Last week saw a bustle of reports showing, once again, that maths learning is not up to scratch in New Zealand.

A report commissioned by the Ministry of Education found that in 2013, 41% of Year 8 students were not achieving in maths at the expected level, with holes in fractions, decimals, percentages, and pro-numerals.

And last Thursday, The New Zealand Initiative released its latest education report Un(ac)countable: Why millions on maths returned little. The title raises a critical question: why did New Zealand pour $70 million and counting into a project that has failed to improve maths learning?

The report covers the history of the Numeracy Project, taking a critical look at this expensive experiment that has failed to return benefits.

But perhaps more necessarily, it uncovers some deeper questions about lines of accountability for schooling outcomes and the roles of various players in New Zealand’s education system.

Namely this one: when a central agency designs and rolls out a programme over the top of a self-managing school system, who is responsible for the outcomes of that programme? And what happens when it fails?

For a little context first, the Numeracy Project was introduced to the vast majority of New Zealand primary schools in 2001, 14 years ago. To be fair, we were not really good mathematicians even back then.

As part of this research, discovered deep in the archives, were communiques to schools from the Ministry in the early 1980s outlining New Zealand’s poor maths performance.

New Zealand has known about its maths problem for more than 30 years. The Numeracy Project was supposed to be the answer to all that, and no doubt there were good intentions.

The Numeracy Project and the thinking of that time saw a pendulum swing away from the step-by-step maths methods many of us remember from our school days, toward more creative maths learning. The latter can be likened to a grasshopper style of learning.

It is big picture, working it out in your head, seeing patterns, estimative, intuitive, and investigative. Grasshoppers. Sounds fun really, and as many critics of the Numeracy Project have pointed out, myself included, there is nothing wrong with grasshopper maths learning.

The problem is the lack of emphasis on the former. The exact, prescriptive, step-by-step, written, formulaic maths learning. Inchworms. May not be as fun but it is certainly useful. And while there has been such an emphasis on seeing the big picture of how the maths game works, the eye has been taken off the ball.

This inchworm style of learning may not be sufficient alone but it is necessary for helping children form the deeper conceptual understanding of maths that the Numeracy Project intended.

The Initiative’s report presents clear evidence that the lack of emphasis on the basics is constraining maths learning. That is certainly not to say we should go back to the old-school ways of learning.

In the words of one critic of those older methods, “at all costs, we should ensure that we never return to the hundreds of algorithms that have made mathematics a wasteland full of the rote learning of incomprehensible rules.”

Indeed, I shouldn’t even be dichotomising old-school and new-school; instrumental and relational; or inchworm and grasshopper learning. Both should build on each other.

But there is a clue in the quote above that shows there wasn’t a lot of economic thinking going on in the minds of the maths reformers 15 years ago when the Numeracy Project was rolled out across the country: “At all costs.”

Of course it’s a turn of phrase not to be taken literally, but if economists had been involved in the Numeracy Project, they might have asked about costs and benefits, and the more pedantic among them might have said “you can’t really say, ‘at all costs’.”

It is 15 years late and too many children have gone through school without getting a proper grasp of maths but now we are asking these questions about costs and benefits. To start with, it hasn’t returned benefits.

The Numeracy Project has probably improved children’s abilities in certain areas of math but the lack of emphasis on the basics has constrained progress.

Though there were some national improvements in the mid to late 1990s, when the more nimble forerunner programmes to the Numeracy Project were in pilot, performance has been in decline since about the time it was rolled out nationally.

And what about costs? The Numeracy Project was both intensive and expensive when it was scaled up, to the tune of $70 million. That was the central cost but, as the report outlines, we do not know what it has cost schools.

It is likely that these methods are much more resource intensive, and we place huge expectations on teachers to teach whole classes of children multiple methods for working out answers to maths problems.

The Numeracy Project has returned little if any benefit, at much cost. But the bigger question that kept coming up during this research was: why is this continuing? Who is responsible? Each of the 1900 primary schools in New Zealand is supposed to be self-managing and responsible to local communities and parents.

Un(ac)ccountable outlines a series of recommendations for solving the maths equation. But it also raises these bigger questions about the roles of different players in the system.

The Ministry of Education should reflect on its role.

If it rolls out a programme nationally, and then sees achievement going into decline, it must be accountable and pull the plug earlier. But the bigger consideration is whether it should be rolling out national programmes in the first place.

What the ministry should do is allow schools to try different methods, programmes, and ways of teaching. It should then identify the schools that are doing well and facilitate the sharing of good ideas. Leave the innovation to the ground and leave schools to be responsible to their students and accountable to local communities and parents.

Whatever the right balance between inchworm and grasshopper teaching is, schools will get it right if they are left to work it out for themselves.