When it comes to teaching mathematical concepts, abstract formulas may be more effective than the familiar examples of speeding trains and tossed coins favored by algebra instructors, according to a study published today in Science magazine.
In the study, which was described in a paper titled “The Advantage of Abstract Examples in Learning Math,” researchers at Ohio State University divided 80 undergraduates into groups and taught a mathematical rule to one group using a combination of abstract symbols. The researchers taught the same principle to the remaining students using one or more “concrete” examples that involved measuring cups of liquid, slices of pizza, or canisters of tennis balls.
When asked later to play a game using the rule, the students who had learned the concept in abstract form were better able to apply their knowledge to the new situation than were their counterparts who had studied concrete examples.
While math teachers need not abandon real-life illustrations altogether, the paper’s authors conclude, the experiment’s results suggest that relying exclusively on concrete examples might limit students’ ability to transfer what they learn to other situations. —Paula Wasley