Discusses suggestions for the learning and teaching of mathematics based on a study examining the mathematics practices of carpet layers. Suggestions are made from the areas of (1) the school mathematics curriculum; (2) the methods used to teach school mathematics; and (3) research in mathematics education. (MDH)

Suggests some questions and prompts that teachers can adapt and use to promote mathematical power in their students. Argues that asking children to share their strategies for solving problems is a simple but powerful learning tool for promoting understanding. Presents four classroom vignettes as an example. (ASK)

Presents an activity that led to the discovery of the role of ratios and percentages in discussions about triple-jump performances, and a range of tasks that provide important information about students' understanding of key mathematical concepts. (ASK)

Investigates the problem of finding all triangles that have natural-number sides for which the area is numerically equal to the perimeter. (ASK)

Notes that knowing how to estimate is crucial to becoming a good problem solver. Suggests that young children be exposed to the concept as early as kindergarten in order to learn to apply the skill effectively. Discusses the values of estimation skills and how they can be developed. Outlines five classroom activities that help students develop…

Addresses the difficulties students have in acquiring graphical problem-solving skills. Presents some techniques and concepts intended to help students overcome them. Contains 15 references. (Author/ASK)

Explains the approach of integrating notions of algebra in problem-solving experiences and the design of instructional activities that integrate nonroutine, nontraditional problems. Presents some problems and students' interpretations, conjectures, and generalizations about the patterns they discovered. (AIM)

Presents a murder mystery in the form of six Calculus II review problems. Students must solve the six problems to determine the murderer, murder weapon, and time and location of the murder. (AIM)

The common teaching practice habit of connecting mathematics classroom activities with reality is still substantially delegated to wor(l)d problems. A growing body of empirical research suggests that the practice of word problem solving in school mathematics does not match this idea of mathematical modeling. Presents some classroom activities that…

Teachers can help students build a disposition to use connections in solving mathematical problems, rather than mathematics as a set of disconnected, isolated concepts and skills. One activity that addresses the criteria that involve problem solving, reasoning, communication, and representation that together create a vision that encourages…

The cross-product is a mathematical operation that is performed between two 3-dimensional vectors. The result is a vector that is orthogonal or perpendicular to both of them. Learning about this for the first time while taking Calculus-III, the class was taught that if AxB = AxC, it does not necessarily follow that B = C. This seemed baffling. The…

An aspect of the long history of the struggle to quantify motion is briefly traced through three extended problem sets suitable for use in first year calculus courses. The sketch culminates with an application of simple mathematics to one of the most current problems in the theory of the universe. (Contains 2 figures.)

This article describes how a presentation from the point of view of differential operators can be used to (partially) unify the myriad techniques in an introductory course in ordinary differential equations by providing students with a powerful, flexible paradigm that extends into (or from) linear algebra. (Contains 1 footnote.)

In this paper, the author looks at some classic problems in mathematics that involve motion in the plane. Many case problems like these are difficult and beyond the mathematical skills of most undergraduates, but computational approaches often require less insight into the subtleties of the problems and can be used to obtain reliable solutions.…

This conference proceedings includes two plenary lectures by Celia Hoyles and David Henderson. Papers from working groups deal with teacher growth, dynamic algebra, and the role of proof in post-secondary education. Topic sessions from the conference examine problems, puzzles, and games; the relationships among parents, children, and mathematics;…