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Monday, 6 October 2014

Teaching Maths the Singapore Way


September 2014 saw the launch of a new National Curriculum with lots of changes. The new maths curriculum was perhaps one of the most controversial:

'New national curriculum to introduce fractions to five-year-olds' The Guardian July 2014

'Is the proposed new national curriculum too much too soon?' The Guardian 1st April 2013

Despite the initial furore teachers all over the country are now getting on with the business of delivering the new curriculum which aims to ensure all pupils žbecome fluent in the fundamentals of mathematics so that they are:
  • efficient in using and selecting the appropriate written algorithms and mental methods, underpinned by mathematical concepts  
  • can solve problems by applying their mathematics to a variety of problems with increasing sophistication, including in unfamiliar contexts and to model real-life scenarios   
  • can reason mathematically by following a line of enquiry and develop and present a justification, argument or proof using mathematical language.
We have to ensure that we are catering for the needs of every child in our class/group. Merely repeating the same instruction ten times does not work for some children. They need to be able to understand the process rather than just rattle off facts. Only then will they have a real grasp of the number system and be able to apply that to a range of problem solving activities. 

The expectation is that the majority of pupils will move through the programmes of study at broadly the same pace. However, decisions about when to progress should always be based on the security of pupils’ understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content. Those who are not sufficiently fluent with earlier material should consolidate their understanding, including through additional practice, before moving on.

But how can this be achieved when there are still pupils who find maths a challenge, they just don't get it! And others find it a chore? How do we raise the bar in terms of competency and engagement?

Findings from Ofsted 2011 provides some clues:
  • Practical, hands-on experiences of using, comparing and calculating with numbers and quantities … are of crucial importance in establishing the best mathematical start …
  • Understanding of place value, fluency in mental methods, and good recall of number facts … are considered by the schools to be essential precursors for learning traditional vertical algorithms (methods)
  • Subtraction is generally introduced alongside its inverse operation, addition, and division alongside its inverse, multiplication
  • High-quality teaching secures pupils 'understanding of structure and relationships in number … 
The Singapore Method may provide some answers. The Singapore method of teaching mathematics develops pupils' mathematical ability and confidence without having to resort to memorising procedures to pass tests - making mathematics more engaging and interesting. It follows and is based upon the CPA (Concrete Pictorial and Abstract model.)
 
 

Concrete - Using solid, hands on resources to help with the understanding of maths/
It is important to use practical resources to ensure children understand the process of calculations, such as making a number ten times bigger or increasing a number by 12 means we now have 12 more of something, rather than maths just being an abstract activity that ‘we just do’
 

Pictorial -  Using diagrams and images to represent numbers and symbols.  Here, children move away from physical, hands on objects and instead use pictures for demonstrations and also recording. 


ž 
Abstract - Moving onto the use of numbers and symbols in a conventional written method. 
 
 
The CPA model is nothing new to Early years and KS1 however where through the guise of continuous provision it has provided pupils with real life experiences of maths. However, I believe it can improve and enhanve the teaching and learning of maths into KS2 and beyond.
 
There is a new Maths Curriculum that we are all beginning to implement. So it is a perfect time to try the CPA approach to teaching maths, starting now! Start by using the main principal of providing the children with the concrete and pictorial before the abstract then if that's successful try the Bar Method. But  that's a whole new blog post!