This digest discusses the unique needs of mathematically gifted students and reasons why curriculum and instruction should be differentiated for these learners in mixed-ability classrooms. Recommendations for differentiation include: (1) give pre-assessments so that students who already know the material do not have to repeat it but may be…

Presents suggestions for opening the minds of children to new concepts and for teachers, who must encourage their pupils to desire to learn about the world. (RK)

A problem involving the search for an equivalence class of triangles is viewed to provide several exciting and satisfying moments of insight. After solving the original problem, there is a brief discussion of a slight variation and several notes regarding related theorems and ideas. References for additional exploration are provided. (MP)

Presented is a method for finding two triangles that have five pairs of congruent parts, yet fail to be congruent. The solution is thought to involve some creative insights that should challenge both the teacher and students to recall and analyze all the congruence axioms and theorems. (MP)

Four specific problems are presented, discussed, and extended to illustrate how diverse instructional strategies, materials, and resources can be used to develop problem-solving skills. (MP)

The problem of finding the maximum number of right angles a polygon can have, given the number of sides, is discussed in detail. (MP)

Learning activities based on a geometrical puzzle that consists of rearranging triangles and trapezoids are used to teach concepts involving area. (MP)

Ideas and examples that support the problem-solving role of computers in the classroom are given: procedures, techniques, and sample problems that can be used with beginning, intermediate, and advanced students have been included. (MP)

Aspects of the instruction of trigonometry in secondary school mathematics are reviewed. Portions of this document cover basic introductions, a student-developed theorem, the cosine rule, inverse functions, and a sample outdoor activity. (MP)

Samples of materials available to students from grades 4 through 12 at a Mathematics Center are reviewed. The examples are part of a collection of more than 200 mathematical tasks using solid materials in a new approach to problem solving. (MP)

A method of discovery learning in which students learn the technique of observing and formulating questions is applied to landscape archaeology. This method demands that the relationship between tutor and student be adjusted so that the tutor becomes a fellow researcher rather than a conveyor of information. (Author/CSS)

Describes how a software package that includes a spreadsheet, a relation grapher, and a dynamic geometry can contribute to teacher training through an exploratory problem-solving course. Discusses the ways in which technology-rich environments enhance and extend traditional topics. Contains 17 references. (DDR)

Presents the problem of points and the development of the binomial triangle, or Pascal's triangle. Examines various attempts to solve this problem to give students insight into the nature of mathematical discovery. (KHR)

Describes problem-solving training provided by the Discovery Program, a series of structured group discussions about common personal and social problems and how to cope with them. Discusses the program's advantages over other methods of teaching problem-solving skills. (SV)