A problem is posed concerning the area of certain parts of a plane geometric figure. The problem was used in a student contest with 71 of 270 mathletes answering correctly. An outline of the general proof is given. (LS)

This paper describes an investigation of problem sequencing as part of a symposium presenting theoretical concerns and research findings regarding several diverse types of strategies for designing and presenting instructional materials. The first step involved analyzing a set of problems, to determine the knowledge (rules) required for solving the…

A series of problems concerning a geoboard with "holes" is suggested. (SD)

Elucidated is the relationship among three threads of mathematical investigations: Kirkman's schoolgirl problems, finite geometries, and Euler's n-square officer problems. (JP)

Techniques that can be used in solving various mathematical problems are illustrated by an optimization problem and the accompanying model and solution. (MP)

The author gives a method for involving students in developing and verifying elementary number theory hypotheses by studying areas and perimeters of primitive pythagorean triangles. (MN)

The opportunity for students to develop formulas that involve tangent lines to a circle and the Pythagorean Theorem and to use approximation and common sense is provided in a suggested distance-to-horizon problem. (MN)

Presents three sample problems related to arithmetic and algebra, geometry, and calculus, indicating, in each case, similar problems that could be posed. Includes a discussion of positive benefits which result by asking students "Can you derive the result differently?" (JN)

GED "Scoreboost" materials target exactly the skills one needs to pass the General Educational Development (GED) tests. This book focuses on the GED Mathematics test. To prepare for the test, the test taker needs to learn skills in number and operation sense, data and statistics, geometry and measurement, and algebra. To pass the test,…

This paper analyses changes in the quality of a mathematical task as a result of its reformulation from a proof mode into an inquiry-based mode. The task is borrowed from the reformulation assignment given to the in-service teachers. The analysis of the task is based on implementation of the task with pre-service teachers. Through the lens of the…

This book contains a set of versatile enrichment exercises that cover a very broad range of mathematical topics and applications in pre-algebra from the Moebius strip to the googol. Several criteria have been used in developing the activities and selecting the topics that are included. All of them bear heavily and equally on concerns for…

Presents results of action research which had the goal of producing concepts and topics that would permit students to get creatively engaged in mathematical analysis and problem solving. The method used, called Turtle Geometry,'' is concerned with programming a moving point to generate geometric forms. (DT)

A discussion of intuition, doubt, and surprise in mathematics arising from a problem involving rational points and lines. (RS)