This is a difficult question to answer- because you are not specifically talking about elementary education, early childhood education, middle school education or secondary education---and I am not sure if there is research looking at teacher burnout in any one of these specific areas. I would be really interested to know if the number of children with special needs being integrated into the regular education classroom is related to burn out or if the lack of "administrative support" is related to burn out- It would seem plausible to investigate- but research and data is sorely needed !
I am not aware of any studies, but from the clinical psychology literature - competence/ incompetence to do the job usually is not considered as a cause for burnout syndrome. Of course, competence/ incompetence could influence the amount of perceived stress and quality of performance.
Thank you for your posting and contributing to the Discussion....Teacher "competence" is a slippery construct---because one teacher may be very competent at teaching normal, well adjusted , average students- but may NOT be very good at working with children with special needs- children with autism, children with vision or hearing impairment, children with dyslexia or some learning disability or attention deficit disorder or perhaps a child who a traumatic brain injury. All too often teachers are confronted with students who have very special needs ( medical, psychological, health ) and feel that they were not adequately trained. In other instances, teachers are confronted with violent, aggressive, assaultive destructive students, and again do not feel well trained or do not feel they have administrative support.