The purpose of this report is twofold. The first is to deliver an accurate portrayal of students' achievement in geometry and measurement as gleaned from the results of the 1986 Massachusetts Educational Assessment Program (MEAP). The second is to provide K-12 teachers of mathematics with activities that have proven to be helpful in encouraging the development of geometric understanding. This report is divided into the following five chapters: (1) the overview in chapter 1 provides an outline of the highly ignored subject of geometry, based on its academic utility for visualization skills, logical reasoning, problem solving, representational power, and measurement abilities; (2) chapter 2 provides an in-depth discussion about the results from the MEAP utilizing 26 illustrated geometry and measurement items; (3) geometry activities for the elementary and middle grades are included in chapter 3; (4) chapter 4 provides activities for teachers of geometry in the secondary school; and (5) chapter 5 discusses the implications from the findings of the MEAP, and proposes recommendations for the curriculum and for teaching methods. (JJK)