WASHINGTON (AP) — It’s the kind of drill that drives math nerds crazy. And it wouldn’t matter so much if these statisticians, scientists and others weren’t parents as well.
The drill, as described in a California workbook for seventh-graders:
Students, in a group, must fill an imaginary recycling container with imaginary phone books. But the books and container have only two dimensions. And the kids also may use a calculator to figure out .75 times 600, part of the exercise. The text gives the answer, right next to the problem, just in case students can’t get it with a calculator.
Critics like Paul Clopton, a 46-year-old statistician and angry San Diego parent, say 1992 changes in California math teaching, prompting such exercises, are creating math dummies. A state board is working on new standards this year.
And the issue has attracted angry parents’ attention beyond California, because some of the teaching philosophy under fire would show up in voluntary national standards and tests that President Clinton supports.
Critics say the math curriculum reflects the handiwork of the National Council of Teachers of Mathematics, which in 1989 called for a national overhaul of math teaching.
The council, worried about America’s math phobia and dropping test scores, hoped to make math more meaningful by changing from a dry-as-chalk focus on drills, postulates, definitions and proofs — the memorization of tables and rules — to a more real-world focus.
The council also recommended that all grades use calculators.
“All of the research that we’ve seen shows that children learn differently,” said Jack Price, professor of mathematics education at California State Polytechnic University in Pomona and past president of the national group. “For some, direct instruction in the classroom works well. For others, it doesn’t.
“We have never said anywhere in any of our publications that children shouldn’t know their basic skills,” he added.
In an interview, though, Price questioned the need to learn the multiplication tables, or at least more than half of them. Why memorize 4 times 3 if you already know 3 times 4?
Why figure a square root without a calculator? Or long division for that matter? Why do a stack of division problems for homework?
Should standards be so specific as to say children in the first grade ought to be able to write every number up to 100?
“Some kids are not going to be able to do that,” he said.
Under the council recommendations, students instead were encouraged to focus on problem solving, generally in groups, as the best way to pick up skills and prepare them for the real world.
The council also recommended that students learn geometry, probability and pre-algebra before they reach high school — a seemingly high standard.
But critics worry how well the children use classroom time, and whether the stress on group activities too often substitutes play-acting for real learning.
Marianne Jennings, a 43-year-old lawyer and professor of business ethics at Arizona State University, has crusaded in newspapers and other publications against a widely used algebra textbook that talks about Maya Angelou’s inaugural poem for Clinton, African tribes, pollution — striving, she suggests, more to be politically correct than educational.
“I was driven to write about this because it became very clear my daughter was becoming a math illiterate,” Jennings said, talking about Sarah, now 14.
Critics also complain there’s too much stress in the early grades on “manipulatives” — cubes, little figures, colored sticks and other pieces that critics call “concrete pacifiers.”
In a San Marcos, Calif., classroom, for example, third- and fourth-graders mark out each others’ height on the floor, then make cube “trains” for each student’s height. They line up the trains side by side and derive a mean height by subtracting cubes from the longest train and adding to the shorter one.
Pupils estimate, then actually measure, the length of a train, then use that mean to measure the height of various animals in kid-sized units of 54 inches.
Teacher Eunice Hendrix-Martin, writing about her classroom in a teachers’ magazine, said the project helped kids see that “measurement is never exact.”
Although Clopton sees value to that particular exercise, he questions whether so much time should be spent on so little arithmetic. “Do they really have to lie on the floor and spend a whole day on this?”