Philosophy of Math and Math Education

Conception of mathematics.

How would you describe or define what math is?
Philosophers, mathematicians, and others have described the field of mathematics in a number of compelling and sometimes contradictory ways; my personal conception of the field draws from several of these:

On Learning

Learning is a Process

I think it's important to describe learning as an ongoing process, not as an end result or goal. It is a process that neither starts not stops in the classroom; learning occurs from the moment we wake up in the morning until the moment we go to sleep at night. Formal education is but one avenue through which we "gain knowledge or skill" (the common dictionary definition of learning).

A response to David Tyack's "Seeking Common Ground"

Unity

"Our schools of learning, by producing one general, and uniform system of education, will render the mass of the people more homogeneous, and thereby fit them more easily for uniform and peaceable government." - Benjamin Rush, 1798.

In the earliest days of our republic, Benjamin Rush concisely stated what has become a persistent theme in American public education--the desire for unity and homogeneity among the people; the desire to create "good citizens". In the late 18th century, this desire stemmed from concern over the various countries of origin found in the citizens of the United States (and Pennsylvania specifically); a half-century later, Rush's sentiment can be felt in Calvin Stowe's call for a "national assimilation" of recent immigrants; a call repeated once again following waves of early twentieth century immigration, postwar periods, and other eras of cultural change.