Describes an activity connected with mathematical definitions that illustrates the process of gradual refinement as a way to understand and construct knowledge. Presents a gradual construction of a specific geometry concept that was the result of interaction between participants in a mathematical discourse. (KHR)

Describes a low-tech, hands-on activity to improve student understanding of irrational numbers. Each student creates a number line from adding machine tapes and uses a square and a precisely folded triangle as the only measuring device. (KHR)

Presents interactive parabolas created from straight segments using a dynamic geometry software and its web component. (Author/KHR)

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)

Describes the maximum-volume-box problem designed to lead students to a deeper understanding of the problem and its solution. Uses the Geometer's Sketchpad as a learning tool. Illustrates some examples of constructing and using the sketch. (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)

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

Relates one secondary geometry teacher's experiences learning and using the computer program "Geometer's Sketchpad." The article describes the program and provides examples of ways this teacher uses it in combination with more traditional teaching tools. (SM)

Presented is an activity which examines an arithmetic concept from a geometric point of view. Objectives, prerequisite learning, and procedures are discussed. Four worksheets are provided with answers. (CW)

Subjects forced to process redundant material or split their attention between multiple sources of information may encounter extraneous cognitive load. Results of 4 experiments involving 125 fourth graders in Sydney (Australia) provide evidence for the inadequacy of conventionally formatted instructional materials and emphasize debilitating…

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)

The National Council of Teachers of Mathematics (1989) proposes using everyday objects, such as paper, to enable students to explore geometric relationships and vocabulary. Paper-folding and other types of hands-on activities have been found to increase students' ability to communicate mathematically and foster their understanding of mathematical…

This yearbook focuses on the role of technology in school mathematics. Chapters are replete with classroom-tested ideas for using technology to teach new mathematical ideas and to teach familiar mathematical ideas better. Chapters included: (1) "Using the Graphing Calculator in the Classroom: Helping Students Solve the "Unsolvable" (Eric Milou,…

This volume attempts to bring together a collection of reports on the Geometric Supposer, a series of computer software environments which can be a tool for exploring particulars and generalizations in geometry. The book contains the following chapters: (1) "A Personal View of the Supposer: Reflections on Particularities and Generalities in…

A system for categorizing components of geometry class discussions is described. The unit of observation is the teacher question; responses are coded at four cognitive levels. The system is easier to use than many in the literature; use of it can help teachers develop questioning techniques. (SD)