id: 06466660
dt: j
an: 2015e.00525
au: Johanning, Debra I.; Mamer, James D.
ti: How did the answer get bigger?
so: Math. Teach. Middle Sch. 19, No. 6, 344-351 (2014).
py: 2014
pu: National Council of Teachers of Mathematics (NCTM), Reston, VA
la: EN
cc: F43
ut: fractions; fraction division; mathematical concepts; concept formation;
numeracy; number sense
ci:
li: http://www.nctm.org/publications/article.aspx?id=40498
ab: Summary: When students begin work with fraction division in fifth grade or
sixth grade, they bring with them experiences from whole-number
division. Many students think that a division problem should lead to a
quotient that is smaller than the dividend. It is also common for
students to believe that the dividend should be larger than the
divisor. Many, if not most, of the whole-number division problems that
students have worked with are of the form $15 \div 5 = 3$ or $666 \div
18 = 37$, where “division makes smaller.” When students begin to
study fraction division, it is important that their understanding of
division is expanded to address why it is possible to divide two
numbers and find a quotient that is larger than either dividend or
divisor. Supporting students to develop efficient procedures for
fraction division, although important, should not be the only goal.
Instruction should also support the development of number and operation
sense. Fraction magnitude is a prerequisite for developing such number
sense and operation sense. With fractions, number sense includes
understanding magnitude or the size of an individual fraction in
relation to a whole and in relation to other fractions. With fraction
division, understanding what a reasonable quotient might be involves
being able to compare the magnitude of the dividend with the magnitude
of the divisor when the operation of division is carried out. This
article explores both modeling and equivalence as reasoning tools to
support students’ developing number sense and understanding of the
measurement interpretation of fraction division. (ERIC)
rv: