The Van Hiele level theory offers an explanation and a remedy for student difficulty with higher-order cognitive processes required for success in secondary school geometry. This document reports results of a study which involved about 2700 students in 13 high schools, selected to provide broad representation of community socio-economics in the United States. The investigation looked at: (1) How are entering geometry students distributed with respect to the levels in the Van Hiele scheme; (2) What changes in Van Hiele levels take place after a year's study of geometry; (3) To what extent are levels related to concurrent geometry achievement; (4) To what extent do levels predict geometry achievement after a year's study; (5) What generalizations can be made concerning the entering Van Hiele level and geometry knowledge of students who are later found to be unsuccessful in their study of geometry; (6) To what extent is geometry being taught to students appropriate to their level; and (7) To what extent do geometry classes in different schools and socio-economic settings differ in content appropriateness to student level. (MP)