Computing with rational numbers: Not easy even for college students


Many individuals, including school children and adults, struggle with rational numbers, especially in fractional and decimal format (Hartnett & Gelman, 1998; Humberstone & Reeve, 2007; Jacobs & Gelman, 2010). A preliminary study with undergraduates revealed difficulty with problems where a price increase of x% is followed by a decrease of the same percent, for example, “x increases by 50% and then decreases by 50%”. More than 75% of these problems were answered incorrectly (Jacobs, 2010). A second study, where N = 1629, presented percentage problems in either an algebraic or numerical format. The focus was on analyses of trends between and within subjects, including systematic error patterns, the effect of problem-solving representational formats, and problems that were easy. These data highlight the fact that even undergraduates can have persistent problems with rational number concepts and notations.

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