## Making Mathematical Connections

Connected Mathematics is an example of a middle-school instructional series developed in part with NSF funds. In 1999, these materials were being used in more than 2,200 school districts across the country. Connected Mathematics was judged the best of four—and only four—sets of middle-school mathematics materials receiving an excellent rating from Project 2061, a curriculum reform effort of the American Association for the Advancement of Science. The three other top-rated instructional materials—Mathematics in Context, MathScape, and Middle Grades Math Thematics—were also developed with NSF funds. None of these materials, however, are as yet in wide use.

What's so different about Connected Mathematics and the other top-rated materials? Ask Linda Walker, a teacher at Cobb Middle School in Tallahassee, Florida, who participated in the development of Connected Mathematics and whose school district implemented the series with the help of an NSF grant.

"When I went to school," she says, "there was one way to do a mathematics problem—the teacher's way. He'd show you how to work the problem, repeat it, and move on. With Connected Mathematics, I set up a problem and then let the kids explore for answers. They gather data, share ideas, look for patterns, make conjectures, develop strategies, and write out arguments to support their reasoning. Instead of getting bored, they're getting excited."

In one recent eighth-grade class, Walker asked her students to redesign a brand-name cereal box to use less cardboard while putting the same amount of cereal in the same number of boxes on a grocery shelf. There was no single right answer—the goal was just to come up with a more environmentally friendly box design and, as a result of the exercise, learn about the ratio of surface area to volume.

Walker says she could have had her students just crunch out formulas, but too much would have been lost in the process. "The importance of a student's exploration is that you, as the teacher, can see what they're really understanding," she says. "Getting a correct answer is only one goal. Are they comfortable with fractions or do they avoid them in their calculations? What do their guesses tell you about what they know and don't know?"