Graham taught at Unley HS (1968-72), served in PE Branch (1972-1989) & UniSA (1990-2009).
He was National Secretary-Treasurer of the Australian Council for Health, Physical Education, & Recreation (ACHPER 1975-1980), and National Coordinator, Co-author, and Editor of the ACHPER Daily PE Program (1978-1984).

He was co-founder of Kindergym Australia (1980), co-creator Jump Rope for Heart program & schools resources (1983), co-founder PE Week Australia (1984), Program Director (1996-2009) PE and Human Movement/Exercise Science degrees & Studies Co-ordinator JP/P/MP Major in HPE at UniSA.

He was principal author-editor of the South Australian Curriculum Frameworks (SACSA) for HPE 1999-2001. In 1990 he created TriSkills Australia to provide schools with support in HPE and is currently it's active Director.

Graham is a Fellow and Life Member of ACHPER, and received the National 2006 Individual Carrick Award for his University Teaching. His thesis,‘Toward a Broader Appreciation of Human Motion in Education’, exposed the impact of mind-body dualism on education practices that devalues PE in schools. 

Graham was the Program Director for the 21st ACHPER National Biennial Conference'Key into Life'in Adelaide 1998, and the 27th ACHPER International Conference‘Moving, Learning, and Achieving’also held in Adelaide 2011.

He is a past Vice-President of National ACHPER & presented the 23rd Fritz Duras Memorial Lecture at the 29th ACHPER International Conference -'The Unrealised Value of Human Motion: Moving back to movement'. In 2015 he presented the opening keynote'Moving Back to Movement'at the inaugural Asia Pacific Physical Education Conference (APPEC) in Hong Kong.