Recent changes in approaches to the teaching of introductory multiplication reflect current trends in arithrnetic instruction which lay greater stress upon an early development of understandings of principles and properties central to mathematics as a whole. This is seen as a part of what may be termed the modern mathematics trend which is characterized by an increased concern for teaching arithmetic as a branch of mathematics. Central to this view seems to be au assumption that a recognizable structure underlies mathematics, much of which can be learned with initial instruction in the elementary school and which, when understood, can serve to render children more independent in their approaches to quantitative situations. This influence is reflected in the newer approaches to the teaching of multiplication by the considerable attention given to developing an understanding of the operation and its special properties. In the newer arithmetic programs, multiplication is introduced and explained in such terms as repeated additions, mappings, arrays, and Cartesian products. The commutative, associative, and distributive properties for multiplication are developed extensively.
Dr. Gray is a member of the faculty of education at the University of British Columbia.
* See Roland F. Gray, “Au Experimental Study of Introductory Multiplication” (unpublished doctoral dissertation, University of California, 1964).
1Cf. Dorothy M. Fraser, Current Curriculum Studies in Academic Subjects (Washington: The National Education Association, 1962), pp. 27–42. The School Mathematics Study Group Newsletter No. 4 (March, 1960), pp. 3–5. Kenneth E. Brown, “Tho Drive to Improve School Mathematics,” The Revolution in School Mathematics (Washington: The National Council of Teachers of Mathematics, 1961), pp. 15–29.
2Cf. Robert L. Morton, et al., Modern Arithmetic through Discovery, Grade Three, Teachers' Manual (Morristown, New Jeraey: Silver Burdett Co., 1963). Robert E. Eioholtz, et al., Elementary School Mathematics, Book Three, Teachers' Edition (Reading, Massachusetts: Addison-Wesley Publishing Co., Inc., 1963). Science Research Associates, Greater Cleveland Mathematics Program, Teachers' Guide for Third Grade (Chicago: Science Research Associates, 1962).