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.
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 classmates.
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 explains.
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 symmetry.
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) E-mail: JBECKER@SIU.EDU