Successful performance in mathematics rests not only on general skills but also on general attitudes and traits such as perseverance, self-confidence, willingness to try out a hunch, and appreciation for exactness. (MM)

Thirty-eight sixth graders were trained in fraction calculation through progressive transformation dialectics (PT) whereas a control group of 38 was taught through a traditional mathematics education framework. The PT group, encouraged to form network-type knowledge representations, performed better on problems that required more than mere…

Discusses the process and the usefulness of translating empirical logic puzzles into mathematical problems which may be more easily solved, then translating the answer back into the context of the original problem. Presents nine logic puzzles devised by Lewis Carroll, with answers. (AIM)

Shows how attention to transcending functions provides a new integrative approach to mathematics that can improve the critical thinking and problem-solving skills required for addressing large-scale problems. Contains 38 references. (DDR)

Presents an activity that requires middle level students to use mathematics and measurement skills to estimate the mass of an extinct dinosaur using museum-quality models. (JRH)

Presents a typical cost-allocation problem with possible solutions, including geometric and combinatoric ones. Provides students with a real-life application of the mathematics that they know. (KHR)

Discusses the nature of tasks used to elicit the development of such systems by middle school students. Analyzes mathematical reasoning development of students across tasks and the diversity of thinking patterns identified on problem tasks. Discusses student reasoning about the relationships between and among quantities and their application in…

Presents a case study in which two 8th grade students developed knowledge for modeling a physical device called a winch. Demonstrates that students have and can use criteria for evaluating algebraic representations. Explains how students can develop modeling knowledge by coordinating criteria with knowledge for generating and using algebraic…

Investigates the differential effects of cooperative learning with or without metacognitive instruction on lower and higher achievers' solutions of mathematical authentic tasks. Results indicate that students exposed to metacognitive instruction within cooperative learning (COOP+META) significantly outperformed their counterparts exposed to…

Presents some ideas about how teachers can foster mathematical communication by encouraging students to find multiple solutions to problems. Discusses three problems that help develop communication ability in mathematics. Views communication of multiple solutions as an instructional strategy to help students make sense of mathematics. (KHR)

Uses poems incorporating mathematical terms to help students apply their knowledge of mathematics to another field and give evidence that what they had learned had become a useful and easily accessible part of their general experience. Includes assignment sheets. (KHR)

Describes a group project that involves geometry and falls into an area of mathematics known as operations research, which is crucial to making decisions in business and industry. Includes problem statements and project assessment guidelines and illustrates solutions. (KHR)

Explores why it is impossible to make a square from six tangram pieces and, in the process, develops insight into the nature of learning mathematics as well as strategies for teaching. (YDS)

Describes similarities and differences between modeling cycles and stages of development. Includes examples of relevant constructs underlying children's developing ways of thinking about fractions, ratios, rates, proportions, or other mathematical ideas. Concludes that modeling cycles appear to be local or situated versions of the general stages…

Investigates student learning in a mathematics enrichment program offered via the Internet. Describes a course aimed at fostering students' capabilities to work like a mathematician. Examines students' correspondence and work for evidence of how students were working mathematically. Explains how to design both face-to-face and on-line teaching to…