A multiple-probe-across-problem-sets (tasks) design was used to evaluate the effects of the Detect, Practice, and Repair (DPR) on multiplication-fact fluency development in seven third-grade students nominated by their teacher as needing remediation. DPR is a multicomponent intervention and begins with a group-administered, metronome-paced…

The authors investigated the performance on simple multiplication and division problems of 8-year-old children longitudinally to determine the developmental trajectories of both operations. Twice a year, during 2 consecutive school years, children performed a multiplication and division verification task and a number-matching task. All effects…

Presents a study in which participants were trained on nine single-digit multiplication problems over three sessions. Transfer of practice was tested with nine different multiplication problems in the fourth session for half the participants. Interprets problem-size, transfer, and retention effects within a network-interference model of mental…

How multiplication is usually taught in school and how it could be taught are discussed. Development of understanding is illustrated through children's words and work. (MNS)

Three experiments were conducted to examine children's use of multiplying and proportionality rules in judgments of area. In the first two experiments, 7- through 8-year-olds were asked to judge the area of rectangles. In the third, 8- through 11-year-olds were tested on ratio of a rectangle compared to a horizontal line. Results indicated…

Investigates the effect of mental schemes corresponding to additive and multiplicative situations in the process of interpreting and solving problems. Classifies relative difficulties of problems according to their situations which are considered through a written test administered to pupils in grades 2, 3, and 4. Supports the assumption that…

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…

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)

Describes the psychological analysis of the instruction of the concept of multiplication in the former Soviet Union. Presents a system of instructional situations in introducing multiplication and the main results of instruction for grade two. (MDH)

Applies the Lesh Translation Model to develop conceptual understanding by showing relationships between five modes of representation proposed by Lesh to learn multiplication of fractions. Presents five teaching activities based on the translation model. (MDH)

Six Piagetian-type tasks, designed to examine associated topological groupings, were examined to determine if a hierarchical relationship existed among them. The groupings examined were: the partitioning of sets and addition of subsets, reciprocity of proximities, one-to-one multiplication of elements, order of placement, symmetrical interval…

This paper studies the difficulties children have solving word problems that correspond to one of the situations modeled by multiplication; that of a ratio (e.g. "candies per box"), multiplied by an extensive quantity (e.g. "boxes") (I x E). Sixty children were individually observed solving and repeating I x E problems. Various…

Discussed are preservice elementary teachers' misconceptions and inconsistent beliefs about multiplication and division with decimals. Sources of inconsistencies and recommendations for overcoming inconsistencies are included. (KR)

The processes and strategies used by Finnish second graders in solving verbal multiplication and division tasks were investigated, and the relationship of these processes and strategies to Piagetian abilities, memory capacity skills, and rational number concepts was charted. Three categories of strategies were classified: operations based on…

Discusses the two overgeneralizations "multiplications makes bigger" and "division makes smaller" in the context of solving word problems involving rational numbers less than one. Presents activities to help students make sense of multiplication and division in these situations. (MDH)