In 1992, Mattel Toys put the first talking Barbie doll on the market. The first words out of her perpetually smiling plastic mouth were, "Math class is tough." Mattel designers thought they were just expressing the feelings of most school-age girls. They didn't anticipate the storm of protest from parents, sociologists and educators that resulted in talking Barbie being yanked from store shelves. The blonde with the doe eyes fell silent again.
She might not have made such a gaffe, however, if she had said, "Math class gets tougher and tougher." In that case, major studies would've backed her up.
According to the Third International Mathematics and Science Study, for example, American fourthgrade children rank with the topachieving two or three countries in the world, judged among students from 41 nations. But by the time American students graduated from high school, they are almost last-about two or three from the bottom in that same list of nations. "In other words," said then-Senator John Glenn during his presentation of the September 2000 report to the federal Department of Education, "our kids are losing ground in mathematics and science compared-now that's compared. It doesn't mean that our scores have not been moving up. I think we should point that out."
As time goes by
Why do American students "lose ground" in mathematics through the years? University professor Brian P. Chinni says it's an outcome of the "mile-wide and inch-deep syndrome."
"Coverage tends to be the emphasis," says Chinni, who teaches a course at Fairleigh Dickinson University in Teaneck, N.J., in critical thinking, quantitative reasoning and problem solving as they apply to mathematics in the elementary classroom. "We emphasize one point and neglect another."
In an effort to provide coverage, American students in middle grades and higher are required to take classes about separate topics in mathematics. Nowhere else in the world do students have a year of algebra, a year of geometry, another year of algebra, and so on. Chinni agrees with the spirit of mathematician and education theorist Seymour Papert's observation that math started as a way to solve problems, and now it is taught for years before students are able to see that it can be used to solve problems.
Making math important
As early as 1902, E.H. Moore, in his outgoing presidential address to the American Mathematics Society, called for integrating school mathematical topics. Then, as now, supporters of integrating mathematics argue that it makes essential connections for students, helps make mathematics more usable, avoids long gaps in learning, allows a balanced curriculum, and addresses differences in learning styles.
"Students begin to understand that math is a way of thinking," says David J. Whitin, a mathematics professor at Queens College, City University of New York, with an emphasis on linking mathematics with literature and science. "They begin to see that it's useful in terms of its applicability to life, useful in answering questions they're curious about, that it's not confined to the pages of a textbook. It also eases some of the math anxiety that kids begin to develop as they progress through school. As they see it as a natural part of school-another way of answering questions."
But what is integrated mathematics?
Actually, the concept of integration can take many forms, depending upon personal or school purposes. Integrated mathematics learning may refer to concept connections within or across mathematics courses, for example. In Singapore, operations in arithmetic, algebra and geometry are taught as part of the overall curriculum every year, with an emphasis on practical problem-solving.
The other approach is the one favored by the National Science Foundation through its funded programs for integrated mathematics curricula. These have a different focus, trying to teach mathematics in the context of real-world problems. These connections can be made through various approaches, including single-course integration, broad planning across or within departments, team teaching, short- or long-term projects, thematic projects/units, and even academies devoted to math and science.
Unfortunately, because teaching integrated mathematics has involved cooperative learning, alternative assessments, and the "teacher as a guide" methodology, it has sparked "math wars" that question its value. In addition, when teachers take on the challenge of teaching integrated mathematics, sometimes they are not as well prepared as they should be, giving rise to the accusation that "fuzzy math" is being taught instead.
The first way to avoid problems like these, says Whitin, is to realize that integration for its own sake is not the goal. "Teachers have to feel the value of it as learners before they see the benefit to kids. Workshops that engage teachers where they can see mathematics emerging as a tool, then they begin to see its relevance."
Even getting to that first step can be difficult, however, says Hope Martin, author of a number of math integration activity books for teachers and a consultant to the Illinois Math and Science Academy.
"Math teachers feel the need to tie mathematics, but I find there is a great deal of unhappiness when English and math teachers are brought into a math integration workshop," says Martin. "My focus is how can we tie math to real-world focus."
As an example of real-world focus, Whitin described an interdisciplinary activity in an article he co-authored with his wife, Phyllis Whitin, also an instructor at Queens College, called "Where Is the Mathematics in Interdisciplinary Studies?" The Whitins describe a first-grade class going outside to hunt for insects in early spring, leading to investigations about insect life cycles (time), how far grasshoppers can jump (length), and why spiders build webs in corners (spatial relations).
"The problem is that when you look at how math is viewed when people are doing interdisciplinary units of study, the math is often forced in a contrived way," says Whitin. "Counting the number of blocks in a pyramid during a unit on the Egyptians-so what? It doesn't serve real function or a burning question. Mathematics follows an inquisitive mind. It comes on the heels of that. It doesn't have to be forced in."
Chinni recommends that teachers interested in math integration via manipulatives or other constructivist approaches "look back to Dewey. He always emphasized the importance of teaching in a meaningful context." Second, he says, it's important to keep on eye on National Council of Teachers of Mathematics standards to make sure objectives are being met. Careful development of mathematical concepts should build on one another. "It depends on your overall curriculum for the district. You might be able to integrate math in the context of other subjects easily. Or, you want to examine your core curriculum against state standards and use those standards as ways to bring in math."
In the workshops on math integration she holds in the Chicago area, Hope Martin uses two approaches to get teachers thinking. First, there's facilitating a whole group working together-usually a department or interdisciplinary team. The second way is to pair just a math and science teacher together, for example, and let them find links in what they teach. In either case, she says, the goal is to teach related skills through application. "There's a lot of decisive research that shows we do not learn in isolation. Nonsense syllables don't mean anything, and rules about operations by themselves don't make any sense, either."
Or, as Barbie could have asked and voiced the feelings of many adolescents, "When are we ever going to use this?"
Charles Shields, firstname.lastname@example.org, is a freelance writer and 20-year veteran educator based in suburban Chicago.