I love maths. I’m not ashamed to say it. I took maths and further maths at A-level and went on to spend three years doing a maths degree at Oxford before training as a primary school teacher. After ten years teaching, I have spent the past two years writing and implementing a new maths curriculum, running a peer coaching project in mathematics teaching, and teaching maths to groups of students at risk of underachievement.
So, you’d be forgiven for thinking that I might welcome Nicky Morgan’s new focus on primary maths teaching.Unfortunately not. When I first heard that every child will sit an externally-set, standardised times tables test at the end of primary school, my heart sank.
The entire policy is grounded in a basic confusion between the complex and intricate subject of mathematics and memorising lists of facts. Of course, the government doesn’t explicitly state that they are one and the same. While the Neanderthals from the Campaign for ‘Real’ Education may be calling for every child to memorise all their tables before they start school along with reciting hymns from memory, and declaring that understanding is irrelevant to education, Nicky Morgan hopefully (surely!) understands that there is more to maths than ‘knowing your tables’. However, when you introduce a high-stakes test of a very specific skill, you send a strong signal, to students and teachers, about what matters in the world of mathematics.
Now don’t get me wrong, I am not against children learning their times tables. Indeed, in my classroom, as in many others up and down the country, children work hard to learn times tables, division facts, additions and subtraction strategies and many other things. That is because they are useful tools for solving mathematical problems. But they are just that – tools. And we cannot substitute these tools for maths itself. Real maths is about proving that there are an infinite number of numbers between one and zero, it is about independently deriving the formula for the area of a triangle, it is about being able to add up your weekly shopping and work out if you have enough money in your account at the end of the month. It is not simply the memorising and regurgitation of facts, however useful those facts may be. By confusing the complexity and depth of mathematics with the ability to memorise lists of facts, we contribute to the misunderstanding and mystification of the subject.
Because it is based on a misunderstanding of mathematics, this test is likely to reinforce existing weaknesses in the education system. Successive reports into maths teaching in England have highlighted the same issue – maths is too often taught as a series of disconnected skills and techniques, with insufficient focus on students’ conceptual understanding. As the 2012 OFSTED report Mathematics: made to measure puts it, “too much teaching concentrates on the acquisition of disparate skills that enable pupils to pass tests and examinations, but do not equip them for the next stage of education, work and life.”
Of course, we cannot blame teachers for this. They teach within a framework; a framework which, with league tables, OFSTED and now performance-related pay, exerts more and more control over their professional lives. Unfortunately, that framework is driven by high-stakes testing which, as Finnish educator Pasi Sahlberg has so passionately argued, leads inevitably to low-risk strategies for learning. Too much teaching focuses on shallow learning for the test because teachers are assessed on whether their students pass tests, not the depth of their conceptual understanding.
This issue will only be made worse by more high-stakes testing of basic skills.
Worst of all though, is the impact this test will have on those students who struggle to learn their tables. I know because I was one of them. You see, I haven’t always loved maths. At primary school, I struggled with times tables. Rote learning did not work for me and, no matter how many times I repeated my tables, no matter how many times I was tested or made to recite them, they wouldn’t go in. As I fell further and further behind my peers, I became convinced I couldn’t ‘do’ maths.
Fortunately, I had teachers who encouraged me, who taught me to find creative ways to solve problems. Those teachers showed me that there was much more to mathematics than learning (or not learning) times tables and, bit by bit, they developed in me a real love of the subject.
In the long run, that proved much more important than my inability to remember my times tables. These days, my mental maths is pretty good. I use a range of strategies to work out complex calculations and can usually beat a calculator. But I would still struggle to recite my twelve times table – and I’m no worse off for it.
This policy amounts to a dumbing down of mathematics. Quite the opposite of the stated aim of the primary maths curriculum – to give students the opportunity to experience “the beauty and power of mathematics.”
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