The entry, attack, and review/extension stages of problem solving are discussed. A project for children aged 9-13 was developed; some student reactions to problem solving are included. (MNS)

Brief articles on a linguistic approach to learning mathematics vocabulary, designing cross-figure puzzles, an activity with probability, and a problem with an erroneous solution are included in this section. (MNS)

The use of exercises that students can perform independently of any calculating aids and in a reasonably brief space of time is promoted, so that pupils can concentrate on the processes involved and any relationships of interest. Some examples are presented with the goal of increasing learning promoted. (MP)

Several examples of using divergent questioning techniques in elementary school science lessons are provided. The use of divergent questions (as contrasted with use of convergent questions) places students in the role of producing many possible solutions stimulating creative thinking. (Author/JN)

Describes problem-solving activities in the Unified Sciences and Mathematics for Elementary Schools (USMES) and Elementary Science Study (ESS) programs. Indicates that these curricula serve as excellent sources of activities to develop and improve their students' problem-solving skills. (Author/JN)

Describes a laboratory course, modeled on the approach developed by Robert Karplus for physics laboratory courses, emphasizing discovery learning. (SK)

Approaches to extrema that do not require calculus are presented to help free maxima/minima problems from the confines of calculus. Many students falsely suppose that these types of problems can only be dealt with through calculus, since few, if any, noncalculus examples are usually presented. (MP)

Analogies between topics in algebra and in arithmetic are noted. It is suggested that algebra teachers should consider how to take advantage of student backgrounds in arithmetic by exploiting these analogies. (MP)

Hypotheses from self-efficacy theory in the area of children's arithmetic achievement were tested. It was hypothesized that compared with didactic instruction, cognitive modeling would result in higher arithmetic achievement, self-efficacy, and accuracy of self-appraisal. (Author/GK)

Having pupils create their own mathematical-application word problems is promoted as a powerful teaching strategy. Teachers are encouraged to make creative pupil applications an integral component of day-to-day learning in mathematics. Research is cited that strongly favors the approach presented. (MP)

An approach to teaching geometry is promoted that allows students to decide for themselves what they could prove from given information. Such an approach allows pupil involvement in the personal process of discovering mathematical ideas and formulating problems. It is noted these methods will not work for all. (MP)

The subtraction ideas presented are designed for elementary and junior high school children, yet are felt to be flexible enough to offer some challenge for high school students, particularly in algebra. (MP)

Reports on the use of videotape recordings illustrating experienced problem solvers working out solutions to typical introductory physics problems. Includes brief summaries of student response to the recordings. (SK)

Ways are identified in which typical textbook word problems can be used to better fulfill their role in the development of mathematical concepts and a sound instructional program of mathematical problem solving. (MP)

The need for improving the dialog between teacher and student is promoted as an important step towards improving the mathematics curriculum. (MP)