### Abstract:

This study investigates mathematics for teaching, specifically in the case of
functions at the grade 10 level. One teacher was studied to gain insights into the
mathematical problem-solving a teacher does as he/she goes about his/her work.
The analysis of data shows that the mathematical problems that this particular
teacher confronts as he goes about his work of teaching can be classified as
defining, explaining, representing and questioning. The resources that he draws
on to sustain and drive this practice can be described as coming from aspects of
mathematics, his own teaching experience and the curriculum with which he
works. Of interest in this study are those features of mathematical problemsolving
in teaching as intimated by other studies, particularly restructuring tasks
and working with learners’ ideas; which are largely absent in this practice. This
report argues that these latter aspects of mathematical problem-solving in teaching
are aligned to a practice informed by the wider notion of mathematical
proficiency.
The report concludes with a discussion of why and how external intervention is
needed to assist with shifting practices if mathematical proficiency is a desired
outcome, as well as with reflections on the study and its methodology.