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National education spokeswoman Nikki Kaye has gone so far as to call for the ministry to scrap the changes to English for speakers of other languages (Esol) funding.
The ministry is now reaching out to schools affected by the changes, to address any negative impacts.
Federation executive member and Esol authority Deidre Alderson said many schools across the country were disgruntled there had been little consultation about the changes.
She also said informing schools in December 2018, of a funding change to hit in March 2019, was ''far too late''.
''Any funding change should have been notified to the sector in July or August .
''Particularly because schools are in a crisis of funding and not being able to get the right teachers - things are a bit tough.
''Most schools would already have made their Esol teacher appointments for 2019. So then to have a cut in their funding would have been quite difficult.''
Federation executive member and Musselburgh School principal Debbie Smith agreed.
''It's not until you start crunching numbers that you realise the impact, especially at schools that have got so many refugee children. They're being impacted.
''There was no consultation.''
Ms Kaye said the late notification was ''incompetent and careless''.
''If the system is going to change, then at least there needs to be a transition period so schools can work out how to deal with the funding shortfalls.
''The Education Minister needs to step in and sort this out.''
Ministry of Education sector enablement and support deputy secretary Katrina Casey said the number of pupils needing Esol-funding had increased rapidly over the past five years, from 31,800 pupils in 2014 to 47,807 in 2018 - about 9% per year.
Budget 2018 provided an additional $34.5million over four years to address the increased demand, but volume increases had ''outstripped'' the funding available, and it was anticipated the number of applications would continue to grow with the increase in refugees and migrants.
She said the ministry had hoped to delay making the changes until 2020, to give schools more time to plan for the implementation of the new rates.
''However, the volume increase and budget pressure became apparent recently which, unfortunately, meant that late notification was given to schools.''
Ms Casey said 1485 schools received Esol funding in August 2018, and under the new system, most would receive about the same funding.
However, a small number of schools with large refugee rolls would lose funding.
''This can be replaced through the Refugee Flexible Funding Pool.
''We have reached out to the affected schools this week to arrange to meet with them as early as possible in January to address any impacts.''