Presents a portfolio assignment giving students an opportunity for creativity in designing their portfolios to demonstrate their progress in the course. Presents examples from student portfolios and outlines portfolio goals. Concludes with student reactions to the class portfolio, information on the grading procedure, and candidate courses for…

Recounts a sequence of activities that occurred in a senior high school geometry class and helped students to engage in creative reasoning. All student suggestions were discussed by the class, and pursuing alternative solutions was not only encouraged but required. (MKR)

Presents algebra course curriculum that utilizes a symbolic algebra system called PAD (Power, Application, and Depth). Demonstrates an example using PAD and points out that mathematics courses using this software present new ways for students to launch the power of algebraic thinking. (ASK)

Describes the use of an extended problem-solving assessment task with a Japanese secondary class. Argues that extended problem-solving tasks have the potential to illuminate a much wider range of student performance and to offer learning opportunities almost never realized with more traditional--albeit often quicker--forms of assessment. (ASK)

Described are activities in the study of techniques used to conceal the meanings of messages and data. Some background information and two BASIC programs that illustrate the algorithms used in a new cryptographic system called "public-key cryptography" are included. (CW)

Presented are two examples of real-life examples that can be used to promote or exemplify concepts of probability and statistics. Details of the calculation of these probabilities are given. (CW)

Examines teachers' judgments of the difficulties of algebra problems. Offers classroom-tested instructional approaches that build directly on students' mathematical intuitions and inventions. (KHR)

Presented is a problem involving a real-life situation involving simple ideas, computation, and a proof. A variety of other situations in which this type of problem may be applied are discussed. (CW)

Discussed are some applications of mathematics involved in actuarial science which may be taught in high school mathematics classes. Described are the importance of approximate solutions, multiple answers, and selling the solution to a problem. (CW)

Presented is the problem of determining alternative schedules for major league baseball. Equations of the schedule, conditions on the solutions, and solutions are discussed. (CW)

The study of trigonometric functions in terms of the unit circle offer an example of how students can learn algebraic relations and operations while using visually oriented thinking. Illustrations are included. (MNS)

Described is an approach to teaching algebra in a meaningful context by using problem solving to motivate students and increase their retention. Examples of this approach are given. (CW)

Presents six construction problems in which key parts of the figure are made inaccessible, that is, a lake or an obstruction is inserted. Encourages creative thinking while improving problem-solving skills. Students are to show the construction, describe the solution, and verify correctness of the solution. (LDR)

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)

Gives an example of an open exploration using trigonometric relationships in which the law of cosines can be deduced from the law of sines. Discusses the characteristics and value of the exploration process. (MDH)