Geometric interpretations and derivations of the six trigonometric relationships are demonstrated. Selected for discussion are limiting values, geometric verification of trigonometric identities, a one-dimensional illustration of the Pythagorean relationships, and the geometric derivation of infinite-series relationships. (DE)

Discusses educational materials on the World Wide Web related to mathematics and science education. Also provides some resources. (ASK)

Examines the nature of prior mathematical knowledge that facilitates the construction of useful problem representations in the domain of geometry. Indicates that high achievers build schemas that are qualitatively more sophisticated than low achievers, which in turn helps them construct representations that are conducive to understanding the…

Presents a medley of proofs and topics related to the Pythagorean Theorem. Provides a resource for teachers and students in high school and undergraduate liberal arts education as well as a starting point for in-class research projects in geometry and the history of mathematics. Contains 20 references. (Author/ASK)

Provides a set of classroom activities or steps that can be used to determine the area of a triangle on a sphere. (ASK)

Compared Japanese and U.S. geometry curricula using the van Hiele model, U.S. National Council of Teachers of Mathematics Standards, and Japanese Course of Study by Mombusho, examining how the students regarded van Hiele levels and determining differences in geometry instruction. Japanese curricula and students were ahead of U.S. curricula and…

Shows how the joint use of a dynamic geometry program and a spreadsheet can provide a computational environment for exploring geometry on plane lattices that lessens the risk of developing the false empiricist view of mathematics often associated with the use of information technology. Contains 17 references. (Author/ASK)

Presents the University of Chicago School Mathematics Project's (UCMSP) Every Day Mathematics Program as one current reform-based elementary curriculum incorporating geometry throughout the K-6 curriculum, with an emphasis on hands-on and problem-solving activities. Measures the longitudinal effects of such an approach. (Author/CCM)

Considers how well cerebral palsy students learn high school geometry. Finds that one student needed a lot of time to process visual information. Concludes that the orientation of angles, complexity of the diagram, and the length of the side of an angle all had an impact on understanding. (Author/CCM)

Presents an extension of a Japanese mathematics lesson involving the area of a triangle and introduces concepts from trigonometry. (ASK)

Discusses students' use of visual considerations in doing geometrical proofs. Studies ninth-grade students (n=17) in an academically-selective high school in Jerusalem. Concludes that only three out of 16 students who turned in their papers chose symmetry considerations when working on a proof. Contains 16 references. (ASK)

Investigates the development of shape concepts within an instructional unit on geometric paths, including the role of noncomputer and computer interactions in that development. Concludes that the computer environment and the activities facilitated students' development of their conceptualizations of the properties of geometric shapes and their…

Reports on the results of a summer institute for middle school teachers on informal geometry which sought to meet the needs of teachers with regard to aspects of change. Concludes that it is important for teachers to be able to acknowledge their emotions about change to facilitate their own learning. Contains 13 references. (ASK)

There are several possible approaches in which dynamic computerized environments play a significant and possibly unique role in supporting innovative learning trajectories in mathematics in general and geometry in particular. Describes an approach based on a problem situation and some experiences using it with students and teachers. (Contains 15…

Discusses software for geometric construction, measurement, and calculation, and software for numerical calculation and symbolic analysis that allows for new approaches to the solution of geometric problems. Illustrates these computer-aided graphical, numerical, and algebraic methods of solution and discusses examples using the appropriate choice…