Recently, I participated in a collaborative research study which investigated the prospects of reconstructing the established belief system that underpinned a didactic, teacher-centered, "transmission-type" pedagogy of a colleague, an experienced high school teacher of science who was teaching "out of field." Ray was teaching Grade 12 mathematics for the first time and had completed the first of four 10-week terms that comprise the school year in Western Australia. Apart from incidental encounters with mathematics in his science teaching, Ray's previous formal experiences with mathematics had been as an undergraduate student, about 20 years ago.