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 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!


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 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