Difficulty levels of 168 randomly generated multiplication problems were obtained by testing 238 fifth-graders. Variables concerning the number of operations, digits carried, and magnitude of the digits were defined, and a least-squares procedure was used to construct structural models accounting for 60-70 per cent of observed problem difficulty…

Twelve fourth-grade classes in two schools were taught division using either the subtractive approach to the Greenwood algorithm or a partitioning approach to the standard algorithm. Analysis of class means on immediate, retention, and delayed retention tests indicated that use of the standard algorithm was more effective. (JP)

Fifty Brazilian children aged seven-13 were individually given addition and subtraction exercises. Counting was the preferred procedure, with use of school-taught algorithms limited. Some children decomposed numbers into tens and units and then worked at both levels. They rarely referred to previous results when doing related exercises. (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…

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)

The time at which component skills are taught is studied to see whether it is a significant instructional variable. This research involved the instruction of a multiplication algorithm to 15 below-average first graders. (MP)

The authors attempt to determine the effects of the use of direct and "combinations of tens" methods of two column-addition, ability, and grade level as factors in column addition efficiency. (MN)

Sixteen Brazilian third graders aged 8-13 were given problems involving multidigit computation. School-taught algorithms were likely to be used in school-taught problems, with little carry-over to real problem situations, but resulted in more incorrect answers. (MNS)

In a two-year study, frequencies and descriptions of systematic errors in four algorithms in arithmetic were studied in regular and special education classrooms. (Author/SD)

Students from six fourth-grade classes were paired and randomly assigned to computer or worksheet treatments on multiplication and division. Those using computer-based drill-and-practice programs made greater gains on some tests of basic facts, but had no higher retention of algorithms. (MNS)

Computational strategies and estimating abilities of 466 Japanese students were tested and interviews with a subsample of that group were used to compare with a theoretical model based on a sample from the United States. Results of the comparison of computational and estimating abilities are presented. (CW)