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A teacher was excited when all of his fourth-grade students were able to reduce fractions to their ...

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A teacher was excited when all of his fourth-grade students were able to reduce fractions to their ...

A teacher was excited when all of his fourth-grade students were able to reduce fractions to their lowest common denominator. On a test he had given, the students were able to reduce, for example, 18/20 to 9/10 and 18/24 to 3/4 correctly. The teacher told his class how pleased he was with their performance, then he said, "For a review, let me ask you which you would prefer: 18 pieces of a cake that has been cut into 24 pieces or 3 pieces of a cake that has been cut into 4 pieces?" To his astonishment, the teacher listened as half the class said they would prefer 18 pieces because there were more pieces, and the other half said they would prefer 3 pieces because they were bigger. Explain what happened with the students, by discussing rote versus meaningful learning.

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