Discusses the use of manipulative materials to model operations and algorithms. Indicates that they clarify the several interpretations of each operation, establish a basis for correct mathematical language, and show why algorithms work. (JN)

Twelve fourth-grade classes in two schools were taught division using either the subtractive approach to the Greenwood algorithm or a partitioning approach to the standard algorithm. Analysis of class means on immediate, retention, and delayed retention tests indicated that use of the standard algorithm was more effective. (JP)

A strategy to make the transition from manipulative materials to a written algorithm for division is outlined in dialogue form. (MNS)

Described are two methods of calculating developed by the Dutch WISKOBAS Project: addition and subtraction with a loop abacus and multiplication using a grid model. (MP)

Renaming fractions with the dot method is described with illustrations. It can be used to introduce renaming at the manipulative level in a meaningful way prior to moving to a more abstract level where prime factorization will be involved. (MNS)

This article discusses the use of concrete materials as conceptual models which serve as references for later learning of algorithms. (DT)

The purpose of this study was to compare the repeated subtraction method of long division of a partitioning distributive method, both taught by recording manipulation of popsicle sticks. Two instructional units were prepared. Twelve fourth grade classes were used, with six being taught one approach and six using the other. Tests consisting of…

Helping teachers to build a strong bridge from concrete experiences to algorithms is the focus. A detailed sequence of activities is described. (MN)

The use of developmental algorithms to develop skills is described. Children make the transition from using concrete materials to using a standard algorithm. (MNS)

Describes a research project designed to monitor the transition from work based on concrete materials to the more formalized aspect of mathematics found in secondary schools. The topic of subtraction was chosen by three teachers who were involved in the investigation. (PK)

A method is presented for helping children make a smooth transition from using manipulative materials to using symbols only in solving multidigit addition problems. (MP)