Presents an example from the combinatorial theory of partially ordered sets. Discusses algorithms of on-line antichain partitioning problems, a topic in discrete optimization. (YP)

Describes investigations of quick cancellation problems in two-digital integers. Generalizes the results to n-digital integer problems. (YP)

Described is the subject of biological scaling for physics teachers including examples and in-depth reading. Topics are elements of scaling, terminal velocities, Lilliputian and Brobdingnagian, brain evolution, dolphin echolocation, surface tension, gravity change, food and oxygen, and seeing. Ten references on physics and size, and ten questions…

An aspect of the long history of the struggle to quantify motion is briefly traced through three extended problem sets suitable for use in first year calculus courses. The sketch culminates with an application of simple mathematics to one of the most current problems in the theory of the universe. (Contains 2 figures.)

This paper describes a proportional reasoning problem set within a real-life context and a complete analysis of one small group discussion of this problem over the course of a 90-minute block. The seventh-grade students' discourse is described to provide insights into typical mathematical interpretations of this problem, as well as some…

The aim of this monograph is to describe a program of research investigating the problem-solving responses of young children and to present in summary form the results of the analyses completed so far. Attention is given to characteristics of clinical studies which are thought to make the clinical method particularly useful with young children.…

This yearbook is a reference source of direct applications of mathematics for use in grades 7-12. Topics are listed alphabetically in each of four sections: arithmetic, algebra, geometry, and trigonometry. An explanation is given as to the plan of the book, making the location of desired material easier, and an index is included. In many cases the…

Outlines various misconceptions about problem-solving (PS) and several strategies to improve intellectual skills and strategies. Also describes the Covington Productive Thinking Program (designed to help develop PS skills) and several lesson problem sets from this series of 15 books. (JN)

Explored are various aspects of drawing graphs on surfaces. The Euler's formula, Kuratowski's theorem and the drawing of graphs in the plane with as few crossings as possible are discussed. Some applications including embedding of graphs and coloring of maps are included. (YP)

Discusses how to express an n factorial as a product of powers of primes. Provides two examples and answers. Presents four related suggestions. (YP)

Provides several problems and their solutions for a descriptive statistics course. Included are problems related to measurement, data collection, sample construction, applications, and computation. Discusses the misleading nature of statistics. (YP)

Discusses geometric construction problems. Presents four ways to construct a regular octagon using different conditions. Provides drawings showing the constructions. (YP)

The author discusses the definition of the ordinary points and the regular singular points of a homogeneous linear ordinary differential equation (ODE). The material of this note can find classroom use as enrichment material in courses on ODEs, in particular, to reinforce the unit on the Existence-Uniqueness Theorem for solutions of initial value…

Discussed is the benefit of the inclusion of historical material in a student's text. Several geometry problems are used as examples. A suggested list of problem sources is provided in the appendix. (YP)

Determines which chessboards contain a chromatic rectangle having all four corners the same color for any black-white coloring. Expands the problem to a three color problem. (YP)