The author calls attention to four neglected aspects of gifted children's education in scientific thinking: problem finding, problem solving, problem reevaluation, and scientific reporting. (SW)

Examples are given of problems which can be solved pictorially, thus aiding in the general development of geometric intuition and in developing some of the basic ideas of probability. (MP)

Presents the reflections of students on a problem given in May, 1996 issue of this journal in order to share the thinking of middle school students. The problem concerned weighing on a double per balance if given a clump of clay, and a 20-gram and 50-gram balance. (ASK)

The relation between Lakatos' theory and issues in mathematics education, especially mathematical problem solving, is investigated by examining Lakatos' methodology of a scientific research program. (AIM)

Presents many problems involving scheduling after-school activities and tournaments that bring the topic of Euler paths to a level of understanding for elementary students. (MKR)

Presents responses to the Stair Skipping problem that appeared in the April, 2000 issue of this journal. (KHR)

Analyzes the problem-solving process and presents the dominance of the conjecture or theoretical aspect as a subtle relation between the data and the conjecture. Argues that conjectures are not necessarily subordinate to the data but play active roles in mathematical problem solving. Discusses the meaning of this dominance in the context of…

Investigates students' use of imagery in their mathematical activities. Findings indicate that image forming is crucial in doing mathematics. A student who fails to construct an image in a problem-solving situation is severely limited in giving meaning to the situation. Contains 21 references. (JRH)

Describes a pattern-based approach to subtraction that enables students to find the amount of change from a purchase "faster than a cash register." (Author/YDS)

Demonstrates what it might mean to engage students in problem posing and how teachers might begin to create classroom environments that encourage, develop, and foster mathematical curiosity. (Author/NB)

Presents a hands-on investigation for students to measure the flow of water through a waterway. Involves problem solving and reasoning, develops communication skills, and connects various mathematical concepts and principles. (Author/NB)

Explains "Mathematical Mind Journeys," a lesson format that promotes computational fluency through variable practice that relies on mathematical memory rather than rote memorization. (Author/NB)

Explores trapezoidal numbers, which are the result of subtracting two triangular numbers. Includes classroom activities involving trapezoidal numbers to help students develop their problem-solving skills. Includes reproducible student worksheets. (MKR)

Underprepared college freshmen (212 in control group; 178 in experimental group) were monitored through 1 year of college mathematics in a study that showed cooperative learning and problem solving had a significant effect on mathematical success. An appendix contains sample problems. (MKR)

An approach is presented for determining unidimensional scale estimates that are relatively insensitive to limited inconsistencies in paired comparisons data. The solution procedure--a minimum-cost network-flow problem--is presented in conjunction with a sensitivity diagnostic that assesses the influence of a single pairwise comparison on…