A study to determine if "random" or "careless" errors in multiplication made by individual students take on discernible patterns is described. Implications for teaching are discussed. (MK)

Describes a microcomputer-based system for diagnosing children's multiplication errors which incorporates the knowledge base of all known systematic multiplication errors, and utilizes a modular approach to cope with the program's complexity. Each module's function, how the programs interact, and the design of pupil-machine interaction are…

This study compared the error patterns of third- and fourth-grade children on addition, subtraction, and multiplication exercises in horizontal and vertical formats. The research design used parallel eight-item tests for each operation; the only difference between items on parallel forms was the formal (horizontal or vertical) of the computational…

Using R. S. Siegler's retrieval-required task, 19 male and 22 female third graders were examined before they had been introduced to multiplication in school. Examination of error patterns suggests that the basic assumptions of the distribution-of-associations model need to be tested directly and that the retrieval-required task confounds retrieved…

Recall of multiplication number facts is a major educational objective in elementary grades, yet some children never acquire total mastery. A microcomputer multiplication number facts training program was developed which incorporated programmed instructional features including feedback, positive reinforcement, vanishing, branching and pairing.…

Investigated was how easily pupils aged 12 and 13 who were initially unaware of the invariance of an operation (with decimals) modeling a situation could be led to such awareness. Results from clinical interviews are reviewed and a protocol presented. It appeared difficult to induce conservation. (MNS)