Parents question math strategies
They fear schools focus too much on talk, not enough on facts
As third-graders sat in a circle around her, teacher Jane Ehrenfeld outlined a math problem: If you put 275 pennies into rollers holding 25 pennies each, how many penny rollers would they fill?
Hands shot up, but Ehrenfeld, a teacher at Nathan Hale School in Roxbury, halted students trying to give the answer and urged them to think first.
''The most important thing you do as you're reading a math problem is to try to picture it," she said. ''You're trying to get a little movie going in your head of what's going on. What kind of math is happening in this problem?"
For the next several minutes, students talked about different ways to solve the problem, but they didn't add, subtract, divide, or multiply. Calculating the answer would come later.
Elementary schools across the state are taking such an approach, emphasizing discussion, hands-on solutions, and the idea that there is more than one way to solve math problems. But to parents, this approach to math instruction doesn't always make sense. They, and some teachers, worry that encouraging students to come up with strategies on their own doesn't work for all students. They want teachers to mix in math drills because they fear some children will not learn to quickly recall math facts.
''I get the concept. You should understand math," said Cathy Moylan, whose son, Owen LiPuma, is a third-grader at Edward Everett Elementary School in Dorchester. ''But there's just a lot of groping around. I feel like there's one answer in math and you should get it, not talk about how you're going to get it."
This war over math instruction -- the mathematical equivalent of the reading wars of the past (Should schools use whole language, a more conceptual method of reading, or phonics, which is more rote?) -- has been simmering for about a decade. One of the latest battlegrounds is Boston, which began using a new math program in some schools in 1999 and, by last year, had instituted it in every elementary school. Boston uses Investigations in Number, Data and Space, a curriculum produced by TERC, a Cambridge nonprofit. Wellesley, Reading, Shrewsbury, Braintree, Lynnfield, Ipswich, and other towns have been using similar math programs for several years.
The push for a new approach came from the National Council of Teachers of Mathematics, which, in 1989, issued a set of standards for math instruction. The math teachers' group wants people to know that 3 times 4 equals 12, but it also wants them to realize that they're figuring out the area of a rectangle when they do that equation, said Jim Rubillo, the organization's executive director.
''If that were firmly understood, people would have a lot less trouble buying carpet in our society," Rubillo said.
In response to the council's standards, the US Department of Education endorsed several new math programs, including Investigations, MathLand, and Everyday Math, as ''exemplary" or ''promising." The programs are used widely in Massachusetts, but not as much around the nation, Rubillo said.
The goal of the Investigations curriculum is that children develop a high level of mathematical proficiency and make sense of the mathematics they are doing, said Susan Jo Russell, who directed the development of the program for TERC. The newer math programs do not deemphasize computational skills, Russell and Rubillo said.
But many parents lament that they cannot help their children with even second- or third-grade math homework.
''Homework is just a huge struggle," said Karen Gaylord, whose youngest daughter, Emily, is a fourth-grader at the James F. Condon Elementary School in South Boston. When she or her husband, a mechanical engineer, tries to help her with math, Emily tells them, ''No, I can't do it that way."
Gaylord recalls one assignment in which Emily had the option of solving a problem with pictures, words, or numbers. She chose pictures and drew numerous balloons, which she then miscounted.
''There are too many opportunities for mistakes," Gaylord said. While stressing that her daughter has a good math teacher this year, she said, ''It's a nightmare. There's a lot of crying. My daughter is struggling, and I feel I can't help her."
Sid Smith, Boston public schools' director of curriculum and instruction, said he is convinced that the program is a good one. Fourth-grade MCAS scores in math have improved since schools began using the new approach, he said. The percentage of fourth-graders scoring proficient or advanced on the math MCAS -- the highest categories -- nearly doubled, from 14 percent to 22 percent between 2000 and 2004, and the percentage failing decreased from nearly half of the students to about a third.
Wayland and North Andover schools, though, are reviewing their use of the same program Boston uses because of concerns that students are not learning basic math facts.
North Andover School Committee member Charles Ormsby, a calculus professor at the University of Massachusetts at Lowell, wants a return to more traditional math instruction. He said he routinely sees college students who are incapable of doing basic long division and fractions.
''In order to do higher-level math, the basics have to be automatic. They have to be second nature. And you have to understand them," he said.
Smith said school systems need to provide training for parents and teachers if they want the new approach to succeed. In Boston, the school system offers ''math nights" a few times a year and workshops for parents. In Wayland, parents can attend PTO meetings to see examples of math games they can play with their children.
But many parents said they have to do more. They are drilling their children in math facts, hiring tutors, or enrolling their children in Kumon Centers or similar programs. Some specialists say mixing approaches will confuse children, but parents say they want to be sure their children can compute equations with ease.
William Pike, a Wellesley parent who led an unsuccessful fight against a curriculum called MathLand many years ago, found tutoring for his sons. He also did drills with his youngest son, now a 10th-grader. ''We had to play catchup with tutors," said Pike, an MIT graduate. ''It's infuriating."
Back in Ehrenfeld's class, students working on the penny roller question did eventually produce answers.
''I counted by 25s until I got to seven," said Sharon Moy, 9.
''Until you got to seven?" Ehrenfeld asked.
Sharon and the teacher count by 25s up to 275 and realize that the answer is 11, not seven.
Then 8-year-old Dakota Watts raised his hand to explain his strategy: He already knew that 12 times 25 equals 300 and since 275 is 25 less than 300, he knew the answer was 11.
''The concern among parents is that the way they know how to solve the problem is not the way their children are learning it," Ehrenfeld said.
But when she was in fifth or sixth grade, she learned about computers, a topic her parents knew nothing about.
''I don't think that's a reason to stop teaching it," she said.
Nor do many parents, as long as more of the basics return to math class, just like phonics eventually came back to reading classes in many schools.
''What's going to happen when they go into a store? Are they going to say, 'Do you happen to have 25 Cheerios so I can break it down?' " said Jacqueline Azulay of Roslindale, who sees her two daughters going to great lengths to break large numbers into manageable pieces. ''I think they need to teach basic math."