There was something strange about this particular math lesson. The students were laughing and actually seemed to be enjoying themselves.
Meet Paul Oliverio, math humorist.
Teacher, too. But Paul Oliverio has this notion that teaching--and learning--math can be fun, so he takes his math gig on the road and teaches math--specifically, geometry--on stage.
This particular day he was at the Christ the King Academy, a small, private nondenominational Christian school in Fallbrook, and he stood in front of 45 kids.
An Italian, he dressed nattily and introduced himself with an exaggerated accent as "Godfather" of the Parallelo family, and he selected three students to play his sons.
Their names were Rectango, Squarini and Rhombo, and they're debating over the size of their territory, the story line goes. Rectango wants his territory's boundary to include a right angle--so he gets four. Squarini likes right angles, too, but he's a product of a liberal arts education and believes in equal rights, so he argues for the sides of his territory to be of equal length. He gets it. Rhombo, the black sheep of the family who seems headed for a career as a diamond smuggler, gets his territory shaped like one, a rhombus.
There are a lot of one-liners thrown in along the way ("A right angle is 90 degrees? Wow, that's hot. Four of them are 360 degrees? Wow, you can cook a pizza in that one!") The kids giggle and laugh, and when Oliverio's 15 minutes on stage is over, they applaud. And they probably will never forget the properties of a rectangle, square and rhombus.
The principal of the school, Pat Savas, was delighted by the performance, however corny.
"So many of us see math as a great onus, so anything we can do to make it fun and enjoyable, versus a burden to get through, is great," she said.
Oliverio may be more extreme than most math teachers in his approach, but he reflects a growing trend among educators to come up with new ways to teach math, and to focus not on rote memorizing of math rules and equations but on understanding the dynamics of math.
Two plus two is still four, but instead of looking at the numbers on a sheet of paper, kindergartners are counting four buttons or four toothpicks or four building blocks.
Two times three is still six, but instead of looking at numbers on a sheet of paper, primary-grade students are looking at three people with two ears each, or two legs each, or two eyes each, to come up with the answer six.
"We're definitely trying to get away from rote memorization because it appears that hasn't worked for the general population," said Janet Trentacosta, mathematics coordinator for the San Diego Unified School District. "Now, we're working more with manipulatives--actual concrete models (such as toothpicks, buttons, etc.) to show students the concept of what we're trying to teach.
"Rather than having our students memorize the fact that four plus five is nine, we're finding it's far more beneficial to show them four objects and five objects and have them put them together and realize there are then nine objects. It's concrete. They can see it."
And they'll remember it.
It's a simple concept in teaching--trying to move from the abstract, which generates anxiety, to the concrete--but it's been a long time coming in math and the advancement is critical in helping young children get a better grasp of what may be America's most feared classroom subject, experts say.
"We should always have been doing it this way," Trentacosta said. "The days are gone when we sat there obediently in the classroom and memorized what the teacher said. Now, we have students living in the generation of TV and video; it's a very exciting world, and kids don't want to just memorize anymore."
The new buzz phrase in math is "teaching for understanding," she said. It's no longer good enough for a student to know that 2 plus 2 is 4; now he must understand why the answer is 4.
To that point, the state Board of Education several months ago rejected virtually every mathematics book submitted for its approval, sending them back to the publishers with orders that they develop better concepts of understanding math versus the old-fashioned rote teaching of principles.
"Mathematics research has told us all along that we've needed to do this," Trentacosta said. "What has finally really pushed us in this direction is all the studies that compare us to other countries (in math skills) which show us declining.
"We've just completed the back-to-basics movement, and we still aren't any better at it. Our children need to better understand , not just know , the answers."