school's "Wall of Fame."

"We don't care more, but we have fun more," added Lindsay Anderson, 8.

Nevertheless, John Durrer, who taught math to rising fifth-grade students, warns against teachers relying too much on physical teaching tools.

"I would not want to conduct my entire class during the regular year using only manipulatives," Durrer said. Some math problems, such as multiplication of long numbers, are easier solved with a pencil, he said. "Manipulatives need to be supplemented."