Some students leave high school never quite sure of the relevancy of the mathematics they have learned. They fail to see links between school mathematics and the mathematics of everyday life that requires thoughtful decision making and often complex problem solving. Is it possible to bridge the gap between school mathematics and the mathematics in…

Paper folding, or origami in Japanese, is a traditional craft that has been enjoyed by both children and adults for hundreds of years. Mathematicians have long studied the mathematics of paper folding. They use square papers to construct mathematical shapes (for example, folding an equilateral triangle from a square paper or trisecting an angle),…

One of the primary expectations that the author has for her students is for them to develop greater independence when solving complex and unique mathematical problems. The story of how the author supports her students as they gain confidence and independence with complex and unique problem-solving tasks, while honoring their expectations with…

In their years of teaching geometry, Wong and Bukalov realized that the greatest challenge has been getting students to improve their reasoning. Many students have difficulty writing formal proofs--a task that requires a good deal of reasoning. Wong and Bukalov reasoned that the solution was to divide the lessons into parallel tasks, allowing…

The National Council of Teachers of Mathematics (2000) recommends that students at all grade levels be provided with instructional programs that enable them to "create and use representations to organize, record, and communicate mathematical ideas; select, apply, and translate among mathematical representations to solve problems; and use…

Materials designed to promote student investigation of factoring quadratic polynomials over the integers through using a physical model are presented. Pupils are expected to discover regularities that will permit them to factor such polynomials at the symbolic level. Worksheet masters designed for classroom use are provided. (MP)

Monte Carlo methods are used to simulate activities in baseball such as a team's "hot streak" and a hitter's "batting slump." Student participation in such simulations is viewed as a useful method of giving pupils a better understanding of the probability concepts involved. (MP)

Certain properties of lenses provide a physical model of the mathematical concepts of multiplication of integral numbers and of similarity transformations in geometry. Further, they can provide a realistic concrete representation for rules governing multiplication of signed numbers. Suggestions for problems and classroom demonstrations involving…

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

Suggests a model for teaching mathematics with three dimensions: facts and skills, understanding, and problem solving. Geometric examples are used to illustrate each dimension and suggestions for integrating the teaching of the three dimensions are given. (PK)

Presents an analysis of the question in the title which involves a discussion of fractions, number theory, and probability through modeling, exploring, and other mathematical connections. (MKR)

Discusses research involving instruction to help students develop their mental managerial processes or metacognition, the role of a framework for problem-solving activities, the teacher as model or moderator, problem solving involving groups or pairs, and weaving writing into problem solving. (Contains 18 references.) (MKR)