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.
What will be an ideal response?
The teacher's students used rote learning to complete the fraction test. There was little connection between the reduction of fractions and real world experiences. The exercise of reducing fractions was meaningless to the students outside of memorizing to take the test.
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