Presents an approach for illustrating, on an intuitive level, the significance of loop invariants for algorithm design and analysis. The illustration is based on mathematical games that require the exploration of regularities via problem-solving heuristics. (Author/MM)

Four different types of problems from graph theory are presented and discussed. (MK)

Considered are what discrete mathematics includes, some parallels and differences between new math and discrete mathematics (listed in a table), and lessons to be learned. A list of references is included. (MNS)

A statistical model for investigating predictive validity at highly selective institutions is described. When the selection ratio is small, one must typically deal with a data set containing relatively large amounts of missing data on both criterion and predictor variables. Standard statistical approaches are based on the strong assumption that…

The problem of finding cube roots when limited to a calculator with only square root capability is discussed. An algorithm is demonstrated and explained which should always produce a good approximation within a few iterations. (MP)

States a convenient algorithm for temperature scale conversions and shows how performing the successive steps improves the accuracy of the results. (DDR)

Details are given of a simple computer program written in BASIC which calculates the sine of an angle through an application of DeMoivre's Theorem. The program is included in the material, and the program's success is discussed in terms of why the approximation works. (MP)

Three teaching ideas are presented: how to present changes between scientific notation and decimal form that eliminate some student confusion; an analysis of an incorrect algebra equation that produced a correct answer; and aspects of a standard calculus problem dealing with minimum and maximum values. (MP)

This reprint of a Project Solo curriculum module discusses graphing by computer, gives an example of a BASIC program used to graph a second degree polynomial, and provides suggested exercises in programing. (MK)

Describes the use of Moe's Mall, a locational device designed to be used by learners, as a simple algorithm for solving mole-based exercises efficiently and accurately using dimensional analysis. (DDR)

Examines solutions presented by preservice teachers for solving graphical and numerical problems involving the arithmetic mean. Participants presented two methods: algorithmic computation and balancing deviations about the mean. A significant difference was found between science and mathematics preservice teachers in the use of balancing…

Ideas on the long-term effects of using microcomputers in mathematics are presented. The changing perception of mathematics, the role of algorithms, the use of short computer programs, the effects on mathematical understanding, implications for teaching methods, logistic problems, examinations and assessment, and planning for the future are…

A procedure for constructing a magic cube is presented, with related teaching activities appropriate for students familiar or unfamiliar with the algorithm covered. (MP)

Addresses the distinction between conceptual and algorithmic learning and the clarification of what is meant by a second-tier student. Explores why novice learners in chemistry and physics are able to apply algorithms without significant conceptual understanding. (DDR)

The intent of this paper is to suggest and illustrate how electronic hand-held calculators, especially non-programmable ones with limited data-storage capacity, can be used to advantage by students in one particular aspect of work with polynomial functions. The basic mathematical background upon which calculator application is built is summarized.…