Overcoming Pedagogical Barriers Associated with Exploratory Tasks in a College Geometry Course

With the advent of dynamic geometry software, and a current trend towards the exploration that such software facilitates, textbook authors have in some cases introduced geometric concepts intended for college students by means of exploratory tasks. The strengths of this approach are offset by the disadvantage that many students are thereby convinced of the veracity of a geometric statement without feeling the need for a proof, and without having the knowledge of inner structure that will illuminate why the statement is true. This chapter explores examples of exploratory tasks from a college geometry textbook with a view to connecting these tasks with formal geometric proofs that will not only prove but explain principles that underlie the explorations.