Many developed nations have a serious problem with a shortage in the supply of numerate graduates, fuelled by their school students' negative attitudes towards their future study of mathematics. At the same time, the smart phone and other personal sensing technological devices are becoming commonplace amongst students in schools and universities.…

By translating inequalities into equations (e.g., x greater than 0 can be written x- absolute value of x = 0) and forming equations for unions and intersections of solution sets, students can develop equations for polygons. The method can be generalized to yield equations in three dimensions. (SD)

The material examines areas generated by combinations of: (1) Circles and Triangles; (2) Closely Packed Circles; and (3) Overlapping Circles. The presentation looks at examples of certain areas and at logical ways to generate the necessary algebra to clarify the problems and solve general cases. Ideas for extension are provided. (MP)

Presents content and approaches for teaching geometry at the K-6 level. By use of the discovery technique, the author demonstrates how various topics can be taught beginning in three-dimensionalspace with the study of solid shapes. The sequence begins with the sorting of solid shapes, is followed by the ordering of solids by size and leads to the…

Examples are given of problems which can be solved pictorially, thus aiding in the general development of geometric intuition and in developing some of the basic ideas of probability. (MP)

An example is given of a problem-solving approach by outlining the development of a generalization of the Pythagorean Theorem as applied to points on a unit circle. (MP)

This project endeavored to develop a high school course for use in the classroom and for use with a computer-controlled system of programed lessons. Many difficulties such as those in the display and control of figures were encountered in trying to organize and prepare the material for the computer. The conclusion reached was that the solution to…

The author outlines a possible approach to the discovery of Euler's Theorem that results from a search for a classification of polyhedra. (MN)

The present problem was derived from the knowledge that if the midpoints of the sides of any quadrilateral are connected, a parallelogram would be obtained. The author explores what would happen if similar procedures were applied to pentagons, hexagons, and other geometric forms. (RP)

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

Beginning with a construction problem admitting a classical solution, the authors provide other solutions based on algorithmic estimation and transformational geometry. The latter methods are generalized to suggest solutions to other problems; hints to these solutions are provided. Teacher-student discussion could lead in many directions. (SD)

This article presents, in the context of solving a specific mathematical problem, an argument to indicate how problem posing can lead to a deeper understanding of what is involved in the act of problem solving. (DT)