Research Problem

My research is all about the discovery function of proof. It is presented most of the Mathematics textbooks as verification to obtain certainty and to eliminate doubt. It also has many functions such as explanation (providing insight into why it is true), discovery (the discovery or invention of new results), intellectual challenge (the self-realization/fulfillment derived from constructing a proof) and systematization (the organization of various results into a deductive system of axioms, concepts and theorems). It is also about the specializing to a triangle, generalization to similar parallelograms and to similar cyclic quadrilaterals.
Its purpose is to develop a holistic perspective and understanding of the role of proof. To give an illustrative example of the latter discovery function of proof, this might be accessible to high school students as well as prospective and in-service teachers. To discover mathematical results experimentally and prove it with several examples.
I started thinking about this research last Tuesday (January 07, 2009).
The field of my research belongs to Geometry specifically (reasoning) or proving it to verify if the answer is correct or not.
My target is thirty (30).