Following "numerous complaints" about the record of needs, which applies to the 2 per cent of the school population with the most difficult learning problems, Ms Jamieson announced its replacement with a new "co-ordinated support plan".
This would like the record have statutory backing but would only be activated where a child's needs were found to be beyond the school's resources under a "staged intervention" process.
The proposals, which follow a consultation exercise last year, will set up a new appeals system for parents who object to the level of support suggested for children. This will take the form of an independent tribunal of experts to speed up the process.
Ms Jamieson, who made the announcement during a visit to a special needs unit at Lochgelly High, said these were "significant long-term improvements", particularly the greater say for parents. Authorities will be under a legal obligation to inform parents and young people of the assessment process, the provision that is available and their rights of appeal.
The plans were welcomed by Children in Scotland which described them as bringing Scotland "a step closer to developing a more inclusive education system". Kay Tisdall, its director of policy and research, said: "If we get education right for children with special educational needs, there is a much greater chance that we will get it right for everyone."
But the organisation has found gaps in the proposals, particularly the failure to establish national minimum standards to tackle inequalities across authorities.
Ian Liddle, chairman of the Association of Principal Educational Psychologists, also welcomed the replacement of the record by a support plan which he envisaged would only be for those in greatest need, where schools required the backing of outside agencies.
But Mr Liddle has serious doubts about a tribunal system. "If it mirrors what is happening in England, it will be even more costly, bureaucratic and adversarial than anything we have here just now."
The Scottish Executive says tribunals will be "open, accessible, user-friendly and efficient". But parents and authorities are urged to try mediation first. Currently the system allows appeals to local education committees, Scottish ministers and the sheriff court.
The Executive's decision to ditch the record follows years of complaints that it is inflexible and cumbersome, focusing on pupils' strengths and weaknesses rather than what should be done to make progress. It also fell into disrepute when authorities could not put in the resources identified for each child.
Brian Monteith, the Tories' education spokesman, said the role of authorities was still confusing. They had a conflict of interest as the providers of assessment and the providers of education.