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 REFERENCES Linked references are available on JSTOR for this article: https://www.jstor.org/stable/41198061?seq=1&cid=pdfreference#references_tab_contents You may need to log in to JSTOR to access the linked references. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at https://about.jstor.org/terms National Council of Teachers of Mathematics is collaborating with JSTOR to digitize, preserve and extend access to Teaching Children Mathematics This content downloaded from 202.65.64.82 on Tue, 04 May 2021 02:22:18 UTC All use subject to https://about.jstor.org/terms 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 This content downloaded from 202.65.64.82 on Tue, 04 May 2021 02:22:18 UTC All use subject to https://about.jstor.org/terms opment that will support farther understanding and I concept building at the intermediate grades. Sharing situations can assist with number devel- ShillerMath is a proven four-yea I guarantees your 4-7 year old wil I only Montessori-based home math opment as well as fractions. But aren't we talking about whole-number division when we share a set I of items? If you think of the quantity to be divided as a collection of individual entities, the number of I long math success. The ShillerMat I books containing over 470 activit I that set is important, as well as the number in each subset. But if you think of the quantity to be divided as a unit - a whole or one - each subset is a part, and this thinking strategy begins to foster a vocabulary for naming the fractional parts in relation to the whole. The actions of assembling discrete items includes audio CD, everything and a full set a of parent needs Montessori ■ ShillprMath Wlllll^l ■IWlllll^l mail I or visit www.shlllermath.com ■ HOW KIDS LEARN MATH Ca«i«forourcun«rtNCTMi|»ciaLTMcto^^ man mail Calculators for the Classroom into equal groups and disassembling them are We stock calculators from the basic to math labs, appropriate experiences both for multiplication and plus overhead systems, batteries, workbooks, etc. division of whole numbers and for fractions and Call us for information or quotations! ratios. These topics are closely connected. 1-800-526-9060 Primary-grade instruction can present the concept of fractions relative to students' informal under- standing of sharing. As for what is developmentally FC EDUCATIONAL ELECTRONICS appropriate, children's understanding of fractions as sharing should "build upon what children already 70 Finnen Drive, Weymouth, MA 02188 know and are able to do ... and include a broad Fax:781-340-6742 range of content across disciplines that is socially relevant, intellectually engaging, and personally meaningful to children" (Bredecamp and Coppie 1997, p. 20). The teacher's challenge is to identify or 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 / This content downloaded from 202.65.64.82 on Tue, 04 May 2021 02:22:18 UTC All use subject to https://about.jstor.org/terms September 2003 7