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…

This activity for grades three through six determines how to identify the gross tonnage of a ship by measuring volume in cubic feet. During the problem-solving process, students construct and use a tool for measuring volume, derive a formula based on data collected, and compare their data with a given set of statistics. (AIM)

Discusses an approach to learning that uses well-selected problems to capture student interest and challenge their intellect. Presents an example of the problem-centered approach and discusses ways in which it helps all students learn important mathematical concepts and skills. (KHR)

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)

Presented are problems that teachers can use to stimulate students' thinking about the subject of mathematical scaling. Food and eating examples are used to illustrate this concept. (CW)

Outlines a possible framework for allowing teachers to explore how children learn mathematics. A mathematical modelling process and three domains, including content, process and pragmatic domain, are described. Twelve strategies for encouraging children to translate between the domains are suggested. (YP)

Presents a problem in which the incorrect application of the Law of Sines leads to an erroneous solution. Demonstrates that the commission of this error by an ophthalmologist using laser trabeculoplasty could lead to patient injury. (MDH)

Uses projectile motion to explain the two roots found when using the quadratic formula. An example is provided for finding the time of flight for a projectile which has a negative root implying a negative time of flight. This negative time of flight also has a useful physical meaning. (MVL)

Analyzes the notion of structuring resources and their role in shaping mathematical activity. Examines ways in which nurses conceptualize ratio and proportion problems and provides a case study of two nurses discussing conflicting strategies when monitoring the fluid balance of a patient. Draws out some implications for the design of viable…

Reports on an intensive study of problem-solving activity of female students at the senior secondary level. Focuses on both the mathematical processing and the underlying cognitive and metacognitive activities that led to that processing. Concludes that all successful groups displayed a high number of key points where metacognitive decisions could…

In this article, the authors explain how curriculum-based measurement (CBM) differs from other forms of classroom-based assessment. The development of CBM is traced from computation to concepts and applications to real-life problem solving, with examples of the assessments and illustrations of research to document technical features and utility…

This paper is the sixth in a series designed to supplement the statistics training of students. The intended audience is social science undergraduate and graduate students studying applied statistics. The purpose of the applied statistics monographs is to provide selected proofs and derivations of important relationships or formulas that students…

Mathematics should be taught in everday terms, not as a series of wispy, bloodless abstractions. (Editor)

Problem solving that both requires and develops higher-order thinking skills is illustrated in the EQUATIONS Challenge Matches program, which consists of computer diskettes at the elementary, intermediate, and advanced levels plus a multi-level diskette. Samples of computer output are given, with the results of various types of experimentation…

This material assumes the user has the background provided by a good undergraduate course in applied probability. It is felt that introductory courses in calculus, linear algebra, and perhaps some differential equations should provide the requisite experience and proficiency with mathematical concepts, notation, and argument. The document is…