I have a copy of the paper Bostonian mentioned today. If anyone wants it, PM me with your email address and I'll send it to you. It was a decent-sized study with ~4,300 kids from two countries (US and UK). The two cohorts were born in different decades (1970 in the UK and the mid-1980s in the US). Each group was tested twice (around ages 10-12 and as high school students).

From the Discussion:


Originally Posted by Siegler et al Early Predictors of High School Mathematics Achievement
Over 30 years of nationwide standardized testing, mathematics scores of U.S. high school students have barely budged (National Mathematics Advisory Panel, 2008). The present findings imply that mastery of fractions and division is needed if substantial improvements in understanding of algebra and other aspects of high school mathematics are to be achieved. One likely reason for students’ limited mastery of fractions and division is that many U.S. teachers lack a firm conceptual understanding of fractions and division. In several studies, the majority of elementary and middle school teachers in the United States were unable to generate even a single explanation for why the invert-and-multiply algorithm (i.e., a/b ÷ c/d = ad × bc) is a legitimate way to solve division problems with fractions. In contrast, most teachers in Japan and China generated two or three explanations in response to the same question (Ma, 1999; Moseley, Okamoto, & Ishida, 2007).

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