This document plus diskette product provides nine interactive puzzles and games that both teach and provide practice with simple addition and subtraction concepts. The activities address these skills through carrying in addition and regrouping in subtraction. The activities address cognitive skills such as problem solving, planning, visual pattern…

A subtraction algorithm for numbers having several digits is described. The algorithm requires that, for digits in the same place, the smaller is always subtracted from the larger. (SD)

An attempt to introduce subtraction of negative integers early in the secondary school curriculum is described. The attempt was not successful, and several aspects of the experiment are discussed. (SD)

A new subtraction algorithm is described and illustrated. Research by the author has shown the method to be easier for low achievers, as well as useful as enrichment for average students. (SD)

This paper is concerned with the role of meaning and understanding in the acquisition of computational skill in subtraction. Evidence on the syntactic nature of subtraction errors is reviewed, with common "bugs" described. Then, data collected from interviews with four children are summarized in terms of their semantics of concrete…

This study involved the development and experimental tryout of 22 lessons designed to teach 23 primary grade children a set of specific procedures, focusing on the drawing of meaningful diagrams, for analyzing and solving arithmetic story problems. Major dependent variables studied were gain on (1) a 20-item test on stories of the eight types…

The purpose of this study was: (a) to develop a learning hierarchy for rational number subtraction using intraconcept analysis, and (b) to validate that hierarchy using the Walbesser technique and pattern analysis. Skills required to complete tasks within the hierarchy were operationally defined and ordered from both a mathematical and…

This investigation sought to determine the effect of emphasizing mathematical structure in the acquisition of computational skills by seven- and eight-year-olds. The meaningful development-of-structure approach emphasized closure, commutativity, associativity, and the identity element of addition; the inverse relationship between addition and…

Interaction between pupils' cognitive styles and instructional method in effecting achievement was studied. The instructional variables were sequencing and use of manipulative materials. Ninety sixth-grade students were ranked on Sigel's Cognitive Style Test. The upper and lower 36 were defined as high and low analytic pupils, respectively. Nine…

The relationship between children's performance in solving open sentences and the factors of sentence type, number size, and context was investigated. The study also identified and classified the methods of solution used. Thirty-two third graders were individually given an orally administered test on open sentences. Four types of open sentences…

Allowing students to examine different ways of performing an operation is suggested as a means of increasing their understanding. (MP)

A demonstration-plus-feedback technique was applied in an attempt to reduce the systematic inversion errors in subtraction in nine learning disabled students (ages 9-11 years). Journal availability: see EC 112 927. (DLS)

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 author urges that subtraction be introduced by "taking away" rather than by equal addition; multiplication be first demonstrated in sets; division be understood as sharing; and unit fractions be denoted at first by using the written word for denominator. (MN)