A Proposed Model for Teaching and Learning Common Fractions, and the Operations of Multiplication and Division of Fractions.
Suzanne K. Damarin · 1976
MF-$0.83 HC-$1.67 Plus Posta/e. Division; *Elementary School Mathematics; Elementary Secondary Education; *Fractions; *Mathematical Models; *Mathematics Education; Multiplication A model for fractions derived by an operation of scattering into subunits is hypothesized. Fiye stages in the model are discussed. Assumptions underlying the development of the model, features of the model, and disadvantages of the model are listed. (DT) *********************************************************************** Documents acquired by ERIC include many informal unpublished * materials not available from other sources. ERIC makes every effort * * to obtain the best copy available. Nevertheless, items of marginal * * reproducibility are often encountered and this affects the quality * * of the microfiche and hardcopy reproductions ERIC makes available * * via the ERIC Document Reproduction Service (EDRS). EDRS is not * responsible for the quality of the original document. Reproductions * * supplied by EDRS are the best that can be made from the original. * *********************************************************************** A Proposed Model for Teaching_and Learning Common Fractions, and the Operations of Multiplication and Division of Fractions Suzanne K. Damarin The Ohio State University U.S. DEPARTMENT OF HEALTH. EDUCATION II WELFARE NATIONAL INSTITUTE OF EDUCATION THIS DOCUMENT HAS BEEN REPROOUCEO EXACTLY AS RECEIVED FROM 1 THE PERSON OR ORGANIZATION ORIGIN1 ATING IT. POINTS OF VIEW OR OPINIONS, 1 STA TEO DO NOT NECESSARILY REPRE. SENT OFFICIAL NATIONAL INSTITUTE OF EOUCATION POSITION OR POLICY. In the model proposed below a fraction is considered to be an answer to the question = q x ? where p and q are counting numbers with q nonzero. Defining a fraction in this manner we must assume that the child has an understanding of multiplication of counting numbers, and that, in some sense, we can desciibe thatunderstanding. Thus the model for fractions presupposes a-model for multiplication of counting numbers. The two most ' common models for this operation are the Cartesian.Product Model and the Repeated Additions Model. These models are illustrated below. Cartesian Product Model for p x q q elements per row (q columns) p TOWS Paper prepared for GCSLTM workshop on Models for Teaching and Learning,Mathematics, Atlanta, Georgia, April 24, 1976