Sorry for the late entry of this month’s blog, it has been a particularly busy few weeks down at the Primary with many exciting trips taking place! This month’s focus in maths has been on the use of concrete resources to support understanding.

This focus on concrete resources is something that stems from the CPA approach to maths (devised by Jerome Bruner) – the belief that children, and indeed some adults, can find maths a struggle because it can be quite abstract in nature. The CPA approach suggests children should first be taught maths in a concrete way, which is the hands-on, ‘doing’ stage of the process. Objects and resources are used to bring maths to life and give the children a concrete base for each new concept. The second stage is pictorial, and is thought of as the ‘seeing’ phase. Instead of using actual objects, children use representations of them to help solve problems. Drawings and pictorial representations are used to bridge the gap between physical objects and abstract problems. The final stage of the process is the abstract phase, also known as the ‘symbolic’ phase. By this point the idea is that children should have had enough hands on experience of manipulating objects, and then of using drawings and pictures to represent these objects, that they are now able to access the maths at an abstract level. Here children use numbers and mathematical symbols to represent their maths.

In Year 1, we have been using the CPA approach this week to help with word problems. First we began observing ‘maths in action’ and talking about what was happening, for example someone having 9 pens and giving 4 to another person. We focused on the numbers in the story and began applying language like ‘adding’ or ‘subtracting’ straight away so that we could ‘see’ the maths. Nothing was written down at this point though, it all involved concrete objects and real people. It was then time for the children to practise solving word problems on their own, using cubes to support them. They began by finding the key information in the number sentence and circling the numbers themselves, before deciding what the number story required them to do (either add two sets of cubes together or take some away from a set). It really helped the children visualise the maths in the problem, and they were very good at imaging the cubes were dogs, strawberries or even monkeys!

Some children even managed to write their own number stories, with the cubes and real-world objects having helped them build a secure understanding of this concept. Below you can see the word problem one of our lower-ability children created – ‘(Child’s name) have ten Spidermen and my friend takes six off me’. He was then able to assign an abstract number sentence to it, showing a really deep understanding.

Concrete resources have also been used in a variety of other ways across school:

· Using each other as resources to gain an understanding of position!

· Using counters and 10 frames to match written numbers to values

· We even used each other to represent tens and ones, standing as tall soldiers to represent a stick of 10 and curling up small to represent a one!

Next month’s focus will be on the next stage of the process, the pictorial stage of maths. We will be particularly focusing on use of the Bar Model as a way of representing maths.

Krissie

This month at the Primary we have been focusing on challenge in maths, using it to both deepen the learning and stretch the more-able pupils. I delivered some training before Christmas that split challenge in maths into 4 main areas: ‘Prove it’, ‘Teach it’, ‘Spot it’ and ‘Predict it’. This has helped staff focus their daily challenge on a skill, ability or concept that links well with that particular lesson. Below are some examples from across the year groups that we are proud to show off!

EYFS

 In EYFS a lot of the challenge is through conversations with the children that encourage them to think deeper or apply their learning. This forms excellent building blocks for the move into Year 1 when the children can then capture these sorts of ideas themselves. In the example below the child had been learning about time, and through conversation with the teacher was able to apply this to their daily routine at home as well as showing understanding of how to read the time too.

Year 1

In Year 1 we have been experimenting with each of the 4 areas of challenge to see what sorts of questions we can think of and how well the children respond to these. We have been particularly enjoying using ‘Spot it’ and ‘Predict it’ challenges, encouraging the children to make their maths quicker and easier by looking for patterns and using these to predict other answers. In the first example below, the child was asked to spot the pattern and use it to predict the next answers. He has then written his observations: ‘It is the 2 times table and so the answer goes up by 2 more every time’. In the second example, a different child had been set an ‘Teach it’ challenge where he had to explain his reasoning for solving a problem in his chosen way. The child has responded ‘I will do the biggest number first because it will be easier’. It gave great insight into how he is approaching problems and showing, even at 6, he is able to think about how to make his maths more efficient!

Year 2

 In Year 2 the focus has been on challenging the children to draw out maths from number stories as opposed to just formal number sentences. In the example below, the children had been adding 3 one-digit numbers and so were encouraged to find the ‘hidden’ number sentence in the written problem. Their further challenge was then to deepen their understanding by writing their own number story for a similar problem.

  

Year 3

 Year 3 have also been making good use of number stories in their challenge, encouraging the children to apply their learning and show a deeper level of understanding by being able to put it in context. They have also been trying out the ‘Teach it’ challenge area, being encouraged to explain the way they have approached a problem and why. In the below example the child explains she ‘counted in threes’ to get the right answer, giving insight into how she is applying her understanding of times tables to multiplication.

Next month we will be focusing on the use of concrete resources in maths, as part of the CPA approach from Singapore Maths.

Krissie

A big thank you to Krissie for her first contribution to our Primary bulletin, especially at this very busy time – even busier than usual for this time of year as our Primary colleagues are moving into their new building for the start of the new term. It’s all very exciting. I can’t wait to come and visit! ~ Matilde

I’ve been collecting pictures and information from staff about what their children have been up to in Maths over the past few weeks:

EYFS

In EYFS, the theme this half-term has been Traditional Tales. The children have been carrying out measuring and practising writing by making recipes for Goldilocks and measuring how much their beanstalks have grown each day. They also began matching numbers to quantity by giving Cinderella the right amount of jewels on her slipper. It has been so much fun the children barely realised they were learning!

Year 1

Over the past few weeks Year 1 have been focusing on the numbers to 20. We began by writing them in numerals and in words, and then using the language of ‘more than’ and ‘less than’ to compare them. We moved on to adding numbers within 20, applying what we had learnt to solve Christmas-themed problems. Over the few weeks we used lots of practical resources, as encouraged by the Singapore Maths style, to help us visualise the numbers.

Year 2

In Year 2 the children have had a few weeks working on their subtraction skills. They have been using practical resources to support a variety of methods helping them subtract one- and two-digit numbers within 100. I can’t believe how far they have already come since Year 1, keep it up Year 2!

Year 3

In Year 3 they have been focusing on number and place value. The children have been counting, comparing and ordering numbers up to 1,000, as well as adding and subtracting three-digit numbers using a range of strategies. These included bar modelling, number lines and the column method. The bar model is new to the Year 3s but they are getting their heads round it quicker than some of us grown-ups!

 

 

Moving forward we will choose a theme each month so we can focus on different areas of practice across the school.

Have a lovely Christmas break,

Krissie

The teachers and children at Bluecoat Primary love their Maths lessons.  Over the past year, the teachers there have been developing the use of the Maths No Problem schemes which is based on the Singapore model for teaching mathematics.

The links below explain about the Maths No Problem approach:

• What is Singapore Maths?
• Teaching Maths for Mastery
• Why Use the Singapore Approach?
• The Bar Model Method
• Concrete>Pictorial>Abstract
• Number Bonds

To get a feel for what this looks like in real life, Krissie Dickens, the Maths Lead  will be writing regular updates for this site.

Hopefully everyone will benefit from seeing the fantastic work that is going on from Foundation Stage up to Year 3.