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)

When two methods of transforming numbers from one base to another were taught sequentially, the first interfered with learning of the second. (SD)

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)

Two studies investigated the effects of verbalization of discovered generalizations on the retention of those principles. (SD)

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)