Before judging a student's diagram correct or incorrect, the mental associations made by the student between his diagram and the problem should be known. This is a follow-up to the author's article in the November 1970, Arithmetic Teacher." (RS)

A model for division of fractions using money as manipulative material is presented. Eight levels are described, ranging from the development of language and concept introduction through types of problems to rule discovery and application. (MNS)

An approach is illustrated that introduces selected models of addition and subtraction to students who have previously learned a model for either operation. (JT)

A model that can be effectively used to develop the notion of function and provide varied practice by using "real world" examples and concrete objects is covered. The use of Popsicle-sticks is featured, with some suggestions for tasks involving functions with one operation, two operations, and inverse operations covered. (MP)

How children can be guided to see and feel the power of thinking with and about mathematical symbols is discussed. A strategy to help them bridge the gap between manipulative models and symbols is detailed. (MNS)

Using manipulative materials and pictures is considered valuable, but the need to use models appropriate for individual children is stressed. Suggestions for using well-structured physical space are given. (MNS)