
Making Mathematical Connections
Connected Mathematics is an example of a middleschool
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 middleschool 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 toprated 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 toprated 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 eighthgrade class, Walker asked her
students to redesign a brandname 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?"

