Abstract
As we go into the second quarter of the twenty-first century, we enter a troubling time
for mathematics education in educational institutions at all levels. This troubling time
comes with a multitude of challenges that seem to restrict how mathematics educators
can incorporate research-based understandings into their practices. Using Bernstein’s
pedagogic device, I discuss where possibilities for identifying the “unthinkable” lie at
the curriculum level, the institutional level and in the classroom, using examples from
my own research. These possibilities can be linked to both advocacy with participants
to create new spaces as well as to subversion in which existing spaces are used in
unexpected ways, to proactively find alternative ways to act upon the unthinkable, so
we can respond to the challenges that affect our practices.