New Zealand faces a serious maths problem - and at last there is also a serious will to solve it.
Unfortunately it's a complex problem - a bit like the simultaneous equations that our students struggle to solve.
Can we somehow lift our average maths knowledge, close our shameful gaps between ethnic groups and school deciles, and yet keep the best elements of creativity and local innovation in our system without succumbing to the memorise-and-regurgitate culture of some countries that top the world's educational tests?
It's not a new problem. We have been slowly sliding down the international league tables since global testing started in the 1990s, not just in maths but also in reading and science.
But the latest results of the Trends in International Mathematics and Science Study (TIMSS), released in December, were so bad that everyone seems to have decided that the problem finally has to be solved.
The Principals' Federation, at its first meeting of the year in Taupō, agreed that "top of our agenda was concern about our national achievement rates, and particularly mathematics achievement".
And the Ministry of Education has called in a Royal Society expert panel to advise on "the mathematics knowledge and skills learners need to know, and when, and what needs to be changed in the NZ Curriculum to achieve this".
There are four main surveys that measure how well our education system is doing. All show that we're in trouble.
TIMSS and its companion Progress in International Reading Literacy Study (PIRLS) are run by Boston College for the International Association for the Evaluation of Educational Achievement (IEA). They test maths, science and reading at age 9 (our Year 5), and maths and science again at age 13 (our Year 9).
The Programme for International Student Assessment (PISA) tests maths, science and reading at age 15 (our Year 11). It's run by the Organisation for Economic Cooperation and Development (OECD).
Finally, our Ministry of Education funds our own National Monitoring Study of Student Achievement (NMSSA). It tests primary school students in all school subjects on a rolling basis in Years 4 and 8, omitting high school students because they have always been tested in external exams.
In maths, we have been bottom of the English-speaking countries and far below the top countries led by Singapore in every TIMSS survey since they started in 1994 at Year 5, and in every one since 2002 at Year 9.
Our trend at Year 5 was upwards until 2006 and has since levelled off with a most recent score of 487 against a world average of 500.
At Year 9, we have plunged straight downhill from 501 in 1994 to 482 in 2019.
Giving students specialist maths teachers when they get to high school seems to help, and our 2018 PISA score at Year 11 was 494, slightly above Australia (491) and well above the United States (478).
But even in PISA, our score has dropped in every year since 2003, from 523 to 494.
Our own NMSSA actually showed a slight improvement at Year 8 between its first maths survey in 2013 and the second in 2018 - but only from 41 per cent of students achieving at the expected curriculum level in 2013 to 45 per cent.
It found that 81 per cent of Year 4 students achieved at the expected level in both surveys, but something is clearly going wrong in the later primary and intermediate years.
Similarly, our reading scores have been bottom of the English-speaking countries at Year 5 in every survey except one since PIRLS began in 2001.
As in maths, we did better by Year 11 when PISA started in 2000, with a reading score of 529 - well above the average. But our scores have declined in every subsequent PISA survey to 503 in 2018, now below all other English-speaking nations.
In science, our scores have been flat at just above 500 in Year 5, declined in Year 9 from 511 to 499, and declined in Year 11 from 530 to 508 - although at two out of three year levels we are still just above the world average.
Looking more closely at Year 9 maths, which has sparked the latest concern, TIMSS shows that our students are strongest in statistics and "number" (basic arithmetic), weaker in geometry and weakest in algebra.
We are stronger on problems that require "reasoning" and "applying" knowledge.
We are weakest on actually "knowing" stuff - not necessarily knowing the times tables, but knowing basic mathematical terms, knowing how to measure and how to read tables and graphs, and knowing how to add, subtract, multiply and divide.
There are huge ethnic and decile gaps. Our Asian students are as good as Australians (10th-best in the world) and our decile 9-10 students are slightly above them; but our Pacific students fall below Lebanon (eighth-lowest) and our decile 1-2 students do worse than Oman (fifth-lowest).
Boys did slightly better than girls in the latest survey, but girls have done better than boys in three of the six TIMSS surveys and there's not much between them.
What's going wrong?
Principals' Federation president Perry Rush told Ministry of Education head Iona Holsted in an urgent letter last week that our decline is partly due to "a lack of system level curriculum and pedagogical leadership".
"We have little thought leadership available to enable important ideas and approaches to curriculum to be debated, established, and implemented in a co-ordinated manner across the sector," he wrote.
"If there are such thought leaders available, I am unaware of who they are."
Our national curriculum advisory service was abolished when schools became self-governing in 1989. Advice was contracted out initially to the universities, but in recent years schools have been left to buy their own advice from a list of hundreds of approved "facilitators".
"It's a competitive thing where you are trying to get schools to bid for you," she says.
"There is no account taken of need, it's just how nice the application was. Some schools would get 50 hours, some would get 100 hours.
"Anyone can set themselves up as a maths facilitator, there are some checks but not a huge amount. It's a huge mess, really - profit-driven is how education became."
Principals face a bewildering variety of options. Rush says the 20-year-old "Numeracy Project" is still official policy, but many principals have rejected it because it confused students by giving them multiple ways to solve every problem - but there is no clear alternative.
"There is a complete information void around advice to schools about whether [the Numeracy Project] still has efficacy or not," he says.
"Schools are grabbing resources - 'Bobbie maths' [from Hunter's Massey University unit], Prime Maths, a commercial provider out of Australia with the Singapore Ministry of Education and Scholastic [a US publisher]."
Many teachers need support. TIMSS found that only 14 per cent of NZ Year 5 primary teachers specialised in maths in their training, compared with a global average of 43 per cent.
Even in Year 9, only 63 per cent of New Zealand maths teachers actually trained in maths, compared with 89 per cent globally. NZ Association of Maths Teachers president Dr Gillian Frankcom-Burgess says we have never had enough maths teachers.
"So many maths teachers in secondary schools are not trained to be maths teachers, they are trained to be PE [physical education] teachers or something," she says.
Kiwi kids spend the same amounts of time doing maths each week as the world averages - 4.2 hours at Year 5 and 3.6 hours at Year 9.
But Frankcom-Burgess, who trains student teachers at Auckland University, says her students often come back from practicums in primary schools saying, "I didn't see any maths taught this week."
"There is actually a maths period, I don't know what they are doing in that time," she says.
TIMSS found that Kiwi kids learn all the main maths areas about as much as the global averages in Year 5, but in Year 9 only half of the Kiwis (52 per cent) learn both algebra and geometry, compared with global averages of 68 per cent for algebra and 76 per cent for geometry.
Hunter says many kids miss out because New Zealand teachers stream students into ability-based groups - 68 per cent do this in at least about half their maths lessons in Year 5, compared with 42 per cent globally.
"Some intermediate schools we work in, kids have never done fractions, because we've had them in ability groups where they have just been given addition and multiplication and they have never been given access to higher-level maths," she says.
As for algebra: "It's not covered, it's not taught necessarily, just not taught."
What can we do?
It's possible that the sharp drop in numbers achieving at the expected level between Year 4 and Year 8 is because we're expecting too much at Year 8. But Holsted told Rush in a response to his letter on Friday: "We do not believe there is a significant issue with the curriculum expectations."
Distinguished Professor Gaven Martin, who has been brought in to chair the Royal Society expert panel, says that at the panel's first meeting last week: "Our feeling was that the basic curriculum was good, so the real disjunct is what is promised from it and what is delivered against it. That is a big issue."
The ministry's chief scientific adviser, Professor Stuart McNaughton, has suggested that we could hire specialist maths teachers for upper primary and intermediate classes, and Holsted has told the Herald in a written response that this is being considered.
But Rush, Hunter and Frankcom-Burgess all argue against this, saying every primary and intermediate teacher should be able to teach maths.
Rush, who is principal of Hastings Intermediate, says: "You're able to integrate those [subject] curriculums together in a way that contextualises learning and gives young people the capability to make sense of the world outside of curriculum silos."
Hunter insists: "Everybody can learn maths, and teachers are just the same."
"I just don't believe in this notion of ability in maths, because it's such a wide area - this whole idea that if you are low-ability you are always going to be low-ability," she says.
She has worked with decile 1 schools such as Koru School in Māngere where she has helped the teachers to get all students "level-pegging with decile 8 and 9" in maths.
She says the trick is to see maths not as rote learning of times tables and formulas but as patterns that the kids can see in the world around them, in kōwhaiwhai lattice work, Cook Island quilts or the way flowers grow.
"Maths is the study of patterns," she says, holding up a 10 x 10 number board in which all the multiples of 3 show up in straight diagonal lines.
"They [student teachers] are very unhappy with their own ability in maths and it shows up in huge anxiety," she says.
"We are trying to help them see the joy in maths that they never had."
Hunter runs school-holiday programmes and parents' workshops, as well as training the teachers, to bring in the whole community when she goes into a school.
"It's making a school-wide commitment to grow, to pushing through the barriers, getting the community involved and having high expectations," she says.
The Government has also promised to re-establish a "Curriculum Centre" within the Ministry of Education and to revive regional subject advisers in the proposed Education Support Agency. The first 38 advisers are already being hired in the mental health and wellbeing area, prioritised because of Covid.
The ministry is also working on a "refresh" of the NZ curriculum, which Rush expects will spell out what students need to know in more detail - reflected in the ministry's request for the Royal Society to advise on "the mathematics knowledge and skills learners need to know, and when, and what needs to be changed in the NZ Curriculum to achieve this".
The pattern is being set by the new Aotearoa NZ Histories curriculum, which will spell out for the first time what students should learn about our history.
"There is growing recognition that the curriculum is too generic, and therefore has not enabled the degree of national consistency that is required," Rush says.
"That is why we are seeing that NZ Histories is coming in and we're saying we can't leave it to chance.
"If you accept that that is appropriate in that dimension, you have to accept that there has to be greater specificity in other key areas of learning."