After practice in making cross-section cuts on four solids, 90 sixth-, eighth-, and tenth-graders were tested on ability to select appropriate drawings for designated cross sections. Sixth graders had significantly lower mean scores than upper graders; boys scored significantly higher than girls; lower-ability students generally scored lower. (MS)

First graders' length conservation was measured using a verbal and nonverbal test, and the results were compared as predictors of mathematics achievement. Findings showed that verbal conservation scores were superior to nonverbal conservation scores and to intelligence scores for predicting achievement. (DT)

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)

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)

Children aged four through eight performed a series of tasks involving two-dimensional isometrics to determine the amount of compatability between a mathematically-based organization of Euclidean transformation concepts and the existing cognitive structures of the children. Results confirmed that mathematical and cognitive structures are not…

Secondary geometry students were tested for van Hiele level of thinking, geometry knowledge and achievement, and proof-writing achievement. Proof-writing achievement correlated significantly with van Hiele level entering geometry knowledge and geometry achievement. The predictive validity of the van Hiele model was supported. (Author/DC)

Presented is an alternative method for analyzing the van Hiele level of students' geometrical reasoning. The accuracy of students' answers may afford a description of acquisition and/or expertise for each of the van Hiele levels simultaneously rather than the traditional assignment and evaluation of one level at a time. (JJK)

The investigation reported pursued the possibility of cross-cultural differences between American and Swiss children in terms of how they perceive and conceptualize spatial figures. There was statistical evidence that the preferences of American and Swiss children were different when compared as a whole or by sex and test version. (MK)

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)

Twelve middle school students, working in pairs, used a computer microworld to explore introductory geometric transformational concepts. Despite a tendency for symbolic overgeneralization, the students were able to use visual feedback from the microworld and discussions with partners to correct their own mistakes. (Author/JJK)