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Unpacking the division interpretation of a fraction. (English)
Teach. Child. Math. 22, No. 3, 178-185 (2015).
Summary: One of the challenges in learning fractions is understanding how and why a fraction can have multiple interpretations. As presented in one textbook, a fraction is “a symbol, such as $2/3$, $5/1$, or $8/5$, used to name a part of a whole, a part of a set, a location on a number line, or a division of whole numbers” [{\it R. I. Charles} et al., enVisionMATH common core, grade 4. Glenview, IL: Pearson (2012), p. 475]. How can a fraction take so many forms? In particular, why is a fraction also a division of whole numbers (e.g., $13/7 = 13 \div 7)$? In this article, the authors will present examples of classroom lessons that support children in developing conceptual understanding of the division interpretation of a fraction by building on children’s knowledge of whole-number division. Children demonstrate conceptual understanding by: (1) using the partitive interpretation of division to construct a definition for the division of any two whole numbers; and (2) using established definitions and observations to show why the fraction $m/n$ equals the division $m \div n$. (ERIC)
Classification: F40