Much more important than specific
mathematical results are the habits
of mind used by the people who create
those results. We envision curricula
that elevate the methods by which
mathematics is created and the techniques
used by researchers to a status
equal to that enjoyed by the results
of that research. Our goal is not to
train large numbers of students to be
university mathematicians, but rather
for students to become comfortable
solving mathematical problems, to see
the benefit of being systematic and
using abstract reasoning, and to look
for and develop new ways of describing
situations. We want students to
gain the tools they will need to use,
understand, and even make mathematics
that does not yet exist.