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)

Suggests that, although questions are often used to help students or stimulate student thinking, questions can also be used to help evaluate student thinking and attitudes about problem solving. Sample problems and questions are given. (PK)

Illustrates how one mathematics department has added courses to widen pupils' views of mathematics and to improve their problem-solving ability. (PK)

Describes an approach which helps sixth-grade students become excited about word problems. By using the approach (which involves categorizing a problem before solving it), students master skills in the problem and also develop more positive attitudes toward solving problems. The approach is equally applicable to any intermediate/junior high grade…

Discusses a computer program requiring students to find an object on a grid by using location coordinates. The program, which provides a wide range of problem-solving activities, is a highly motivating approach to hands-on metric measurement, rounding off numbers, and plotting points on Cartesian coordinate systems. Includes complete program…

An approach to teaching the exponential function using discrete methods, rather than continuous analysis, is presented. A model for simple geometric growth is explored, with a computer program given. (MNS)

Fourteen probability activities are presented, categorized as activities with impossible and certain events, mystery bags, decks of cards, dice, spinners, and flipping. They help children develop an intuitive understanding of probability. (MNS)

Common mathematical errors of pupils as identified by the Concepts in Secondary Mathematics and Science Project are identified and traced to the use of methods invented by students rather than formally taught methods. (MP)

The author discusses mathematics problems given to a group of primary teachers studying properties of numbers. Using a milk crate and bottles as a problem, the teachers diverted to exploring extrapolations. (MP)

The use of exponentiation as a starting point for an open-ended exploration of real number ideas is presented. (MP)

Considers how the domains of mathematics education and history of mathematics may interact in the process of mathematics teaching. Focuses on the teachers' role and explores the relationship between research in mathematics education and the history of mathematics. Contains 24 references. (DDR)

Presented is an example of a question that can be used to investigate probability and random triangles. Included is the question, analysis, and procedure for solving the question. (KR)

Described is a geometric view of Singular Value Theorem. Included are two theorems, one which is a pure matrix version of the above and the other that leads to the orthogonal diagonalization of certain matrices, i.e., the Spectral Theorem. Also included are proofs and remarks. (KR)

Described is a decomposition theory from which the Cayley-Hamilton theorem, the diagonalizability of complex square matrices, and functional calculus can be developed. The theory and its applications are based on elementary polynomial algebra. (KR)

Selects five critical elements for success in problem solving in mathematics and in computer programing: general strategy; planning; logical thinking; variables; and debugging. Describes the role of the five elements based on a literature review. Forty-one references are listed. (YP)