A collection of games and puzzles that teachers can use to replace or supplement the usual textbook subtraction examples involving large numbers is given. Most of the nine activities are self-checking. (MNS)

Several subtraction algorithms are analyzed to see if they involve borrowing. The main focus is on an analysis of a procedure called the residue method. The operational arithmetic which underlies the symbolic manipulations is examined and conditions where the method does and does not use borrowing are highlighted. (MP)

Data indicated that high percentages of fifth- through eighth-grade low achievers had high algorithm confidence for the operations of addition, subtraction, and multiplication. A substantial proportion in each grade expressed a low degree of confidence in their computational method for division. (CM)

A process for helping students in the elementary grades develop their own algorithms for subtraction with carrying is described. Pupils choose their own times and ways to move from manipulative materials to written notation. (MP)

A method is presented for determining cube roots on a calculator with square root facility that has a rapid rate of convergence. (MP)

Solutions to difficult equations are illustrated with numerical techniques that can be used easily on calculators. Flowcharts and programs for computers and calculators are included. (MP)

Examines the philosophy behind the issue of computational fluency in "Principles and Standards." (Author)

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)

Fourth graders' (n=117) solutions to addition problems were analyzed in terms of standard or idiosyncratic written algorithms. Students had not previously been taught pencil-and-paper algorithms. Preference for horizontal layout, working from left to right, and a wide variety of written algorithms were found. (Contains 48 references.) (Author/MKR)

Compares traditional mathematical models with computer simulations. Shows the strengths and flexibility of algorithmic computational simulations through a program designed to investigate and extend understanding in one of the most enduring questions in social choice research. Discusses solutions to this problem from each approach--analytic and…

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

One difficulty that mathematically naive subjects encounter in solving arithmetic word problems involves the limitation on short term memory (STM) capacity. It is hypothesized that naive subjects, not having access to formal problem solving strategies, may find visualization useful in reducing strain on STM. Two experiments are reported. The…

Investigating properties and characteristics of unary operations is shown to be facilitated by using calculators. Several avenues for instructional exploration are suggested and examples given. These include questions relating to relations, inverses, commutativity, distributivity, and iterations. A discussion of the calculator algorithm for…

Five reports from a 2-year study are presented. Frequencies and descriptions of systematic errors in the four algorithms in arithmetic were studied in upper-middle income, regular, and special education classrooms involving 744 children. Children were screened for adequate knowledge of basic facts and for receiving prior instruction on the…

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)