# Leaving a legacy worth billions

I have said very little in public about the New Zealand flag referendum, apart from suggesting that the referendum should have been funded by the sale of tea towels. If everyone who voted correctly in the first referendum bought a tea towel of their preferred flag for approximately \$25, that would have covered the estimated \$26 million. Given the Prime Minister’s financial acumen, I’m surprised he didn’t think of that himself.

Instead, New Zealand’s coffers are \$26 million poorer and our Prime Minister is still chasing a legacy.

It’s not too late for John Key to leave a legacy. Instead of worrying about New Zealand’s branding and the “billions” a new flag might be worth, he should worry about the 59% of Year 8 children who are struggling to grasp fractions and decimals. He could Bring Back Column Addition and give the 48% of Year 5 children who cannot add two three-digit numbers a fighting chance. He could allow children to learn their times tables without requiring them to use “number properties” to work them out. Perhaps then, more than 8% of Year 5 children would be able to multiply two two-digit numbers.

Since the Union Jack remains embedded in our national flag, let’s look at what Britain has been up to in recent years. They’ve brought back column addition, they’ve introduced testing of times tables, they’ve brought in teaching expertise from Shanghai, they’ve created a Mathematics Mastery curriculum inspired by Singaporean methods. You may not agree with everything they’re doing, but at least they’re doing something.

Our mother country has recognised the widespread impact of adult innumeracy in the UK. If John Key’s government fixed our primary school maths curriculum, how much would that be worth to New Zealand’s future economy? Billions. Think about it, John.

Dr Audrey Tan, Mathmo Consulting
April 2016

# What are the chances of completing a Disney-Pixar Domino Stars collection from a fixed number of packets?

It’s a strange thing for a mathematical person to say, but some people are luckier than others. Luckily for our son (or his parents), we shop at Countdown, which means he received a regular supply of Disney-Pixar Domino Stars throughout the 6.5 week promotion.

It was all a bit of a yawn to me, this time round. Having calculated the chances of collecting a full set of Dreamworks Heroes Action Cards, I was neither surprised nor frustrated by the increasing number of duplicates as his collection grew. The theoretical hyperbolic growth of the number of packets he would have to open to find a new domino implied a spend of \$4480 to complete a set of 50. Almost \$700 per week?? Not very likely.

To cut a long story short, on the last day of the promotion, we trudged home from a swap meet needing just two more to complete the set. Our chances of finding those last two looked bleak…except that a neighbour had just dropped off a big bag of 22 packets in our letterbox.

As I said, some people are luckier than others, and to our amazement, our son actually found the very two that he needed! Now how lucky is that?! I mean, what are the chances…?

Without going into too much detail, you can either focus on what you don’t want to happen, i.e. you get none of one of the coveted dominoes and any number of the other:

or you can focus on what you do want to happen, i.e. you eventually find one of the two that you’re looking for, and then hope to find the other one amongst the packets remaining:

But a friend of ours came up with an expression that best reflects what really happened, i.e. our son stopped opening packets as soon as he found the two he needed:

Reassuringly, all three expressions evaluate to this rather impressive looking fraction:

So it was very close to a 1 in 8 chance. Our son doesn’t realise just how lucky he is.

Dr Audrey Tan, Mathmo Consulting
September 2015

Over the past two weeks, there has been a flurry of public discussion about primary maths education in New Zealand.  Two reports, released within a week of each other, came out with the same message: our primary school children are performing very badly in maths.  Not exactly news, but it’s good to see the nation talking about it.

Releasing the Crown’s National Monitoring Study of Student Assessment on Mathematics and Statistics (2013?!) late on a Friday before the long Queen’s Birthday weekend was a possible reason for the muted response to the latest depressing statistic: only around 41% of approximately 2000 Year 8 students in 2013 met the expected level of achievement.  Our primary school leavers are struggling with decimals, fractions and percentages, and don’t I know it…

But what really got people riled up was The New Zealand Initiative’s report, “Un(ac)countable: Why millions on maths returned little”, written by Rose Patterson.  As the Minister of Education said herself, it provided a “fresh perspective” on New Zealand’s maths learning woes.

Now that the media hullabaloo is settling down, let’s try to set the record straight.  The report investigated and established the failure of the Numeracy Project by:

• providing evidence of a decline in student maths performance that aligns with the roll-out of the Project;
• debunking the myth that it’s not such a bad thing that Kiwi kids don’t “know” anything anymore because their strength lies in the higher-order areas of “applying” and “reasoning”, unlike their east-Asian rote-learning counterparts. Sorry, but it turns out those east-Asian kids are not only better at “knowing”, they’re also better at “applying” and “reasoning” because they’ve actually got some knowledge to work with.

The report also investigated maths teaching quality in our primary schools, citing a study in which a significant proportion of 125 student teachers were unable to answer some basic primary-level maths questions.  Personally, I feel this raises some serious questions about the quality of the Bachelor of Education degree.  Is it not reasonable to expect that all graduating primary school teachers should be able to do primary school maths?

Critics called it unfair, but Rose Patterson was professionally compelled to examine teacher quality after interviewing curriculum writer Vince Wright and maths education researcher Jenny Young-Loveridge.  Both interviewees prefer to blame the failure of the Numeracy Project on its poor implementation by teachers rather than its flawed ideology.  It really wasn’t the Herald’s finest moment when it accused the report, and by association the Minister of Education because she agreed to launch the report, of criticising teachers.  Not one single journalist mentioned the report’s actual conclusion: that teacher quality was unlikely to have changed over the past 15 years, and that the decline in student maths performance was due to the Numeracy Project’s multiple strategy approach to numeracy and the loss of emphasis on the basics.

I am pleased that I had the opportunity to speak publicly in support of our teaching workforce.  Frankly, it is shameful that the people who are supposed to be looking after our teachers chose to not defend them.  Instead, the NZEI Te Riu Roa president said underfunding for teacher professional development (PD) was to blame for the poor results, even though the report pointed out that New Zealand spends a lot of money on maths PD – more than most other countries, in fact.  Even after the Minister of Education responded to the “maths problem” by promising to raise the quality of maths teaching through more PD, the NZEI president still wasn’t happy, saying things would only improve if the training was better than what’s currently available.

Sigh. Result. By the way, has anybody thought about the children lately? When political and professional pride get in the way of helping our kids, it is really sad.

Had certain things happened or not happened, the political response to the Un(ac)countable report might have panned out quite differently.  But, having been to Wellington and heard with my own ears the Minister of Education’s response, it is clear there is more work to be done.  Nobody could have held the Minister accountable for the mistakes of past governments.  In her own words, the Numeracy Project “was in line with international thinking at the time”, so she missed a great opportunity to renounce it and become the public hero.  Instead, everything’s gonna be alright now that we’ve got National Standards.  Erm, would these be the same National Standards that her Ministry just deemed as lacking dependability?

What has been truly heartening, however, is the public’s response.  The Herald’s suspiciously unoriginal editorial and the unrepentant curriculum writers’ opinion editorial have been met with mockery akin to the Emperor’s New Clothes.  It’s good to see the public ain’t buying it any more.

I am proud of this campaign’s role in bringing the debate to this point, but merely talking about it won’t help our children.  A shocking amount of taxpayers’ money has been spent on what can only be described as a failed experiment.  By allowing it to continue, we are failing our children.  From here on, we are all accountable.

Dr Audrey Tan, Mathmo Consulting
June 2015

# Open letter to Hon Hekia Parata MP, Minister of Education

Dear Minister Parata,

I write in response to your speech at the launch of the New Zealand Initiative’s report “Un(ac)countable: Why millions on maths returned little” on 4 June 2015.

With respect, the Crown’s recently released National Monitoring Study of Student Achievement has NOT shown that the system is failing a minority of students. To quote: “The curriculum expectation at Year 8 is that students will be working solidly at Level 4. About 41 percent of [approximately 2000] Year 8 students achieved at Level 4 or higher on the KAMSI assessment.” In actual fact, the system is failing the majority of primary school students in New Zealand, not a minority.

It is incorrect to suggest that the Un(ac)countable report continues the age-old debate in education between those who believe in rote learning and those who place a higher value on critical thinking. By doing so, you have precisely proved the report correct: “Rather than striking a good balance between instrumental learning and relational learning, and enabling the two to build on each other, they tend to be falsely dichotomised. They should work in tandem.

Looking at the graphs, we can see that Year 5 student performance in TIMSS has been on the decline since 2002, Year 9 student performance in TIMSS has also been on the decline since 2002, and PISA 2012 showed a sharp decline in the performance of 15-year-old students in mathematical literacy, in stark contrast to the OECD average. To say that New Zealand student performance in these international assessments has “declined slightly in recent years” is something of an understatement.

Striking the right balance between the practice and mastery of basic skills and developing higher-order thinking is much easier than you claim, and should be guided by evidence. A report released last month, written by mathematician Assoc. Prof. Anna Stokke for the C.D. Howe Institute in Canada, explains that “studies consistently show direct instruction is much more effective than discovery-based instruction, which leads to straightforward recommendations on how to tilt the balance toward best instructional techniques.

Your commitment to raise the quality of maths teaching in New Zealand is welcome. However, the Un(ac)countable report shows that teacher quality is unlikely to have changed over the last 15 years, and the true reason for the decline in New Zealand student performance in mathematics is the loss of emphasis on the basics. Until the Ministry acknowledges the overwhelming evidence and addresses the deficiencies in curriculum content and delivery, throwing more money at professional development for teachers will, sadly, have little effect. That is why I have decided to share this letter, so that parents, teachers and principals can also examine the evidence and make appropriate choices for the children in front of them. By working together, I am confident that we will bring back column addition to New Zealand’s early primary maths curriculum.

Yours sincerely,

Dr Audrey M. Tan
Mathmo Consulting

# Live interview on TVNZ’s Breakfast

“As an (old) ex teacher I absolutely applaud your appearance and comments on Breakfast TV this morning. You were better than excellent and I couldn’t agree more with EVERYTHING you said.” – G Blackwell

“For me, the most encouraging aspect you shared was that it is possible to turn things around quite quickly, even after all the years that have been wasted trying to teach maths using a method that clearly doesn’t work and also disadvantaged the students. In other words, because you were so very specific about what needed to change and how, you brought a sense of hope, not only to the students who may have been listening to the interview, but to the parents who have felt anguish seeing their children robbed in their mathematical education and knowing this would negatively impact their futures. Thank you Audrey.” – S Maxwell

Numeracy Project was a failed experiment
A report shows Kiwi kids are failing maths in higher numbers than ever before. Dr Audrey Tan says the \$70M Numeracy Project was a failed experiment, and gives her recommendations on how to fix the current New Zealand primary school maths curriculum.

# Kiwi kids are failing to grasp maths fundamentals

Pardon the cynicism, but why on earth would the Ministry of Education release a report late on a Friday before a long weekend, if not to bury bad news?

The National Monitoring Study of Student Achievement 2013 found that only 41 percent of [approximately 2000] Year 8 students achieved at Level 4 or higher on the KAMSI assessment. The curriculum expectation at Year 8 is that students will be working solidly at Level 4.

It is hardly any wonder that older primary school children are failing to grasp maths fundamentals such as fractions and decimals. Too many of them are still muddling their way through the list of whole number strategies, such as “doubling and having”, “tripling and thirding”. Assuming they have already learned how to perform column-based multiplication (which many of them haven’t), their time would be better spent experiencing decimals, fractions and percentages in a variety of ways. And I don’t mean colouring in pictures of fractions; I mean learning how to actually do maths with these numbers.

A curriculum that emphasises practice and mastery of the basics would give all children, regardless of their ethnicity or socio-economic background, the best chances of success with maths. Just look at what one Decile 1 school teacher and her students, mostly Pasifika and Maori, achieved in just five months.

We don’t have to wait for the Ministry to tell our teachers what to do; we can’t afford to. The path ahead is obvious. Let’s just get on with it.

Dr Audrey Tan, Mathmo Consulting
May 2015

Report finds Kiwi kids are failing to grasp maths fundamentals – National – NZ Herald News
Maths standards achieved by New Zealand children are sliding dramatically between their fourth and eighth years at school. – New Zealand Herald
nzherald.co.nz

# Ministry’s concern over gaps in NZ maths teaching

Readers will be pleased to know that we already have a name for “space and shape” mathematics. It’s called geometry.

I put it to the Ministry of Education that students’ lack of exposure to “formal maths” is a direct consequence of students’ over-exposure to numeracy strategies. There are only so many hours in a school day, after all.

But let’s remain optimistic. The Ministry may never admit that the Numeracy Project was an abject failure, but the report paves the way for them to quietly sweep it under the carpet. The term “formal maths” suggests more direct teaching and less discovery-based learning.

Concern over gaps in NZ maths teaching – National – NZ Herald News
Students are not being taught enough “space and shape” mathematics and the “huge” learning gap is hurting achievement, the Ministry of Education says. – New Zealand Herald
nzherald.co.nz