Compared to math teachers in the high-achieving nations of Hong Kong and Japan, teachers in the United States offer less of certain supports that could help students learn more. This could contribute to the lower performance among U.S. students on international math tests, a UCI researcher discovered.
The study analyzed how analogies -- a reasoning practice that involves connecting two concepts, often a better-known concept to a less familiar one -- are used in the United States, Hong Kong and Japan. They are known to be helpful for learning mathematical concepts, but only if teachers use enough imagery and gestures that students' attention to the analogous relations. These strategies, or cognitive supports, are necessary to ensure that students notice and understand the analogies.
U.S. teachers incorporate analogies into their lessons as often as teachers in Hong Kong and Japan, but they less frequently utilize spatial supports, mental and visual imagery, and gestures that encourage active reasoning. Less cognitive support may result in students retaining less information, learning in a less conceptual way, or misunderstanding the analogies and learning something different altogether.
"There is no guarantee that without these cues, the students are actually benefiting from the analogies and thinking about math in a comparative way," said Lindsey Richland, assistant professor of education and co-author of the study.
Richland and research colleagues analyzed videotapes of math lessons from the large-scale video portion of the 1999 Trends in International Mathematics and Science Study. That study found U.S. teachers engaged students in complex connected reasoning and problem solving significantly less than teachers in countries where students score higher in math. Richland examined the instructional uses of analogy in the videotapes and coded the frequency of teaching strategies that provide cognitive supports for students' reasoning.
The "teaching gap" with respect to analogy could be attributed to different cultural orientations to relational reasoning. However, the authors conclude U.S. math teachers could improve the effectiveness of their analogies through slight adjustments in their instruction.
"Teachers are already using analogies; we're not recommending going into the classroom and changing the way they're doing things. But if teachers could be more attentive to the use of these kinds of supports, the students would be likely to benefit and learn a lot more," Richland said.
The findings are published in the May 25 issue of Science.
Richland's co-authors for this study were Osnat Zur and Keith J. Holyoak. Holyoak is a Distinguished Professor of psychology at UCLA. During the research Zur was a postdoctoral researcher at UCLA, and now is director of research and evaluation at the Los Angeles Universal Preschool.
The study was funded by a grant from the Institute of Education Sciences in the U.S. Department of Education.
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