Part of my learning process as I go round on my school visits is the impact of Maths Recovery of the teaching of maths in our primary schools.
Keen to find out more I asked Mhairi (proncounced Vhairi) Stratton of Humbie primary School to come into the office yesterday to give me a greater insight into what it’s all about.
What followed was one of the most exciting conversations I’ve had about teaching for some time. What I like about the Maths Recovery Programme is that it’s based upon a developmental approach to the teaching and learning process. Here’s what Dr Penny Munn has to say about this:
According to teachers who have studied developmental psychology – usually in the context of continuing professional development (CPD) in early years education – the following features characterise teachers who take a ‘developmental’ approach to teaching in general:
• They start where the children are, not where the textbook thinks the children should be.
• They take account of the way the children learn. Sometimes this is a matter of looking at the child’s developmental level. Sometimes it’s a matter of looking at a child’s individual learning style.
• They develop an active role for the children’s learning, because they know that active involvement in learning will engage young children’s cognitive processes.
• They use settings that will engage with children’s ideas of themselves, and that will motivate them to become independent learners. They decide on their settings by carefully watching for children’s preferences and self-identification.
I love this – particularly the notion of starting where people are – which is also a characteristic if our Grounded Strategy approach.
Teachers who take this kind of approach say that it helps them to be better teachers in the following ways:
• It produces greater depth of observation, which in turn gives a more informed response that facilitates reflection.
• It stops them jumping into a teaching situation too quickly, and gives them a framework for problem solving on children’s difficulties.
• It produces more powerful planning, especially of the long-term variety.
Mhairi went on to explain some of the techniques of Maths Recovery which build upon this developmental approach. Here are just a few:
Finger patterns – children should use their fingres – it helps them to generate their own strategies
Spatial patterns – I learned a new word here – “subitizing” which is about recognising number patterns such as those on a dice. – this a powerful and important stage in understanding number
Screening – this is where the teacher perhaps has four items and three other items each group of different coolours – the teacher then screens or covers the four items and asks the children to put the “number in their heads” – then cover up the three – in this way the children start to add numbers in their head – without even being aware of what they are doing.
Forward number WORD sequence – don’t confuse this with counting which is usually done from the number one – start from different places. The teacher starts to realise how complex addition -is for children.
Backward number WORD sequence – just as important as forward number word sequence – children need to able to do this at the same as they start forward sequencing – don’t leave it too late
Numeral sequencing – which is relating number word seqencing to numerals, e.g.
1 2 3 4 5 — 5 4 3 2 1- children start to sequence with cards – then take away a number and get them to fill in the gap
Multiplication – in Primary 1 – Mhairi told me about P1 children in Longniddry who can do 4 x 3 mulitiplication.
Help them first to understand what 4 x 3 looks like – four discs with three spots on each – turn over the 4 discs – cover the four discs with a card – “under this card I have four discs each with three spots” – it’s a short step from here to getb the children to work out how many spots there are in total – all withouth seeing the spots
Division – is all about grouping and sharing – I’d never thought about division as being linked to sharing but if I have so many chips and I need to share them equally onto so may plates it becomes quite obvious.
We are investing in training 25 teachers in east lothian in this approach but what I found even more relevant to what it is we are trying to do on an authority basis is the developmental approach which can traslate to any teaching situation – regardless of subject.
I would like to point out that in the example given screening is used instead of teaching the trick “put the number in your head”. By screening the first amount the teacher can guide the child towards a count-on strategy based on real understanding (they learn in their own time that they don’t need to count the first amount for themselves) and not by teaching a trick like “put the first number in your head.”
This of course is only one example of screening. Screening can be used in a variety of ways to guide children from the concrete to the abstract through understanding the reality of number.
Mhairi, Where can I find out more about the screening you talk about here? A colleague mentioned recently the “put the first number in your head” thing and I used it with great success with a couple of P4s. When they want to retrieve the number you can see their eyes going up to where they touched their heads when they “put it in”, and sometimes their hand even goes up as well. It’s very effective. But I didn’t realise it was part of a more structured approach. Can you give me some refs please?
The problem with teaching children to “put a number in your head” is that there is no underpinning understanding required. Although it may appear effective to begin with this can be problematic when children are presented with new problems. If they do not understand what they are doing they are not likely to relate this understanding to different settings. Screening allows children to understand counting-on strategies for themselves and therefore they are far more likely to apply/adapt this skill to different settings/problems.
There are several Maths Recovery Books that go into this in detail but most are course books and difficult to read . A more reader-friendly book is “Teaching Number in the Classroom with 4-8 year olds” ISBN 1412907586.
In East Lothian we are introducing MR Tracker which is basic training in Maths Recovery Techniques. This is a good starting point to understanding the potential of screening tasks. Training in Maths Recovery is highly recommended!
Thanks for this Mhairi. I hope I didn’t misrepresent our conversation too much?
Thanks Mhairi. That’s very useful. I’ll follow it up after parents nights and PLPs next week.
Hadn’t realised until it was pointed out to me today that I had referred to myself as Mrs Stratton. It is unlike me to be so formal. Mhairi will do fine!
Hi, delighted you have picked up the fantastic potential of Maths Recovery to our pupil’s learning in maths. Dorothy’s comment was an interesting one as it pinpointed a crucial aspect of Maths Recovery.
The child who is being taught to put a number in their head and count on ‘appears’ to be counting on but in reality has no abstract concept of that number they still have it as part of a number sequence. It is only when a child moves on from this through the teaching and devlopment Mhairi describes that they can be judged to be truly counting on. If this aspect of a child’s number development is not recognised then the child and the teacher will struggle to develop more complex strategies and many children go through their school lives still only being able to count by ones because the numbers they are using only make sense to them within a number sequence. Developing a part whole concept of numbers becomes a rote learning task and children struggle and so do teachers.
I’m in my first term at Strathclyde Uni and working through the first Module (Looking forward to meeting you in a couple of weeks, Jane) I am absolutely hooked already – the problem is I think of all the children I have met but didn’t know hod to get to the route of the problem. We are training four teachers in Angus this session, but I’m sure it will be rolled out in the coming terms.