The Five Big Ideas at Secondary – Coherence
Why is coherence one of the Five Big Ideas in Teaching for Mastery?
04/12/2024
As we continue our series on The Five Big Ideas at Secondary, we speak to Dr Mary Stevenson, Assistant Director for Secondary, about the importance of having a coherent curriculum and how maths departments can work together to achieve this.
What do we mean by coherence and why is it important?
Coherence is all about carefully designed curriculum sequencing that supports all students to progress. This is important not only in terms of the content of the curriculum, which is what most people think of, but also in the teaching approaches that are used. For example, are we going to use bar models to help students understand multiplicative structures? And, if so, is every teacher in the department going to use them in a similar way?
For maximum impact on student learning, teachers need to work with a curriculum or scheme of work which offers clear and coherent sequencing of mathematical ideas, both within each year and across the year groups. This coherent view of maths highlights unifying ideas and makes links between concepts, so that students can experience maths not as a collection of separate topics but as a connected whole.
What does coherence look like in a secondary maths classroom?
We know that certain images, techniques and concepts are precursors to later ideas, so sequencing these correctly is an important part of planning and teaching. When we introduce new ideas, we need to make connections with earlier ideas so that students can build on concepts that they already understand well.
When that new idea has been understood and mastered, it should be used in the next steps in learning, so that students become fluent with it. Some teachers find it helpful to think about maths as a story that unfolds as the students learning grows and deepens. The story has a direction, a narrative, key characters and reference points. We need to think about these characters and how and when they're introduced and developed.
What can teachers do to bring greater coherence to their curriculum planning?
The key to this is collaboration: teachers working together to agree curriculum sequencing and approaches. Now, this can feel daunting, but it's helpful to just start small. For example, members of the maths department might start by looking at where they want to improve student learning in one topic area. This might be done by breaking it down into a sequence of steps and considering, ‘What is the prior learning required for students to access this topic?’, ‘What key language and vocabulary is needed?’, ‘Are there any key representations we should use?’. It's also important to anticipate and discuss likely student misconceptions that will occur during the learning process and discuss productive ways of working through them.
What are the benefits?
I'm sure every maths teacher knows what it's like to have to reteach a topic when the students haven't really learned it properly the first time. This common problem can be mitigated by allowing students sufficient time to develop key knowledge and understanding when the new idea is introduced for the first time. Then, when they meet these ideas again, students can build on their understanding more effectively. Teaching time is limited, and it makes sense to use that time as efficiently as we can.
Another benefit is what happens to the maths team when they are working collaboratively. It is great professional development for everybody, irrespective of their level of experience. We also find that, when the curriculum is collaboratively planned, teachers are more invested and feel supported, and that has a positive impact on staff morale and retention.
What are some of the challenges that teachers might face?
I think a key challenge is finding the time during the regular working routine for team meetings and departmental curriculum planning. Maths departments across the country are using a variety of different approaches to this. The most important thing is that the school's senior leaders understand the necessity of planning for coherence and the positive impact that this can have on the quality of teaching and learning.
Teachers need the time to sit together and take ownership of the curriculum. Although it's a challenge, the benefits are huge. Team planning draws on the ideas and experiences of everybody, so it leads to higher quality learning and a stronger department. It reduces the need for individual planning and, although it might seem at first like an extra task, it very quickly becomes a time saving mechanism and leads to greater efficiency.
What are your top tips for teachers who want to improve curriculum coherence?
Agree your common goals and what you want to achieve. All teachers should be working from the same set of principles and towards common goals. Developing the scheme of work and the individual lessons requires ongoing discussion and debate. It's a live endeavour that never stops!
Make use of the NCETM and other materials. Teachers can use The Essence of Mathematics Teaching for Mastery as that stimulus to think about their goals and long-term vision. It is also worth having look at the DfE’s Key Stage 3 non-statutory guidance for ideas about what makes a rigorous and connected curriculum and how this might be created. Ofsted makes some useful recommendations in its subject report, which we explore in our Ofsted explainer on curriculum coherence.
Establish some form of collaborative planning, which might be as a whole team or within subsections of the team. Collaborative planning takes different forms in each school, so find a way that works and be consistent with it – start small, but start talking!
To find out more about the Five Big Ideas, and to discover how your school could start collaborating to develop a coherent curriculum, contact your local Maths Hub or explore some of the professional development available.