Concern is expressed that trigonometry is being de-emphasized at the secondary level, and that even incoming college students with excellent mathematics backgrounds and aptitudes appear to be "drawing blanks" on even the most fundamental trigonometric concepts. Teaching trigonometry as the ultimate high school subject is promoted. (MP)

Investigated how 14-year-old students (N=84) perceived good and bad learning experiences in school, how and why they judged specific learning experiences as good or bad, and what they perceived to influence these judgments. During interviews, students told stories of an actual event and feelings expressed at that time. (Author/MP)

Discussed are the: (1) Notion of Mathematical Objects and the Realist Approach; (2) Psychological Need for Mathematical Realities, A Psychological Point of View; (3) Formalist Approach; (4) Meaning of Mathematical Existence; (5) Relative versus Absolute Existence; (6) Psychological Need for Mathematical Realities and the Offer of Mathematics; and…

Problems involving multicolored cubes are discussed with examples of Instant Insanity and Rubik's Cube cited. Sections cover defining chameleonic cubes, producing such a cube, and extending understanding to multidimensional cubes. One theorem proved is that for each positive integer, every cube of that size is chameleonic. (MP)

Details about mathematics education in China, what changes are underway, and the direction these changes are taking at the middle school level. The curriculum at this level is viewed to be quite demanding. It is felt Americans may ponder the great strides of the Chinese in 25 years. (MP)

Approaches to extrema that do not require calculus are presented to help free maxima/minima problems from the confines of calculus. Many students falsely suppose that these types of problems can only be dealt with through calculus, since few, if any, noncalculus examples are usually presented. (MP)

The mathematical nature of the product barcode that now appears on many supermarket goods is discussed. Particular attention is given to the nature and formula of a "check digit" used to verify that product numbers are correctly scanned. Several possible student activities related to this code and others are suggested. (MP)

Programmable calculators are useful tools in the classroom that are often overlooked. This report gives examples of problems and activities that can be brought within the scope of such calculators. (MP)

Data from longitudinal studies of high school students who took the Annual High School Mathematics Examination sponsored by the Mathematical Association of America (MAA) indicate that 56 percent of the top achievers pursued careers in mathematics or mathematically related fields. (MP)

Many students appear to enjoy mysteries at the same level that they hate proofs. It is felt that the solutions of the two can be so alike that their diagrammatic forms will coincide. One geometry and three mystery problems involving logic for solution are presented. (MP)

Describes techniques intended to provide the teacher (or student) with insights to the solution of the problems of constructibility of squares of area c and determination of the numbers of squares, and a method for the construction of constructible integers of area c. (DS)

A discussion of the reasons for the new design of international standard typing paper (AY) with dimensions of 210 mm by 297 mm leads to a discussion of the ratio of the sides and geometric concepts involving similar rectangles. (MP)

A set of activities designed to help students discover properties about order-3 spirolaterals on square grid paper is presented. The materials are prepared on worksheets designed for easy duplication. The lessons can lead to investigations involving spirolaterals of many other orders and shapes. (MP)

Some uses of a computer in a high school statistics class are presented. The increased student involvement in the lesson is seen as a result of the line demonstration of the mathematical concepts involved. A special application program written in BASIC is included. (MP)

An excursion in applied mathematics is detailed in a lesson deemed well-suited for the high school student or undergraduate. The problem focuses on an experimental missile guidance system simulated in the laboratory. (MP)