Student letters, November 2013

Teacher from previous post: “The children’s writing is all post assessment. I have had zero input to the writing and without exception they all poured their hearts out. This is what I have been working towards all year. The boys (and I don’t think it is peculiar to our school) rarely get excited about writing, so your presentation back in June has had, if somewhat belatedly, a follow-on effect on literacy as well as maths!!”

Fantastic progress in a classroom

Remember the Decile 1 school teacher who attended my NZEI presentation, whose pupils now wanted to do maths above anything else? Well, she got in touch again:

“Hi Audrey, I thought I would catch up with you and let you know how things have turned out in my room. I am astounded at the ongoing desire of ALL my students to do maths. If for any reason we have to miss out there is uproar!! I have attached the IKAN results for my students. I think you will agree it is an amazing document.”

(If you don’t know what IKAN is, go to http://www.nzmaths.co.nz/ikan-forms and try one of the tests yourself!)

Well, my eyes nearly popped out. In April, before my presentation and after two years of input from a numeracy advisor, all students but one were working at Stage 4. In November, five months after their teacher adopted my approach to teaching maths, two-thirds of the class had raised their performance by as much as THREE stages. In each of the four domains, at least a quarter of the class were working at Stages 7 or 8, which is where they should be. And most importantly, the whole class has gone from hating maths to loving maths!

20131206_IKANdata

There has been no direct input from me. This was done quickly and easily by a teacher claiming to have no specialist knowledge of mathematics.

“I keep trying to get my head around this whole thing that has exploded in my room since June……. I think I hear your name mentioned most days! They keep asking will she come and see us?”

“Well, why not?” I thought. I was given such a warm welcome and they presented me with some truly touching letters they had written, which I will post later. I was treated to a great performance of McFly’s “Love Is Easy”; I’ve been do-do-doing ever since! I dedicate these modified lyrics to these amazing students:

“If this is maths,
Then maths is easy,
It’s the easiest thing to do,
If this is maths,
Then maths completes me,
Cause it feels like I’ve been missing you,
A simple equation,
With no complications,
To leave you confused,
If this is maths, maths, maths,
Hmm, it’s the easiest thing to do,
Do, do-do-do, do do…”

What have we Achieved?


We have a spat between our tertiary engineering schools and our secondary schools/NZQA. It’s time to bang some heads together.

Unfortunately, it’s true. I respect NCEA, but its structure does not support student achievement in algebra, and hence calculus, and recent revisions to NCEA standards have reduced the examinable content in these core topics. It’s a real concern because New Zealand desperately needs more science, technology and engineering.

On the other hand, the engineering schools should raise the bar if students attaining “Achieved” grades are under-prepared. The bar should never have been lowered in the first place! Every NCEA student wanting to continue with their studies should be aiming for “Merit” or higher.

But wait a minute. Secondary students are under-prepared for their studies too! PISA 2012 results are out and New Zealand’s rankings have plummeted (and not just in mathematics). It all starts at primary school…

New Zealand mathematics education is in trouble.

We need to turn things on their heads if we want to prepare school students adequately for tertiary study. The impetus must come from the top. University lecturers should influence what is taught in secondary schools, secondary school teachers should influence what is taught in primary schools. There needs to be a division of responsibility in designing a school mathematics curriculum. The mathematicians should determine the content, the educationists should determine how to deliver that content and ensure that teachers deliver it effectively.

This is my idea for a brighter future for maths education in New Zealand.

Dr Audrey Tan, Mathmo Consulting
December 2013

Manitoba, Canada brings back column addition!


In Manitoba, Canada, it’s the start of a new school year, and a revised mathematics curriculum for their elementary school children.

According to wisemath.org they will see:

  1. All four standard algorithms have been put back in the curriculum (vertical addition with a carry, subtraction with a borrow, vertical multiplication and long division).
  2. There is a specific requirement for times table memorization now.
  3. Most of the language from the preamble, which describes the instructional philosophy, that disparaged practice or pencil-and-paper math has been removed. Language discussing the importance of practice, efficient computation and knowing math facts automatically was added.

WISE Math was founded in 2011 by mathematicians campaigning for improved mathematics education in schools in Western Canada, and who were subsequently involved in discussions with Manitoba’s Deputy Minister of Education. To date, nearly 1000 people have shown their public support for this initiative. It’s heartening to see a government education department paying attention to public concern and putting things right.

I’d like to remind everyone that this campaign also needs a strong voice, so please speak up! Leave comments and make our own Ministry of Education pay attention!

Dr Audrey Tan, Mathmo Consulting
September 2013

A teacher making a difference

Teachers, please read and share this exciting feedback with your colleagues!

“Hi Audrey, I attended the NZEI workshop in June and was so inspired by your presentation. I teach at a decile 1 school and all my year 7/8 students are performing below the National Standards in maths – whatever that means!

I just wanted to let you know that I went straight back and started teaching maths in a way that makes more sense to me – the way I have wanted to teach since the Numeracy Project started. Since the June workshop, my class have learned to use family of facts, including decimals, division of fractions, COLUMN ADDITION AND SUBTRACTION and we have touched on some basic algebra and they are loving it! I have just started a group on multiplication – we are up to three digits!

The children want to do maths above anything else now. In fact today I met with two presenters of an exciting new health/fitness programme and my class shrieked ‘Not now, we’ve got maths!’ I think the staff are getting a bit tired of me constantly raving about the maths in my room!

So, thank you for making it OK for me to teach maths in a way that the children want to learn it.

Also, the comprehension is coming from the children, not from me.”

This teacher has done something very special, possibly life changing, for her pupils. I hope that by spreading the word, other teachers will find the courage to do what’s right for the children in front of them. We don’t need to wait for the Ministry. Let’s just get on with it!

Dr Audrey Tan, Mathmo Consulting
August 2013

Update: Fantastic progress in a classroom

New English primary maths curriculum rewards pupils who use column-based methods


Last week, the United Kingdom’s Department for Education published a revised national curriculum to be implemented in English state schools in September 2014. It will expect a great deal more of its younger pupils, but along with it comes the recognition that that is what it will take to catch up with the top-performing countries.

So what’s in the new English primary school mathematics curriculum? Well, the content is fantastic! There is a good balance between written and mental calculations, with a strong emphasis on repeated practice of methods over a number of years to gain fluency. I have already talked about revisiting methods over many years to improve and deepen understanding in my Review of March 2013.

Best of all, the column-based methods have been restored to their rightful place and treated as fundamental. Methods known as gridding and chunking (they are taught in New Zealand too, in preference to long multiplication and long division) have been dropped.

The curriculum is quite specific about what is expected of pupils at each Year level. I was excited to see curriculum requirements and guidance notes such as:

Year 2: “Recording addition and subtraction in columns supports place value and prepares for formal written methods with larger numbers.”

Year 3: “Pupils use their understanding of place value and partitioning, and practise using columnar addition and subtraction with increasingly large numbers up to three digits to become fluent.”

Year 3: ”Pupils develop reliable written methods for multiplication and division, starting with calculations of two-digit numbers by one-digit numbers and progressing to the formal written methods of short multiplication and division.”

Year 4: “Pupils should be taught to recall multiplication and division facts for multiplication tables up to 12 × 12” (The current requirement is that pupils know all multiplication tables up to 10 x 10 by the end of Year 6.)

Year 5: “Pupils practise and extend their use of the formal written methods of short multiplication and short division. They apply all the multiplication tables and related division facts frequently, commit them to memory and use them confidently to make larger calculations.”

Year 6: “Pupils practise addition, subtraction, multiplication and division for larger numbers, using the formal written methods of columnar addition and subtraction, short and long multiplication, and short and long division.”

“By the end of Year 6, pupils should be fluent in written methods for all four operations.”

And if, by this time, the reader has any remaining doubt about how pupils should add, subtract, multiply and divide, an appendix is supplied with examples of column addition, column subtraction (both regrouping and borrowing), short multiplication, long multiplication, short division and long division.

Apart from the strong focus on arithmetic (both written and mental), there is plenty more to like about this curriculum. By Year 6, pupils will be working with fractions, decimals and percentages. They will also be introduced to a more formal treatment of algebra, using symbols and letters in already-familiar contexts. These are precisely the foundation areas of mathematics that I focus on when working with primary school children, for early success in these areas generally leads to a more successful outcome at high school.

Naturally, there would have to be a reduction in content somewhere, and that “somewhere” is Statistics. I completely agree with this. A Year 8 student’s ability to analyse data is not going to be affected by the lack of an early focus in this discipline; natural maturation will be the biggest influence in outcome here. On the other hand, we already know that a Year 8 student’s mastery of basic numeracy (and general success with mathematics thereafter) can be severely affected by what happens in the early years.

So what has brought about these bold and ambitious changes? Well, like New Zealand, the United Kingdom was dissatisfied with its performance in TIMSS 2011, but unlike New Zealand, they’ve done something about it. British MP, Elizabeth Truss, delivered an excellent speech in January this year. The section “Teaching the most efficient calculation methods” is crucial reading. It is an unapologetic damnation of the “tortured techniques” that confuse both pupils and parents. It acknowledges that the column-based methods are the most efficient methods of calculation and what I love is that “tests will be designed to reward pupils whose working shows they have used the efficient methods”. This is a striking contrast to the Numeracy Project diagnostic assessment, where the column-based methods are considered to be the least acceptable.

The United Kingdom has recognised the failure of an “untried method for teaching maths”. It has looked at various countries, plus 20 of its own schools, that are successful in teaching mathematics and adopted their common approach. A well-resourced country has done all the research for us; all we need to do now is follow their lead.

When the draft curriculum was released earlier this year, the United Kingdom held a public consultation period in which expert opinions were sought. The idea of seeking input from professional mathematicians supports my wider campaign for a brighter future for mathematics education in New Zealand. It would potentially save New Zealand from another decade of disappointing results.

It would appear that the United Kingdom’s Department for Education is unwittingly implementing everything that I want for New Zealand’s mathematics education system. How does that make me feel? Excited, vindicated…and on the wrong side of the world. What will it take for New Zealand’s Ministry of Education to do the same?

Dr Audrey Tan, Mathmo Consulting
July 2013

Is professional development our only solution?

Last month, I received a letter from the Minister of Education, Hekia Parata, in response to my proposal for an improved primary school maths curriculum. In her letter, she wrote:

“We know that we still have some work to do to raise the overall achievement of students in literacy and numeracy. We have learnt a great deal from the Numeracy Projects in the last decade, and central to this is the importance of teacher content knowledge.

“Although there is an expectation that written methods, including traditional algorithms are used officials inform me that many teachers have been so focused on mental strategies they haven’t paid sufficient attention to this. Continued attention to building teacher knowledge will be required both in schools and in teacher training.”

So far so good! But then she goes on to say:

“Officials also inform me that while algorithms are efficient and reliable, there is no guarantee that students will understand, especially if they are learned by rote and before the student has sufficient understanding of the concepts that underpin the algorithm. There is also evidence that premature drill is ineffective, and for some students contributes to a dislike for, and a faulty view of, learning mathematics.”

Oh dear! Well, I wish to inform the Minister that her officials’ claims have little substance. The same pejorative arguments could be applied to any methods, including the “mental strategies”. In any case, they are criticisms of the manner in which these methods are taught, not the methods themselves. If Ministry officials are committed to building teacher knowledge, then there should be no rote learning without understanding, or ineffective, premature drill. Therefore, such criticisms are unfounded.

In the last month, I have also had some welcome correspondence with Dr Naomi Ingram, College of Education, University of Otago, who teaches pre-service teachers (both primary and secondary). Naomi and I agree on many things, including the current lack of emphasis on the teaching of fractions and proportional reasoning, and the importance of teacher-parent communication. She took my concerns to a meeting with her colleagues and has kindly given permission for her feedback to be posted on the Bring Back Column Addition Facebook page. I encourage everyone to read her valuable comments (posted by Mathmo Consulting on her behalf).

It worries me a great deal that the teaching profession as a whole continues to muddle through the problems with the Numeracy Project without asking some very tough questions. I wonder how many other professional bodies would get off so lightly when a largely untested system is released and the results, ten years later, are so poor. If this was something to do with healthcare, there would be a public inquiry. In the software companies I worked for, there is no way we would have released something like the Numeracy Project without stringent testing to provide evidence that it would meet the requirements and do the job effectively. In software terms, it was an alpha release, not even a beta. When untested, bug-ridden software is released, what do you get? You get something like Novopay. I hope I’m not the only one to see the irony here.

But since this is education, not health or wealth, there is no inquiry, no sense of urgency. There is nothing more important than a person’s health, financial mistakes are also very serious, but I rate a child’s education and future as pretty important too…and something we only get one chance at.

The topic of professional development of teachers keeps cropping up, so let’s discuss it now. On one hand, Hekia Parata emphasises the importance of teacher content knowledge and providing professional and learning development programmes to build teachers’ confidence and capability. On the other hand, Naomi Ingram also calls for ongoing professional development and support of teachers but informs us that the Government has reduced funding in this area. It would seem we are caught between a rock and a hard place.

I agree that teachers should have ongoing professional support and development, and it is a concern if funding in this area has been reduced. However, if the consensus is that a significant proportion of teachers are inadequately prepared to teach Numeracy Project concepts without ongoing professional support, then there has been a grave misjudgement somewhere along the line, probably because expectations were too high initially. Certainly, in the early days, there would have been a nation of practising teachers who would have needed re-training, but after more than a decade, there must now be a significant proportion of graduate teachers who were trained to deliver the new methods. Can we not expect these teachers to interpret and deliver the curriculum effectively? If not, then this raises many questions in my mind: What does the B.Ed. qualification mean? Do we need to raise the entry level requirements for student teachers? Is the curriculum too complicated if it cannot be understood in three years?

The more I learn about the Numeracy Project, the more convinced I am that teachers cannot be blamed for the misinterpretation or poor implementation of the curriculum. I’m blown away by how the four basic operations can be made to look so complicated! It must be completely overwhelming for teachers, especially those who don’t like maths, and it must be completely off-putting for many children. Who knows, it might even contribute to a dislike for, and a faulty view of, learning mathematics.

Again, drawing on my experience in the software world, if there is widespread misinterpretation or poor implementation of a product, then it is considered to be a fault of the product, not the end-users, and the vendor would take it upon themselves to make the product more robust. If the funding isn’t there to successfully support all features, then functionality would simply be reduced. In the commercial sector, you cannot get away with producing something that fails in part.

So if we are saying that teachers need more professional development to deliver the curriculum effectively, but the money for professional development isn’t actually there, then what are going to do? We have no choice but to address the curriculum. And unlike with the software analogy, simplifying the curriculum won’t necessarily reduce its functionality. In fact, I believe a simpler approach will improve greatly our chances of producing more effective teachers and more children with higher levels of numeracy.

So let’s ponder over that, because I wouldn’t like to see the topic of professional development become a convenient excuse for not examining the curriculum itself.

More encouraging are the bigger changes I am hearing about on the street! Congratulations to Mark Newman and his school for embracing the traditional methods and inviting feeder primary schools to discuss how to teach the basic operations.

There are other positive developments in the pipeline, and I hope to be able to talk about them in the future.


Dr Audrey Tan, Mathmo Consulting
May 2013

Maths tutor offers solution to Novopay’s problems

The Minister Responsible for Novopay, Steven Joyce, remains confident that the remaining bugs in the school payroll software will be fixed and every teacher will soon be paid the incorrect amount.

Since the new payroll system was introduced last August, thousands of teachers have been overpaid, underpaid, or not paid at all. The latest pay run delivered the lowest number of mistakes to date, but there are still a small number of teachers who are being paid the correct amount.

Novopay’s payroll calculations are based on new methods of calculation taught in New Zealand primary schools through the Ministry of Education’s Numeracy Project.

“It wouldn’t be sensible for us go back to the old payroll system now,” said Joyce. “The problem with the old system was that everybody was consistently paid the correct amount using traditional methods of calculation, but nobody understood why. With Novopay, our aim is to ensure that everybody gets paid the incorrect amount but at least we understand why.”

Maths education consultant, tutor and former software engineer, Dr Audrey Tan, said she was too busy at present trying to fix problems in New Zealand’s maths education system to fix bugs in Novopay, but did offer a possible solution.

“In the old days, people used to add numbers by lining up the columns, but nobody understood why they kept getting the right answers. The new methods of calculation improve understanding by getting the wrong answers. I think Novopay’s bugs might have something to do with the strategy ‘Addition Using Equal Subtractions’. If used properly, it should give you the incorrect answer every time. If there are a small number of cases in Novopay where the correct answer is obtained, it means the software writers didn’t understand the strategy well enough to ensure they always got the wrong answer.”

A spokesperson for the New Zealand Educational Institute said teachers’ opinions of Talent2, developer of Novopay, are still low. “We’re just aghast with the sheer incompetence of Talent2. ‘Addition Using Equal Subtractions’ is a highly effective strategy; it’s so complicated that even a child could understand it. How can they keep paying us correctly?”

A spokesperson for Talent2 says the company has accepted Dr Tan’s recommendation and hopes to implement it incorrectly some time before 2023.

A brighter future for mathematics education in New Zealand

In the NZ Herald, Peter Hughes asks how TIMSS 2011 and PISA 2009 can produce “such wildly contradictory results” reflecting New Zealand children’s performance in mathematics.

We can argue endlessly trying to compare two assessments of children of different ages, taken at different times, assessing different aspects of understanding mathematics. It is pointless, not least because PISA 2009 points to a population no longer representative of 15-year-olds in New Zealand today. Whatever PISA may tell us, it should not detract our attention from the “very depressing” results produced by New Zealand primary school children who have known no other approach to learning maths than that of the Numeracy Project, the very curriculum Peter Hughes helped to write.

Hughes says we urgently need to work on algebra and geometry rather than “number”. I couldn’t agree more. So much for the pioneering curriculum that was supposed to develop “algebraic thinking” in children! Why are our primary school children spending so much time taking numbers apart and putting them back together again? This introspective over-analysis of numbers is not a good use of a young child’s time.

Curriculum co-writer Vince Wright says the Numeracy Project’s failure to deliver improved pupil performance is due to the insufficient maths knowledge of our primary school teachers. We can continue to beg for more funding to up-skill our teachers, but wouldn’t it be more practical to simplify the curriculum to meet the skill set of the teachers we have, present and future?

A bright future for maths education in New Zealand depends on bright beginnings, hence my campaign to Bring back column addition to New Zealand’s early primary maths curriculum. The aim is to redress the balance between written and mental methods of computation, and to make the curriculum more accessible to a wider range of students. I do not advocate teaching column-based methods exclusively, but it’s a good place to start. As Sir Vaughan Jones says, “We have this wonderful decimal system which took tens of thousands of years to bring to perfection and to not take advantage of it for basic operations is nothing short of folly!”

When recent untested ideologies about learning take precedence over the principles of mathematics, which by their very nature are the most logical of all, one has to wonder where things are heading. There should be a division of responsibility in writing a mathematics curriculum: content and delivery. Those with true, long-term mathematical knowledge and experience should determine the content. The educationists should determine how to deliver that content, and ensure our teachers deliver it effectively.

Our university mathematics lecturers should influence what is taught in secondary schools. They, together with well-qualified and experienced secondary school teachers, should influence what is taught in primary schools. This is my idea for maths education reform, and a brighter future for maths education, in New Zealand.

Dr Audrey Tan, Mathmo Consulting
April 2013