Adapts Stanic and McKillip's ideas for the use of developmental algorithms to propose that the present emphasis on symbolic manipulation should be tempered with an emphasis on the conceptual understanding of the mathematics underlying the algorithm. Uses examples from the areas of numeric computation, algebraic manipulation, and equation solving…

The calculator is used to explore the distributive property of a unary operator over a binary operator. This is an extension of an earlier paper. The emphasis is on student discovery of the property for various combinations of the operators. Instructional material contained in the report include a reference sheet of questions for potential…

Stochastic approximation algorithms for least square error approximation to density and distribution functions are considered. The main results are necessary and sufficient parameter conditions for the convergence of the approximation processes and a generalization to some time-dependent density and distribution functions. (Author)

A method for finding any integral root of a number using a four-function calculator is given, along with a justification of the method and root-finding exercises. (MN)

The concept of prime factorization is discussed and two rules are developed: one for finding the number of divisors of a number and the other for finding the sum of the divisors. (MP)

Chio's method of evaluating determinants by successive reduction of size is explained. (MN)

A conceptually elementary and geometrically based algorithm is presented to indicate how trigonometric functions can be calculated without using calculus. (MN)

Significant differences were found favoring skill-deficient second-graders (N=10) provided with repeated preteaching trials on a selected component skill of a subtraction algorithm before they worked the entire algorithm over students (N=10) who, from the beginning of training, received systematic instruction on working the entire algorithm.…

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)