Goal Sketches in Fraction Learning

To examine how conceptual knowledge about fraction magnitudes changes as students' learning progresses, 5th and 7th-grade students were asked to solve fraction magnitude problems that entailed finding a fraction between two given fractions and then to evaluate solutions for similar problems that were modeled for them. When the given fractions share a common denominator or numerator, a simple strategy is to keep the common value and choose an intermediate value for the other component. 5th graders used this strategy on both common-numerator and common-denominator problems, and judged it "very smart" when it was modeled. 7th graders typically converted common numerator fractions to a common denominator and often judged the strategy of picking an intermediate denominator "not smart." (Contains 2 figures.) [For complete proceedings, see ED500860.]