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Topic: Psychologists/New Programs - Boosting Math Scores
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Jerry P. Becker

Posts: 16,576
Registered: 12/3/04
Psychologists/New Programs - Boosting Math Scores
Posted: Sep 4, 1998 7:25 PM
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From the APA Monitor, American Psychological Association


Psychologists reinvigorate math lessons for children

New programs may help boost the math scores of American children.

By Bridget Murray, Monitor Staff

In the old-style mathematics classroom, young children robotically plowed
through columns of addition and subtraction problems. But few of them saw
any connections between math and real life.

In the modern classroom, children learn how math relates to their everyday
experiences-that eating three more cookies will add three to the two
they've already had, that moving back two spaces in a board game is like
subtracting two spaces and that staying up an hour later at night means
losing an hour of sleep.

Rooted in research by psychologists and other educational researchers, this
"learner-centered" approach to math education makes math meaningful by
connecting the learner's real-life experiences with formal math concepts.

With psychologists' help, a growing number of math teachers are trying this
approach in response to the government's Goals 2000 educational reform
effort, the legislative initiative intended to dramatically improve
American children's learning of the basics by the year 2000. In addition, a
set of educational standards issued by the National Council of Teachers of
Mathematics calls for greater attention to learner-centered teaching.

A demonstrated need

A report last year helped spotlight the need for changes in math
instruction, pointing out that American students' math achievement falls
below the international average. The Third International Math and Science
Study (TIMSS)-a cross-national comparative study of children's educational
achievement in 41 countries-showed American students' math scores lagging
behind those of students in Russia, Japan and other major U.S. competitors.

Learner-centered curricula can rejuvenate American math education by
allowing students to shape their own learning, say educational theorists.
Teachers who employ learning-centered principles act like coaches on the
sidelines, says Sharon Lynn Kagan, EdD, a consultant to the government's
National Education Goals Panel and a senior associate at the Yale
University Bush Center in Child Development and Social Policy. These
teachers engage children using math-related activities and questions that
make them think.

"The teacher shapes the playing field and the children do the playing,"
says Kagan.

Number worlds

Psychologists have focused mostly on learner-centered programs that boost
math skills of low-income, inner-city and minority children. Orchestrating
one of the most comprehensive of these programs are Sharon Griffin, PhD, of
Clark University and psychologist Robbie Case, PhD, of Stanford University.
Griffin and Case propose that children "construct" their math knowledge,
using what they already know about numbers to add new knowledge.

Unfortunately, though, most math classes are geared for middle- and
upper-income children, who gain a sense for numbers by playing board games
or helping their parents measure ingredients in cooking, says Griffin.
Low-income youth in inner-city or rural communities have much less access
to such enriching activities, she says. Each fall, when they return to
school, these youngsters' math performance drops further below that of
their peers, and they lack the numbers sense and language of their

Called Number Worlds, Griffin's program seeks to fill in these children's
knowledge gaps with a series of group-oriented games. In versions of the
program geared for kindergarten and first and second grades, children learn
to apply math practically-using it to understand time, temperature and
space. To gain a sense of the number line, students stand on a mat-size
game board and move between numbered squares using a large dice. And in a
pretend picnic activity, children determine how many places they need to
set for themselves. For all of these activities, teachers travel between
groups, gently nudging students toward more efficient strategies as needed.

The program yields impressive results. A three-year study in Worcester,
Mass., (in press, Journal for Research in Mathematics Education) is proof.
The study, conduct-ed between 1991 and 1994, track-ed 54 Number Worlds
kindergartners from low-income urban communities and 78 middle-income
kindergartners. The high-risk group had significantly lower math knowledge
when they entered kindergarten. But, after participating in Number Worlds,
the group caught up to their higher-income peers at the end of
kindergarten, and they outperformed a matched control group for the next
three years of school.

Understanding how young children think about math is the key to effective
learner-centered instruction, says psychologist Thomas Carpenter, PhD, of
the University of Wisconsin-Madison. For example, most children in
kindergarten can figure out that if 12 children share 24 lollipops, they'll
each get two lollipops, he asserts. Instead of automatically dividing as
adults do, children will count out the lollipops in sets of 12, Carpenter

Carpenter believes teachers need to build on these rudimentary abilities:
He has developed a teacher development program called cognitively guided
instruction (CGI), geared for those who teach math to children in
kindergarten through third grade.

The program urges teachers to use story problems that help children
explore, define and refine their problem-solving strategies. Teachers can
also turn routine activities into math opportunities, says Carpenter. For
example, if 12 students out of 20 are eating hot lunch, the class can
determine the number of children eating cold lunch, he says.

A four-year study published last year in the Journal for Research in
Mathematics Education (Vol. 27, No. 4, p. 403-434) indicates that the CGI
approach improves students' math understanding. The study tracked 21
first-, second- and third-grade teachers using CGI instruction and found
that their new methods boosted students' math achievement and
problem-solving skills significantly.

Giving teachers tools

Work by Herbert Ginsburg, PhD, of the Columbia University Teachers College,
adds more evidence that teachers can build on the math that children learn
outside class. For the past two years, Ginsburg and his colleagues have
observed and interviewed low-income 4- and 5-year-old African-American and
Latino children in a New York City day-care center. They find that the
children naturally explore mathematical questions during play, such as
counting up to the highest number they know, or counting the number of
shapes in a coloring-book activity.

Based on these observations, Ginsburg is planning a curriculum that gives
day-care teachers tools to tap children's natural math thinking. Some
possibilities are giving children pennies to help them tackle addition
problems or plastic shapes that they can arrange to gain a sense of

Psychologists at Vanderbilt University's department of teaching and
learning are also helping teachers develop materials for math learners. One
of them, Paul Cobb, PhD, finds that children learn best when they write
down a sequence of logical steps for solving problems and explain them to
their class. Working with students in the first, second and third grades,
Cobb finds that when students consider multiple ways of solving the same
problem, they build deeper math understanding and greater math confidence.

A teaching focus on problem-solving strategies is likely the source of high
math achievement in Japan, Cobb asserts. Japanese teachers urge students to
explore all angles of key math concepts, instead of giving them formulas to
memorize, Cobb says.

Jerry P. Becker
Dept. of Curriculum & Instruction
Southern Illinois University
Carbondale, IL 62901-4610 USA
Fax: (618)453-4244
Phone: (618)453-4241 (office)

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