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…

This study examined how six experienced teachers got information about students' knowledge and used that information to adjust their instruction while tutoring the students in addition. Each teacher tutored five simulated students and one live student. (RB)

Presents an activity that engages children in thinking about the results of combining numbers. (ASK)

An investigation is given of exceptions to the rule for adding fractions. The use of such exceptions in instruction is discussed. (MP)

The problem solving performance of 24 learning disabled and 24 non-disabled second and fourth grade children was investigated using embedded irrelevant linguistic and numerical information within addition word problems. Irrelevant numerical information but not irrelevant linguistic information affected performance of all groups; however, LD…

We compared alternative instructional strategies for integrating knowledge of decimal place value and regrouping concepts with procedures for adding and subtracting decimals. The first condition was based on recent research suggesting that conceptual and procedural knowledge develop in an iterative, hand over hand fashion. In this iterative…

Includes sample diagrams. (SP)

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…