This paper addresses the continuing need for mathematics teachers to enrich their mathematical knowledge beyond the school curriculum, in order to effectively engage students in creative and imaginative thinking, particularly, but not exclusively, students who show exceptional promise. The author, a retired university professor, works staff and students in a girls' private school in Sydney for this purpose. The paper provides examples of imaginative problem solving gathered over a 5-year period, which has led to significant mathematical insight for both staff and students. It promotes the realization of mathematical potential of students concurrently with the professional development of teachers. It is argued that this best happens in mathematics classrooms with experienced mathematics educators working alongside teachers.