The Maths Hubs have recently shared information on The Five Big Ideas and how it can be used in Fluency at Secondary level.

Schools and teachers engaged with teaching for mastery are focused on achieving a consistent approach. Coherence is the ‘Big Idea’ that holds everything together. It’s important to avoid students who go from one teacher to another and encounter completely different teaching approaches, and completely different sets of representations. They need to have a seamless experience and that is developed within the department and within whichever phase of learning they’re in. It is an approach which links to previous learning from Key Stage 2 and anticipates future learning in Key Stages 3 and 4, and into post-16.

The other ‘Big Ideas’, such as variation, representation and structure, mathematical thinking, and fluency, are all key concepts in teaching for mastery. They work together to support the development of a mathematical toolkit of conceptual understanding, flexibility, mental structures and deep knowledge that students can use to become engaged and active participants in their learning. But this all starts with teachers, working together, in their departments to develop their approach and get the most out of their curriculum.

What do they mean by fluency?

Fluency is related to how well we know something and can easily access it, but there are different ways of ‘knowing’. We could say, ‘I know’ meaning, ‘I’m aware of’. For example, I know there’s a place called Australia, but I’ve never been, so I can’t picture it in detail or imagine what it would really be like to be Australian. We could also say ‘I know’ to mean that it’s been part of my experience. For example, a visitor to Australia would know much more about it because they’ve experienced life there and could probably engage in a meaningful conversation about it.

Being mathematically fluent is an essential element in thinking mathematically. It means that each element of maths is not in isolation; it’s not put into different disciplines. People can appreciate the interconnectedness of mathematical structures. Fluency, in terms of rapid recall, reduces the burden on working memory and allows thinking capacity to be channeled towards the new, challenging part of a concept.