We know a heck of a lot about learning. Approaching teaching armed with humanity’s cumulative knowledge about teaching means we can be forensic rather than random, we can be sustained rather than faddy, and we can be unswerving in our belief that all pupils can learn well. I think that’s no bad thing.

Time and time again, it has been shown that all pupils, regardless of wealth, sex or ethnicity, can learn well. For thousands of years, it has been understood by the great commentators on teaching and pupillage that all human beings can learn well. With expert teaching and serious application and effort combined, over the necessary and appropriate amount of time for an individual, it is within the grasp of everyone to succeed. All human beings are born with, for all intents and purposes, limitless cognitive potential. At birth, we are blessed with a brain so unknowably complex and wonderous, so capable of extraordinary achievement, so full of potential that the whole of school learning represents a mere iota of its capabilities.

A short post about time and mastery.

All human beings can learn well. But all human beings learn from different models, metaphors, examples and instruction. And, crucially, all human beings learn at different rates.

In a mastery approach, time is the key variable.

I spent nearly all of my teaching career seeking out and working in schools in economically deprived communities – what used to be euphemistically referred to as ‘schools facing challenging circumstances’. These are my favourite types of schools and favourite types of communities.

A couple of decades ago, I taught in a school in a small, working-class town where the main employer was the local food processing factory. Rumour had it that the most soul-destroying job in the giant metal building was to continually pack sausages for eight hours every day.

The state broadcaster in the UK, the BBC, has lately been campaigning to have additional public funding appropriated for the further expansion of its child targeted television channel under the guise of education output. The BBC has long since created television shows for children, many of which have been given the education badge and many of which have endured for decades. They are good television programmes. Because that is what television producers are in the business of producing – good television. This is not the same thing as a good education.

Many people have asked me over the years why I so often use the phrase ‘models, metaphors, examples and instruction’ when talking about mastery approaches to teaching. This short blog is a high-level response to that question.

This week sees the launch of my new book, ‘Teaching for Mastery’. Later this year, another new book, ‘Curriculum and Task Design’, which I am writing with Chris McGrane will also go on release. I am currently working on another new book, ‘Teach, Do, Practise, Behave’, which will be available in 2020 – this book is a response to the many teachers who have asked me to put together examples of my phasing model of learning. The book takes several mathematical ideas and explores in depth how they would appear in the classroom during the four phases of a learning episode, with exemplar instructional materials, worksheets, tasks and inquiries. So, then what?

Children are antifragile, not fragile. They need to encounter problems and harm – carefully and deliberately and appropriate to their developmental stage – such that they learn to adapt and become strong, not weak, adults.

It is a surreal experience to sit in a small room with a stranger and listen as they tell you that the cancer is aggressive and unpredictable, that it is time to think in months, not years, and that you should begin to get your affairs in order. When the consultant told me that I did not have much time left, I did what I assume most people do in the situation; I considered my life and thought of things left undone and then I tried to do them all.

In October 1995, bushy bearded and unkempt, I travelled the length and breadth of Britain – with some unexpected detours to France, Germany and Belgium – by bus, by train, by the kindness of travelers who stopped to pick up an unknown hitchhiker, by long, long walks in sun, rain and snow, by ship and by sky. I set out to meet those who were like me and those who were not, set out to speak with strangers and find, in their stories and touch, some new direction in life. For eight months, with not a penny in my pocket, I had the immense privilege of spending just a little time in the lives of so many varied people. When I finally decided to return home on the last day of May 1996, I boarded a ferry at Zeebrugge and watched England approach on the horizon with new eyes.

I have noticed a lot of people talking about ‘weaker pupils’ on Twitter. There are suggestions, for example, that certain representations of equations cannot be accessed by weaker pupils or that concrete of pictorial modalities for exploring a mathematical idea are only suitable for ‘weaker pupils’.

My problem with this is that I don’t believe there is such a thing as a ‘weaker pupil’. There are just kids learning maths and, except for those children with the most severe learning difficulties, all pupils can learn the whole of school level maths.

I have often heard it said that when a loved one dies, the grieving process takes time. And that, over time, the hurt and loss diminish.

I don’t think that is true.

Part 1 and Part 2 of this blog concerned the background efficacy of the approach, its history, evidence base and evolution over the past 100 years in particular, and how schools could go about adopting the approach in practice.

In this part, I will consider the key logistical and pedagogical considerations for ensuring a mastery approach has as great an impact as possible. The blog is broken into chapters, which have been written in a narrative but can also stand alone should you wish to dip in and out.

The tiles can be used in a wide range of ideas from counting, area, perimeter, arithmetic, through to solving equations, factorising quadratics, algebraic long division and simultaneous equations. In this blog, I will look at a small number of uses that have been helpful in introducing teachers to the use of Algebra Tiles.

It should be noted that Algebra Tiles have been used in the mathematics classroom for many, many decades (I recall many lessons as a child using the tiles myself) and that this blog is not meant as a comprehensive description of their use. It should also be noted that Algebra Tiles are simply one representation of some ideas in a wide range of representations. The intention is not to replace ways of teaching ideas by the exclusive use of Algebra Tiles, rather it is to augment the teacher’s current multiple representations with another model and another way of discussing and thinking about ideas. The physical nature of the Algebra Tiles makes them easy to manipulate – that is, to change mathematical systems and structures easily and witness the impact of doing so. However, it is not the intention that pupils are then expected to work with Algebra Tiles whenever faced with the ideas outlined here. The use of the tiles is one step in a scaffold towards efficient, symbolic representations and a way of convincing pupils to accept an abstract idea.

Yesterday, 400 maths teachers from across the UK descended upon Kettering in Northamptonshire for #MathsConf14.

The day follows months of planning and organisation by my fantastic team at La Salle, with a flowchart of logistical issues to address as long as my arm. The team tirelessly put together an event of the highest standards – and they do this four times per year!

When I started MathsConf, I wanted to introduce a new forum to the mathematics education landscape – one where practicing classroom teachers were given a platform to discuss, explore and refine their own theories. All teachers of mathematics have theories, though many don’t realise that they do. All teachers of mathematics carry out thousands of complex decisions each day, gradually refining their practice based on these micro-experiments, reading, research and learning from other teachers and experts.