Understanding conceptual relationships is an important aspect of learning arithmetic. Most studies of arithmetic, however, do not distinguish between children's understanding of a concept and their ability to identify situations in which it might be relevant. We compared 8- to 9-year-old children's use of a computational shortcut based on the…

For over a decade, research studies of mathematics education in high-performing countries have pointed to the conclusion that the mathematics curriculum in the United States must become substantially more focused and coherent in order to improve mathematics achievement in this country. To deliver on the promise of common standards, the standards…

Procedures for using an abacus to teach addition to learning disabled children are described. Considerations in choosing, constructing, and doing basic problems with an abacus are discussed. (CL)

Describes a study which compares the abilities of 130 first graders in responding correctly to open (Computational) addition exercises to their abilities in responding to equivalent problems stated in the closed form. No statistical difference between levels of correct responses to opened or closed exercises was indicated. (PR)

The study addresses the relational reasoning of different-aged children and how addition reasoning is related to problem-solving skills within addition and to reasoning skills outside addition. Ninety-two 5- to 8-year-olds were asked to solve a series of conceptually related and unrelated addition problems, and the speed and accuracy of all…

This programed mathematics textbook (Volume I) is for student use in vocational education courses. It was developed as part of a programed series covering 21 mathematical competencies which were identified by university researchers through task analysis of several occupational clusters. The development of a sequential content structure was also…

This programed mathematics textbook is for student use in vocational education courses. It was developed as part of a programed series covering 21 mathematical competencies which were identified by university researchers through task analysis of several occupational clusters. The development of a sequential content structure was also based on…

Viewing the number system as a complex of interrelated words, three studies are described: (1) a study of the difficulty of simple addition and subtraction in different decimal positions; (2) a study of variations in the number of digits in the addend or minuend; (3) a study of the effect of irregular morphemes occurring in some number words.…

Two sequences of activities were developed to provide instruction on the algorithms for addition and subtraction of two-digit numbers. In the integrated sequence (I) the mechanics of "carrying" and "borrowing" were treated as a single process "regrouping." In the sequential treatment (S) the addition algorithm was developed before the subtraction…

Two sequences of activities were developed to provide instruction on the algorithms for addition and subtraction of two-digit numbers. In the integrated sequence (I) the mechanics of "carrying" and "borrowing" were treated as a single process "regrouping." In the sequential treatment (S) the addition algorithm was developed before the subtraction…

The use of a toy adding machine in teaching addition to fifth grade students is described. (DB)

The cognitive processes of seven children solving arithmetic problems were accurately classified as reconstructive or reproductive according to the child's verbal report of his thought processes. Classifications of thought processes by means of verbal reports can also be used to improve the analysis of latencies. (SB)

Two experiments investigated extent to which English- and German-speaking childrens' mental arithmetic was constrained by working memory. Found higher mental addition spans when numbers were visible throughout calculation than when not. Variation in addition span with age and arithmetical operation difficulty approximated to a linear function of…