Equivalent Fractions: Their Difficulty and Educational Implications.

Abstract Fifth and sixth graders ( n =120) were individually interviewed to find out whether they compared parts of rectangles by reasoning that 3 4 = 6 8 , for example, or by making perceptual judgments. Two identical rectangles were folded and cut differently in front of the child. One was folded horizontally into 4 parts, and 1 4 was cut off. The other rectangle was folded vertically into 8 parts and cut into 8 strips. The question posed was: If the paper were chocolate, how many of the 8 strips (eighths) would make the same amount of chocolate as 3 4 ? The children approached the task perceptually instead of making use of equivalent fractions, which they had studied in school. The findings are explained in light of Piaget's theory, and the pedagogical implications are discussed.

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