Geometry is an essential part of mathematics. Unfortunately, according to evaluations of mathematics learning, such as the National Assessment of Educational Progress (NAEP), students are failing to understand basic geometric concepts and are failing to develop adequate geometric problem-solving skills (Carpenter et al. 1980; Fey et al. 1984; Kouba et al. 1988). This poor performance is due, in part, to the current elementary school geometry curriculum, which focuses on recognizing and naming geometric shapes and learning to write the proper symbolism for simple geometric concepts (cf. Carpenter et al. [1980]; Flanders [1987]). In contrast, we believe that elementary geometry should be the study of objects, motions, and relationships in a spatial environment (Clements and Battista [1986]; cf. Trafton and LeBlanc [1973]). First experiences with geometry should emphasize informal study of physical shapes and their properties and have as their primary goal the development of students' intuition and knowledge about their spatial environment. Subsequent experiences should involve analyzing and abstracting geometric concepts and relationships in increasingly formal settings.
A School Geometry. (Containing Plane and Solid Geometry, Treated Both Theoretically and Graphically)