“….but now they have got that they won’t use anything else!”
3 December 2017
Author: Mari Palmer
On Friday 3rd November the EEF released its latest guidance report: Improving Maths in Key Stage 2 and 3. This meta-analysis has produced a clearly written and highly focussed set of guidelines that point the reader towards the elements of teaching that could have the greatest impact on children’s development.
In this blog we will examine comparing and selecting methods – taken from
Strand 3 of the report: Teach them to use and compare different approaches and
Strand 4: Teach pupils to consciously choose between mathematical strategies
If we are completely honest this is one part of the Maths Guidance Report that, when we read it, we felt we needed to refocus on.
We, as I am sure many other teachers do, spend not a small amount of time bemoaning children who, once they are taught a method they are comfortable with, then use the same method for every single calculation – even if it would be far simpler and easier to use an alternative. This is most typically evident after teaching vertical subtraction and addition but can be found across children’s work.
We feel very confident that we teach the children to use a variety of methods and discuss these in nearly every lesson. We have spent a long time working with the children so that they understand there is more than one way to solve a problem and we then regularly compare these. Currently we do this in the sense of considering that different pupils have used different approaches, that these may well all give us the ‘correct’ answer and that if we can use more than one method ourselves we can be surer that our answer is right. In addition by using more than one method the children are beginning to show that they are moving towards a mastery of a level of calculation as they can recognise and use the skills in different situations.
However, when recently asking students which was the most suitable method for a particular calculations the children were not as articulate as we would hope.
Examples include the following:
Year 4 child (after giving several examples of methods for 7351 + 2462 =):
“I think the best way to do it would be to do column addition and then column take away to check. If it was 5 + 6 I would still do it this way to check.”
Year 6 child (when asked what would be the best method for the same problem as above, again after being able to write many different examples of approaches) said:
“Doing it in my head is my favourite as it requires no paper so no cost – I am a businessman! If it was more than 10 000 000 I would use paper.”
Both of these children were able to use many methods, able to use inverse operations to prove their calculations were correct and draw parallels between the different approaches. However when asked to assess which would be the most effective they were unable to articulate this through a well thought out process of reasoning.
The picture was similar in the younger age groups.
When asked how they would calculate 6 + 5 one child was able to say:
“ I could have 6 in my head and count on 5 on my fingers….
(or) I could do 7 + 4 as I know 7 is 1 more than 6 and 4 is 1 less than 5 so they would make the same – you could do that with 8 and 3 like that to.
You couldn’t do it with doubles because it is odd (but) I could make up ‘an add’ with the counters.”
All of these would be very successful methods and show a deep understanding of the concept of addition and also could be used as a form of description, evidence and proof.
However, when asked which of these methods was the best, she replied (with much enthusiasm):
“I think the best way to do it would be 6 + 3 + 2 – I would do it this way as I like 3 numbers – it is my favourite sort of adding!”
Despite the obvious delight in being able to add three numbers (which to this age child was proof to them that they were being very successful!) there was no logical reason as to why this would be the most efficient or simple method for achieving an answer.
We have therefore decided that if we are going to expect the children to select the most appropriate method for a particular problem we need to spend more time modelling this for the children, letting them work in small groups to discuss this and then evaluating their choices. We would also like to work with the children on using STEM sentences and expanding their vocabulary in order to enable them to be able to express their reasoning when they have learnt how to recognise them most efficient method.
This will then be a step forward from the point we have currently reached.
I had a first experiment with using STEM sentences to express preferences this week and one child produced this (though not entirely sure about the explanation of the method!):
The text in the bottom left says:
“My method is easier because it is more simple because there are less stages.”
We will let you know how we get on as we develop this further!Posted on 3 December 2017
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