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…

In this article, an attempt is made to find all linear transformations that map a standard Pythagorean triple (a Pythagorean triple [x y z][superscript T] with y being even) into a standard Pythagorean triple, which have [3 4 5][superscript T] as their fixed point. All such transformations form a monoid S* under matrix product. It is found that S*…

This study focused on unprompted changes in children's analogical reasoning on geometric tasks and the additional effect of a short training procedure. Participants were 36 grade 1 level children (M = 6;8 years) divided over a not-trained and a trained condition. The study was a 5-sessions migrogenetic procedure, with a follow-up test session…

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)

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…

The Maine Learning Results (MLR) expects the state's students in prekindergarten through grade 2 to describe two-dimensional shapes as well as use positional language. Requiring translations of two-dimensional shapes supports this expectation. Students in grades 3-4 are expected to "use transformations," while students in grade 5-8 are…

In some elementary courses, it is shown that square root of 2 is irrational. It is also shown that the roots like square root of 3, cube root of 2, etc., are irrational. Much less often, it is shown that the number "e," the base of the natural logarithm, is irrational, even though a proof is available that uses only elementary calculus. In this…

For two given vectors of the three-dimensional Euclidean space we investigate the problem of identifying all rotations that transform them into each other. For this purpose we consider three types of rotation matrices to obtain a complete characterization. Finally some attention is paid to the problem of obtaining all rotations taking two vectors…

An easy way to present the uniqueness of the square root of a positive semidefinite matrix is given.

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)