An algorithm is defined here as an unambiguous procedure which will always produce the correct result when applied to any problem of a given class of problems. This paper gives an extended discussion of the definition of an algorithm. It also explores in detail the elements of an algorithm, the representation of algorithms in standard prose, flow…

The purpose of this study was to determine differences in achievement of fifth-grade students in 16 classes taught two of four mathematical algorithms by one of four instructional strategies. Computational skills and ability to extend the algorithm were tested. The instructional strategies were: pattern, algebraic, pattern followed by…

On the basis of analytical and observational work during Phase 1 of this project, an experiment was developed to test the effects of systematic variations in the level of the independent variable "instructional cue" (I.C.). The first phase of the research consisted of the development of a precise operational definition of the variable. This was…

This study investigated two methods used to teach multidigit multiplication to fourth-grade students: the lattice method and the distributive method. Classes from four schools were randomly assigned so that the two treatment groups contained two each or urban, rural and inner city classrooms. A series of 15 lessons was prepared for each treatment…

Computational algorithms appearing in early American arithmetic text are discussed. (SD)

Described is a case in which a young student stumbles upon the "integer" technique for subtraction which differs from the techniques of decomposition and equal addition. (MN)

The conceptual difference between understanding and algorithmic performance is examined first. Then some dilemmas that flow from these distinctions are discussed. (MNS)

Second-grade students were randomly assigned to either an instructional unit within which addition and subtraction of two digit numbers were treated as a single integrated process of regrouping or one which developed the addition and subtractive algorithms sequentially. Periodic assessments favored the sequential approach, but differences were not…

A strategy to make the transition from manipulative materials to a written algorithm for division is outlined in dialogue form. (MNS)

The following ideas are shared: (1) a low-stress subtraction algorithm that eliminates the traditional borrowing process, and (2) an approach to graphing circular functions that looks at the process of modifying simple functions as a series of shifting, sliding, and stretching adjustments, with its biggest advantage viewed as its generality. (MP)

Results of this study indicated calculator algorithms can serve as an effective alternative instructional strategy where computational skill is an instructional goal. (MP)

The author feels teaching division of fractions is worthwhile because it will help students understand other algorithms. (MK)

Three short essays provide teaching suggestions for lessons on base two, order of operations, and ratios used to motivate a number of mathematical ideas. (MK)