Using Analogy in the Math Classroom

June 1, 2007

A comparison of mathematics instruction in different countries reveals that teachers in the United States generally fail to make effective use of analogies in the classroom, researchers say. The findings may have implications for improving U.S. math education.

Learning by analogy typically involves finding a set of correspondences between a better-known source and a more novel target, the researchers note. Mathematical reasoning often requires understanding abstract relations that can appear in different contexts.

Lindsey E. Richland of the University of California, Irvine and her colleagues analyzed videotapes of math lessons from the large-scale video portion of the 1999 Trends in International Mathematics and Science Study (TIMSS).

Reporting in the May 25 Science, the researchers say that, in their study, U.S. math teachers introduced analogies into their lessons, but they offered significantly less in terms of cognitive backup to help their students benefit from the analogies than did teachers in Hong Kong and Japan.

Math teachers in Hong Kong and Japan, they note, made more effective use analogies because they offered appropriate visual and spatial cues to aid comprehension of abstract relations, including hand or arm gestures, diagrams, and mental images or visualizations.

"There is no guarantee that without these cues, the students are actually benefiting from the analogies and thinking about math in a comparative way," Richland says.

"U.S. teachers provide high-quality learning opportunities to their students but provide less of the support that would enable their students to reap maximal benefits," Richland and her colleagues conclude.

Source: Science, May 25, 2007; University of California, Irvine