A group of unsolved geometry problems is presented. Several problems that were unsolved for a length of time and then solved are also discussed. (MK)

The conditions necessary for a circumscribable quadrilateral also to be inscribable are discussed. Three propositions are presented and proved. (MK)

This article presents problems to challenge students over and above the standard curriculum problems assigned at a Course I level. Every additional problem in the article can be solved using only the tools provided by Course I. (AIM)

Explores a variety of approaches to solving one geometry problem illustrating the work of teachers, the flow of their ideas, and the diverse areas of mathematics they applied. (KHR)

Argues that proving something begins with an assumption and proceeds logically to a conclusion, thus convincing by offering arguments. Describes some pitfalls involved in proving through examining several case histories. Offers suggestions for teaching the proof process. For example, sometimes an extreme example or counterexample will do more to…

Suggests several approaches that allow students to explore the implications of Varignon's parallelogram theorem. (KHR)

Explains the Geometric Standard of the "Principles and Standards for School Mathematics" (NCTM, 2000) which emphasizes the usefulness of geometric ideas in representing and solving problems across the mathematics curriculum. Discusses this Standard and illustrates it with classroom examples. (Contains 45 references.) (YDS)

Presents the Perfect-Square Geometry Partners problem to teach students about patterns. (Author/NB)

Reports on a study in which three 3rd grade students were presented with the volume of cuboids. Examines the problem solving actions students demonstrate and analyzes students' strategies and solutions. Explores the connection between spatial structuring and the use of numerical operation. Considers perseverance and control emerging when solving…

Contains an analysis of the activities of 12-year-old students solving problems of polygonal tilings and presents two categories of the thinking processes of these students: instantaneous thinking resulting in perceptions of simple structures and discursive thinking appearing in drawing activities and arguments of proofs. (13 references)…

Reports, in French, an investigation on the use of graphic representations in problem-solving tasks of the type in Spanish Mathematical Olympiads. Analysis showed that the choice and interpretation of the first graphic representation played a decisive role in the discovery of the solution. (34 references) (Author/MKR)

Presents an analysis of written solutions to geometry exercises in the last year of Greek Lyceum which showed relatively low performance on vector methods. Justifies pupils' false preconceptions with regard to the concept of vectors, and the strong influence of classical geometry teaching in the previous years. (Author/ASK)

Many students view mathematics as a collection of theorems and facts that were discovered by intelligent mathematicians and all they have left to do is to study them carefully. Some believe it is important to help students change this view (Lavy & Shriki, 2003). One possible way is to enable students to modify the attributes of a given situation,…

Here we give an example of a problem that could be beneficially investigated by AS/A level students. It is a geometry problem that they can profitably tackle by geometric (especially geometry software) and algebraic means. Such problems naturally lead students to the need for proof--an essential part of mathematics that is often lacking in current…

Interesting problems sometimes have surprising sources. In this paper we take an innocent looking problem from a calculus book and rediscover the radical axis of classical geometry. For intersecting circles the radical axis is the line through the two points of intersection. For nonintersecting, nonconcentric circles, the radical axis still…