This paper deals with a set of geometrical problems for mathematical problem-solving at different difficulty levels. All of these are presented as national flags and one has to investigate invariant area proportions when changing the locus of any corner of the flag. This dynamic element suggests the usage of dynamical geometry environments.…

By working through well-designed tasks, students can expand their thinking about mathematical ideas and their approaches to solving mathematical problems. They can come to see the value of looking at tasks from different perspectives and of using different representations. This article discusses four tasks that encourage high school students and…

In early 2008 researchers from the University of Melbourne's "New Technologies for Teaching Mathematics" project created a lesson for the Year 10 students at their Victorian research schools. Two important goals of secondary school mathematics education are to build students' conceptual knowledge and to teach students to think…

Using a microcomputer to test high school mathematics students for areas of weakness can save teachers' time, eliminate paperwork, and make testing enjoyable for the students. Results are immediately accessible and in several forms. (Author/TG)

This monograph was developed with the intention of addressing the concerns of high school mathematics teachers in Alberta (Canada) who want to base their programs on problem solving but have questions about effective and efficient ways to do so. Considered are the most basic philosophical questions, and a framework is provided to use in solving…

Discusses figurate number learning activities using patterns and manipulative models. Provides examples of square numbers, triangular numbers, pentagonal numbers, hexagonal numbers, and oblong numbers. (YP)

Describes investigations of quick cancellation problems in two-digital integers. Generalizes the results to n-digital integer problems. (YP)

This article describes a problem-centered curriculum for grades 9-12, using problem sets developed by a mathematics department and designed to take the place of textbooks. The students discover mathematical concepts in the context of the problems and activities in the materials.

This yearbook is a reference source of direct applications of mathematics for use in grades 7-12. Topics are listed alphabetically in each of four sections: arithmetic, algebra, geometry, and trigonometry. An explanation is given as to the plan of the book, making the location of desired material easier, and an index is included. In many cases the…

Discusses geometric construction problems. Presents four ways to construct a regular octagon using different conditions. Provides drawings showing the constructions. (YP)

Discussed is the benefit of the inclusion of historical material in a student's text. Several geometry problems are used as examples. A suggested list of problem sources is provided in the appendix. (YP)

Discusses problem solving in mathematics instruction and examines the role of students, teachers, and computers in the problem solving process. Seven sample problems that require high school mathematics and some knowledge of a programing language are offered for use in exploring the problem solving process. (LRW)

Argues that there is a sense of surprise and wonder that can result from looking back at problem solutions and there is a potential for then creating unexpected, even memorable, alternative solutions. Example problems with routine solutions and alternative approaches uncovered while "looking back" at the solution are given. (PK)

Describes three teaching activities for secondary school mathematics classroom: designing a house; guessing the slope function in a calculus course; and solving the six problems of bisymmetric matrices. (YP)