Interpreting student understanding in geometry: A synthesis of two models

There is increasing evidence that many students in the middle years of schooling have severe misconceptions concerning a number of important geometric ideas (see, e.g., Burger & Shaughnessy, 1986; Dickson, Brown & Gibson, 1984). There are many possible reasons for this. A clear divergence of opinion exists in the mathematics community about the methods and outcomes of geometry and, as a result, textbook writers and makers of syllabuses have failed to agree on a clear set of objectives. Anecdotal evidence suggests many teachers do not consider geometry and spatial relations to be important topics, which gives rise to feelings that geometry lacks firm direction and purpose.