Explores 80 sixth- and seventh-grade students' self-reported use of 14 categories of strategies for processing mathematical word problems and the relationship of strategy use to academic achievement, problem-solving behaviors, and problem-solving success. A chart of categories of strategic behavior and examples from middle schools students is…

Covers a project conducted by the Freudenthal Institute in which observation of student behavior supported the premise that the graphics calculator can stimulate the use of realistic contexts, the exploratory approach to mathematics, a more integrated view of mathematics, and more flexible behavior in problem solving. (AIM)

Reports on a study that focused on three teachers and their ways of teaching problem solving. Findings indicate that the participants unconsciously constructed personal metaphors that became the basis of their conceptualization of problems. "Community", "adventure" and "game" were the key metaphors. The outcome…

Introduces Hogben's adaptation of Zeno's paradox, "Achilles and the Tortoise", as a thinking and writing exercise. Emphasizes engaging students' imagination with creative, thought-provoking problems and involving students in evaluating their word problem-solving strategies. Describes the paradox, logical solutions, and students' mathematical…

Describes the history of the unsolved moving sofa problem, presents one possible solution, and gives several suggestions for how this problem can be used in the classroom. (Author/NB)

Describes how mathematical puzzles and riddles can be implemented in the classroom to engage students in rich mathematical explorations and logical reasoning. (YDS)

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)

Discussed is the tendency of students to equate the concepts of continuity and connected graphs based on their lack of an understanding of such concepts as limit points, closed sets, and connected sets. Included is a theorem with three lemmas with their proofs. (KR)

Discussed is the problem of inscribing a rectangle of maximum area in a given right triangle. Answered is whether there is an advantageous orientation and whether a corner of the rectangle of maximum area can lie on the midpoint of a leg of the triangle. (KR)

Significant changes in the General Educational Development Math Test require a change in teaching methods. A structured problem-solving approach focused on applying principles and interpreting abstract data will stress process as well as content as required by the test. (SK)

Describes an activity for developing an understanding of the unit rates associated with a proportional relationship. Provides the material, objectives, directions, four worksheets, and answers of the activity. (YP)

Discusses the use of mathematical modeling. Describes types, examples, and importance of mathematical models. (YP)

An instrumental technique is presented to help students create a symbolic representation that may aid the process of choosing an appropriate operation to solve a problem. Current research and practice are discussed; then the part-part-whole model is presented. (MNS)

Describes principles for constructing mathematics exercises that challenge students. Presents examples of good problems in differential equations. (MKR)