The topics of angle construction, angle trisection, and regular polygon construction with only a straightedge and compass are discussed for angles with integer measure. (MP)

A method is developed for finding the equations of two circles that intersect at points with integral coordinates. Such equations are useful for the introducing systems of quadratic equations. (MP)

Two units are developed that provide the student with experience in constructing auxilary lines that are often needed in formulating geometric proofs. (MP)

An investigation of these numbers is shown to give students an opportunity to make use of such mathematical skills as algebraic substitution, modular arithmetic, counting arguments, and mathematical induction. (MP)

Detailed descriptions are given of two procedures for measuring the radius of the earth, one using a rule and the other a stopwatch. (MP)

Three approaches to the same geometrical problem are presented to demonstrate the role of intuition in mathematics and to clarify the concept of insight. (MP)

The five mathematics problems to be solved by high school students participating in the Fifth U.S.A. Mathematical Olympiad are given. (DT)

A method is given for generalizing Pascal's triangle to three dimensions. (DT)

A geometric approach to the solution of quadratic equations and more general polynomials is based on finding points with minimum distance from the x-axis. The approach is useful in motivating the definition of complex numbers. (SD)

Presents results from two skills surveys of Build a Book (BAB) classes in which students learn geometry by writing and editing their own textbook. Points out that this approach is reasonable and that students who had BAB classes in prior years could identify important areas of learning in addition to geometry. (ASK)

Presents an activity on soap-bubble geometry using a guessing contest, explanations, and demonstrations that allow students to mesh observation and mathematical reasoning to discover that mathematics is much more than just number crunching. (ASK)

Cooperative groups were given transparencies of eight regular inscribed polygons and overlays of corresponding circumscribed polygons and were asked to find the perimeters and ratios of perimeter to diameter. Transparencies give students a graphic illustration of limits. Includes reproducible worksheet. (NI)

Children 3.5 to 5 years old were asked to judge which of several possible sets of parts matched a configured target form and to copy the target forms. Found a significant association between age and performance on the perception task and consistency across the two tasks. (MDM)

Introduces a room air-exchange activity designed to assess student understanding of the concept of volume. Lists materials for the activity and its procedures. Includes the lesson plan and a student worksheet. (KHR)

Explores what is involved in the teacher's work of engaging students in producing a proof. Analyzes what teachers do to create a task in which students can produce a proof and what teachers do to get students to prove a proposition. Indicates that traditional, formal, two-column proofs place contradictory demands on teachers regarding how ideas…