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Circle in the square

They were given a 3-by-5-inch index card, a pair of scissors and the

task of cutting a perfect loop that they could fit their bodies


This was a lesson in thinking outside of the box.


The eighth-grade students in Jay Duval’s science class at Mesa

View Middle School took on their assignment with gusto.

“This is easy!”

“Oh, I can do this!”


After little success, the students balked.

“You want us to do what?”

“This is going to take a while.”

Duval’s exercise in creative thinking allowed his students to

diverge from their usual methods of scientific experimentation and

look at matters from a new perspective.

“In learning, not everything involves steps,” Duval said.

Inspecting an array of imaginative quasi-origami figures and


confetti, Mr. Duval took stock of his class’s progress.

“Look what we have here!” Duval exclaimed as he motioned a student

to share her work.

After examining it further, he sounded disappointed.

“Too small,” Duval said. “Do you think you can pass your body

through that?”

Another student delivered a big loop but was disqualified for

having loose ends.


“It needs to be one continuous loop,” Duval reminded them.

After a short comparison and analysis of their peers’ work, the

students returned to the task. Learning from the results of others

can be important in science, according to Duval.

More folding and cutting produced a fresh round of results for the


“It looks like you got it,” Duval said, eager to check out a loop

being held up by a beaming student.

The loop was perfect, and the student moved it across his body

with satisfaction.

“You see, it can be done!” Duval said.

A sense of victory filled the room as other class members also

found success.