The power of bar modelling

I am delighted to have completed the Train the Trainer course from White Rose Maths Hub. It's incredibly exciting; I can now share this fantastic training. The blog is an attempt to show what a powerful tool it is.

Bar modelling does two things:

1) Provides a pictorial support for understanding mathematics
2) It gives a scaffold for children to access problem solving

This problem is often categorised as trial and improvement. We choose a number for day 1. Then work from there. Quickly realising that the number has to be less that eighty. Quite significantly less than 80 as day 1 and 2 are two numbers quite close together. Eventually, through trial and improvement we will find an answer. This a year 3 or 4 problem.

How does Bar Modelling support problem solving?

1) A starting point. The model helps me understand the structure of the problem identify knowns and unknowns.

2) What's changing? Day 2 has 4 fewer castles than day 1. While day 3 has 4 fewer castles than day 2 but also 2 lots of 4 fewer than day 1.  Day 4 will have 4 fewer than day 3 but 2 groups of 4 fewer than day 2 and 3 group of 4 fewer than day. Here, the image supports the more abstract explanation.

3) 5 bars of equal length! I can use my multiplicative reasoning. N divided by 5 gives the length of each bar.

4) I am making progress, but have I answered my question? The question marks in the model help students to check they have completed the question.

I believe that the power of bar modelling lies in helping highlight the structure of problems. It helps children to identify patterns and use what they already know. The incredible @mrnickhart has written some excellent articles on this and the inadequate use of RUCSAC. Now I realise how accessible, simple and empowering bar modelling is I cringe at memories of my former (non-bar modelling) self pointing at the RUCSAC display. As Dylan William says, "This job you’re doing is so hard that one lifetime isn’t enough to master it. So every single one of you needs to accept the commitment to carry on improving our practice until we retire or die. That is the deal.”

Nick Gibb: building a renaissance in mathematics teaching. But what about the foundations?

In 2016, Nick Gibb stated that:

In countries such as Korea and Singapore, and cities such as Hong Kong and Shanghai, the percentage of low-performing 15-year-olds is below 10%. There is nothing different about children in these countries, but there is something different about their approach to teaching maths.


Pisa results don't lie. The UK came 27th in 2015

There has been a real change in the teaching and learning of mathematics in the last 3 years; there is no doubt that Mr Gibb is having a huge influence in our classrooms. The new National Curriculum and the term mastery have caused schools to evaluate their processes and some long-standing facets of educational DNA have disappeared. My words. Nick Gibb's words below:

Today, I want to celebrate a renaissance in mathematics teaching that is taking place in our schools. Currently happening on a small scale, it has the potential to revolutionise the teaching of the subject in this country.

At this point, I'd like to address the term mastery. A term Nick Gibb uses quite liberally. Some schools and teachers use the term, I believe, without much substance. Is it a noun? Is it an adjective?

Is that a mastery lesson? Is that mastery? Can you give him some mastery questions? Is he at Mastery?

The NCETM discuss the different terms here. Even better, read @emathsuk excellent and accurate overview of mastery via Bloom and Washburne here. @mistersetchell rather elegantly navigated this problem at a course I attended by using the term, messages around mastery.

It's my belief that those messages around mastery have improved aspects of teaching:

• Reasoning 
• Problem solving 
• Not placing limits on learning through prison-like grouping 
• CPA 
• Teaching for understanding 
• Concrete-pictorial-abstract approach 
• A belief all children can succeed - although my previous post disputes this somewhat

So, our classrooms are changing, our practice is changing, both myself and the Secretary of State for schools notice the difference. Surely, we will catching up with the high performing jurisdictions that Mr Gibb eulogises about?


2016 KS1 Mathematics results

Look closely white British 73% at the expected levels and 17 percent at higher standard. Children of Indian origin 82% at and 29% higher. Finally, Chinese 88% at and 40% at higher standard.
Similar patterns can be found in the 2016 KS2 results:


92% Chinese at the expected level.

There is a stark difference in attainment between the different groups. We live in a culturally diverse country; there's no doubt this is a very reductionist approach to looking at the education of young people. However, when the Minister for schools is hailing education systems from around the world with such reverence, it would be remiss not to dig a little deeper.

In 2016, Nick Gibb stated that:

In countries such as Korea and Singapore, and cities such as Hong Kong and Shanghai, the percentage of low-performing 15-year-olds is below 10%. There is nothing different about children in these countries, but there is something different about their approach to teaching maths.

I conjecture there is something different. The data shows that students of Chinese origin perform incredibly well in our system. The difference is not just the approach to teaching maths, but in the approach to learning maths as well. Nick Gibb may be building a renaissance in mathematics teaching - but what about the foundations?