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So, you are thinking of introducing bar models to your school? It’s an exciting feeling. We know as we’ve spoken to and supported many schools in implementing a whole-school bar modelling approach all over England.
But while it is an exciting time, there are a few things to consider before implementing the approach, and a few more points to cover while your teachers are formally introducing bar models to pupils in your school.
As we visit more and more schools trying to introduce the bar modelling approach in their settings, we can see that many are making a number of mistakes, so after the initial excitement and eagerness to reveal a fantastic strategy to their staff and children, it can quickly feel like an uphill task.
So, what are these mistakes, and how do you get past them?
Not fully using the CPA approach is the first major mistake when introducing bar models.
Why does this happen? Well, you may have seen bar models on our website and in books, but that may mean you’ve only seen them as pictorial representations.
When introducing bar models to your pupils it’s imperative that the teachers follow Jerome Bruner’s Concrete Pictorial Abstract (CPA) approach.
This means that it’s important for teachers and children to use concrete materials for bars when attempting to use this strategy to solve problems.
There are more commercial products available recently, which has meant some teachers using the bar model approach are also using concrete materials when modelling some questions, but are they doing it consistently?
Ask yourself: Are your teachers consistently using concrete materials? Are you letting your pupils use concrete materials? How can you consistently use concrete materials? When should you let your pupils move to pictorial representations? Is there a transition technique that allows my pupils to smoothly and accurately understand and draw bar models?
If your school doesn’t use the CPA approach consistently then what is likely to happen is that your pupils will not understand the key elements of the bar model approach and they will not be able to generalise, and therefore master, the approach.
We always aim for consistency in what we say and do in our schools, but when it comes to bar models we’ve seen many schools forget about consistency. Why? Well, we think it’s mainly because bar models all look the same – like bars, right?
So as long as my teachers are drawing bars it should all be consistent, surely? Wrong!
So what do we mean by consistency? Have a look at the picture below.
It shows different solutions in a seminar with a group of delegates from over 10 schools.
They came up with various different ways to draw the Singapore model solution for one questions. The actual question was a very simple subtraction question yet even for one of the most simple model questions we had various different solutions offered to us, and this happens in every training session we deliver.
Should we allow the teachers to draw them how they think is best? Is that a good whole school approach? Is there a problem with allowing teachers that freedom? What should we do?
A consistent approach will always result in a more efficient use of bar models throughout the school and lead to fewer pupils being confused and fewer mistakes from both teachers and pupils.
So is there a need to be consistent but what is the best approach from the above pictures? Is there a better option than the ones the teachers have suggested above? What would the National Institute of Education subscribe in Singapore? Are we training the teachers in the same way? Is there room for flexibility, if so what would that look like? All points for us to consider before we start to introduce bar models to our school.
In many schools, there is a lack of focus on the two core bar models. The Part-Whole and the Comparison models are the two core models and at upper KS2 level, where many schools are using Singapore Maths textbooks, teachers have jumped into the top end of the model questions even though the schemes are relying on pupils having experience in using the model in the previous years of primary education. As pupils don’t have this experience many are not too sure about bar models as we’ve forgotten to go through the basic concept of part-whole and comparison models. Even within these models, there are core foundations which have to be carefully taught through high-end questioning and visual modelling to get the most out of the model approach.
An example of a part-whole model
Before formal approaches to bar modelling kick in around Year 2, many schools are not sure how to support EY and year 1 teachers. In fact a common gripe amongst EY teachers is that they feel left out in almost every CPD in which their school invests.
This is why we developed the ten-frames training, which has supported hundreds of EY and Year 1 teachers all across England.
The use of ten-frames and number bond diagrams (also known as part-whole diagrams) are prerequisite of bar modelling, yet many schools jump into teaching bar modelling without this foundation.
The use of games such as the trump cards (below) is also a very useful and engaging way of using bar models at a young age. In fact the use of the model in the trump cards is very subtle as it just feels like playing a game.
When things are not going well in a lesson using bar models, many pupils and teachers start blaming the model approach for the failure to solve a question. In many of these incidents, it is the failure to understand basic models and also choose the appropriate model.
When do we use the part-whole model? Should I use the comparison model? How do I know which one to use?
This is the first issue many pupils will face, but let’s say we get over that issue. With some questions, pupils may not be able to solve them because they can’t visualise the world problem.
In other cases, they won’t be able to do the maths to solve the questions (but this should be very few pupils, as with most questions you will only need to be able to confidently use the four operations).
So how do we overcome the first problem, as the second problem (not being able to add, subtract, multiply and or divide) should be covered before pupils look at such word problems?
This is two-fold – from a teacher’s point of view, and also from a pupil’s. In both cases, we lack experience.
Many schools jump in to the textbooks without thinking about the lack of experience children have in using the model approach. But equally as devastating, in some schools, is the lack of experience teachers have, and the fact that they feel they have been flung in to the high-end bar model questions, meaning they sink rather than swim.
How can we prepare pupils for the high-end questions before we get to those chapters? How do we allow our teachers to build their own confidence, or shall we just let them dive in whenever they come to a chapter on bar models?
We know from the research done by Zoltan Dienes and Jerome Bruner, that using the CPA approach (Bruner) and constructively-active learning (Dienes) is an effective way of teaching.
What Zoltan Dienes goes on to say is that the mere use of concrete materials is not enough, that our questioning and modelling has to be strong. So, can we question the children to edge their thinking forward so that by the end of a question they feel they are the ones that solved the problem? Or are we just giving too much away, so that when we do let go our pupils still seem lost, and like they are not making as much progress?
We’ve briefly mentioned in one of the above points about the importance of being engaging, but as bar modelling is something very new, it may be a tricky ask for some teachers to maintain.
One way is to use animated videos like the ones we’ve created to engage your pupils and make bar modelling less daunting and much more accessible to all your pupils.
Click here to view one of the Bar Model Company’s Singapore maths videos on Vimeo.
Mohi Uddin Ahmed is a Singapore maths consultant and trainer for The Bar Model Company.
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