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Gaps
Fraction understanding is one of the key gaps in American elementary education.
Fraction Understanding
What number is 12/13 + 7/8 closest to..?
1, 2, 19, 21, or none of these?
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If this is challenging, you’re not alone. Only 24% of the more than 20,000 eighth graders answered the correct answer, 2 (Carpenter et al., 1980). And though this study was done in 1980, little has changed since then. Only 27% of 8th graders in an affluent suburban school district could answer the same problem correctly when it was presented 35 years later (Siegler & Lortie-Forgues, 2015).
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Other measures of fraction understanding are similarly stark.
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50% of eighth graders cannot correctly order the size of 2/7, 1/12, and 5/9 (NAEP, 2004)
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< 30% of US eleventh graders translated .029 into the correct fraction (NAEP, 2004)
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70% accuracy when comparing which of two fractions is larger among community college students (chance was 50%) (Siegler, 2016)
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In a nationwide sample of 1,000 US algebra teachers, the fractions were rated as the topic that most student learning, second only to word problems (Hoffer et al., 2007).
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Teacher Understanding
What is more, gaps in fraction understanding exist for students and as well as for teachers. When asked to illustrate the meaning of a fraction division problem, such as 7/4 ÷ 1/2, only a minority of US teachers can provide an explanation other than stating the invert-and-multiply algorithm. In contrast, roughly 90% of teachers in East Asia (eg. Hong Kong & Singapore) can provide a coherent explanation to the same question, and many can provide more than one explanation (Depaepe et al. 2015).
This is important because teachers’ understanding of number arithmetic is strongly related to their knowledge of how to teach it effectively.