A model was proposed to examine the effects of mathematical aptitude and academic orientation on performance. The calculated path coefficients did not strongly support the model. Mathematical aptitude has a direct effect on college performance, whereas the effect of academic orientation was mediated by high school performance and mathematical…

The use of basis matrix methods to rotate axes is detailed. It is felt that persons who have need to rotate axes often will find that the matrix method saves considerable work. One drawback is that most students first learning to rotate axes will not yet have studied linear algebra. (MP)

National assessment data on student performance in several phases of algebra are reported. It is noted that this performance has not reached the point of mastery even for most students with two years of algebra and a year of geometry. However, the data are not thought to suggest complete failure. (MP)

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)

A problem is detailed which has a solution that embodies geometry, trigonometry, ballistics, projectile mechanics, vector analysis, and elementary computer graphics. It is felt that the information and sample computer programs can be a useful starting point for a user written code that involves missiles and other projectiles. (MP)

A sample problem shows some pitfalls in approximating square roots when working with calculators or computers. (MP)

Teaching ideas related to the instruction of decimal division as the opposite of multiplication, an approach to approximating logarithms that help reveal their properties, and the simple creation of algebraic equations with radical expressions for use as exercises and test questions are presented. (MP)

Several methods of numerical mappings other than the usual cartesian coordinate system are considered. Some examples using parallel axes representation, which are seen to lead to aesthetically pleasing or interesting configurations, are presented. Exercises with alternative representations can stimulate pupil imagination and exploration in…

A problem-posing approach is used to change a door problem that involves a linear hallway into one in which doors are in a circle. The new problem is noted to relate mathematically to concepts behind the spirograph. It is hoped the material will encourage teachers to use problem-posing. (MP)

Masters of three worksheets are provided which require students to name selected polygons, compute areas of triangles, rectangles, squares, and trapezoids, and compute cost per square unit. (MK)

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)

A set of activity sheets designed to provide experience for pupils in estimating products, quotients, and powers is provided. The material is designed for calculator use, and problem-solving abilities of students are developed as individuals focus on finding game-winning strategies. (MP)

Three ideas are shared: using geometric figures in motivational practice of order operations with prealgebra students; constructing a test with a holiday theme to increase student interest; and coding greeting cards for students that can be solved mathematically through the use of previously learned concepts. (MP)

Two examples are given of ways traffic engineers estimate traffic flow. The first, Floating Car Method, involves some basic ideas and the notion of relative velocity. The second, Maximum Traffic Flow, is viewed to involve simple applications of calculus. The material provides insight into specialized applications of mathematics. (MP)

Lessons given to a group of mathematically talented eleventh and twelfth graders enrolled in a problem-solving course that provided practice in applying the heuristic strategy of working backward are detailed. Special attention was given to the process of formulating generalizations that represent large problem classes. (MP)