Fractions in the Early-Years Curriculum: More Needed, Not Less
Author(s): Carol A. Powell and Robert P. Hunting
Source: Teaching Children Mathematics , SEPTEMBER 2003, Vol. 10, No. 1 (SEPTEMBER
2003), pp. 6-7
Published by: National Council of Teachers of Mathematics
Stable URL: https://www.jstor.org/stable/41198061
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Carol A. Powell and Robert P. Hunting
Fractions in the Early-
Years Curriculum: More
Needed, Not Less
and international measures of mathematics achieve(2001) has argued that the
teaching of fractions should be
ment
elimiwith topics of fractions, ratios, and proportions,
nated from the primary mathematics
it makes sense to devote more time to developing the
curriculum, based on issues related to foundations
curriculum,
of these topics in appropriate ways, in
light We
of research
development, and instructional materials.
dis- results on young children's ideas of
agree, for the following main reasons:sharing
First,and
this
distribution.
approach overlooks young children's developing
Teachers can begin to establish important ideas
multiplicative structures, which have their
roots in
informally.
As an example of how fraction lanpart-whole relationships. Second, although
guage
we
can
agree
be introduced seamlessly into problem
that the teaching of formal symbolism situations
and notation
involving division, imagine a teacher
for fractions can be delayed, conversations
and abetween
small group of students who have designed
teachers and children can establish important
a farm consisting
ideas
of fields, pens, roads, and
from which formal symbols later will flow
fences,
naturally.
possibly on a large sheet of paper or in a
Third, sharing situations can help young
sandchildren
tray. The farmer has bought some sheep for
develop whole-number knowledge and can
his lay
two founchildren, and he wants equal numbers of
dations for the rational-number system. sheep in each of two fields or pens. The children's
Young children are quite capable of solving
shartask is to
take a quantity of toy animals and figure
ing problems. Fraction concepts are indeed
out how
developthis might be done. Because there are
mentally appropriate for primary-age children
only two(four
fields or pens, the teacher might say to
theand
children,
to eight years old). Research by Hunting
Davis"The farmer wants half the sheep in
this field
and half in this field." The children can
(1991) and Miller (1984) shows that many
children
as young as three years old can divide a count
set of
the
items
quantity of animals that they need to
divide
as well as the animals in each field after the
into equal subsets using a powerful and
consistent
distribution method called the dealing
division.
strategy
They can write about the results. Divid(Davis and Pitkethly 1990). We do not know
ing different
pre- numbers of animals in half will lead
cisely where children get this ability, but
towe
fraction
are sure
equivalence: Half can be two of four,
six, five of ten, and so on. Students can
that it does not originate in classrooms.three
Of of
course,
not all children can or will use the dealing
investigate
procedure
similar situations involving three fields
andproblems
thirds, four fields and fourths, and so on. Note
when solving a sharing problem. Sharing
may offer teachable moments as childrenalso
arethat
invited
young children can consolidate their
to explain their methods of distributing
whole-number
items and knowledge in the process. Dividing
argue about which methods are superior:
items
trial
between
and two fields might offer children
error or systematic dealing.
basic experience with multiplying by two as they
If part-whole reasoning has dual aspects
find fractional
- addi- equivalents of one half. Table-settive and multiplicative - why delay problems
ting and
involvcard-game activities also might help chil-
ing the multiplicative aspect until the intermediate
dren explore sharing in equal portions and discuss
fractions.
grades, when young children clearly can
deal with
sharing and division tasks in the earlier years?
Although
Given
primary students, and probably many
the difficulties that children encounter on national
primary teachers, are not ready to discuss fractions as
linear, area, or discrete models, other sources of frac-
experience
arise from
physical models,
such of
as
Carol Powell, carolp@heronetne.jp, has tion
more
than
twenty
yean
ele
rience. She currently teaches third grade
at
Sollars
Elementary
Schoo
dividing
toast,
sandwiches,
or other edible material.
in Japan. Robert Hunting, huntingnPmail.ecu.edu, is professor of m
A part-whole understanding of number is an imporBast Carolina University. He is interested in how young children learn
tant breakthrough in children's mathematical devel-
6 Teaching Children Mathematics / September 2003
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opment that will support farther understanding and
I
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Sharing situations can assist with number devel-
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Calculators for the Classroom
into equal groups and disassembling them are
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Primary-grade instruction can present the concept
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range of content across disciplines that is socially
relevant, intellectually engaging, and personally
meaningful to children" (Bredecamp and Coppie
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pose appropriate problem situations that will foster
growth of mathematical knowledge. The concept of
fractions is important; the earlier it is taught, the
more personal the mathematical power that children
will bring to higher education and discovery. The
development of fraction concepts should not be The
Society of National Association Publications (S
recently awarded Teaching Children Mathematics
tured and built on throughout students' school
Award in the 2003 SNAP EXCEL Awards competiti
careers.
won the award in the Scholarly Journals, Editorial
gory for "Bumper Stickers/ an "In My Opinion" pi
References
Robert Callahan that appeared in the February 200
delayed until the intermediate grades but rather nur-
Bredekamp, Sue, and Carol Coppie. Developmentally
Appropriate Practice in Early Childhood Programs.
Washington, D.C.: National Association for the Educa- "Bumper Stickers" outlines the author's misgiving
the use of technology in elementary school classro
tion of Young Children, 1997.
Davis, Gary Ernest, and Anne Pitkethly. "CognitiveCallahan
points to the high cost of computers and
quickly they become obsolete, a? well as the quest
educational value of some computer mathematics p
grams. The article concludes that schools need bet
funding sources for technology, and that technolo
cannot replace real-world activities. Callahan encou
educators to reflect on their own use of technolog
classroom and to implement changes that will incr
Aspects of Sharing." Journal for Research in Mathe-
matics Education 21 (March 1990): 145-53.
Hunting, Robert P., and Gary Davis, eds. Early Fraction
Learning. New York: Springer- Verlag, 1991.
Miller, Kevin. "Child as the Measurer of All Things: Measurement Procedures and the Development of Quan-
titative Concepts." In Origins of Cognitive Skills,
edited by Catherine Sophian, pp. 193-228. Hillsdale,
N.J.: Erlbaum, 1984.
Watanabe, Tad. "Let's Eliminate Fractions from Primary
Curricula!" Teaching Children Mathematics 8 (Octo-
student achievement.
ber 2001): 70-72. A
Teaching
Children
Mathematics
/
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September
2003
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