What Michael wants..........

Michael Gove is in the media a lot at the moment: Headlines concerning poor and failing schools dominate.

But what constitutes failure? For Gove and the government the answer is 60 percent. (Primary schools are judged as failing if less than 60 per cent of pupils meet the expected level in reading, writing and maths over the past 5 years.)

“For years hundreds of children have grown up effectively ...innumerate.” Michael Gove

He is, of course, absolutely right - although thousands rather than hundreds would probably be a more accurate figure for this dismal failure.

So - one way or another - Michael Gove is seeking change, be it to the naming and funding of a school (Academy status) or to the topics taught (overview of the National Curriculum). In a speech to the Royal Society (June 2011) he considers where best to concentrate his efforts:

One of the lessons from the international evidence is that in East Asia there is much greater focus on fundamental number concepts, fractions and the building blocks of algebra in primary school. They have minimum standards that they aim to get practically all children to reach so they have a firm foundation for secondary. It may be, therefore, that we will adopt the same approach and have much more emphasis on pre-algebra in primary and remove data handling and some other subjects from the primary curriculum.

Pre-algebra?  I think this is an Americanisation but if he simply means - let’s just get stuck in and do more algebra without being afraid of it - and more significantly - without passing on any of ‘our’ fear to the children - then I couldn’t agree more.

Algebra is delightful. To appreciate this, it just needs to be taught well. Why is algebra so jaw droppingly good? Put simply it is the essence of mathematics; it is the language of maths; it is precise, exacting, rigorous and succinct. At a basic level algebra is an efficient form of short hand; at an advanced level it is the sole vehicle for expressing and examining theories and discoveries. We can no more easily seperate out and ignore Algebra than we can Geometry or Topolgy or any other strand of the subject. 

If none of this is enough to persuade a typical teenager (or parent or reluctant teacher) of the merits of the matter, I simply say… algebra is good for you, it strengthens the mind and encourages precise logical thinking – skills any employer would appreciate.

In Arabic the word ‘algebra’ simply means ‘restore’ or ‘balance’.

Bizarrely........

Just because algebra can (eventually) become complicated and complex, it  discourages some from ever stepping out on the start of the journey.

Playing the piano can be highly intricate, football skills can be extremely challenging. but few of us would shrink from encouraging our children to take part. We know very few of them will ever perform live ballet at the... but we are still happy to take them to their weekly class and cheer their termly progress. Why, as a nation, do we actively discourage our children from properly engaging with algebra just because one day it could become quite tricky!!!!!!!!! 

So on this matter alone, I agree with you Michael: train and support primary teachers to appreciate the beauty of algebra; encourage and enthuse the teachers to enjoy the elegance and eloquence of the language; and ensure that algebra is universally taught well.

Can The Tiger Come to Tea?

I shouldn’t think so! You see - there are no play dates for tiger cubs, the offspring of so-called Tiger Mums.

The term Tiger Mum was coined by Amy Chua in her memoir, Battle Hymn of The Tiger Mother, a book about Chinese parenting published a year ago. Tiger Mums believe in hard work and often rigorously schedule their children’s after school activities; four hours of extra study is not uncommon. Organisation, hard work, dedication, effort, these are their watchwords; ‘practice, practice, practice’ their mantra. All of this comes at a cost of course; play dates are simply prohibited.

England may be languishing in league tables – we are currently in 28th position worldwide for the maths performance of our fifteen year olds - but China is the rising star and number one.

Even in England, Chinese children achieve the best maths GCSE results. And maybe it is all thanks to their Tiger Mums.

But is there more to the Chinese success story than sheer hard work? Well, yes, I believe so. Something as simple as the way we say our numbers can have a massive impact on early learning.

Just think about our naming of numbers: ‘Fourteen’ for example, or ‘sixteen’. So why not ‘oneteen’ or ‘twoteen’ or ‘threeteen’’ or ‘fiveteen’? Similarly we have ‘sixty’ and ‘seventy’ but not ‘twoty’ or threety’. Even ‘forty’ isn’t ‘fourty’! It’s just a bit odd.

Even more significant for small children is that the names can also be counterintuitive.

Think about ‘fourteen’ again. We say the ‘four’ bit first BUT write the teen bit first: 14. Likewise for all the teen numbers. But then we reverse that process So for ‘twenty four’ we write the 2 first (representing two lots of 10) and then the 4. No wonder when you are aged 5, distinguishing between 21 and 12 takes some thinking about.

Compare this with the Chinese system of naming numbers. Eleven is quite simply ‘ten-one’; twelve is ‘ten-two’; thirteen is ‘ten-three’; and so on. Likewise: twenty-one is ‘two-tens-one’; twenty-two is ‘two-tens-two’; twenty-three is ‘two-tens-three’; and so forth.

The upshot of this beautifully simple system is that, on average, Chinese children can count to forty by the time they are 4. English speaking children are usually 5 before they master this skill.

So by the time English speaking kids reach school they are already a year behind their Chinese peers. And that’s not all. Because the Chinese system is so clear and so straightforward, basic number operations (such as adding and subtracting) are just that much easier.

Imagine you are six years old. Now try adding, in your head, twenty-seven and twelve.

Before you can begin you must be able to interpret the words, i.e. twelve actually means one ten and two units, likewise twenty-seven is actually two tens and seven units. Then perform the addition, adding the tens and adding the units*, and then translate back into words; 3 tens and 9 units being thirty-nine. (*Note when performing mental maths most of us do add the tens first, followed by the units.)

Now try the Chinese way: two-tens-seven and one-ten-two. The solution is literally embedded in the question. Answer: three-tens-nine. How much easier is that for a 6 year old? A similarly simple and sensible system exists for fractions. 

Does this mean Chinese children have an easier and more successful start to the subject? Could this explain why, in China, there is no culture of negativity surrounding maths? 

And of course success breeds success.  No wonder by the time English pupils sit their GCSE’s, Chinese pupils are on average two years ahead.

Hard work has its place of course; So too an aspirational desire to succeed. British children of Chinese ethnicity do after all perform best in GCSE exams even without the linguistic advantage. It seems Tiger Mums can drive their children to conquer even our opaque number system.  Amidst much media hoo-ha about Chua’s tough parenting style, she emerges as a loving and caring parent. Maybe Tiger Mums should be given some credit. Maybe, as the sun sets on the West and we contemplate the future of our economy and education, we should learn some lessons from the Eastern stars.

Naomi Sani

Move it!

Meeting my son and his best friend from school, I asked how their day had been. Expecting the usual pre-teen, 10 year old mumbles, I was taken-aback by their: “Really good,........ maths was great”. Music to my ears  - but what wonderful, inspiring, creative lesson had their teacher crafted?

Measuring.

Measuring! Measuring what? Anything, everything, all sorts....it didn’t matter. The point was they were up, out of their seats, trying things out, experimenting, making decisions, in control.

This is not rocket science: Kids just love to move around, be hands on and try things out for themselves. This is a classic case of kinaesthetic learning.

Kinaesthetic learning sounds complicated but it simly means learning through touch and movement. Children, especially of primary age, love to move around: This will be of no surprise to anyone who has spent any amount of time with young children. But most children do also learn best when they are allowed to be active!

Talking to children at length can be so counter productive. It is however a very tempting tactic - because children are in the seats, quiet and the teacher can be comfortably in control. Allowing children to move is more unsettling, more noisy and more risky. But the rewards can be great: the learning so much richer, deeper and engaging; the pupils more curious, interested and motivated. For maths to become a more joyful experience for many, the kinaesthetic approach is a must.

Boys in particular benefit from kinaesthetic learning. Generally as children get older fewer and fewer opportunities for kinaesthetic learning are offered. This can be a problem, particularly for boys. So if you want to kickstart a group of sluggish boys, consider upping the kinaesthetic content.

Linking together mathematical concepts, joining up the dots and seeing the big picture can also be enlightening.

I was blown away by an inspirational talk by Christopher Lloyd (author of ‘The What On Earth Wallbook’). He summed up the whole history of the earth, all 13.7 billion years of it, in just under one hour. Simply amazing. I learnt (and re-learnt things that I had once known but long since forgotten) stuff which all made so much more sense when fitted together and joined up.

I used this idea - of zooming out and seeing a big picture as opposed to zooming in and focusing on one particular concept - when working with a group of forty pupils on an intensive revision maths residential. Linking together .... (big breath)...... number bonds with adding and subtracting (and sum and difference) with summing numbers to 180 with angles in a triangle with different types of triangles with different types of polygons with interior and exterior angles of a polygon with the area of a rectangle with factor pairs (making up the dimensions of rectangle) and multiples with the area of a triangle with BODMAS with square numbers and cube numbers and indices with standard form and very big numbers such as a billion, and so on,....... all in one session. Interjected with some loud music and some snappy YouTube clips - it really worked!! 

But what is a billion anyway? After all we hear a lot about the billions and billions of debt in the Euro-zone. 

A billion used to be a million lots of a million and look like this:

1 0 0 0 0 0 0 0 0 0 0 0 0

and this is still the case in large parts of Europe.

In the United States however, a billion is a thousand lots of a million and looks like this:

1 0 0 0 0 0 0 0 0 0

(and in fact the United States’ trillion is the same as a European billion!!)

So whose billion are we (and our media) using??

Perhaps we best ask the movers and shakers - the politicians. (But I have a sneaky feeling that many wouldn’t have a clue!)

Naomi Sani

A maths problem: Winning hearts and minds.......

My 3 year old has just started preschool. An amazing, award winning, inspirational preschool, led by Lizzie, one of those ‘special few’. I was delighted to meet her. A like minded teaching soul, we shared some ideological stuff about the Government’s absurd insistence on assessing 3 year olds, along with the undeniable benefits of outdoor learning. Then Lizzie asked me my subject - and that is when I saw her literally shudder.

MATHS 

Why does the word provoke such a reaction? And what, if anything, can we do about it?

Can we tackle raising standards in maths and deal with the devilish problem of altering deeply embedded attitudes?

We can, if we focus less on test results for a moment and imagine children knowing maths in quite a different way. Envisage maths in the class room being creative, fun and engaging; envisage children in the class room being busy, curious and interested.

Buckets and buckets of money have been thrown at the thorny issue of raising mathematical standards. Government drives, national strategies and endless initiatives have all been thrust on teachers with limited success. But now the pots of cash are drying up and austerity measures have hit hard. 

We need to forget about big, top down, expensive strategy policy makers and learn to manage the problem at a micro level - in schools and within schools. The answers lie with the teachers themselves.

But the truth is, through no fault of their own, a lot of teachers have a very negative view of maths often stemming from their own experience at school. These teachers are not in a position to teach the subject with confidence, enthusiasm and creativity. And in many cases their own maths is simply not up to scratch. (By that I mean a primary teacher’s own mathematical ability should easily outclass that of a bright 11 year old; the expected high standards may surprise a few teachers as well as parents.) 

With time, energy and focus, we need to invest in our existing teachers and change the way many children are taught maths. The Government acknowledges this and in the Schools White Paper “The Importance of Teaching” (2010) announced the Government’s commitment to improving the maths skills of existing teachers. But it goes on to say that the primary responsibility for this rests with the schools.

With an enlightened outlook, schools can do this - we can invest in ourselves.

Firstly and fundamentally, we need to be honest; we need to ‘own’ the problem and be prepared to do something about it. Then we can take responsibility for raising our ‘game’.

Getting the basics right is the best start. Teachers need to be aware of the expected maths skills for the pupils within their school (for primary teachers this would be up to at least Year 6 level maths). Currently, and maybe somewhat surprisingly, this is not always the case. And then teachers need to regularly challenge and hone their own maths skills and be prepared to ‘own up’ when skills are lacking. (Good senior management will be essential to render an atmosphere for creative candor.) Working together on maths problems is a simple start. A five minute maths focus at the start of every staff meeting is a good idea. (Be prepared to discuss answers and compare them with how your pupils are expected to show results.)

I know, I know! 

.....I can already hear the dissenting voices in the staff room. Why maths? ‘Other subjects are just as valuable.’ So true - but no other subject suffers from the huge shuddering cultural handicap meted out to maths.

Why we need to tackle maths NOW..........

because more than one in five children leave primary school having failed to grasp basic maths*; because failing to master the fundamental skills at primary school leaves you with only a one in ten chance of catching up by age 16; because league tables now demand that maths be included in the 5 A*-C statistic; because there are plans to abolish the modular (try as many times as you like) maths GCSE; because the Government is planning to make studying GCSE maths compulsory for any 16 to 18 year-olds in education without a grade C or above in the subject; because if you do not secure a basic level of numeracy you can feel the negative effects on your lifestyle, your income and your health; because we need a shift in culture if we are ever to tackle the huge tail of underachievement in the UK; because although there has been some improvement in the UK over the last 20 years, standards have been rising much faster in other countries; and just because ..... because we owe it to our kids.

Tackling questions a bright 11 year old is expected to do could create much needed discussion and debate. The Channel 4 Dispatches website have some very good examples stemming from an excellent programme shown last year ‘Kids don’t count’. 

I recently used a typical question from the teacher quiz on their website, 1.4 ÷ 0.1, whilst delivering INSET.  It caused problems.

Actually it isn’t a difficult problem at all and was really only my starting point for    1.4 ÷ 0.01. I just think sometimes all the notation can get in the way and we can easily panic or freeze. A very common reaction in stressful (exam!) situations. For 1.4 ÷ 0.1, I suggested this: Imagine you are in the car watching the SAT NAV showing you getting closer and closer to your destination. As you get close it starts counting down in 0.1’s of a mile. You are 1.4 miles away from meeting all your friends and family. How many times do you count down before you get there?(1.4, 1.3, 1.2,..................) Answer: 14.

(Often rephrasing the question is enough: How many 0.1’s go into 1.4?)

(For 1.4 ÷ 0.01, the answer is 140)

Another typical question which can wreak havoc: 2 1/2 ÷ 1/4

Many of us need to retrain ourselves to picture or visualise the problem. Stop looking at the numbers and symbols and instead picture a scenario. Try imagining two and a half green apples. How many children could each have 1/4 of an apple? 

Answer: 10 children could each have 1/4 of an apple.

(Each whole apple could be cut up to give 4 quarters, so the two whole apples would be a snack for 8 children. And the 1/2 apple could be cut into 2 quarters.)

So do we always have to relate maths problems to everyday life? No absolutely not - but sometimes when there is a ‘block’ or a habitual resistance to learning maths - it can certainly help.

I believe that pure or abstract maths should be taught - and from an early age. Maths is a robust, economical and efficient language. When taught well the intrinsic beauty of maths is wholly satisfying.

The ‘new’ methods of the Numeracy National Strategy are, on the whole, great and a massive improvement on the mysterious algorithms many of us were taught at school. However there are two big problems. One - parents don’t always follow the new methods and therefore can feel deskilled and anxious. Secondly - I think some primary teachers have misunderstood the intent. The intention is not to bombard the pupils with a plethora of methods and then leave it up to them to ‘choose’ which to use. No. The intention is to gradually introduce written methods based on the previously practiced mental methods, refining and abbreviating the methods until the most efficient method is mastered. Some children will obviously go faster and further along this path than others.

Giving parents clear guidance on the methods currently used in the class room simply makes sense. Parents are very keen to help and are often a massively underused resource. We also need parents ‘on side’ if we are serious about rewriting the script for the instinctive response to the word ‘maths’. Some schools provide better information than others. Often, at the end of the day, there is little time and energy to devote to parents constant queries. With this in mind, and after being asked by countless parents if there was a book to help them, I decided to write the book ‘How To Do Maths So Your Children Can Too’. 

Together - parents, teachers and anyone involved in educating our children - we can make a difference.

A sea-change to how many of us view ‘maths’ really is possible and there could be a whiff of it in the autumnal air. Now is a great time to inject optimism into the staffroom. All that is needed is someone to channel some positive energy: An Advanced Skills Teacher (AST) would be great (and free).

We’re done with battling with strategies; now we’re battling for hearts and minds. 

Teachers are an incredibly bright resourceful bunch of people. Once we put our collective minds to something we can be invincible. The knack now is to persuade a critical mass of the teaching profession to want to become more proficient at maths.  And it is a very doable proposition. All we have to do is create the space and afford the focus to getting the basics right. Simple maths resources will suffice, for example: step-by-step guides(see ‘How To Do Maths So Your Children Can Too’); worthy websites (try www.cimt.plymouth.ac.uk; www.bbc.co.uk/skillswise; www.bbc.co.uk/schools/ks2bitesize; www.bbc.co.uk/schools/ks3bitesize; www.bbc.co.uk/schools/gcsebitesize; www.nrich.maths.org; www.teachitprimary.co.uk). It’s not rocket science - we can do this. And if we do, teachers will feel more confident, more comfortable and more empowered in the classroom every single day. The cultural cycle of negativity towards ‘maths’ may even stop spinning!

Why write a maths book?

As a teacher I had been asked countless times if there was a book I could recommend to help parents help their children with maths. There just wasn’t one - so I thought it would be a really good idea to write one. But the catalyst which pushed me to put pen to paper was an article ridiculing David Beckham for not being able to help his 6 year old son. A little harsh I thought as there are lots of parents who do not feel confident helping their children with maths: Even very numerate parents can be unsure of the ‘new’ way of doing things.  So HOW TO DO MATHS SO YOUR CHILDREN CAN TOO is for anyone who wants to help children with maths: parents, teachers, teaching assistants and student teachers; for those who feel numerically confident and for those who don’t. HOW TO DO MATHS SO YOUR CHILDREN CAN TOO explains things simply and clearly -  highlighting new methods, terminology and teaching methods. It is packed full of helpful advice and examples: Everything from mastering ‘number bonds’ and ‘number lines’ to dividing by ‘chunking’, ‘partitioning’ with confidence and using the ‘grid method’ to multiply. In fact many primary teachers are already finding the book to be an accessible and essential resource.