Investigated was student inability to understand mathematics across concepts, focusing on the processes by which students solve problems. In-depth clinical interviews were used with students during ninth-grade general mathematics. Mathematical abilities investigated were information gathering, generalization, reversibility, flexibility, and…

A special calendar chart is presented that can be used to find out what day of the week any date falls on during the 1980s. (MP)

The idea that females may be born with less mathematical ability than males is explored. Data from Benbow and Stanley, as well as from the Education Commission of the States, are considered. (MP) Aspect of National Assessment (NAEP) dealt with in this document: Results (Interpretation).

The process skills discussed include: observation; estimation; communication; mensuration; and graph construction and interpretation. Two activities for grade 6 and beyond are suggested. (MK)

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)