For many educators, encountering Shulmanʼs 1986 articulation of "pedagogical
content knowledge" (PCK) brings an epiphany. It names something we are sure exists, and
recognises that "there really is something special about what I know for teaching my discipline
area". Despite these feelings of resonance and identification, however, debate about PCK in
mathematics education and how to develop it in teachers continues. It has proved elusive to
define, there have been arguments about how to measure it, and, significantly, showing that it
makes a difference to learning outcomes has been difficult, despite the fact that we all feel
certain it should and does.
Many of us claim that PCK is central to our teacher education courses. As educators
of future mathematics teachers we find ourselves as demigods in a fallen world. The fallen
world constrains the design of teacher training programs and the number of contact hours we
have; our studentsʼ mathematical backgrounds are never quite what we desire; assessment
opportunities are limited; and we often have to address content knowledge before we can
tackle PCK. The path leading to enlightened mathematics teachers is often thorny and
Yet even in this fallen world, we demigod-like educators think we have power to direct
people on this path to enlightenment. We choose what aspects of PCK to emphasise, based,
if you like, on our PCK for PCK. We cannot do all we would like (we are not omnipotent) but
our expertise is the basis for choices about what to include. We exhibit a self-asserted
omniscience that we are doing what is best.
Yet do we, as demigods, make the same choices? Will future teachers receive the
same enlightenment from different demigods? Do different demigods have different
expectations about what comprises enlightenment?