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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.
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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.
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