Types of errors made by children in addition and subtraction are presented and discussed. Suggestions are given for testing, diagnosing, and prescribing for instruction. (MNS)

Reported are the results of a study to determine if specific errors in subtraction occur when students demonstrate ability to apply selected decimal numeration system principles. A secondary purpose was to examine and compare errors made by various subsets of the sample population characterized by grade level, arithmetic achievement, mental…

This study explored the effects of visual (vertical and horizontal) and oral presentation modes upon simple mathematical computations (addition, subtraction, and multiplication). Seventy-two undergraduate education majors were employed as subjects. The placement of the process sign (left, middle, right) and whether a one or two digit number…

The early use of the distributive law can aid students in learning addition of fractions and provide rapid approaches to computation involving other operations. (SD)

Two methods of adding columns of single digits were compared in terms of the speed and accuracy with which sums are produced. The direct method (successive addition) was found to be better than the method of looking for combinations which sum to ten. (SD)

Develops a division algorithm in terms of familiar manipulations of concrete objects and presents it with a series of questions for diagnosis of students' understanding of the algorithm in terms of the concrete model utilized. Also offers general guidelines for using concrete illustrations to explain algorithms and other mathematical principles.…

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)

Symbols and shapes used in flowcharting are defined, reasons for incorporating flowcharts into instructional activities are listed, and eight different flowcharts are presented. (DT)

The role of division of whole numbers in problem solving and the implications for teaching division computation are examined. Deleting the teaching of division facts, and obtaining solutions by using multiplication facts, is advocated. (DT)

This response to Usiskin's editorial comment on calculator use in the May 1983 issue considers why arithmetic is taught. The belief that mathematics improves thinking and the humanist position that it is part of our cultural heritage are noted. The role of mathematics in the curriculum should be reconsidered. (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)

The hypothesis investigated is that understanding of the long division algorithm requires a higher cognitive level than understanding of fundamental division concepts. Sixth-grade children were tested on performance and understanding of a given algorithm and concepts of division. (MP)