After a discussion of philosophy and learning processes and theories, the author presents rationale for teaching axiomatics in geometry including traditional and modern transformational approaches. (JG)

The basic ideas of the theory of manifolds is illustrated using elementary geometry. (MM)

A description of visual aids which are useful in discussing rotations of geometric figures is presented. (FL)

A procedure using calculators is described to test Ulam's conjecture that all positive integers converge to 1, if subject to certain iterated transformations. (MNS)

The effects of under and overrotation on common factor loading stability under three levels of common variance and three levels or error are examined. Four representative factor matrices were selected. Results suggested that matrices which account for large amounts of common variance tend to have stable factor loadings. (Author/RL)

Details of the investigation of a device that produces unusual transformations in the plane are provided, along with the directions several students took in their studies. (MP)

A replication study was conducted to determine whether conservation-of-number performance would be improved by questioning the subject only after the transformation is performed, rather than before and after the transformation, as is done in the standard conservation test. Subjects were preschoolers, aged 0-4 to 5-7. (Author/MP)

Presents a way of using greeting cards created by graphing calculators to teach the transformation of functions. Illustrates the steps of making a calculator greeting card and students' descriptions of transformations. (KHR)

The general transformation approach to time series analysis is extended to the analysis of multiple unit data by the development of a patterned transformation matrix. The procedure includes alternatives for special cases and requires only minor revisions in existing computer software. (SLD)