By Shannen Doherty
Effective early Maths teaching is vital for students to be able to progress through the curriculum quickly. Shannen Doherty explains why prioritising mental maths methods over written methods might be a better use of time in the long term.
As a primary Maths coordinator and a Year 2 teacher, I despair when I see schemes of work directing teachers to teach written methods of calculation earlier than necessary. Schemes of work and textbooks should be leading from the front. They should be pushing for high-quality practice, not jumping to what seems the easiest way.
The National Curriculum (2014) states that children in Year 2 should be able to ‘add and subtract numbers using concrete objects, pictorial representations, and mentally, including:
- a two-digit number and ones
- a two-digit number and tens
- two two-digit numbers
- adding three one-digit numbers’
The key words here being ‘concrete’, ‘pictorial’ and ‘mentally’. The non-statutory notes go onto say that recording addition and subtraction in columns will prepare them for formal written methods later on, but many mathematics curriculums seem to have taken that tiny nugget of guidance and run with it. They’ve run straight to column addition and subtraction without pausing to consider the consequences. The National Curriculum for Year 3 then goes onto explicitly state children need to learn the formal column method. So why do so many schemes, textbooks and teachers rush into column addition and subtraction before then?
As far as I can tell, there are a lot of potential explanations for hurrying into teaching a formal written column method for addition and subtraction in Year 2. I suspect that the use of column method in Year 2 is due to the presence of end of KS1 assessments. Teachers feel under pressure to deliver results and see column method as a quick and easy win without teaching the depths and structures of calculation.
It could also be a case of poor subject knowledge. This links to a lack of confidence found in some teachers, especially when it comes to teaching Maths. If teachers haven’t got a strong Maths lead or haven’t been part of high-quality CPD then they’re likely to teach Maths as they learnt it, which was probably with an emphasis on procedures rather than concepts.
Lastly, a reason I’ll probably get into hot water for writing about… some teachers will believe that getting their children to the written method finish line will make them look good. I’ve seen it in schools. I’ve seen it on social media. It definitely exists. There will be teachers who think that their ability to teach a class of six or seven year olds a procedure and have those children perform that procedure without error is a sign of an outstanding teacher.
So why is this a bad thing? Why do I feel so strongly about it? I imagine most primary teachers will have worked with a child who uses column addition and subtraction as a crutch as soon as they’ve been taught it. If work has been done on their mental arithmetic, then it is often forgotten once the written method is introduced.
We are doing our children a disservice if we jump into formal written methods too soon. The National Curriculum places importance on fluency. Fluency is far more than the ability to rapidly recall facts. It’s the ability to manipulate numbers and calculate mentally. Fluency relies on a deep understanding, rather than surface level fact recall. Without this level of true fluency, our children end up using written methods for the simplest of calculations. I’ll never forget administering the Year 6 SATs two years ago when a student used column addition to work out 6000+90. They were so reliant on a procedure that they could not see the simplicity of what was being asked. Their place value knowledge had been overshadowed by the crutch of a procedure. I’ve seen it with adding 10 and adding 100 regularly. If we don’t push mental calculation, then the children will lose it. We have a duty to stop this from happening, but by introducing a written method too early we are enabling it.
We want children to develop a selection of methods to calculate mentally and improve their mathematical mental flexibility. This should be the goal for addition and subtraction in KS1, and I’d argue in KS2 where appropriate, too. In Year 2 where we teach the addition and subtraction of two-digit numbers, I would expect teachers to be showing their children how to partition addends into tens and ones, for example 35 + 23 = (30 + 20) + (5 + 3).
I would also expect the method whereby we partition one addend and add in stages, for example 35 + 23 = 35 + 20 + 3. For subtraction, I’d again be looking to partition the subtrahend and subtract in stages. There’s also the idea of same or constant difference, something that blows children’s minds! There is such an array of mental methods that we can teach, so I can’t possibly list them all now. But it is absolutely vital that we expose them to the axioms and intricacies of calculation.
I am in no doubt about the damage that introducing written methods too early can have. But what are the benefits? Children who have a handle on mental calculation will have a deeper understanding of place value, which underpins much of the maths we teach in primary school. Children who have spent time exploring constant difference will have a better grasp of how to manipulate numbers to their advantage. A child who turns to column subtraction for 5,000-3,594 won’t have the same level of understanding compared to those who turn it into 4,999-3,593. This runs deeper than just the two-digit numbers we operate with in KS1.
Mathematical flexibility will stay with them for life. As well as a depth of understanding, the children will have a better idea of efficiency and which method suits which problem. They’ll instinctively pick the right method, and yes sometimes that will be a written one!
This isn’t me saying children aren’t developmentally ready for written methods, or that they aren’t capable of learning a procedure. I am quite confident that I could walk into my Year 2 classroom tomorrow and teach them the process of column addition or subtraction and I am sure they’d do fine with it. However, just because we can doesn’t mean we should. We have seven years in primary school. There is plenty of time to teach written methods. Why jump the gun? Why skip the best stuff?