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Peer reviewedJansson, Lars C. – Journal for Research in Mathematics Education, 1986
Ordering theory was used in two studies to empirically determine hierarchies of developmental precedence for Piaget's 16 logical combinations. In study 1, subjects (N=94) responded to statements about odd and even numbers; in study 2, 30 subjects responded to statements about line segments. Results are reported and discussed. (Author/JN)
Descriptors: Cognitive Development, Intermediate Grades, Junior High Schools, Logical Thinking
Peer reviewedBurger, William F.; Shaughnessy, J. Michael – Journal for Research in Mathematics Education, 1986
Describes the van Hiele levels of reasoning in geometry according to responses to clinical interview tasks concerning triangles and quadrilaterals. Subjects were 13 students from grades 1 through 12 plus a university mathematics major. Students' behavior on tasks was consistent with the van Hiele original general description of the levels.…
Descriptors: Cognitive Development, Elementary Secondary Education, Geometry, Higher Education
Peer reviewedDeVecchi, James Martin – Journal for Research in Mathematics Education, 1981
A logically and empirically valid structure of knowledge for differential calculus was made by textbook analysis and by collecting data from a first semester college calculus course. (MP)
Descriptors: Abstracts, Calculus, College Mathematics, Educational Research
Peer reviewedClose, John S.; Murtagh, Fionn – Journal for Research in Mathematics Education, 1986
A hierarchical-clustering technique was used to examine relationships among computation-related skills by pupils in grades one to four in two Irish schools. A clear hierarchical ordering of skills was obtained at each grade. (MNS)
Descriptors: Cluster Analysis, Computation, Elementary Education, Elementary School Mathematics
