Math pedagogy's foundational principle

is that

individual directed self discovery may always occur in those areas of mathematics that are of interest to the individual.

One simply must have a methodology for finding out what is of interest.

And then

an extension into a new and personalizd understanding about the natures of mathematics may happen in as little as two weeks.   One does not learn all of mathematics in two weeks, one learns how to learn; and as a consequence the study of mathematics becomes more interesting and less frustrating.


This understanding, once gained, should apply to all of one's study of mathematics, and any other discipline.  The methdology involves creating set of topics, and then sorting those topics into categories, one of which one is comfortable with.  It is constructive, Socratic and demand side oriented.

We acknowledge the need to cover those topics needed to pass mathematics.  So there is a lot of pragmaticm in the topic discussions.  I will lecture quietly on a white board in the conference room about any topic any student brings to this room, until finals are over.  In this way I hope to help the individual and to form the foundation of a commerical business based on my work. 


We should be clear that the notion of model building over a set of topics is something not expected by freshman mathematics students.  Students already have a model about mathematics and this model does not include his or her learning a great deal. This model may be discarded.