Determined effects of two task types on 12- and 13-year-olds' understanding of applications of multiplying and dividing positive numbers. Results indicate the persuasive nature of certain misconceptions and specific effects of context attributable to such aspects as relative familiarity. Implications of these and other results are discussed.…

This study involved 48 students ages 9 to 12. The 29 experimental group students, divided into small groups, performed learning exercises designed to improve skills in analyzing and processing expressions frequently included in addition and multiplication problems. The exercises helped significantly to improve problem-solving performance. (MNS)

One important finding from recent research on multiplication word problems is that children's performances are strongly affected by the nature of the multiplier (whether it is an integer, decimal larger than 1 or a decimal smaller than 1). On the other hand, the size of the multiplicand has little or no effect on problem difficulty. The aim of the…

Three different models with continuous materials, discontinuous materials, and number lines were used to study the operation concept in six investigations on multiplication with fractions with pupils aged 11-12 in a Penang International School. All approaches could be understood by pupils, but they preferred the area and fractional models. (MNS)

This study demonstrated the effectiveness and efficiency of a constant time delay procedure (four seconds) to teach five elementary students with learning disabilities multiplication facts. Learning generalized to a paper-and-pencil task, to a different presentation orientation, and to reverse facts. (DB)

Numerous studies indicate that performance in solving single step multiplicative word problems is influenced by both problem structure and the types of numbers involved in the problem. For example, including numbers less than one often increases the difficulty of a problem. What remains unclear is how problem structure and number type interact in…

This case study examined the performance of a 13-year-old highly skilled mental calculator on mental multiplication tasks. She solved difficult tasks by using various ingenious calculation methods, including distributing, factoring, and recalling the product directly. Implications for instruction are reported. (Author/RH)

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…

Four methods of solutions and 12 calculative strategies were found from introspective reports of 15 skilled and 15 unskilled students in grades 11 and 12 doing mental multiplication. Unskilled students used strategies more suited to written than mental computation, while skilled students used strategies based on number properties. (MNS)

Over 600 pupils in grades five, seven, and nine in Italian schools were asked to choose the operation needed to solve 26 multiplication and division word problems. The findings seemed to confirm the impact of the repeated addition model on multiplication and of the partitive model on division. (MNS)

Studied were the misconceptions that preservice elementary teachers have about multiplication and division. Results indicated that they are influenced by the same primitive models as students; the most common errors made by both groups are quite similar. (MNS)

This study compared the effects of two cover, copy, and compare interventions on the written multiplication performance of two elementary school students with behavioral disorders. The verbal response condition resulted in greater increases in written multiplication performance and occasioned more than twice the number of opportunities to respond…

Describes the characteristics of progressive schematization with regard to column multiplication and column division. Contrasts this with column arithmetic based on progressive complexity. Presents a summary of research data concerning column arithmetic. (TW)

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)

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.…