Shows the potential of using interactive geometry software to produce a natural environment for formulating and pursuing questions that arise in the course of solving problems. (KHR)

Provides activities that deal with Fibonacci-like sequences and guide students' thinking as they explore mathematical induction. Investigation leads to a discovery of an interesting relation that involves all Fibonacci-like sequences. (DDR)

Describes an activity that utilizes four pattern blocks to help students understand and explain perimeter. Engages students in making and supporting conjectures about a scenario that involves trains composed of various shapes with different perimeters. (DDR)

Presents weekly activities that focus on various forms of transportation in the world. Students investigate transportation through data collection, geometry, and measurement. (KHR)

Offers a cave-mapping problem and discusses how to solve it. Presents the problem and necessary geologic background and a spreadsheet algorithm to solve the problem. (KHR)

Proposes a word problem concerning placing students around triangular tables. Students must determine how to place the touching tables so that everyone can be seated. (KHR)

Describes an activity, The Spaghetti Problem, that shows how statistics could be used to introduce many topics in the secondary mathematics curriculum. (KHR)

Developed is a condition, expressed in terms of an index, that ensures that a quasinormal subgroup is normal. The arguments suggest a variety of exercises for a course in group theory or Galois theory. Included are the definitions, lemmas, and proofs. (KR)

Analyzes fifth graders' approaches for solving the problem of the distance to the horizon. Describes determining the area bounded by the horizon. (YP)

Describes the method that Archimedes utilized to calculate the volumes of spheres and other solids. The method found the volume of a sphere by comparing the mass of parallel slices of a sphere and a cone with that of a cylinder of known mass. (MDH)

A Reuleaux triangle is constructed by drawing an arc connecting each pair of vertices of an equilateral triangle with radius equal to the side of the triangle. Investigates the application of drilling a square hole using a drill bit in the shape of a Reuleaux triangle. (MDH)

Freudenthal was the founder of realistic mathematics education, in which reality serves as a source of applications and learning. Takes a newspaper article about reproducing a Van Gogh painting using plants in a field to exemplify a rich context problem containing elements of all areas of elementary school mathematics. (MDH)

Uses of Dynamic Geometry Software (DGS) are often limited purely to a verifying role. Presents a case study that emerged from a project in which DGS formed an integral part of the pedagogical arrangement. The study demonstrates how the contrasting power of DGS might be utilized in a guided discovery setting. (Contains 17 references.) (Author/ASK)

Two studies involving a total of 66 Australian high school students investigated the effects of training in the use of general strategies on the performance of high- and low-achieving students in trigonometry. The positive effects of management training were identified for both high- and low-achieving students. (SLD)

The author describes a pilot study to investigate the extent to which learners use imagery in a variety of spatial problems. In order to discover how to encourage pupils to use imagery and thus to become better problem solvers, this study set out firstly to explore how pupils are able to use imagery in a variety of tasks. The tasks involved mental…