Presented is L'Hopital's rule for the evaluation of limits in the case when x goes to infinity using geometric concepts. Included are the rule, extensions, counterexamples, and a rule for sequences. (KR)

Discussed are the idea, examples, problems, and applications of convexity. Topics include historical examples, definitions, the John-Loewner ellipsoid, convex functions, polytopes, the algebraic operation of duality and addition, and topology of convex bodies. (KR)

Five geometry experiments with 127 Australian high school students found that guidance provided in a format requiring attention to two sources of information resulted in performance no better than that on conventional problems. A format not requiring split attention resulted in the superiority of worked examples over conventional problems. (SLD)

Illustrates some learning encounters for facilitating first graders' understanding of geometry. Describes some of children's approaches using Cuisenaire rods and teacher's intervening. Presents six problems involving various combinations of Cuisenaire rods and cubes. (YP)

Presents two proofs that only five regular polyhedra exist. The first is a geometric proof, and the second is based on graph theory, using the relationship between the vertices, edges, and regions of the graph model. (MDH)

Applies Pascal's Triangle to determine the number of ways in which a given team can win a playoff series of differing lengths. Presents the solutions for one-, three-, five-, seven-, and nine-game series, and extends the solution to the general case for any series. (MDH)

Presented is a proof where special attention is accorded to rigor and detail in proving the lemma that relates ruler-and-compass constructions to arithmetical operations. The idea that some angles cannot be trisected by a ruler and compass is proved using three different cases. (KR)

Presents a model that relates Polya's ideas on problem solving to teaching practices that help create a mathematics learning environment in which students are actively involved in doing mathematics. Illustrates the model utilizing a high school geometry problem that asks students to measure the width of a river. (MDH)

Ritzville Pyramids are cone-shaped piles of wheat found near the community of Ritzville, Washington. Presents the practical problem of determining the volume and surface area of a Ritzville pyramid to help farmers solve cost-effectiveness questions related to selling the wheat. (MDH)

Explores the role of software tools in geometry problem solving and how these tools, in interaction with activities that embed the goals of teachers and students, mediate the problem solving process. Through analysis of successful student responses, shows how dynamic software tools can not only scaffold the solution process but also help students…

A problem sometimes called Moser's circle problem where a circular region has to be partitioned with chords without any three chords intersecting at one point, is discussed. It is shown that Moser's circle problem makes the students to use a variety of mathematical tools to find correct solutions to problems and gives an opportunity to think about…

"Saxon Math" curricula and materials are available for grades K through 12, with the content and skills designed to meet National Council of Teachers of Mathematics (NCTM) standards and various state standards. This WWC report focuses on middle school math curricula, defined as all Saxon Math curricula for grades 6 through 9. The…

This resource book for geometry contains games, tricks, and quick activities for the classroom. Categories of activities include picky puzzlers, plane figures, constructions, vectors, and measurement. Included are eight picky puzzler problems, 19 activities with plane figures, and 25 geometric construction activities. Three vector activities and…

This is a sample of the final test for students in mathematics at the sixth-grade level in Alberta (Canada) schools. The test contains multiple-choice items and is divided into two sections. Section 1 contains 55 items related to numeration, operations and properties, measurement, geometry graphing, and problem solving. Section 2 consists of five…

This document argues that qualitative graphing is an effective introduction to mathematics as a construction for communication of ideas involving quantitative relationships. It is suggested that with little or no prior knowledge of Cartesian coordinates or analytic descriptions of graphs using equations students can successfully grasp concepts of…