Our reading scores have dropped by more than all except three countries, and our science scores by more than all except eight out of 24 developed nations.
New Zealand also has one of the widest gaps between top- and bottom-performing students.
Hattie said the country had failed to respond even though the days when we almost topped the Pisa ranks had long gone.
"I think it's complacency. We have sat back on our laurels," he said.
"I have been asking for a parliamentary inquiry about the fundamental way in which we run our schools.
"That has been resisted. But if you are running a school and you are not having an impact, you have no right to run the school your own way."
Hattie developed the Assessment Tools for Teaching and Learning (asTTle) tests, and wants schools to use them to measure every child's progress.
He said too many schools took the easy road of shunting weaker students out of the "hard" subjects.
"We are brilliant in New Zealand at getting kids out of science and maths," he said.
"All the evidence shows that all around the world the problem with streaming is that teachers have expectations of what kids can do.
"Imagine a kid that develops later. They can never catch up because they haven't got access [to higher-level subject content]."
Parata said the new communities of learning, in which preschools, primary and secondary schools will work together, were aimed at developing personalised learning for every student rather than large streamed classes.
"If we can do that then it won't be about streaming, it will be about personalising learning," she said.
"Instead of grouping kids into a group of 'This is where they are at' and 'This is where they are at', it's actually using the evidence to understand how this child learns and what approach do they need."
Hipkins said he supported that change.
"I'm not a fan of streaming," he said. "I agree with what Hekia Parata and John Hattie talk about with regard to personalised learning pathways. I think that is actually the way of the future."
But he said personalised learning required smaller class sizes - and that meant more money.
"There is no question that the funding we have got is not enough for schools and early childhood services to do what we ask of them," he said.
Education Ministry deputy secretary Dr Craig Jones said schools were free to decide whether to stream classes.
"We can influence them. We publish Pisa. We identify that we have high levels of same-ability grouping," he said.
"Then it really is for the profession to take hold of that and say, should we really be doing that?"
