In her articulation of the concept of ‘profound understanding of fundamental mathematics’,
(PUFM) Ma (1999) made a significant contribution to the development of theory, which
builds upon earlier work. Her theory has resonance with ideas of procedural and relational
understanding as expounded by Skemp (1976). Ma delves into this area to explore rich
examples of exactly what this profound understanding can mean for teachers, and the ways in
which teachers gain it. Within the original specification for MECs there was an emphasis on
the nature of subject knowledge that should be developed by the courses, which drew
explicitly on the work of Ma (1999), in particular the idea of