A review of 25 years of Piagetian research in intellectual growth as it pertains to the learning and understanding of mathematics and implications for teaching. (MM)

The effects of numerical and visual cues, equality or inequality of initial volumes, size of measurement unit, and order of cue presentation on conservation of liquid volumes by first- and second-graders were investigated. Some findings extend, and others contradict, those of Piaget. (SD)

Evaluates the thinking of third grade students in relation to an instructional program in probability which was informed by a research-based framework that included a description of students' probabilistic thinking. Reveals that overcoming misconceptions in sample space, applying both part-part and part-whole reasoning, and using invented language…

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)

This study investigated the relationship between reflectivity-impulsivity and performance on Piagetian tasks with primary-grade children. Findings indicate that performance was best among the more reflective students but that performance of the normally more impulsive students would increase if they were restrained from answering too quickly. (LS)

To help the reader understand the scope and diversity of the Wisconsin R & D Center's research effort in mathematics, four perspectives are presented: (1) the Center's approach to research, development, and practice; (2) the origins of the current research effort; (3) a description of current research; and (4) a projection for future research. (JP)

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)

This study investigated the ability of middle school children to perform Euclidean transformations mentally. The results indicated that the tasks were more difficult than Piagetian theory would indicate. (SD)

Ninth-grade students were given a battery of cognitive aptitude tests and randomly assigned to verbal or figural mathematics instruction. Learning and retention were correlated with the aptitude measures and other fixed variables; regression analysis indicated the importance of memory, semantic factors, and sex difference. (SD)