Math Texts Are Multiplying
Seven years ago, the National Council of Teachers of Mathematics released a set of student-achievement standards that had the potential to revolutionize the way math is taught in schools across the country. The standards stressed teaching students to reason, think, and communicate mathematically. They called for placing math in the context of students' everyday lives, and they advocated giving students hands-on activities and access to computers and calculators to use as problem-solving tools.
There was one catch: If the new standards were going to take hold, teachers would need new curricular materials and textbooks. In the late 1980s, those kinds of materials were nowhere in sight.
Now, however, many of those hoped-for materials are making their way to the textbook market. One impetus for their development has been a grant program launched by the National Science Foundation. Since 1990, the federal agency has poured more than $25 million into universities, research-and-development agencies, and school-reform organizations to create new curricular materials modeled on the standards.
The 15 math programs that grew out of that effort are either already for sale or are scheduled to be published within the next two years. They range from a middle school curriculum imported from the Netherlands to elementary school units that devote time to teaching students such values as cooperation to high school curricula grounded in realistic problems.
All the materials have one thing in common, says Margaret Cozzens, the director of the NSF's division of elementary, secondary, and informal education: "They really do change the way teachers will have to teach."
One of the new sets of materials, "Mathematics in Context," draws its inspiration from the way math is taught in the Netherlands. The curriculum, designed for grades 5-8, was developed by researchers at the University of Wisconsin's Center for Education Research and the Hans Freudenthal Institute in the Netherlands.
Thomas Romberg, the director of the Wisconsin center, was among a group of educators and mathematicians who re-examined the way Americans learn math in the wake of A Nation at Risk, the hard-hitting 1983 federal report on education.
"One of the things we did was to examine what was happening in other countries," Romberg says. "We looked at the Japanese and the Germans and the French and the Dutch and others. What was happening in the Netherlands struck us as things that needed to be done in this country."
For example, the Dutch were teaching mathematics that was grounded in real-world contexts and applications. Also, rather than test students' comprehension with pages of rote problems, the Dutch generally gave students two or three problems that might take several hours to complete.
"The notion is that there's a context or problem setting, and students are asked to think about something for a long period of time," Romberg explains.
Such methods, in use since the 1960s in the Netherlands, apparently are paying off for the Dutch. Students there generally rank first or second on international comparisons of student achievement in math, according to Romberg.
So the center and officials from the Freudenthal Institute decided to test some of the Dutch units in U.S. classrooms. The venture led to their collaboration on the new middle school curriculum.
Now fully adapted, reviewed by practicing teachers, and revised repeatedly, the 5th-grade materials will be published this summer by Encyclopaedia Brittanica. Materials for the other grades are slated for printing later this year.
The idea of incorporating math into the mainstream of students' worlds is a thread running through all the projects. At the high school level, for example, it is the overriding theme of the ARISE curriculum. Developed by the Consortium for Mathematics and its Applications, or COMAP, a Lexington, Mass.-based mathematics-reform group, ARISE stands for Applications/Reform in Secondary Education.
In one unit on testing blood for diseases, for example, students must decide when it makes sense to pool samples of blood rather than test each sample individually. Along the way, students might use quadratic and cubic equations to arrive at their answers.
And researchers at the Developmental Studies Center, an Oakland, Calif.-based group, have completed elementary school curricular materials that have two goals: They teach children "number sense," while at the same time teaching students to be fair, caring, and responsible.
"Number sense," a notion that predates the national math standards, refers to "children's fluidity and flexibility with numbers, having a sense of what numbers mean, mental mathematics, being able to look at the world around you and make comparisons," explains Laurel Robertson, the director of programs for the Developmental Studies Center.
Embedding values education in the context of cutting-edge curricula has long been a focus of Robertson's center, which has also pioneered a broader school-reform approach for elementary schools.
In its math materials, called Number Power: A Cooperative Approach to Mathematics and Social Development, each unit begins with a "team builder" exercise that enables the children in the group to get to know one another better. The units, which are published by Addison-Wesley Publishing Co., conclude with activities designed to help students reflect both on the math learned and the success or failure of the group's interaction.
Intended as replacement units, Number Power materials can easily fit within most elementary school curricula. But schools will find that, with the other NSF-funded curricula, the fit is not quite so close.
For example, the ARISE program, like many of the other projects, seeks to blur the sharp boundaries between math subjects. It is intended to replace the traditional sequence of algebra I, geometry, and algebra II offered in most high schools. It is also intended to serve all students--not just high or low achievers.
"There's no question that a school that commits to the ARISE curriculum or any of the other curricula that NSF funds are making a dramatic change," says Sol Garfunkel, the executive director of COMAP.
And developers of Connected Mathematics, another middle school curriculum underwritten by the foundation, say students using their program will get more algebra earlier than many students do now.
"High schools are going to have to take a hard look at the mathematics these kids come out of middle school with," says Kathy Burgis, the manager of the project, which is based at Michigan State University.
But even though these projects are a departure from the usual math curricula, none of them has had difficulty attracting publishers.
"There are some smaller publishers that are looking for innovative materials to make their mark," says Garfunkel of COMAP. "And then you have larger companies that are taking a chance. They've already got a standard series, and they're taking a chance for a reform series."
Under the grant program, each project is required to field-test its curriculum in schools. Although the field-tests were conducted primarily to get comments on the materials from teachers and students, some of the projects also gathered statistical proof that their materials can work.
The educators and school officials in Ames, Iowa, who tried out the Mathematics in Context program, for example, decided to compare the algebra achievement scores of 7th graders using the new curricula with those of the previous year's 7th graders.
With the new curriculum, they found, the number of students who were scoring in the bottom 20 percent on the Iowa Algebra Aptitude Test was cut by 20 percent. The number of students scoring in the top 20 percent also rose by 20 percent. Several other developers reported similar improvements.
It should be noted, however, that most of the projects also provided the teachers with training on how to use their programs. Time will tell if the improvements documented so far will last, and whether they can be replicated in schools where no professional development is offered along with the new materials.
But Cozzens of the NSF says professional development may be essential for any school system planning to make use of the new curricula.
"They can't get away with buying a book and handing it to a teacher," she says.
NSF-Funded Math Curricula
Elementary school level
Cooperative Mathematics Project Developmental Studies Center Oakland, Calif.
Investigations in Number, Data,and Space TERC Cambridge, Mass.
Teaching Integrated Mathematics and Science (TIMS) Elementary Mathematics Curriculum Project University of Illinois at Chicago
University of Chicago School of Mathematics Project (elementary component)
Middle school level
Mathematics in Context: A Connected Curriculum for Grades 5-8 Wisconsin Center for Education Research University of Wisconsin, Madison
Middle School Mathematics Through Applications Project Institute for Research on Learning Palo Alto, Calif.
Seeing and Thinking Mathematically Education Development Center Newton, Mass.
Six Through Eight Mathematics (STEM) University of Montana, Missoula
The Connected Mathematics Project Michigan State University, East Lansing
High school level
Applications/Reform in Secondary Education (ARISE) Consortium for Mathematics and Its Applications, Lexington, Mass.
Core-Plus Mathematics Project University of Michigan, Ann Arbor
Interactive Mathematics Project (IMP) San Francisco State University
Math Connections, A Secondary Mathematics Core Curriculum Connecticut Business & Industry Association, Hartford, Conn.
Systemic Initiatives for Montana Mathematics and Science (SIMMS) Montana State University, Bozeman
University of Chicago School of Mathematics Project (secondary component)