Nine children were tested to determine the appropriateness of Piaget's part-whole fraction concept interpretation for both the discrete case and the continuous cases of length and area. (MP)

Eight boys and eight girls from a rural elementary school participated in the investigation. Specific heuristics were adopted from Polya; and the students selected represented two substages of Piaget's concrete operational stage. Five hypotheses were generated, based on observed results and the study's theoretical rationale. (MP)

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)

In elementary grades, word problems that cannot be solved by a routine application of a single arithmetic operation can cause a great deal of difficulty. The role of several factors in children's performance when solving two-step problems of a given structure was probed. (Author/MP)

Research was viewed as needed to establish a classification scheme for the major areas of difficulties individual students have in solving word problems. The results suggest that inability to read problems is a major obstacle for sixth graders, and mastery of components of problem solving ensures process mastery. (MP)

This study investigated the relationship between several Piagetian abilities and an information processing capacity, and first-grade children's performance on verbal addition and subtraction problems. Results pointed to a sometimes small but consistent relationship between possession of a cognitive ability and solving an arithmetic problem. (MP)

High- and low-ability fifth graders were taught multiplication of fractions by one, two, or four methods. On a subsequent transfer test the scores of high-ability students decreased and those of low-ability students increased as a function of number of methods used. (SD)

Area and measurement tasks representative of those used by Piaget were administered to 168 primary students. Data were analyzed to determine effects of sex, age, and task sequence. (SD)

Performance of first and second graders on measurement problems indicated that they are unable to relate the measurements of objects using different units to visual comparisons of quantities. (SD)

Performance was contrasted on mathematical story problems in two formats, a drawn version and the usual verbal one, with 262 fifth graders. The drawn format resulted in superior problem-solving performance. There was a significant ATI between field independence-dependence and format treatments, although the overall treatment effects were not…

Research designed to determine whether the phenomena observed by Piaget were task specific was performed. The results did not confirm Piaget's notion that topological concepts develop prior to the concepts of Euclidean geometry. (SD)

Mastering the basic number combinations involves discovering, labeling, and internalizing relationships, not merely drill-based memorization. Counting procedures and thinking strategies are components, and it may be that using stored procedures, rules, or principles to quickly construct combinations is cognitively more economical than relying…

The author first corrects Baroody's description of the network retrieval model for basic number facts, in which facts are stored in memory and retrieved as needed. He then indicates weaknesses in Baroody's argument. (MNS)

Subjects were 73 first-grade children who were heterogeneous ethnically and socioeconomically. The purpose was to evaluate a component-skill analysis of the child's transition from the solution procedure counting-all to the solution procedure counting-on. The results provide a strong case for the proposed componential analysis. (MP)

Two studies dealing with length conservation and measurement indicate that caution needs to be used when one looks at and makes claims about children's cognitive ability and development with regard to conservation. (MP)