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.

In the last week alone, I have heard an Ofsted inspector call for maths teachers to move to mixed ability teaching and an apparent ‘official’ government body insist that all pupils within a year group should always be learning the same mathematical concepts.

This has been pretty much a weekly occurrence now for the last year or so.

The explanation must be, of course, the striking new evidence that mixed ability teaching in mathematics is more impactful than teaching maths classes in sets, where learning content is targeted at the point in the journey through mathematics that each set has reached, right? There could be no other logical or defensible reason for such influential bodies to call on schools across the country to undertake such a huge change in their pedagogy, curriculum planning, teaching methods, staffing, timetabling, resourcing or fundamental beliefs, right?

I have been in this game a while now. I have the great privilege of working with mathematics educators around the world and visiting schools of all types. Invariably, whenever I meet a maths teacher or teacher educator, I learn something new about mathematics teaching. I love this. I am a bit of a knowledge junkie – I am absolutely addicted to learning. I also love having my views, opinions and thoughts challenged, so that I must consider why I believe something to be true and either change my views based on new information or defend my views because they are well founded and right. I love debate, love having my perspective shaken. I read everything. As a long-term sufferer of awful insomnia, I spend most of my nights, lying next to my snoring better half, reading, reading and reading.

The story of the history of mathematics education in England is also the story of a country moving from a largely laissez-faire position to a dictatorial one. Since the 1858 Newcastle report, mathematics education has changed from a system of great diversity to a highly uniform system controlled from the centre. It is also the story of a battle: a long and far reaching fight for dominance between a mathematics education that focusses on the procedural and one that focusses on the conceptual.

In January 2011, I left my director role at Tribal Group and retired. For whatever reasons – more luck than judgement – I found myself at a time and place in my life with no need to make any more money. Since being diagnosed with cancer in 2006, my other half had continually badgered me to give up work. We had the means to do whatever we wanted. Daily I would be told that we should travel, rest, enjoy ourselves, do all the things we had spoken about doing in life. But, as a complete workaholic, the very thought filled me with terror. So, I threw myself back into work, both at Tribal and the property firm I co-own with my best friend. Following years of pleading, I finally relented. 2011 was a most unusual year – no work, no pressure, no demands on me. We did travel – a heck of a lot – and had a lot of fun. To my surprise, after the initial restlessness, I actually started to enjoy the laid-back lifestyle and became genuinely open to the idea of never working again.

My office is just off Old Street Station. The area throngs with Shoreditch hipsters and naïve privileged kids using daddy’s money to fund yet another start up. Their lives look like magazine covers and their worries sum to getting their hair to stick just right or finding someone selling truly authentic, ethical coffee. Life is good, life is easy, life is superficial, life is at their command.

The Education Select Committee today was the latest body to highlight the issue of teacher workforce numbers. All headteachers know the difficulties in trying to maintain a full staffing complement and we all know the impact on student performance when staffing shortages occur. So, ensuring that there are enough teachers in the system is extremely important.

It was March 6th 2006 when I died.

Mat was a wonderful student and now that he was in his final year, he had become almost a part of the staff on our regular walking trips.

A late blast of winter fell on the Peak District National Park with a sudden and complete freeze. The low afternoon sun danced on the waters of Ladybower reservoir and Lose Hill threw long shadows across the forest. At the banks of the lake, Mat kicked a rugby ball out ahead and we both sprinted after it. The ball bounced awkwardly in front of me, one way then the next, I grappled with it for a second then pulled the ball tight against my chest and ran as fast as I could. But Mat was young and much fitter than his old teacher and he was on my heels in no time. He lunged forward, locking his arms around my shins and toppling me. My body crashed on to the hard, frozen ground. He had triumphed. Mat beamed with delight and laughed at his success. But immediately, something in my eyes revealed the secret that all was not well. His face changed and he leaned down to me to ask if I was okay. I brushed away the concern, puffed heavily to regain my breath and told him that I was fine.

But I was not fine. The two bottommost ribs on the left of my body had snapped angrily as I impacted with the solid earth and were now screaming out in pain. I composed myself and was helped to my feet by Mat. Again, I reassured him that I was okay and we both walked slowly back to the lake’s shore to join the rest of the group.

Benjamin S Bloom developed Carleton Washburne’s ideas and definitions, which Thomas Guskey codified further to result in the list of core elements of a mastery model for schooling, which, in summary, are:

• Diagnostic Pre-Assessment with Pre-Teaching
• High-Quality, Group-Based Initial Instruction
• Progress Monitoring Through Regular Formative Assessments
• High-Quality Corrective Instruction
• Second, Parallel Formative Assessments
• Enrichment or Extension Activities

Each of these elements, as a way of working with students, is not necessarily impactful. It is in the combining of the elements into the cyclical model (shown in the diagram earlier) that brings about the impact. For example, a pre-test alone makes no difference to learning unless it is followed by an action and, similarly, formative assessments do not improve learning, rather it is the action immediately afterwards that truly matters.