# data[].attributes.attachment_link.readable_text
A true understanding of these ideas will probably come about only after discussion with other teachers and by exploring how the ideas are reflected in day-to-day maths teaching, but here's a flavour of what lies behind them:

Coherence

Teaching is designed to enable a coherent learning progression through the curriculum, providing access for all pupils to develop a deep and connected understanding of mathematics that they can apply in a range of contexts.

Representation and Structure

Teachers carefully select representations of mathematics to expose mathematical structure. The intention is to support pupils in 'seeing' the mathematics, rather than using the representation as a tool to 'do' the mathematics. These representations become mental images that students can use to think about mathematics, supporting them to achieve a deep understanding of mathematical structures and connections.

Mathematical Thinking

Mathematical thinking is central to how pupils learn mathematics and includes looking for patterns and relationships, making connections, conjecturing, reasoning, and generalising. Pupils should actively engage in mathematical thinking in all lessons, communicating their ideas using precise mathematical language.

Fluency

Efficient, accurate recall of key number facts and procedures is essential for fluency, freeing pupils' minds to think deeply about concepts and problems, but fluency demands more than this. It requires pupils to have the flexibility to move between different contexts and representations of mathematics, to recognise relationships and make connections, and to choose appropriate methods and strategies to solve problems.

Variation

The purpose of variation is to draw closer attention to a key feature of a mathematical concept or structure through varying some elements while keeping others constant.

Conceptual variation involves varying how a concept is represented to draw attention to critical features. Often more than one representation is required to look at the concept from different perspectives and gain comprehensive knowledge.

Procedural variation considers how the student will 'proceed' through a learning sequence. Purposeful changes are made in order that pupils' attention is drawn to key features of the mathematics, scaffolding students' thinking to enable them to reason logically and make connections.

The Five Big Ideas were first published by the NCETM in 2017.

# data[].attributes.attachment_link.description
The fundamental characteristics that underpin teaching for mastery in all school and college phases

# data[].attributes.attachment_link.description
Materials that will assist you in your professional development and support you in teaching for mastery with confidence

# data[].attributes.attachment_link.description
Materials that will assist you in your professional development and support you in teaching for mastery with confidence

# data[].attributes.attachment_link.title
Research lessons - The Education and Training Foundation

# data[].attributes.attachment_link.description
Key teaching approaches from the Centres for Excellence in Maths (CfEM) programme.

# data[].attributes.headline
Planning collaboratively and learning together as a department

# data[].attributes.subject
Planning collaboratively and learning together as a department

# data[].attributes.attachment_link.title
Planning collaboratively and learning together as a department

# data[].attributes.attachment_link.description
How a secondary maths department includes everyone in the planning process and fosters shared learning

# data[].attributes.wish_content.attachment_props.text
A new S plan in maths for Y4 Geometry and Shape #maths #superbschools #mastery @NCETM @SYMathsHub @MathsHubs https://t.co/Kk9Av4qFW8

# data[].attributes.wish_content.attachment_props.original_text
A new S plan in maths for Y4 Geometry and Shape #maths #superbschools #mastery @NCETM @SYMathsHub @MathsHubs https://t.co/Kk9Av4qFW8

# data[].attributes.attachment_link.embed_code
A new S plan in maths for Y4 Geometry and Shape #maths #superbschools #mastery @NCETM @SYMathsHub @MathsHubs pic.twitter.com/Kk9Av4qFW8
— shell (@mathsmadMK) March 6, 2019

# data[].attributes.attachment_link.metadata.attachment_props_source.data.text
A new S plan in maths for Y4 Geometry and Shape #maths #superbschools #mastery @NCETM @SYMathsHub @MathsHubs https://t.co/Kk9Av4qFW8

# data[].attributes.attachment_link.metadata.attachment_props.original_text
A new S plan in maths for Y4 Geometry and Shape #maths #superbschools #mastery @NCETM @SYMathsHub @MathsHubs https://t.co/Kk9Av4qFW8

# data[].attributes.attachment_link.metadata.attachment_props.text
A new S plan in maths for Y4 Geometry and Shape #maths #superbschools #mastery @NCETM @SYMathsHub @MathsHubs https://t.co/Kk9Av4qFW8

# data[].attributes.headline
A conversation about S-Planning in Maths with Twitter Colleagues May21

# data[].attributes.subject
A conversation about S-Planning in Maths with Twitter Colleagues May21

# data[].attributes.attachment_link.title
A conversation about S-Planning in Maths with Twitter Colleagues May21

# data[].attributes.headline
An effective model for collaborative planning in maths

# data[].attributes.subject
An effective model for collaborative planning in maths

# data[].attributes.attachment_link.readable_text
What if you could spend time planning one top quality lesson rather than eight mediocre ones? What if you had support and ideas from your colleagues in doing so? What if all the students in your school covered the same material in maths, with the same resources, same terminology, and same procedural methods? Would that make it easier when picking up new classes the following year?

At Southfields Academy in Wandsworth, collaborative planning is now embedded in the maths department. Southfields is an 11-18 school (around 1200 students), and the school catchment is challenging on many measures - 49% pupil premium, 56% EAL, and with SEND units specifically to support those with hearing and speech and language difficulties. The maths department consists of a dozen teachers with roughly eight teaching in each year group.

Once a week, all teachers of Year 8 meet during a non-contact period. In another period, all teachers of Year 7 meet. At the beginning of term, they decide the small steps to break each topic into, and discuss common misconceptions and the difficulties students might face. Then they allocate forthcoming lessons for individual teachers to lead on.

Weekly meetings focus in detail on the planning of a couple of lessons. A teacher will have put together an initial set of slides that they will show. Colleagues are then invited to improve, add, challenge, question and polish the work done. The result is a lesson co-planned by the whole department, that everyone is happy to use.

Is directed time used for this? No - teachers willingly use their non-contact periods because they know it will save them planning time. And also because they enjoy the mathematical and pedagogical discussion with colleagues.

What are the benefits?
For students

All students get a consistent diet of maths lessons, helping to even out inequalities in maths provision.

The approach ensures consistency of coverage so staff can be confident in what students have covered and how.

For staff development

This CPD is finely focused on the content of the next few lessons, so it is acutely relevant to all teachers, regardless of experience.

Newer teachers learn from more experienced colleagues, particularly in anticipating misconceptions and areas of difficulty.

More experienced colleagues benefit from the fresh insight that new teachers can bring.

Southfields have found that collaborative planning has really helped to retain staff.

For curriculum development

If changes are being made to the curriculum or teaching style, then this sort of joint planning can embed understanding and develop a common approach.

Southfields have used their collaborative planning sessions to help them make the transition to teaching for mastery and all-attainment groupings.

What are the possible challenges?

Collaborative planning for a year group requires everyone teaching that year group to have agreed, regular time available. Southfields have achieved this by timetabling a common non-contact period for each year group teaching team.

Classes also need to be covering the same curriculum at roughly the same pace. At Southfields, all-attainment groupings in Year 7 and Year 8 make this possible. All teachers pitch in their ideas for support and greater depth, but the basic content coverage is the same for each class.

The meetings require staff to be confident and willing to share their ideas. This trust has been established over time at Southfields, and staff still say that they felt nervous the first time they shared a lesson plan.

What does it look like in practice?

We sat in on a Year 8 collaborative planning meeting at Southfields on a Friday afternoon in March 2019. The teachers discussed two lessons coming up in the timetable. First, Harvey Jones went through his lesson on 'Using multipliers to solve worded increase and decrease percentage problems'.

Harvey's lesson was designed to encourage students to infer either a percentage 'increase' or 'decrease' from questions in which these words were not present. Instead, words such as 'depreciation', 'growth', 'fall', 'loss' and 'accrue' were used.

Colleagues were invited to polish the work he had done in planning. As the meeting progressed, Harvey made changes to his lesson slides as other teachers suggested improvements.

Here are some of the discussions that occurred:

Harvey has planned some 'diagnostic questions' - a question followed by four possible answers. Students will choose which they think is the correct answer. The remaining answers are designed to address common misconceptions.

click image to enlarge
The team consider how a class discussion might be managed after a diagnostic question, to best draw out misconceptions. They also discuss the best time to withdraw the support of multiple choice.

Someone spots an inconsistency across the team's lessons. Some lessons express the multiplier first in a calculation:

e.g. 1.25 × 5 =

Some put it second:

e.g. 5 × 1.25 =

There's a conversation about whether it matters, which way is most instinctive, and what implications this has for their longer-term planning. Someone mentions that commutativity was not sufficiently covered in Year 7. The team decide that their lessons should include both instances and that the equivalence should be made explicit. Colleagues agree to make this change to the lessons they teach prior to Harvey's.

click image to enlarge
Imagine a teacher planning alone late at night, designing five lessons for the following day. This is the sort of nuance s/he is unlikely to notice or spend any time wondering about.

click image to enlarge
One teacher points out that Harvey has included questions containing numbers that are not required for the calculation - red herrings.

Experienced maths teachers know that students often pull numbers out of a question - assuming they know what calculation is needed - without reading the question properly. Putting in extra unnecessary numbers can encourage students to be more critical in their choice of numbers and calculation. It is not necessarily something an inexperienced teacher would think of.

Harvey's main activity is a grid of nine questions to be given to students on a sheet and worked through three at a time. He has also provided working for each answer, as well as the solutions. He suggests that teachers might scaffold the questions by providing either the solutions or the working and asking students to match them. Harvey has done the planning, but what he is providing is far from prescriptive. He has made allowances for teachers using their own judgements and favoured teaching style.

Nicky Frost's lesson is discussed next. She has been charged with creating a lesson for students to practise and discriminate between the four types of percentage calculations they have met to date.

Her colleagues are already familiar with the lesson, having spent some time looking at it in a previous meeting. This time around, the discussion is to fine-tune the lesson. They talk about the best wording for the four types of problem, to ensure clarity. This leads to a drilling down into exactly what the differences are between these various types of calculation, and where they might overlap. They also talk about the use of colour for readability on the whiteboard.

Throughout the meeting, the discussion is highly focused on the mathematics and the pedagogy, continually refining and improving each teacher's understanding of their own philosophy. Through this sort of planning, teachers are able to develop a common approach while also taking advantage of individual strengths.

What do the department say about collaborative planning?

"Going from a training timetable into being an NQT was a real shock and I think that being involved in these planning meetings has really accelerated my progression. It gave me a quick start into mastery teaching that I was then able to adapt to all my other year groups. It's had an impact on cutting down planning time but also on efficiency with my other planning, in helping organise my thoughts."

"It's trying to fast forward that experience thing."

"We all want them [the lessons] to be really good, so you want people to tell you how to improve. I'd rather people tell me 'Well that was a terrible way of thinking about it, have you thought about this way?' because it means I can improve. And it's really nice being able to say that to more experienced teachers too!"

"We speak about how to challenge and support for every different topic. So I've now got this toolkit for every topic."

"As well as our Year 7 and 8 collaborative planning sessions, all our department meetings are spent sharing ideas, resources, teaching approaches and doing maths together. We make a point of rarely spending any meeting time on admin - this is done via email."

And other teachers...?

Southfields welcomes teachers from other schools to see their collaborative planning in action and observe lessons that arise from that planning. Their comments speak for themselves:

"This could revolutionise my practice and my department..."

"Seeing a mixed ability class all access the same content was brilliant."

"I feel inspired to start a collaborative planning meeting."

Gwenda Thomas, Lead Practitioner in maths at Southfields Academy, welcomes contact from any teachers interested in finding out more about collaborative planning - email Gwenda.

Or you could read about how St. Marylebone School in London used a similar model to support their transition to all-attainment groupings.

Or engage with our director, Charlie Stripp, through his blog post advocating collaborative planning by making it a timetabling priority.

# data[].attributes.attachment_link.title
An effective model for collaborative planning in maths

# data[].attributes.attachment_link.description
What if you could spend time planning one top quality lesson rather than eight mediocre ones? What if you had support and ideas from your colleagues in doing so? What if all the students in your school covered the same material in maths, with the same resources, same terminology, and same procedural methods?

# data[].attributes.headline
Ideas for collaboration in secondary maths teaching

# data[].attributes.subject
Ideas for collaboration in secondary maths teaching

# data[].attributes.attachment_link.readable_text
As a maths department, you probably meet regularly, talk often about your planning, and chat over coffee about how lessons have gone. But are you really collaborating? Here we give a few suggestions of what collaboration might involve, and point you towards some features and podcasts which explore how schools have made collaboration work for them in different settings. We also highlight some resources which will enhance your department's collaborative planning, whatever form it takes.

Firstly, let's dispel some myths about collaborative planning. It certainly doesn't mean the topics of a scheme of work being divided up, each teacher given some lessons to plan, everyone dispersing to various corners of the department, then hundreds of lessons being uploaded to a folder on the shared drive a few hours later. Instead, effective collaboration involves teachers thinking deeply about how students will approach, learn and retain the maths that they are being taught.

Often, really thinking about what you will teach involves having a go at it yourself. Whether it's in a department meeting, co-planning time, or just over a cup of tea at the end of the day, try some of the questions you are going to give to your classes.

Instead of glancing over a topic that you have taught dozens of times, make sure you approach the maths as though you were a student, comparing and discussing your answers, and the thinking that you did to get to them. Sometimes, it's useful to do the actual tasks you're going to give your students (that you will therefore approach as an 'expert'), but it's also important to put yourself in the position of the learner occasionally, and do maths that perhaps is beyond your comfort zone!

Going through the process that your students will experience can help you agree some common approaches that you might take as a department, especially when it comes to addressing misconceptions. You don't all need to agree to teach the same things in the same way, but you might agree a particular representation that best models a certain concept, or a task that all students will experience. Sharing your understanding of how students deal with the maths they encounter helps you all create a more powerful sequence of lessons through a topic.

Collaboration can involve teachers of a particular year group coming together, or it might simply mean two colleagues with a shared non-contact period discussing an area of maths that they are teaching. It could also involve more experienced teachers working with those new to the profession, as well as including non-specialists, teaching assistants and learning mentors. These varied perspectives often give a unique view into how questions and problems might be tackled, and are just as useful as the expertise of a head of department or teacher with many years' experience!

And don't forget that collaboration is not just about what happens before you teach. It's also about reflecting on and refining lessons after you've taught them. The non-statutory guidance for Teaching Mathematics at Key Stage 3 reminds us that 'The final piece of the collaborative planning jigsaw is regular post-lesson discussion of how successful the lesson was in terms of students' learning'. Try to make time for a conversation about what went well and how learning took place, so you can feed that new knowledge into future planning.

So, what does the NCETM offer that can support with your collaborative planning? We've picked out our top ten suggestions below. Why not try downloading some of the resources for use in a departmental meeting, or contacting your local Maths Hub to begin collaborating with other local schools? If you're short of time, read a ten-minute feature to get ideas you can explore later with your colleagues and school leaders.

Resources - DOWNLOAD

Departmental Workshops
These one-hour sessions are designed specifically for collaborative CPD in secondary maths departments. Each session contains a PDF of key points and suggested activities, and PowerPoint slides with handouts.

Checkpoints
Our popular Checkpoints diagnostic activities have been downloaded over 15,000 times. With 15 decks now available and more to come, these are ideal materials for teachers to co-plan KS3 lessons that assess students' prior learning from KS2.

KS3 key ideas exemplified
If you've used the Mastery PD Materials and are looking for further professional development discussions, these 52 PowerPoints exemplify some of the key ideas from the materials. They include slides marked for use in the classroom with students, and slides focusing on the pedagogy, designed for discussions as a department or group.

Professional development - PARTICIPATE

Years 5-8 Continuity Work Groups
Maths Hubs CPD projects have collaboration at the heart of them, and this project is no exception. It brings together teachers in both primary and secondary schools to focus on the transition between phases. Get in touch with your local Maths Hub to find out about taking part in 2023/24.

Secondary Teaching for Mastery Development Work Groups
If you're keen to become a Mastery Advocate and lead the collaboration in your department in order to introduce teaching for mastery, join a Development Work Group. You'll work with colleagues from local schools, then take your collaborative approaches back to share in your own department.

Features - READ

Podcast episodes - LISTEN

What mastery has done for our school
In this episode, a secondary deputy head and maths teacher talks about seeing collaborative planning during a visit to Shanghai, and how it was adopted back in her London high school.

The ECT and the mentor
Collaboration in a department can really help an Early Career Teacher to develop both their subject knowledge and pedagogy. Hear from an ECT and her mentor as they discuss how collaboration has made her first year of teaching 'fantastic'!

Videos - WATCH

Planning to teach secondary maths
These twelve videos, plus accompanying notes, are designed to offer advice and guidance to anyone teaching KS3 maths. They cover a range of topics, and would be especially helpful for a department that invites non-specialists, TAs or new teachers to take part in co-planning.

# data[].attributes.attachment_link.title
Ideas for collaboration in secondary maths teaching

# data[].attributes.attachment_link.description
As a maths department, you probably meet regularly, talk often about your planning, and chat over coffee about how lessons have gone. But are you really collaborating? Here we give a few suggestions of what collaboration might involve, and point you towards some features and podcasts which explore how schools have made collaboration work for them in different settings.

# data[].attributes.headline
Planning and sequencing for curriculum prioritisation

# data[].attributes.subject
Planning and sequencing for curriculum prioritisation

# data[].attributes.attachment_link.title
Planning and sequencing for curriculum prioritisation

# data[].attributes.attachment_link.description
Planning and sequencing using the NCETM Curriculum Prioritisation Materials

# data[].attributes.headline
‘Exploding Checkpoints’ – co-planning a KS3 curriculum

# data[].attributes.subject
‘Exploding Checkpoints’ – co-planning a KS3 curriculum

# data[].attributes.attachment_link.title
‘Exploding Checkpoints’ – co-planning a KS3 curriculum

# data[].attributes.attachment_link.description
Discover how the maths department at one Cornwall school went back to the drawing board to develop a new KS3 curriculum

# data[].attributes.headline
Pearson Edexcel Level 1/Level 2 GCSE (9-1) in Mathematics (1MA1)

# data[].attributes.subject
Pearson Edexcel Level 1/Level 2 GCSE (9-1) in Mathematics (1MA1)