The purpose of this study was to document and trace how students' understanding of situations that involve finding a fractional part of a fraction developed during a course of instruction in which students explored and represented various kinds of situations using each of the five representational systems. A class of 5th grade students (n=22)…

A discussion of the various algorithms used for multiplication. Repeated addition, arrays, the distributive law, Egyptian and Russian Peasant Multiplication, Gelosia, Napier's Rods and Genaille's Rods are all described, and examples of multiplying using each method are explained. (DT)

Uses the geoboard as an aid in developing an intuitive "feel for the relationship between sums of numbers in a two by two matrix. Numbers in the matrix are represented as "area numbers on the geoboard. (RP)

Early experience with grouping objects is valuable for later understanding of and work with place value, division, and multiplication. Examples are drawn from the Developing Mathematical Processes Curriculum Project at the Wisconsin Research and Development Center for Cognitive Learning. (RS)

A teacher describes ways in which learning disabled students can learn through tactile-kinesthetic approaches devised by the teacher. Examples are given of multiplication instruction by counting on fingers, and grammar and long division instruction through movement. (CL)

The paper describes a program in which the rate of accurate response by six special education students (10 to 13 years old) to multiplication fact questions was increased by the application of contingent reinforcement procedures. (Author)

Two games and one activity designed to be used with a hand-held calculator are presented. (MK)

A description is given of a game used to give a continuous review of multiplication facts and illustrate certain properties. (MP)

A method of multiplying using fingers is described and an explanation given. The method is then generalized to other number bases. (MP)

Detailed instructions are given for presenting a number of activities that serve to tie measurement and multiplication together. The activities involve length, weight, area, volume, and capacity. (MP)

A method is discussed for justifying to students the fact that the product of two negative integers is positive. (DT)

Describes teaching methods and student-created methods for conceptualizing multiplication with rational numbers. (YDS)