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)

Presents an activity on transformations that employs a story from children's literature. Emphasizes that books and stories that use mathematical problem solving not only engage children in the narrative but also give them opportunities to see how mathematics is used in everyday life. (ASK)

Certain properties of lenses provide a physical model of the mathematical concepts of multiplication of integral numbers and of similarity transformations in geometry. Further, they can provide a realistic concrete representation for rules governing multiplication of signed numbers. Suggestions for problems and classroom demonstrations involving…

An approach to the instruction of maxima and minima problems that works with tools of geometry and algebra is presented. The focus is on a classic pie-cutting problem, which is viewed as an interesting and instructive task that is an excellent application of transformation geometry. (MP)

Presented is a method for solving certain types of problems, with the goal of piquing students' interest in studying affine geometry, which underlines the method. (MNS)

Discussed is an application of number theory to cryptology that can be used with secondary school students. Background on the topics is given first, followed by an explanation for use of the topic. (MNS)

One class of interactive, computer-based learning environments (microworlds) for the exploration of school mathematics (and science) entails the incorporation of appropriate concepts within the engaging context of self-directed discovery learning. The objective of this research was to investigate and describe in detail the constructive learning…

Argues that Turtle Geometry has a great deal to offer mathematics teaching and learning. Suggests that it helps develop general problem-solving strategies and encourages new approaches to teaching and learning. (PK)

Presents 13 examples in which the intuitive approach to solve the problem is often misleading. Presents analysis of these problems for five different sources of misleading intuitive generators: lack of analysis, unbalanced perception, improper analogy, improper generalization, and misuse of symmetry. (MDH)

This guide is designed to help classroom teachers implement the Alabama Course of Study: Mathematics K-12. It is inclusive also of the objectives tested by the Stanford Achievement Tests and the Alabama Basic Competency Tests. One characteristic of the curriculum guide is that it clearly states what students should learn in each grade level. These…