id: 06597706
dt: j
an: 2016d.00566
au: Poon, Rebecca C.; Lewis, Priscilla Eide
ti: Unpacking the division interpretation of a fraction.
so: Teach. Child. Math. 22, No. 3, 178-185 (2015).
py: 2015
pu: National Council of Teachers of Mathematics (NCTM), Reston, VA
la: EN
cc: F40
ut: fractions; division interpretation; understanding; activities;
visualization; fraction concept
ci:
li: http://www.nctm.org/Publications/Teaching-Children-Mathematics/2015/Vol22/Issue3/Unpacking-the-Division-Interpretation-of-a-Fraction/
ab: 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)
rv: