With a painterly eye, eight-year-old Jenny Engelke
scrutinizes the pair of plastic blocks stacked on her desk and
tries to sketch how a box capable of holding the blocks might look
if she could unfold it and lay it flat.
Using graph paper to match the size of the cubes, she first
draws a pattern with two squares in the base attached to a row of
four squares. She cuts it out and tries to fold it around the
blocks, but it won't go all the way around.
"Maybe you should modify your design a little bit," urges her
teacher, Carmen Curtis.
Jenny returns to her pencil and scissors, adding first one,
then two squares to the pattern. Delighted, she runs to show Ms.
Curtis that the cubes fit.
While many of her third-grade peers around the country are
spending their math classes toiling over columns of addition and
subtraction problems, Jenny and her classmates at Country View
School in Verona, Wis., are part of a three-year experiment to make
math something children can see and feel, what Curtis calls "math
Building on children's natural tendency to explore things
visually, elementary school teachers in this district south of
Madison are working with researchers at the University of
Wisconsin-Madison to develop students' spatial skills at the same
time they're learning about numbers.
Students encounter problems in measurement, area, volume, and
way-finding - the fundamentals of geometry - then come up with ways
of defining the problems and explaining the solutions. This differs
from classes that use "manipulatives" - hands-on tools designed to
aid children's understanding of math - which tend to focus
exclusively on numbers, on counting.
Researchers have known for years of the link between spatial
reasoning and success in math. Most recently, researchers at Boston
College found that better spatial skills among boys had more to do
with why they outscored girls on the math portion of the SAT
college-entrance exam than did girls' lower self-confidence in
math. "The best indicator of doing well in math isn't ability to
compute; it's ability to visualize," Curtis says.
Why spatial reasoning?
By encouraging children to come up with their own ways of
solving complex visual problems, students learn the value of making
conjectures and then finding ways to support them through math,
says Richard Lehrer, who developed the curriculum at the
UW-Madison's Department of Educational Psychology.
Besides mirroring the way mathematicians and scientists
think, such an approach forces students to incorporate many
important concepts in math, such as geometry, probability, and
proof, which are often not taught until high school, he says.
Opposition to this "layer cake" approach to teaching math is
what's driving many states to adopt academic standards aimed at
introducing complex reasoning skills at an earlier age.
Mr. Lehrer's work in the primary grades has led to a
collaboration with fellow-researcher Leona Schauble and about 40
teachers here to also change the way science is taught. They are
finding that students with a firm grounding in spatial skills were
better able to create and revise models, the principal way that
scientists explain the world.
In a unit last year, where kids created models of the elbow
using rubber bands and dowel rods, students not in the program
tended to view a good model as one that looked like an elbow,
whether it acted like one or not. …