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

An algorithm for long division is presented that involves only addition and subtraction. (MP)

Suggestions are given for teaching flowcharting at the elementary school level. A short list of sources for free materials on computers is included. (DT)

The arithmetic needed for complex calculation using an electronic calculator is explained and exemplified. Problems involving square roots, number theory, Fibonacci numbers, and electrical resistances are solved. (SD)

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)

A straight forward process for working in fractions on any calculator is presented. The method involves converting a decimal back into a fraction in its lowest terms. (MN)

The use of flow charts in the teaching of college mathematics enhances students' understanding of mathematical processes. Used appropriately in elementary and secondary schools they could also nurture understanding of algorithms. (SD)

The author describes a new graphing algorithm for computing probabilities, and presents problems for these algorithms for use in the classroom. (SD)

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)

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

This volume contains a series of papers on algorithmic learning. Included are six reviews of research pertaining to various aspects of algorithmic learning, six reports of pilot experiments in this area, a theoretical discussion of "The Conditions for Algorithmic Imagination," and an annotated bibliography. All the papers assume a common…

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)

The author proposes that computer programs which are designed to make algorithmic structures accessible and comprehensible be employed as advance organizers in mathematics instruction. These programs would bring clarity and structural integration to mathematical, instructional, and cognitive structures important to the mastery of mathematical…

An algorithm is provided for generating as many desired digits in the decimal representation of a rational number on a calculator. It may be used whenever the number of digits displayed on the calculator exceeds the number of digits in the denominator. (JT)

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