An approach to how to expand explorations of determinants is detailed that allows evaluation of the fourth order. The method is built from a close examination of the product terms found in the expansions of second- and third-order determinants. Students are provided with an experience in basic mathematical investigation. (MP)

Details of how observers on a moving ship can furnish an accurate report of wind velocity are provided. A method employing vector addition and some trigonometry is covered. Wind velocity is initially indicated through an anemometer and a wind vane. Ships are urged to radio weather data. (MP)

The first presentation discusses a way of teaching second-year algebra students that the harmonic series diverges, and notes some issues in instruction on the concept of limit. A second item describes an approach to a warm-up drill claimed to be painless to construct and self-checking. (MP)

Presented is a computer program written in BASIC that covers round-robin schedules for team matches in competitions. The program was originally created to help teams in a tennis league play one match against every other team. Part of the creation of the program involved use of modulo arithmetic. (MP)

The lesson described first involved tossing a pair of dice and recording on a graph the sum produced on each roll. Pupils examined questions such as which sum occurred most often. The second part involved a graph that indicated which types of sums were most likely to occur. (Author/MP)

The first idea discusses the use of Pascal's triangle to discover the total number of gifts presented during the 12 days of Christmas. The second idea looks at an approach to viewing L'Hospital's rule that is geared toward helping beginning calculus students develop a feeling as to why it works. (MP)

Results are presented of an impromptu exploration of polar formulas for volumes of revolution for certain plane regions. The material is thought to be unique, and to offer room for student exploration. It is felt pupil investigation can lead to increased pupil interest in both polar coordinates and calculus. (MP)

Stresses the importance of visualization in mathematics education by reviewing research dealing with the relationship between mathematical and spatial ability, and recommends that such findings be incorporated into mathematics instruction. (JJD)

Details are provided about the American High School Mathematics Examination (AHSME), the American Invitational Mathematics Examination (AIME), and the USA Mathematical Olympiad (USAMO). The AIME will first be offered in 1983 as an intermediate examination between the AHSME and the USAMO. An appendix provides several sample problems. (MP)

Intuitions on selected function concepts presented in diagram, graph, and table settings were investigated. The sample was 443 pupils from grades 6 through 9 of 12 Israeli schools. Different groups had different intuitions, but these intuitions were independent of the settings in which presented and independent of abstraction levels. (MP)

The question is asked, "How many gifts in total were given in 'The Twelve Days of Christmas' song," and is shown to relate to several other problems. Most of the number patterns and partitions dealt with are viewed to be usable with students in junior and senior high school. (MP)

Examples of some geometric illustrations of limits are presented. It is believed the limit concept is among the most important topics in mathematics, yet many students do not have good intuitive feelings for the concept, since it is often taught very abstractly. Geometric examples are suggested as meaningful tools. (MP)

This guide focuses on the role of problem solving in developing mathematical concepts of young children, selected problem situations or tasks for engaging children in problem solving, and criteria designed to provide a guide to teachers and parents of young children in formulating appropriate problem-solving situations. (MP)

The beauty of discovering some simple yet elegant proof either to something new or to an already established fact is discussed. A combinatorial problem that deals with covering a checkerboard with dominoes is presented as a starting point for individual investigation of similar problems. (MP)

Defines the concept of problem and notes that primary-grade teachers need to help nurture problem-solving skills. Discusses six practical ways instructors can promote such skills and views the ability and willingness of teachers to transform typical activities into problem-solving opportunities as essential. (MP)