Motivating For Math: Hands-On Investigations Help Kids "Discover" Mathematical Principles

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REHOVOT - September 1, 1997 - Question: What do you get when you take 25 children, subtract their textbooks, and add dice, matchsticks and chocolate? Answer: an innovative model of math education that has kids discovering mathematical principles all on their own. And best of all, they think it's fun.

The program, developed by Dr. Alex Friedlander of the Weizmann Institute's Science Teaching Department in cooperation with Tel Aviv's Center for Educational Technology, is featured on the cover of the September issue of the U.S. National Council of Teachers of Mathematics journal Teaching Children Mathematics.

Friedlander's approach, designed for grades two through six, offers an alternative to the traditional teaching methods that turn so many children off math. Instead of technical classroom instruction, pupils are presented with structured investigative experiences that motivate them to re-invent mathematical principles. It also provides a way for more talented students to learn at their own pace, without breaking the class into groups according to ability.

The problem with conventional math education, says Friedlander, is that it doesn't reflect the real essence of mathematics. He describes the typical scenario: "A teacher hands kids a toolbox full of abstract concepts, then says, 'Here, in the future you'll use these concepts to solve a bunch of problems you haven't thought of yet and don't really care about.' "

With Friedlander's approach, children explore real-life problems using objects such as dice, matchsticks and dominoes -- "manipulatives" that turn math concepts into something they can see and touch. This hands-on experience gives children the satisfaction of discovering underlying mathematical principles on their own.

The investigative method addresses another problem common to elementary education: children learn at different rates, and more advanced students often get bored waiting for their classmates to catch up. Friedlander's curriculum units consist of a series of eight to ten math-based investigations.
Children work through some of these investigations in heterogeneous groups, allowing each child to contribute according to his or her mathematical ability. Advanced students benefit from the open-ended structure of the activities, which encourages creative problem-solving, not just getting the right answer.

An example of the method is a learning unit on dice. Working in groups, children discover the "magic rule of seven" -- the fact that opposite sides of a die always add up to seven. Once the concept is grasped, it continues to work magic, becoming a useful tool that the children can use to solve more and more complex problems, such as predicting the sum displayed on one side of a "tower" of multiple dice.

"The key to success," says Friedlander, "is letting kids figure things out on their own terms. One child might solve a problem by counting dots on the dice. Another immediately understands and uses abstract concepts. In any case, the kids employ a whole variety of mathematical thinking skills. More importantly, they discover a need for the knowledge of mathematical concepts."

Friedlander stresses that his learning units don't herald the demise of the multiplication table. "Basic skills will always be necessary," he says. But these units may motivate more children to excel in mathematics, by revealing to them their own ability for original, mathematical thought. And if the goals of elementary math education can be achieved through such investigative activities, it may lower the incidence of "math anxiety" in older children and adults.

A big challenge in Friedlander's approach may be the one faced by those elementary school teachers who are accustomed mainly to frontal classroom presentation of mathematical rules. "We suggest that teachers go through the experience of mathematical investigations themselves before presenting them to their students. This way, teachers will get a feeling for the process of learning mathematics rather than simply presenting structured pieces of knowledge."

The Science Teaching Department operates under the aegis of the Feinberg Graduate School of the Weizmann Institute of Science. It develops educational programs designed to raise the level of science education for Israel's Hebrew- and Arabic-speaking students.

The Weizmann Institute of Science is a major center of scientific research and graduate study located in Rehovot, Israel.