This article offers a diversity of approaches for the conceptual development of the summation of the interior angles of polygons. Included are activities that suggest various possibilities for a study of angle sums that build upon an awareness of geometric transformations, particularly dissections and combinations. (JJK)

Various modes of reflection are classified and practical examples of devices, such as cat's eyes, are discussed. Typical light rays are traced through several systems, providing exercises with varying degrees of difficulty. Corner-cube retroreflectors, glass spheres, reflecting luminaries, light concentrators, parabolic reflectors, and off-set and…

Discusses activities to teach Cartesian graphing to young children in a conceptual way. Activities are organized around the concepts of finding one's way around in a plane and using the plane to represent variables in two dimensions by graphing equations in the usual way. (25 references) (MKR)

Presented is an activity designed to help middle school students in their understanding of definitions in geometry. Five definitions involving complex quadrilaterals are discussed. Procedures and expectations for the activity are described. (CW)

Utilized is the technique of expanding circles to explore the truth of the statement that, if the sums of the lengths of the opposite sides of a quadrilateral are equal, then a circle can be inscribed within that quadrilateral. This statement is the converse of a well-known geometric theorem. (JJK)

Examines correct and incorrect student-developed criteria for parallelograms. (MKR)

Introduces a few examples of Mangbetu designs and examines their underlying structure. Describes Mangbetu design and analyzes its geometric features. (ASK)

Presents an activity using dynamic-geometry system software to create an environment in which all students can explore and extend the locus definition of conics. (ASK)

Focuses on teaching in China, concentrating on two particular aspects of teaching: teaching students to prove in geometry and the details of what teachers do in classrooms. (ASK)

Opens with the theoretical construct of figural concepts. Argues that geometrical figures are characterized by both conceptual and sensorial properties. Investigates the effects of interaction between conceptual and figural components. Contains 19 references. (DDR)

Discusses the importance of using children's previous experiences with geometric figures to build foundations for developing geometric thinking. Describes how children's play with unit blocks can be structured to give them experiences with geometric concepts. Contains 12 references. (ASK)

Describes a third-grade class's discoveries when students were asked to develop a method to find the area of a trapezoid on the basis of their prior work with finding the area of rectangles. (ASK)

Presents an activity that utilizes the mathematical models of forest fires and oil spills that were generated (in the first part of this activity, published in the November 1998 issue) by students using probability and cellular automata. (ASK)

Investigates the problem of finding all triangles that have natural-number sides for which the area is numerically equal to the perimeter. (ASK)

Investigates, by conducting individual clinical interviews of 97 children ages 3 to 6, the criteria preschool children use to distinguish members of a class of shapes from other figures, emphasizing identification and descriptions of shapes and reasons for these identifications. Concludes that young children initially form schemas on the basis of…