Some teachers cannot read, write and do maths well enough to do their job, the Education Council says.
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The council has proposed lifting the bar for entry to initial teacher education as part of an overhaul of the sector.
Its consultation document said there was some evidence the literacy and numeracy requirements for people enrolling in teacher training should be raised.
"The Education Council has anecdotal information that some new teachers do not have an adequate level of literacy and/or numeracy to be fully effective in their teaching role - but there is limited evidence about the size and scale of the issue."
It said people could currently enrol in teaching courses if they had University Entrance or equivalent, which required 10 numeracy credits at Level 1 of the NCEA and 10 literacy credits at Level 2.
The document said the numeracy benchmark could be raised to 14 credits at Level 2 of the NCEA, but literacy could be tested using the Literacy and Numeracy for Adults Assessment Tool.
The changes could be implemented in 2020.
Early Childhood Council chief executive Peter Reynolds said a higher standard was a good idea.
"If you look at a child's learning story and it's written in abbreviated English or text speak, that's simply not good enough," he said.
Mr Reynolds said the problem was not widespread, but it did need attention.
The president of the the Auckland Primary Principals Association, Kevin Bush, said its members were aware of the problem.
"There are some teachers who are not good candidates to have in front of the classroom. Sometimes that is related to their literacy and numeracy levels and sometimes it is just that they really don't have what it takes to be a teacher."
Mr Bush said a higher entry standard was a great idea, but he worried it would leave schools with too few new teachers.
"The problem is that we don't have the number of people wanting to get into teaching," he said.
Educational Institute president Lynda Stuart said good maths and literacy were important, but she urged caution because she had seen many cases where people who struggled with maths went on to become great teachers of maths.
"Some of the people that I have seen best, particularly in maths ... are the people who really remember struggling with maths when they were at school and struggled with maths when they were at training college," she said.
The Education Council also suggested more courses should train teachers to work across a range of sectors, for example with children aged 0-8 years.
The spokesman for university deans of education, John O'Neill, said previous experience of such courses indicated they might not work well in practice.
"Sometimes in the sector they're perceived as being neither early childhood teachers nor primary teachers," he said.
"If the sector's not receptive to that, then you may not be setting graduates up for the best employment prospects."
Consultation on the Education Council proposal closes on 7 July.