ABSTRACT
In this chapter, the authors examine initial project of opening up the phenomena of skill and reasoning for direct, real-worldly inspection. They also examine another toolic domain, that of Euclidean straightedge and compass constructions. The authors provide a basic example of a Euclidean construction; several exercises then build on that example. They focus on "Examples and Exercises" has been to problematize and to radicalize their intuitions about skill and reasoning. The authors explain the phenomena of midenic reasoning using tangrams. They describe jigsaw puzzles to try to characterize how they work on them: they found that work on a jigsaw puzzle is the work of continually devising methods for searching the pieces to find how the puzzle pieces fit together.
