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)

Different uses of numbers in natural language and mathematics is argued to have consequences for children's learning of numbers and for primary-grade textbooks. A study using particular properties of Hebrew indicates a crossing of the two language systems in children's reading of an arithmetic textbook. (MNS)

Four experiments are presented to support the theory that the rule system governing the law of large numbers is not tied to a content domain, and that it can be improved by formal teaching techniques. The experiments showed that statistical training enhanced everyday reasoning. Test problems and objective example problems are appended. (LMO)

Findings that six-year-old children perform substantially better in a conservation of number task if they are asked one question instead of two were upheld when mass and volume materials were used and the age range of subjects was extended to include five- through eight-year-old children. (RH)

This teaching guide contains material, for students in grades 6-9, in which a calculator is used in exploring and developing generalizations about quotient patterns generated from various polygons drawn on a hundred square. Includes suggested procedures and four ready-to-duplicate student worksheets. (JN)

Some number investigations on the multiplication table are provided by a sequence of four activity sheets. Beginning with examples of triangular and square numbers, the activities lead to the generalization. (MNS)