Contractions play a considerable role in the theory of fractals. However, it is not easy to find contractions which are not similitudes. In this study, it is shown by counter examples that an affine transformation of the plane carrying a given triangle onto another triangle may not be a contraction even if it contracts edges, heights or medians.…

Preschoolers made numerical comparisons between sets with varying degrees of shared surface similarity. When surface similarity was pitted against numerical equivalence (i.e., crossmapping), children made fewer number matches than when surface similarity was neutral (i.e, all sets contained the same objects). Only children who understood the…

A FORTRAN program for transforming raw scores into square roots, natural logarithms, arc sines, and other transformations is described. Any or all transformations may be made on a data matrix of fifteen columns or fewer, and one hundred rows or fewer. (Author/JKS)

A simulation study demonstrates that transformation of scores to ranks reduces variance heterogeneity when scores with unequal variances are combined and ranked as one set, but not enough to prevent distortion of the probabilities of Type I and Type II errors of statistical significance tests. (SLD)

Concept image and concept definition is an important construct in mathematics education. Its use, however, has been limited to cognitive studies. This article revisits concept image in the context of research on undergraduate students' understanding of the derivative which regards the context of learning as paramount. The literature, mainly on…

Sixty four preservice teachers taking a mathematics methods class for middle schools were given 3 math problems: multiply a three digit number by a two digit number; divide a whole number by a fraction; and compare the volume of two cylinders made in different ways from the same rectangular sheet. They were to a) solve them, explaining their…

Explores whether 5-month-old infants (N=56) develop numerical- or location-based expectations by using a violation of expectation paradigm with possible and impossible events. Reports that infants use a more abstract representation than object location, the numerical nature of which is discussed. Contains 25 references. (Author/ASK)

In three-mode principal components analysis, the P x Q x R core matrix "G" can be transformed to simple structure before it is interpreted. This paper shows that, when P=QR-1, G can be transformed to have nearly all the elements equal to values specified a priori. A closed-form solution for this transformation is offered. (SLD)

The patterns of handmade quilts made in southern United States are utilized for studying the symmetries of the plane and transformational geometry. Quilts are made without sewing and then from the same block, students can make quilts with different wallpaper patterns by using various combinations of transformations and through this geometrical…

Extended Lubin's discussion of ordinal and disordinal interactions by introducing the concept of dual-ordinal. This concept was considered important since a transformation cannot bring about additivity unless the interaction is dual-ordinal in nature. A method is presented for determining whether or not an interaction is dual-ordinal. (Author/BJG)

A general factor analysis computer algorithm is briefly discussed. The algorithm is highly transportable with minimum limitations on the number of observations. Both singular and non-singular data can be analyzed. (Author/JKS)

An experimental procedure involving interaction between subject and computer was used to determine an opitmum subset of stimuli for multidimensional scaling (MDS). A computer program evaluated this procedure compared with MDS based on (a) all pairs of stimuli, and (b) on one-third of the possible pairs. The new method was better. (Author/HG)