The authors challenge some of the conclusions reached about Piaget by Brian Rotman in his book. (MK)

The ability of students in grades 1-12 to generate proofs of theorems in an unfamiliar, one axiom, abstract system was investigated. There were no significant differences in performance of two levels of secondary students; fourth- through sixth-grade students were also able to develop proofs, but needed more time. (SD)

An outline of a model that provides a new perspective on the conceptual foundations of mathematics and a new approach for the study of children's acquisition of numerical operations is proposed. Attention is viewed as a pulse-like succession of moments and is supported by recent data from neurophysiology. (MP)

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)

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)

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)

Investigates, by conducting individual clinical interviews of 97 children ages 3 to 6, the criteria preschool children use to distinguish members of a class of shapes from other figures, emphasizing identification and descriptions of shapes and reasons for these identifications. Concludes that young children initially form schemas on the basis of…

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)

A study with 29 preschoolers showed that a statistically significant number of them successfully reassigned tags in counting (ordinality) but failed to predict that differently ordered counts would produce the same outcome (cardinality). Results indicated that children may not entirely understand implications of their counting actions. (Contains…

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 examined the effects of field dependence/independence and the level of operational development on the mathematics achievement of 450 students in grades 6-8. Field-independent students scored significantly higher on total mathematics, concepts, and problem-solving tests. High-operational students scored significantly higher on all tests.…

Subjects were enrolled in a required science course for elementary education majors at Georgia College during spring quarter 1980. Each student was presented questions during two one-hour interview sessions. Van Hiele's assertions appear to be supported by the investigation, but further examination and development of assessment procedures are…

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)