# Why does 1 + 1 make 2?

15th June 2012, 1:00am

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Why does 1 + 1 make 2?

https://www.tes.com/magazine/archive/why-does-1-1-make-2

A new report, commissioned by Ofsted, has stated that maths isn’t taught very well. Although children might be able to calculate the answer to a problem, too many of them merely know the method of reaching the right answer, rather than the reasoning behind it.

It’s a situation that caused me problems in my first year of teaching, with a class of Year 3s. They needed to learn the basics of addition and subtraction. Addition was fine, but subtraction was tricky once you started carrying tens and units. 24 take away 18? Right, children, units first. You can’t take 8 from 4, so you “borrow” a 10. Pop it up by the 4, which becomes 14. Take 8 from 14, leaving 6 and put that in your units answer column. Now you must pay back that 10, so put a 1 down by the 1 that’s already there, making that ... no Celia, not 11, but 2. Take 2 from 2, leaving nothing on the tens side, so the answer is 6. No wonder my seven-year-olds stared at me open-mouthed. Why do you have to borrow a 10 if you’re paying it back straight away? And once you got into hundreds, tens and units ... well, I could understand where they were coming from.

Even in those days, the pressure was on, and if you spent lots of time making sure your children had a thorough understanding of subtraction, it wouldn’t leave enough time to learn about the Romans, where Australia was and why the sky looks blue. Don’t worry, said my headteacher, so long as the children get the right answer, it doesn’t matter if they don’t understand how they got it. I spent many weekends making lots of coloured blocks and counters, similar to the Dienes apparatus and Cuisenaire rods that were starting to appear, but which my school couldn’t afford.

Understanding what you’re doing in maths is vital. Algebra was ruined for me the moment I joined secondary school. The teacher threw a set of inscrutable textbooks at us, talked his way through the first three chapters, and then set lots of homework. I couldn’t do it. Nor could my parents. Fortunately, the local Scout troop chaplain was a maths whizz, so he did it for me, but that just led me into deeper water. It wasn’t until I met my kindly Welsh PE teacher in Year 10, who also taught maths, that I began to vaguely understand what it was all about.

When the 1967 Plowden report revolutionised primary education, the emphasis was on practical maths. Children could spend more time exploring the reasoning behind the subject. They’d measure distance with trundle wheels, use sand and water for measuring capacity and quantity, undertake traffic surveys and create colourful graphs, before being led, hopefully, to the most expedient calculation methods by a skilful teacher. “Practical maths” created its own problems, though. Secondary schools complained that many 11-year-olds were great with a bucket and spade, but struggled with calculations in an exercise book.

Now, we seem to have returned to the idea that the answer is everything, and understanding how you get it doesn’t matter. Passing the test is all. During a news item, the interviewer asked the report compiler why children needed to learn the mechanics, since calculation is done by machines these days. Well, somebody has to understand it, or we couldn’t build the machines, she said.

Fair point. And even better if lots of children understand it.

Mike Kent is a retired primary school headteacher. Email: mikejkent@aol.com.

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