Describes the stages of a process of reflective thinking. Investigates how geometrical models can be used in learning and teaching mathematics in connection with the process. Identifies two models for children of age four to eight: constant path in the space of shapes and continuous path of varied polygonal shapes. (Author/YP)

Summarizes a reanalysis of the data from an investigation of a test designed to measure a learning sequence in geometry based on the work of van Hiele (1986). Discusses the test based on the Rasch model. (YP)

Provided are activities for creating tangrams. Illustrates how to make tangrams and use them. (YP)

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

Illustrates how to draw a regular pentagon. Shows the sequence of a succession of regular pentagons formed by extending the sides. Calculates the general formula of the Lucas and Fibonacci sequences. Presents a regular icosahedron as an example of the golden ratio. (YP)

Presents 10 space-related ideas, thoughts, and questions represented on the Australian Association of Mathematics Teachers (AAMT) calendar. The ideas are on impossible shapes, fractals, space itself, galaxy, tesselated pigs, spirals, helices, black holes and three-dimensional surfaces, tesseracts, and mobius bands. (YP)

Explores the relationship between high school students' beliefs about mathematics and their mathematical performance. Reports: (1) the students' attributions of success or failure; (2) perceptions of mathematics; (3) comparative views of school mathematics, English and social studies; (4) motivation; and (5) personal performance. A questionnaire…

The College Preparatory Mathematics: Change from Within Project (CPM) was created to develop a rich, integrated mathematics curriculum, based on the best current wisdom of how people learn and the mathematics needed in an era of computers, and involving teachers in materials development. (MKR)

Features the concepts of optics and geometry of eclipses. Presents the "eclipse rule," suggesting classroom activities in which students derive this rule. Includes some triangles activities for outdoors that illustrate eclipsing and sighting phenomena. (ET)

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)

Reviews research literature leading to design of a new LOGO environment, Geo-LOGO, tailored for elementary students' learning of geometry. Presents empirical data from the first field test of the Geo-LOGO environment, which generally support the efficacy of the software design. (Author/MKR)

Describes two types of star charts commonly available for astronomical viewing and outlines a strategy by which teachers can have students use a computer spreadsheet to prepare their own easy-to-use star charts appropriate for the location, date, and time of viewing. (Author/MKR)

Presents activities using three-dimensional geometry to develop spatial skills. Includes reproducible student worksheets. (MKR)

Describes the use of infometry, or informational geometry, to meet the challenges of information service businesses. Highlights include theoretical models for cognitive coordination and genetic programming; electronic information packaging; marketing electronic information products, including cost-benefit analyses; and recapitalization, including…

Discusses the use of activities demonstrating connections between algebra and geometry, which helps students gain a conceptual understanding of important calculus ideas and gives a historical appreciation of how mathematics evolves. Uses distance, speed, and time problems as an example. (MKR)