A Winning Formula
An innovative K-6 math program emphasizes problem solving, not rote memorization
Students at Munsey Park Elementary School in Manhasset, N.Y., love math—and why wouldn’t they? During math time, they read stories, play games, and solve mysteries. In their search for answers, they use calculators and other tools. Long gone are the activities of most traditional mathematics programs: memorizing times tables, trying to remember when to borrow and when to carry, struggling through strings of long division problems. Instead of focusing on rote memorization, teachers at Munsey Park emphasize mathematical thinking. They encourage their students to look for patterns and relationships, to apply logic and reasoning, and to seek multiple paths to a solution.
It’s all part of the Comprehensive School Mathematics Program, an innovative K-6 curriculum currently in use at Munsey Park and hundreds of other schools in 35 states. Created more than two decades ago by researchers at the Mid continent Regional Educational Laboratory, a federally funded facility in Aurora, Colo., the program stresses problem solving and concept development.
On this rainy morning, students in Inara Hirn’s 4th grade class at Munsey Park Elementary are busy cutting sheets of paper into strips; they mark one in half, another in fourths, yet another in eighths, and so on. After they’re finished, they line up the strips to look for relationships. They can see for themselves that two fourths is the same as four eighths.
“In this stage of development,” Hirn says, “the purpose is not to have equivalents memorized. They need to be able to take a ruler and visualize where the fractions would fall.”
Downstairs, Diane Potente’s 1st graders have just met Eli the Elephant, a furry pink and gray hand puppet. Eli, it turns out, collects regular peanuts and “magic peanuts” (negative numbers). When each of the two types of peanuts interact, poof, they disappear.
The concept of negative numbers, Potente explains later, is a hard one. In a traditional program, she says, 1st graders learn numbers one through 25 and how to perform simple addition and subtraction. With CSMP, however, the very first lesson of the year introduces numbers greater than 25 in a cat and mouse game. By the end of the year, students will be dividing and multiplying. “Children love numbers,” Potente says. “They love to experiment with them. You’re limiting them if you go with a regular textbook approach.”
One of the program’s overarching goals is to get students to apply the concepts they learn in a variety of situations. Math is approached as a unified whole, not as a series of isolated topics. Logic, probability, geometry, and computation are all woven together. In program jargon, this is known as the “spiral approach” because the concepts keep cycling back. “A lot of kids won’t get the concepts the first time around, or they won’t get every one,” says Richard Koebele, principal of Shelter Rock Elementary, also in the Manhasset district. “But it’s going to come back again, maybe later on this year, sometimes on another level, and that will reinforce it.”
Some teachers using CSMP in their classrooms describe it as a kind of whole language for mathematics. “If you think about whole language strategies—the writing, the many ways to get to an answer, the real life applications—they’re here,” says Munsey Park math specialist Marilyn Tahl. “Instead of learning multiplication because today we’re going to multiply, you learn to multiply because you have a problem that you need to multiply in order to solve.”
Munsey Park 6th grader Jennie Lin describes the program as “one big game.” “There are spy games where you have different routes to a place, and you have to try to figure out how many routes there are to one place,” she says, her words tumbling out excitedly.
“And when we’re learning that,” adds classmate Colleen Clemency, “we’re also learning Pascal’s triangle.”
“They basically made math fun,” says 6th grader Chris Mucciolo, “because there’s always a story in the lesson.”
Fantasy, real life problems, and manipulatives all play a role. “We try to make math an appealing subject that keeps children excited by using situations and experiences that are interesting,” says Clare Heidema, who directs the mathematics program for the Colorado laboratory.
The program has no textbook. Instead, participating districts order classroom learning kits from the lab that range in price from $160 for kindergarten to $400 for 6th grade. Among other things, the kits include teachers’ guides, manipulatives, classroom visuals, story books, and activity sheets.
The lab often provides inservice training for teachers or math specialists from districts that are using the program. In Manhasset, for example, all elementary teachers—including substitutes and aids—receive intensive training for one or two weeks in the summer until they are comfortable with the program and the accompanying materials. Math specialists and administrators offer feedback and support throughout the school year.
Many teachers using the program find that it demands more of them than traditional approaches. For example, marking papers and going over homework can be challenging since children approach problems and arrive at solutions in many different ways. “Correcting takes time,” Hirn acknowledges, “but it’s worth it to see them understand.” Teachers also have to be willing to let go of the reins a bit and let kids reason their own way through problems. Students are encouraged to work together and talk openly with classmates about how they come up with their answers. “The biggest thing is that they get to explain how they solve a problem,” Hirn says. “It’s not me telling them you will solve the problem this way. It’s ownership, which gives them a wonderful sense of responsibility.”
Although CSMP was developed in the 1970s, program officials say it is in line with the standards approved in 1989 by the National Council of Teachers of Mathematics. Those standards urge teachers to emphasize problem solving, discussion, reasoning, and real world applications and to use cooperative learning, manipulatives, and technological tools such as calculators and computers in their classrooms.
“If you look through the standards,” says Marilyn Chiarello, math specialist at Shelter Rock, “there are some examples in there that just happen to resemble CSMP problems exactly. It almost felt like, ‘Wow, the NCTM is validating what we’ve been doing for 10 years.’ “
Validation has come more officially from the National Diffusion Network, a division of the U.S. Department of Education, which has given the Comprehensive School Mathematics Program its stamp of approval three times, most recently in 1992. According to the diffusion network, only “exemplary educational programs that work” warrant this distinction.
CSMP officials note that this outside recognition merely confirms what they already know. Studies show, they say, that participating students are better able to apply what they have learned to new situations and have a greater enthusiasm for mathematics than their non program counterparts. What’s more, they learn traditional math skills and concepts at least as well as other students.
At Munsey Park, students’ standardized test scores have improved since the program was adopted there a decade ago. In fact, according to Tahl, the school switched to the Stanford Achievement Test after the majority of its students began scoring in the 90th percentile on the Comprehensive Test of Basic Skills. In addition, no one in the regular school program has scored in the unacceptable range on the New York State Pupil Evaluation Program test, given to 3rd and 6th graders.
But perhaps even more telling is the way mathematics now extends into many aspects of students’ lives. Fifth and 6th graders crowd into the school cafeteria in the mornings to do math activities before their classes begin. Students inserted a math column in their school newspaper. And poems written by students about math are proudly displayed on a bulletin board in a school corridor. “What we’ve found,” says Munsey Park principal Irene Hurst, “is that children have a tremendous interest in math. When you take the approach that math is fun, that it’s part of everyday life, that it’s relevant and a useful way of thinking rather than just a skill, kids adopt that attitude.”
Of course, the program also has its critics. Some parents who are unfamiliar with CSMP see that their children are not being taught math the way they were. As a result, they worry that their kids are not learning the subject properly and that they will fall behind as they advance in school. “Many of the parents think we should be teaching algorithms,” Hirn admits.
To address such concerns, the Manhasset school district has made a concerted effort to reach out to parents and educate them through workshops. “After a while,” Tahl says, “when the test scores are so wonderful, the resistance wanes.”
Elizabeth Short, a parent and human resources manager for a large corporation, is a program booster. She believes one of the most important skills children need to learn is the ability to solve problems creatively. “CSMP gets children to think about the fact that there’s one right answer, but there may be many ways to get to that right answer,” she says. “The ability to have a mind think like that is very valuable.”
As for the students, math has become so much fun that they don’t always realize they’re learning. After a normal day of school that included CSMP, one parent asked her son what he did in math that day. “We didn’t do math today,” he responded.
Vol. 06, Issue 01, Pages 17-19