ABSTRACT
This chapter focuses on what might be called the “cognitive support structure” underlying competent performance on straightedge and compass construction problems in Euclidean geometry. The current section begins with a brief introduction to the issues addressed in this chapter. The subsequent discussion provides an attempt to place those issues in a larger context, in order to provide a unifying framework for examining the issues described in this chapter and in the chapters that precede it. At first glance, the subject that is the focus of this chapter, Euclidean geometry, may appear to differ substantially in kind from the subject matter of other chapters. It is more advanced, and the obstacles to mastering it may seem different from the obstacles to learning more elementary mathematics. From the appropriate vantage point, however, the issues of understanding versus performance are seen to be the same in Euclidean geometry as they are in every other subject area dealt with in this book. This opening section is designed to sketch the view from that vantage point.
