This investigation concerns the repeated application of the rule "take the sum of the squares of the digits." (MP)

The author redefines basic numeracy as the ability to use a four-function calculator sensibly. He then defines "sensibly" and considers the place of algorithms in the scheme of mathematical calculations. (MN)

Suggestions for teaching the concept of division by zero are given. (MK)

The method described here converts a given problem in a base other than ten to a related problem in base ten, solves the related problem in base ten, and converts the answer back to the original base. Limitations are discussed. (MP)

Strategies for rapid mental computation are explained, including multiplying by 11 (or 21, 31, etc.); adding columns of numbers; and multiplying 2-digit numbers. Rapid mental computation is suggested as a motivator for investigating the underlying mathematical principles. (DB)

Work with recurring decimals provides pupils with an opportunity for exploration and examination of a wide variety of mathematical ideas and strategies. Examples of work done by one group of pupils who were presented with an opportunity to explore such decimals is featured. (MP)

Three alternative methods of finding averages of two numbers are presented. (MP)

These three brief articles concern problems students encounter in solving simple linear equations, children's conceptions of number, and the distinction between adding objects and adding numbers as illustrated by students' problems with Euler's formula. (SD)

Students who were unsuccessful in performing long division were taught to use a successive subtractions algorithm. (SD)

In one school, algorithmic development has been infused in the mathematics curriculum. An example of what occurs in mathematics classes since the teachers began using the computer is given, with two students' conjectures included as well as the algebraic justification. (MNS)

A method is described for working multiplication problems by counting on fingers. (DT)

Arithmetic programming for students with mild mental disabilities requires a comprehensive perspective that includes attention to curriculum, instruction, and appraisal. Arithmetic computation should not dominate educational programming, but should be included in ways that are functionally relevant and meaningfully presented within a framework of…

Activities are described in which number patterns in two-digit multiplication exercises are investigated. (DT)

Argues that the type of calculator that is used in mathematics instruction is very important. Suggests that four-function calculators fail to give correct values of mathematical expressions far more often than do scientific calculators. (PK)

Describes the Approaching Algebra Numerically (AAN) Calculator as a computer-based simulation of a hand-held calculator designed with novice learners in mind. Includes a complete description of the calculator and suggests uses for the calculator, including exponentiation, order of operations, scientific notation, concept of variable, and problem…