A change of circumstances often provides a good opportunity for reflection. I have found myself in this position after taking early retirement from my primary head’s role and a teaching career spanning 34 years.
I did take two years off in 1990 to cycle around the world; it was during this time, that I developed a fascination for numbers. Towards the end of the trip, a favourite way to pass the time was to make fairly pointless calculations. For example, how many hours I spent actually sitting on my bike (3,128) or how many different places I slept in (437), or how many dogs I was chased by (287). To work these numbers out was relatively straightforward, but some calculations are a little more demanding. A recent discussion with a friend centred on how many cubic millimetres there were in a cubic kilometre (year 6 measurement?) After a while, we realised we’d need a bigger piece of paper.
One of my reflections is that, although done with the best intentions, adults and especially those who don’t teach in our schools, tend to overcomplicate things for children. This is certainly true of the architects of the maths curriculum and the way we teach maths in schools. Of course, the end result is too much content and, unsurprisingly, not enough time to teach it.
Consider the following scenario, which I suspect will be familiar to most primary teachers. A teacher plans to teach a topic, possibly over a two or three-week block, and targets the teaching accordingly depending on the ability of the children and their prior learning. After the block, the topic isn’t nearly complete, but pressure of time is building and the next teaching block in the sequence is knocking persistently on the classroom door.
If you ask the children what they have learnt, the higher ability children will probably be able to give a reasonable synopsis of the content, but the middle and lower ability children will be pretty vague about it, in many cases purposely so, since they will want the conversation to end there. This process usually starts sometime in year 1 after the excellent practice of continuous provision has finally petered out; no blame should be apportioned to the year 1 teacher here, since the directive comes from above.
From year 1 onwards, maths foundations are already quite unsteady for many children. During the subsequent years, many middle and lower ability children gradually lose ground and their learning slows, due to uncertain conceptual understanding, especially of number.
Some children begin to sink at a rate of knots. They openly say they don’t like maths and develop a mental block, triggered just by the mere sight of a number. By the time the child is in year 6, the process is almost irreversible.
These are children who will become adults with a real antipathy towards maths. Actually, it is not maths that they have an aversion to but the way it has been delivered to them. Teachers and heads should plead “not guilty” here – they have been saying this all along.
The new curriculum does, however, promise much better outcomes than the Primary Framework and the National Numeracy Strategy ever did. At last, we have a maths curriculum that attempts to clarify for children what maths is and how it fits together. It has been deconstructed and the separate components and joining points are visible at last.
This must be the first step in understanding how maths works. Too often, children are subjected to “mixed maths”, where they are expected to bounce mentally from one mathematical concept to another or to apply a half-learnt idea to another half-learnt idea.
The basic principle of learning about number and place value before moving on to other concepts seems to be a very simple and sensible one. It is impossible to have an understanding of number and subsequently other maths topics without a clear understanding of place value.
I hope that schools will teach the new maths curriculum as it is presented and I presume, intended. To split the content blocks and re-arrange them into topics that look more like they belong in the previous framework is, I believe, a mistake.
It will lead to continued confusion. Most adults and some children understand that maths is a discipline where concepts are inextricably linked. Children who are directed to see these links too early will fail to see them. Their lack of understanding, due to the burden of a content-heavy maths curriculum, will prevent them from recognising these relationships.
The new curriculum offers some relief. Number has pole position and must stay there. Schools should focus very heavily on number until it is embedded in children’s learning. There is very little point in children moving onto measurement or statistics, for example, if they haven’t got a firm hold on number.
If you can’t tell the difference between tens and tenths in your place value understanding, you haven’t got a hope of knowing how many cubic centimetres there are in a cubic kilometre.
This means advocating teaching that continually reinforces the foundations of maths. Primary schools need to be bold and focus almost exclusively on the acquisition of solid number understanding through constant repetition and over learning.
Consider the much discussed 10,000 hours rule; according to several studies, this is the number of hours’ practice it takes for an adult, by the age of 20, to have mastered a discipline to a very high level, be it computer programming or playing the violin.
Why is maths any different? A child in school from the ages of 4 to 16 will spend, at most, about a quarter of this amount of time on maths and even less specifically on number. Little wonder that many of our children fail to grasp even the basics.
I remain unconvinced that it is possible to develop a love of learning in all children. What is more realistic, however, is to instil a love of achievement. I have witnessed many children, with quite severe learning difficulties, succeed in learning all the times-tables. The difference in the self-esteem of these children, after achieving this success, was palpable.
Although they may not go on to study maths at degree level, some even said that they actually began to enjoy the subject. At the school I left this summer, with happy memories and a heavy heart, the principle focus of number acquisition was a constant in every maths lesson (and throughout the day).
Staff skilfully delivered the maths curriculum, always underpinned by an unfaltering concentration on number. I saw constant number bond and mental maths games and practice, repeated in so many different, exciting ways. The rhythmic chanting of tables permeated the walls – not to gimmicky music either but simply as a chant. A tune is easy to forget; a chant tends to stick in the memory for longer.
An almost exclusive focus on number throughout key stage 1 and lower juniors, will equip children with firm foundations upon which they can build. Many areas of maths should be reserved until year 5 or 6, even though they are on the “official” curriculum for younger children. Once number is embedded, children can acquire the “higher” maths skills much more effectively and quickly.
In conclusion, don’t be afraid to embrace the Mavis Beacon approach to maths teaching. Many years ago, I learnt to touch type with my £5 CD and fingernail stickers provided by Mavis Beacon. Mavis suggested repeating “asdf” around 10 times until confident and then move on. I didn’t count, but I think the number of times I pressed “asdf” with my stickered fingers was nearer to a thousand times before I moved on.
Let’s start to look at maths from a child’s point of view and take a hint from a word that they learn very early: again.
- Peter Sumner is a former headteacher who has now founded HeadStart Primary, a publishing company with a focus on producing maths materials to help schools deliver the new curriculum. Visit www.headstartprimary.com or email info@headstartprimary.com