Yes but the F-1 visa is issued for 18 months. Education that you undertake must go for atleast 6.5 months, the remaining 11.5 months can be CPT (curricular practial training) which can be employed as a CFI by the school you trained at for those 11.5 months. Effectively giving you 23 months of work. As I said, only the second lot of 12 months allows you to roam freely.