Place Value – The Foundations of Mathematical Understanding

As the summer holidays draw to a close, primary teachers across the UK will turn their thoughts towards planning the first unit of work for their new class.  For many teachers, this will be a unit of work on place value – but how effectively will it be taught?  Ofsted’s recent report (Mathematics – Made to Measure – states that children who are working below age related expectations at the end of Key Stage 1 often have misconceptions around place value, which can linger throughout their time in Key Stage 2.

Too often, the first piece of work in children’s maths books is a list of partitioned numbers.  Repetitive.  Shallow.  All correct. Effective teaching requires skilled task design that reveals information about the child’s understanding.  Of course, children need to be explicitly taught how to partition numbers.  They need to practise it.  They need to be taught to read and write numbers.  They need to practise that too.  Some children will need to spend more time practising than others.  It is at this point that some teachers move on to the next unit citing one of two reasons:

  • The children understand place value.  Time to move on.
  • I have so much to cover that if I don’t move on now I’ll never get to probability!

But this is the crucial point of a unit work.  What’s the point of place value?  To calculate?  To order and round numbers? Or simply to appreciate the patterns and intrigue that numbers possess?   The teacher must delve deeper into children’s understanding by creating tasks that require, reasoning, explanation and the forging of links between different areas of mathematics. The repetitive, partitioning stuff can be done quickly, on whiteboards for many children.  They will get it.  Teaching children to reason along with tasks that require explanation sheds further light upon misconceptions as opposed to shallow tasks where misconceptions can lurk unspotted, ready to undermine most future maths learning.

So let’s have explanations; photos of children playing mathematical games; evidence of application of place value in calculating; and open ended problem solving instead of example after example of partitioned numbers on those first few pristine pages of maths books.


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