The article includes a discussion of counting and counting strategies. In addition, there are eight problem sets appropriate for use with groups of different age and ability levels. Suggestions are given for finding variations of the problems. (PK)

The author advocates a return to "traditional" elementary algebra content. Several roles for algebra manipulation are identified, including making arithmetic more interesting and understandable and providing facility indispensable for both the technician and the mathematician. (PK)

Presented is a rationale for the importance of estimation. Strategies used by good estimators, and teaching strategies for computational estimation are considered. (PK)

Argues that calculator activities, even in the early grades, can present situations in which basic mathematical thinking processes come into play. The activity described involves developing efficient calculator guess-and-test strategies and requires only an introductory notion of the four basic operations of arithmetic. (PK)

This activity for grades 6-12 is designed to promote an increased interest in mathematics and its study. Directions for the game "Math Trivia" are given, with questions ready for cards and additional questions listed. (MNS)

The first aim in school might be to help children become more aware of the algorithmic processes they use; then, ensure that they can devise algorithms and define them. Many examples of how these aims can be met are given, including the use of calculators and computers. (MNS)

Programs (using Logo) developed by children to produce multiples, the Fibonacci series, and square numbers are presented, with graphical representations of functions introduced. Another investigation involves drawing a circle using turtle graphics. (MNS)

Computer algebra systems (such as MACSYMA and muMath) can carry out many of the operations of calculus, linear algebra, and differential equations. Use of them with sketching graphs of rational functions and with other topics is discussed. (MNS)

Five-frames are proposed as manipulative material to increase children's ability to identify the number of objects without direct counting. How to use frames and beansticks to construct basic facts without counting is discussed. (MNS)

Included are brief articles discussing chain letters as an example of exponential growth, a box technique for factoring, and integrating the inverse of a function whose integral is known. (MNS)

Fourth-grade students' understanding of the order and equivalence of fractions was investigated in an 18-week teaching experiment. Three related characteristics of thinking are hypothesized to be related to success of such tasks, involving flexibility and reasoning that becomes increasingly independent of specific concrete embodiments. (MNS)

Some answers are given to questions that teachers ask about the preprimary mathematics program. A point of view is presented and a model provided outlining a scope and sequence for choosing experiences for children about five years old. (MNS)

Four worksheets for levels one-eight are included. Practice on addition, multiplication, fractions and decimals, and integers is provided through activities involving puzzling patterns. (MNS)

Five exploratory activities arising from work by sixth-grade students are described. They concern geometric ideas and number concepts, including fractions. Illustrations are included. (MNS)

An example is given for deriving mathematical content from a game. The game and eight activities are included for both basic and advanced versions. (MNS)