The most beautiful thing we can experience is the mysterious. 
It is the source of all true art and science.
 Einstein, What I  believe, 1930.

Certainly few things are more mysterious to a high school freshman than trying to link physical relationships and measurement to the world of mathematics and arithmetic he/she has previously experienced.  Yet if science is just a "refinement" of everyday thinking, how can it be such a mystery?  Probably a paradox there somewhere.

What we are trying to do here is provide a context for beginning a process of reflexive thinking and operant conditioning to crystallize the mathematical principals to which the student has been previously exposed, and enable him/her to  justify the mathematical principals and the scientific principals to start answering the question: How Do We Know?.

It seems to me that the reflexive nature of most of the precision teaching
exercises is an introduction to  a reflective or meta cognitive process.

Operant conditioning in the form of Precision Teaching,  and reflexive thinking in the form of justification tables reminiscent of formal geometric proofs. Trying to link reflexive thinking and operant conditioning, probably a paradox there somewhere also.

Precision Teaching is a powerful tool for motivating students to learn.  It has found wide acceptance in the field of Special Education.   Extensive research has validated this approach to operant conditioning in educational settings. I hope I have presented a structure to help introduce this system to mainstream teachers.