What has 50 fingers, 12 ears, 12 legs, 6 heads, and no tails?
That question was posed by a second-grader, assigned to compose a riddle rather than simply add up numbers.
Meanwhile, in a fifth-grade classroom, teams of students slid together plastic shapes to build polygons.
Both exercises were part of the the investigatory approach to math education employed at the Richard J. Murphy Elementary School in Boston.
That investigative focus impressed Johnny Lott, president of the National Council of Teachers of Math, who toured the school last week before kicking off a three-day NCTM regional conference in Boston.
"There's more to math than learning by rote," says Mr. Lott.
The Murphy School's approach isn't typical, according to a report on math education released this year by The Education Trust, a nonprofit organization in Washington. The report described math education in the US as a "mile wide and an inch deep," covering more topics than do other nations, but in far less depth.
Part of the problem, The Education Trust found, was the level of math education teachers themselves receive. The average US education major in the 1990s completed only two semesters of math - less than the three to five courses recommended by the Mathematical Association of America.
Making sure teachers get more math education - both before and after they start working in classrooms - is a top priority for the NCTM, Lott says. "Math does change. Teachers need to keep learning," he says.
So during three days packed with 350 instructional sessions, math teachers attending the NCTM conference could learn how to help students move from arithmetic to algebra or use cheerios in data analysis.
The NCTM also offers more intensive two- to five-day institutes on geometry and algebra throughout the school year.
At the Murphy School, principal Mary Russo says teachers arrive with "spotty training" in math. But new teachers may be more open to new teaching approaches, she suggests, because they have not wedded themselves to certain methods the way veteran teachers sometimes do.
Instead of just following their math textbooks as they might have done in the past, Russo says new teachers get more guidance. They have 30 hours of curriculum instruction in the summer or fall of their first year.
Teachers learn to emphasize student investigation - starting with simple questions such as how many pockets are there on the clothes their classmates are wearing.
Russo says the focus on developing teacher skills helped boost the school's scores on the fourth-grade math exam to the second best in the Boston public school system. The school's failure rate on standardized tests overall dipped from 50 percent in 1999 to 19 percent in 2002.