Mathematics education uncovered and recovered

Calculators are not allowed

My son sat the Key Stage 2 tests this year. It was the second run of the tests based on the new primary curriculum. In mathematics, two “reasoning“ papers and an “arithmetic” paper replaced two written general mathematics papers (one allowed use of a calculator, the other did not) and a mental mathematics test.

The changes were largely driven by the intention to eradicate calculators from primary schools, promoted by Liz Truss, a Conservative MP who later became the education and childcare minister. Eager to leave her mark on maths education policy, she spoke about the harm of calculators, insisting that because children in Singapore don’t use calculators, children in England shouldn’t use them either.

The calculator ban in maths tests for 11-year-olds has been challenged by respected  academics, but, as it often happens, the ministers keep ignoring the opinion of the experts.

Trying to trace this significant change back to its origin, I have come across a speech that Ms Truss made  in Parliament in November 2011. Since her amateurish claims laid the foundation to the calculator ban, it would be interesting to analyse some of her statements in detail.

We need to look at teaching standards, the curriculum and pupil motivation, but we can say—and there is significant academic evidence for this—that calculator use too early has a negative impact on mathematical ability

Indeed, inappropriate use of anything can have a negative impact.

Having observed eight-year-olds being taught multiplication on calculators in an English classroom before they have fully grasped and practised key mathematical operations, I am concerned that things are going on in our schools as a result of Government policy about which we need to be mindful and careful

I do not understand what exactly “being taught multiplication … before they have fully grasped and practised key mathematical operations” means. Multiplication IS a key mathematical operation and sometimes it is a good idea to teach multiplication using a calculator.

A calculator helps to test whether students understand the concept of multiplication and the context in which it should be used. In early stages of learning about multiplication, children can only perform very simple calculations, so the questions they face involve only small numbers. For example, the question could be “How many books are there on 3 shelves with 4 books on each shelf?”. Giving the correct answer does not mean that a child understands and uses multiplication, since they could just quickly add 4+4+4.

Working with small numbers makes multiplication redundant, so it is reasonable to demonstrate the use of multiplication in large numbers, and that is when calculators could help. If children are allowed to use calculators, the right answer to the question “How many books are there on 28 shelves with 17 books on each shelf?” does mean the correct application of multiplication. Then one can be sure that they understand the concept before moving on to routine memorising of their times tables.

Most teachers would consider that consolidating skills at the age of seven or eight in division, multiplication and fractions, and introducing proper, formal methods that can be used for a lifetime, are important in preparing students for life.

I hope most teachers would not consider work on formal methods a high priority for children aged seven or eight.

Many of my constituents report that too-easy access to calculators is available in local schools.

Do they, really?

What is in the national curriculum? For seven to 11-year-olds—key stage 2—there is a separate section in the national curriculum on calculator methods… Not only are calculator methods set out in the curriculum and encouraged as part of what older primary schoolchildren learn, but they are tested at 11.

There is nothing wrong with that. A calculator is a helpful tool, it needs to be used appropriately, and the ability to use this tool should be taught and tested.

However, many questions in the test for 11-year-olds do not require a calculator to answer them.

True, having a tool does not mean that you must use it, but students need to make a decision whether to use a calculator or not, and this is also a skill that is being tested.

I have a sample question from the “calculator allowed” test in mathematics for 2010:

“These are some prices in a flower shop. Tulips: £1.20 for a bunch; roses: 40p each; daffodils, 55p for a bunch. How many roses can you buy for exactly £2?”

Most Members in the Chamber would be able to work that out without using a calculator.

Don’t worry, Ms Truss, most children would, too. And those who couldn’t answer without a calculator, need to know how to enter amounts of money and how to interpret answers like 1.3, which is also a skill that children should acquire.

That kind of question should encourage thinking and mental arithmetic but, unfortunately, in the tests at the moment, students are asked to use a calculator for basic sums.

No, they are not asked to, they are offered a choice.

We should also consider the provision of calculators in the SATs tests. I know that there are questions about the overall standards in the SATs. I also know that the Minister is considering them and that he is keen to see more formal methods applied in the curriculum so that pupils learn proper long multiplication and long division.

Yes, that is what the children now spend their time on: “proper” long multiplication and long division, those dry, time-worn and dusty methods killing any thought. Useless, in fact, because, like it or not, calculators are here to stay, and no adult in their right mind would use long division when a calculator is always at hand nowadays.

Over the course of her speech, Ms Truss praised mental methods a few times, but as a result of the reform she inspired, the mental maths test disappeared from Key Stage 2 tests without any explanation. Prominent in the new curriculum and the SATs are long multiplication and division, the methods that have little to do with mental skills and developing mathematical ability.

I find it incredible that people without any serious knowledge of teaching, who ignore the opinions of academics and don’t listen to teachers, are allowed to make crucial decisions concerning children’s education. However, it’s a reality that we and our children have to live in.

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