A game based on the group of permutations on four symbols is described. The game can be used in the study of many algebraic concepts. (SD)

Typical difficulties involved in solving combinatorial problems are examined and seven common pitfalls are discussed. (MP)

Mathematical modeling is defined. Examples are used to show that there are models available which illustrate both the traditional use of mathematics in the physical science and its newer use in nonphysical disciplines, and which are at a suitable level for teaching in schools. (Author/MK)

This paper reviews the present state, recent trends, and prospective lines of development concerning applied problem solving, modeling, and their respective applications. Four major trends are scrutinized with respect to curriculum inclusion: a widened spectrum of arguments, an increased universality, an increased consolidation, and an extended…

Probability theory can be developed from a theoretical or experimental probability approach. The problem, "The Gambler's Ruin," is used to study whether students are naturally sensitive to learning probability from an experimental probability approach through simulations. Results indicated that use of simulations can contribute to…

Reports a project that incorporated mathematical modeling into a college course. Reports evaluation of the course in terms of criteria derived from the stated aims: modeling performance, modeling framework, pedagogy assessment, and personal growth. Included are two sample problems. (YP)

Children's responses to an alternative model over three lessons were described and their learning assessed in a posttest. Their responses and performances were compared to that of a similar group of children learning through a conventional number line model. The two models were compared from practical and theoretical viewpoints. (Author/CW)

Identified are three obstacles which students must overcome when examining and interpreting diagrams. The resources of the Geometric Supposer, a set of microcomputer tools designed to aid students, are outlined. The advantages of the use of this software are emphasized. (CW)