A simply posed problem suitable for a class studying summations and series, a class in elementary computer programing, a high school mathematics club, or an individual study project is given, with solution and challenges. (MNS)

Geometric activities for junior high school students at the first levels of the van Hiele model of geometric learning (recognition, analysis, and ordering) are discussed. Illustrative problems are included.

The five levels of the van Hiele theory are described. Then interviewing tasks designed to be presented to students in kindergarten through college are presented. Finally, responses from 14 interviews are discussed, with implications for teaching geometry. Extensive references are included. (MNS)

An activity with non-Euclidean geometry, a worksheet with a device based on geometric principles, and a diagram presenting a geometric view of the geometric series are each briefly presented. (MNS)

Activities that provide opportunities for students to investigate solving linear equations using both a physical and a pictorial model are given. Students should discover a method that will permit them to solve such equations at the symbolic level. (MNS)

Data are given on how well 1520 secondary school geometry students wrote proofs. Examples of the proofs on the test are included, and the significance of the data and recommendations are discussed. A "rather low level" of achievement was found. (MNS)

The role of sentential logic traditionally taught in high school geometry is challenged. A rationale for shifting that content to algebra and replacing it with inferential logic, which directly affects proof making, is given. (MNS)

The project described in this article grew from the observation that many geometry students are unable to see anything in a diagram beyond a static presentation. A computerized microworld called "Motions" is described, with illustrations. (MNS)

Some examples are given of geometric exploration and problem solving in which Logo is the primary tool and turtle graphics is the mathematical environment. Students can explore and develop important patterns while building visual intuition. (MNS)

This review of research on secondary school geometry is drawn from the NCTM publication, "Classroom Ideas from Research on Secondary School Mathematics." Considered are the following topics: goals, content, time, textbook use, activity-oriented instruction, teacher communication, homework, student characteristics, proof, problem solving, and…

Computer science may foreshadow some near revolutions in school mathematics, concerning new ways of teaching much of the mathematics curriculum, increased emphasis on discrete mathematics, and the impact of symbolic mathematical systems. Each is discussed, with a distinction made between computer science and computer technology. (MNS)

Ten crucial mathematical concepts with which errors are made are listed, with methods used to teach them to high school students. The concepts concern order, place values, inverse operations, multiplication and division, remainders, identity elements, fractions, conversions, decimal points, and percentages. (MNS)

The study of trigonometric functions in terms of the unit circle offer an example of how students can learn algebraic relations and operations while using visually oriented thinking. Illustrations are included. (MNS)

Two brief articles are included, one on a different method for solving percentage problems, and one on a trick for the calculator involving the sine to find one's age. (MNS)

Activities concern exploring data and using the stem-and-leaf plot for displaying data. The three worksheets present activities, with brief directions for the teacher included. (MNS)