The call came from a Government adviser on attainment at a meeting of Holyrood's education committee.
Brian McAlinden, previously headteacher at Castlemilk High School, in Glasgow, told MSPs: "It is not popular, but I think teachers and headteachers should have a fixed-term contract.
"The biggest incentive is if you know you are coming to the end of your five-year stint and your job is up for re-election.
"You will make sure you are up to date, you will make sure you are delivering to the young people, you will make sure your leadership will be better and you don't sit back.
"If we want to make transformational change, which this country needs to do, then maybe we need to take transformational steps and not try to make it happen in a process and structure that is 10 years old."
Mr McAlinden's comments came as MSPs took evidence on the findings of the recent Scottish Survey of Literacy and Numeracy, which found a marked slump in the progress of pupils from the latter years of primary to the end of S2.
It showed S2 pupils living in areas with lower levels of deprivation were twice as likely to be performing well or very well as pupils living in areas with higher levels of deprivation.
Labour MSP Neil Findlay, the deputy convener of the committee, questioned the wisdom of fixed-term contracts. He said the security of long-term employment was likely to bring the best out of school staff rather than fear of losing their jobs.
Larry Flanagan, general secretary of the Educational Institute of Scotland (EIS) teaching union, said later: "The EIS absolutely rejects the suggestion that the casualisation of the teaching profession is a means to raising pupil attainment.
"The Scottish Government needs to look at ways of supporting teachers and attracting top graduates into the profession. This will not be done by eroding employment rights and offering only short-term contracts.
"Scotland has one of the highest-qualified teacher workforces in the world, but wider problems in society must be addressed to support teachers in working to ensure all pupils achieve their full potential."
Mr McAlinden praised an initiative developed by the former Labour-led Scottish Executive, which gave so-called Schools of Ambition an extra £100,000 to fund improvements.
Castlemilk High was one of the schools chosen in the scheme, which was controversially scrapped by the SNP after it came to power in 2007.
"I have to tell you it was like Christmas. We were already on that journey and someone in the Government was going to give us £100,000 so it accelerated our professional development," said Mr McAlinden. "We focused on learning and teaching and assessment and we could not have funded that over three years if we had not had that."
The committee also heard many schools in affluent areas – which were seen as successful and appeared prominently in league tables – were just as likely to be failing some pupils as those in deprived areas where few went on to succeed in exam results.
There was also praise for schools that "relentlessly track" pupil progress, to establish those slipping behind previous performance and identify what support they need to improve.