Seven forms of a programmed booklet based on an eleven-level hierarchy for addition of fractions were developed. One hundred forty-two fourth graders were randomly assigned to treatments; achievement, transfer, retention, and time were compared. No treatment was consistently superior, but developing sequences from hierarchies validated by test…

The nature and purposes of secondary school mathematics are discussed, with specific analysis of the role of algebra. Appropriate topics are suggested, with elaboration on level of abstraction and usefulness. (DT)

In this study children between the ages of 3 and 6 years were each presented with six number problems in which length and density were varied according to the proposed composition rules. (Authors)

The column presents activities for grades K-8 focusing on the concept of equality. A geometric-puzzle motif is used, with basic number facts reviewed for the lower grades and equivalent fractions for the upper levels. Four worksheets and a problem poster are included. (DT)

A teaching aid called EOPDICA (Electrically Operated Panel for Displaying Illuminated Colored Arrays) is described; suggestions for its use in teaching sets, elementary number theory, and place value and numeration are given. (DT)

Worksheets are provided which use basic geometric forms as a vehicle for student discovery of efficient counting procedures and of counting patterns. (DT)

Patterns for a set of Napiers Bones and for a denominate number slide rule are provided, with instructions on how to use each of the calculating instruments. (DT)