Calculators are to banned in KS2 SATs and their introduction delayed until year 5 but is this a good or bad thing?

Michael Dix's picture
Having spent yesterday listening to the inspirational children's author and former children's laureate Michael Rosen, I returned home to find yet another controversial education story occupying the media and generating a myriad of comment online.

Michael's key theme, as he advocated developing talk through poetry and gave a rousing critique on government policy on reading, was that changes in the way we educate our children should be based on real evidence from research rather than the whims of ministers. I wonder what evidence the latest decision on calculator use has been based on. Yes, calculators are used more in this country than in others, possibly because the National Curriculum requires schools to teach children how to use them. But are our year 6 children so much poorer at mental arithmetic than those of other countries who don't introduce calculators or is the move based on uneducated guesses?

I can't say that I am particularly distressed about the proposed changes. Unless you are completely rooted in that fictional golden age of education, you would want children to be taught how to use anything that helps them to learn, to reason, to solve problems. That includes having good mental strategies and knowledge as well as knowing how to operate a calculator. In my school, calculator use is mainly for children to check the calculations they have already done or to work with real life situations where the numbers involved are so big that children would spend more of their time calculating than carrying out the problem solving learning objective.

I place great score though on children developing mental knowledge and strategies. Knowledge is their number bonds to ten and to twenty, their times tables up to 10 x 10 (not sure why 12 x 12 is still required when we no longer use dozens or have twelve pennies in a shilling.) Strategies are those that allow them to use that knowledge such as 3 + 4 = 7 to solve 30 + 40. If children have these then it frees up time and thinking to tackle the real maths. For instance, if we take two children learning how to multiply using the grid method where one knows their tables well whilst the other struggles, one will get far more practice as they solely have to deal with the new method whilst the other will often lose sight of the method as they struggle to work out each stage of the calculation.

I can't really see what difference taking the calculator away from the second SATs paper will have. There is already a mental maths paper accounting for 20% of the marks. The incentive for schools to develop mental maths is there already. As a KS2 maths SATs marker of many years, I have seen an improvement in scores over the years. What do the national results of the mental papers tell us about children's mental ability in year 6? Has someone done the maths?

The problem with mental maths is that, like all learning, it needs to be used on a regular basis. These days, how many times do we carry out mental calculations as opposed to the pre-computer age. The cash tills at the supermarket work out our change for us, the online internet shopping site adds up our orders. Let's show children how to use calculators and the other electronic ways of calculating, but lets keep that regular use of mental maths going through a child's education.
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Rebecca Hanson's picture
Sun, 11/11/2012 - 20:45

Are you suspecting that the roots of this move are not firmly based in evidence and a deeply grounded rationale Michael?

Indeed you are right.

This initiative is a Gibb/Truss masterpiece of hubris.
Each year I attend the ACME (Advisory Committee on Maths Education) conference.
In 2011 we had the delight of Liz Truss as a speaker. She prattled on spouting ignorant gibberish about the problems in maths education being all due to the lack of social mobility. The audience of about 150 people - typically highly experienced teachers who are also in senior positions (e.g. lecturing at masters level) in maths education generally switched off but I was on alert because I knew she was one of these dangerous people who, although deeply ignorant, can persuade even more ignorant Tories that they know what they're talking about. At the end of here speech I asked her if she could reassure the audience that ACME would be consulted regarding policy in maths education to which her answer was a very clear 'you lot are responsible for the terrible mess maths education is in.' Then the next year we got Nick Gibb who was even worse.

Here is the debate about calculators in education and my comments on that debate:

I hope the blog gives some of the context you are looking for. Please do feel free to post any further questions here.

To the points made in the blog I would point out that respected figures in the maths education community did feel that there was more work which could be done to SATS on ensuring questions where calculators were allowed more precisely tested the skills students are supposed to be developing when they are using calculators. They were keen to do that work but unfortunately the reforms in process were shut down by this government.

Michael Dix's picture
Sun, 11/11/2012 - 21:53

I read your blog and the links attached to it and found them very interesting. This is obviously an area in which you have much expertise. As a head trying to ensure all my children become confident and competent using maths, I have encouraged a three fold approach. The numeracy strategy, for all its constricting faults, did seek to teach children an understanding of the algorithms they need to use as opposed to the way I was taught it at school - taking away by borrowing and paying back. I rather suspect that ministers aren't really bothered about this because, no doubt, they were taught how to use algorithms without understanding why they were doing it. Therefore our children are taught to use a coherent set of algorithms in a logical way.

We then give them plenty of practice on acquiring the knowledge set that contains times table and number bonds so that they can concentrate on developing their skills and approaches to using the algorithms and applying them in problem solving. Our third approach is to try and contextualise their mathematics learning and to make it fun and enjoyable. This approach has seen a change in attitudes towards maths and an increase in confidence as well as a rise in attainment.

Michael Rosen, who also has much experience of meeting ministers, suspects that as they went to school and are now successful people that the way forward is for all children to have the same experiences as they did. I have long thought this, with policy made up on the hoof without any recourse to research.

Rebecca Hanson's picture
Sun, 11/11/2012 - 22:14

One thing the ministers completely misunderstand and misquote is the evidence from China and the Pacific Rim, Michael, of which the best source is LiPing Ma's book - Knowing and Teaching Elementary Mathematics.

It shows a more fundamental teaching of the structures of mathematics which underpin algorithms than we have here.
So for example when teaching division we would want children to be able to picture the splitting strategy, the chunking strategy and also to be deeply comfortable with the nature of the reciprocal (multiplying by 3 is the same as dividing by 1/3 and vice versa as a way of understanding the link between multiplication and division). When learning any algorithm for division it would built upon these structures rather than being taught as an end in itself.

Rather than being taught maths in context, students are required to reify everything - that is they have to come up with contexts for themselves. This is done effectively if students are seeing those visual structures which are underpinning the mathematics and is much more difficult if they are not. But doing it creates tensions and an environment in which the skills are more likely to be developed.

I have a four part blog on a simple teaching technique which helps teachers and students to begin to focus on structures which starts here which you might find interesting.

Unfortunately all the people who knew all this stuff seem to have been sacked and sidelined.

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