A problem shared: how collaboration paves the path to mastery

Blog: Ian Davies, Director of Secondary

A problem shared: how collaboration paves the path to mastery

Posted: 23/11/15

One way or another, I’ve been in mathematics education since I was five years old. I’ve been an ‘Advanced Skills Teacher’, ‘Head of Department’, and a ‘Specialist Leader of Education’ and various other titles designed to classify me as “good”.

But guess what? I still get stuck. Pretty often too. Fortunately, as the years rolled by I’ve learned to deal with this, eventually recognising that “being stuck” is a crucial part of the learning process – for me as well as the students I teach. How I wish I’d know this earlier!

What’s the most important lesson I’ve learned about being stuck? The best solution is talking to someone about it.

For example, I saw this question on Twitter recently:


Whilst working out the answer, I was reminded of a pedagogic tool we’d been discussing recently: instead of finding one way to solve a problem, find three ways. I soon came up with a second and, eventually, a third (the best so far I thought*).

Feeling suitably smug, I then presented the same problem – find three ways – to the Mathematics Mastery team, working in pairs, in a Monday Morning Maths session. Within minutes the room was full of alternatives.

Talk tasks

Working in pairs was key to the success of this task. People came up with different ways of starting and, after establishing one solution, sharing alternative ideas and starting points was easy. “What about if you extend this line?”, “Where can you add a line parallel to this one?”, “If you split the shape here…” etc.

One of our core values is partnership – we listen to each other and show respect for different views and ideas. This task worked so well because we’ve established and nurtured this culture, where giving people a chance to explain their thinking, asking for and giving support, and encouraging feedback is the norm.

This is why our materials at both primary and secondary all include “talk tasks” – to provide opportunities for talking through problems and exploring new ways of thinking.


These tasks enable students to:

  • Develop mathematical language
  • Articulate their reasoning
  • Share ideas on approaches to problem solving
  • Grow in confidence when discussing ideas

(Top tip: an easy way to start talk tasks is through “number talks”)






Departmental Workshops

Collaboration between students fosters understanding and advances learning…and it’s no different for teachers.

Research, by Malcolm Swan for example, has consistently shown the most effective professional development for teachers is co-planning lessons and learning from each other – especially when given some stimulus material to work with.

Our Departmental Workshops do just this. They provide a starting point for discussion on crucial elements within our resources, such as:

  • The mathematical language students will need and how to support this development.
  • What misconceptions might arise within a topic and how these can be avoided/challenged.
  • Alternate forms of representation – and which one(s) are most suitable for particular classes.
  • How to adapt the material and develop questioning to add support or challenge if needed.

National Leadership Days

One of the most exciting aspects of the Mathematics Mastery programme is, you don’t just have some brilliant colleagues to collaborate with, you have hundreds!

Every term we bring together our Mathematics Mastery teachers for National Leadership Days.

Here we share ideas about how to explain and teach different topics, use of different representations, what’s working well and what we can do even better.

As I’ve mentioned, partnership is fundamental to our organisation. We are not a scheme of work or a textbook supplier, but an organic and evolving programme of professional development. We are constantly challenging, and being challenged by, ourselves and our partner schools to continuously improve. The buzz of ideas and discussion during the National Leadership Days are truly inspiring, as we share and learn more about the teaching of maths – and of course the mathematics itself!

Our mission is to transform mathematics education in the UK, so as you can imagine, I get stuck more often now than I ever did before! When it comes to the Mathematics Mastery organisation, if I get stuck on budget matters there’s Michael and Vijaya from our operations team to dig me out of the hole. If I get stuck writing a blog (I’m a mathematician after all!) then Charli, our Head of Communications can translate me into plain English. If I get stuck on a matter of pedagogy or curriculum, there’s a whole team of primary and secondary Development Leads to help me to sort it out. They all help me when I get stuck on maths too.

I feel really lucky to have such a great job and brilliant team, but we all have colleagues and people we can consult in the real and virtual worlds. The trick is remembering to tap into this wealth of knowledge, skills and fresh perspectives.

Collaboration has always been possible and beneficial, and now in some ways it’s easier than ever. One day I’m really going to get the hang of this mathematics education lark…with a little help from my friends, that is!


(*Three possible solutions to angle question – there are many more…)


Looking for more ideas for your lessons? Take a look at our free classroom resources.

View our resources

Schools who join our programme receive a variety of adaptable materials, along with
in-depth training and support, to help you design and deliver lessons more effectively and support your professional development.