Embedding the Model
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.
Each element is therefore like a tool in the teacher’s toolbox, to be used at the correct time for the appropriate job.
As discussed earlier, both Carleton and Benjamin knew that the model would bring about the combination of
- the crucial, successful elements of one-to-one tutoring, which could be transferred to a group based environment
- the dispositions of academically successful students in a group based environment
The core elements take one step to addressing the first point, but there is a final detail to be added: time.
Unlike a conveyer belt approach, which assumes time to be a given, in a mastery model for schooling time is the key variable. A teacher who plans a unit of work in a conveyer belt scheme will label that unit with a year group, perhaps the term or, worse still, the week number, and state how long that unit will last. The teacher is assuming that the instruction will be fully presented in the time allowed and that it will be a result of the students’ ‘aptitude’ as to whether they learn well or not. The teacher will then move on. This is compounded in England by the perception that the national curriculum is rigid and prescribed. As an inspector, I would often hear teachers talking about their concern that they were not keeping up with the curriculum, yet rarely hear teachers talking about whether or not the students were!
This conveyer belt approach is like the old joke:
The teacher is assuming that the unit of work, presented at the students in the allotted time is sufficient.
In a mastery model for schooling, since time is the key variable, teachers are no longer obsessed by what they have taught, rather the focus is on what the students have learnt.
I have always viewed the words taught and learnt as synonyms – that is to say, like Aristotle, I do not consider something to have been taught unless the desired learning has taken place. But conveyer belt approaches have falsely removed the connection between the two words, particularly in the North-Western culture schools systems, where it is common to find teachers talking about ‘getting through the curriclulum’ as though it was some race to tick off a list of lessons.
In a mastery model, the viewpoint is very different: If a student did not learn what I, as the teacher, wanted them to, then the fault and blame lies with me – my teaching was ineffective. So, celebrating the fact that the student has revealed their lack of understanding or skill, I notice that my practice did not achieve what I wanted it to. I look carefully at my own practice, like an outside observer, and question myself: what pedagogies did I adopt and how might I now change these? This means that, for every concept I am teaching, I must have to hand multiple approaches (or at least be able to find information about alternative approaches quickly and without burden).
There is, therefore, a significant need for teacher professional development to allow for the successful implementation of a mastery model for schooling. Teacher training should focus on ensuring that a subject teacher has multiple approaches for every concept they will be required to teach. This becomes the profession’s body of knowledge. The canon of how to teach, if you like.
It is a long and complex process for a school or system of schools to change the embedded model. Carleton and Morrison understood this clearly and were patient in their work, taking over a decade to get to full implementation. More recently, countries such as Japan and Singapore have followed suit, working slowly and deliberately throughout the 1980s and 1990s to shift their national approach gradually to a mastery model. It is clear, given the scale of the challenge and the CPD implications, that the model cannot be implemented without first producing the courses, the assessments, correctives and curriculum structures. Furthermore, because teachers are required to have multiple approaches to the teaching of any given idea, concept or skill, the subject content and pedagogical knowledge of the workforce must meet these demands. Where cohorts of teachers have been trained in conveyer belt systems – which generally train teachers in just one approach for any given concept (or indeed provide no subject specific training at all!) – the successful implementation of a mastery model for schooling will require the re-training of those cohorts.
This is a long but worthwhile process. A mastery model for schooling cannot simply be transplanted into a new system – it is a fallacy to think that one can end the school year in July, having followed a conveyer belt approach for decades and then suddenly switch to a mastery model in September after a day of two of school training. Rather, the implementation of a different model of schooling takes careful long-term planning, building slowly towards a move to a fully embedded approach. This often causes education systems – which are largely short-termist in their administration – to fall into the trap of cherry picking certain aspects of models, which they then attempt to implement in a superficial manner. Such attempts repeatedly fail.
A head teacher can, however, choose a long term vision for schooling and move towards a mastery model. The starting point is to share the model (in the diagram above) with all teachers and to explore the cyclical nature of the approach. It is key that all teachers appreciate that all students can learn all things expected of them given the right amount of time and the appropriate conditions. This often represents a paradigm shift for many teachers as well as reframing epistemology itself. This is possible to achieve given the right professional development. In our 2010 book, Epistemological Transformation, Jean McNiff and I set out the strategies and processes we carried out in Qatar over a two-year period, which resulted in the shifting of teachers’ (often deeply held) beliefs around the nature of knowledge and knowledge acquisition. We were lucky in that we had complete carte blanche to do what we knew would work and that the Supreme Education Council of Qatar (SEC) required every school in the country to take part in the programme. SEC was, and is, in the process of implementing Education for a New Era, a 30 year, long-term reform programme. With such a long-term approach, it is possible to ensure that the entire workforce receives sufficient professional development and that new entrants are trained in such a way that they arrive into the profession prepared for the chosen model for schooling. In this case, the country was not choosing to move to a mastery model – there are many models of schooling, which a country or system can try to adopt – which I felt was a missed opportunity.
A countrywide adoption of a different model for schooling requires long-term, consistent support from government. The nature of parliamentary democracy in the UK makes this impossible to achieve. However, at a smaller scale, an individual school or group of schools working together, can take a long-term view.
Having shared the vision, a head teacher can begin the process of moving towards a mastery model for schooling by supporting their subject experts to build the body of knowledge required for their subject area. This is a laborious task if started from scratch, which is why it is crucial to recognise that all of those intelligent questions, correctives, assessments and teaching approaches are already defined and exist within the teaching profession, so the task is really one of collating the knowledge.
Subject experts need to know and have access to the entire journey through learning their subject.
Carleton Washburne was a science teacher and science is, largely, a hierarchical subject. This is true too of mathematics, grammar, languages, economics, the skills for studying history and some of the humanities. Hierarchical subjects are easier to define as a curriculum journey, but it is also the case that the less structured subjects can be plotted out for the particular country and school system in question.
Schools should not aim to reinvent the wheel, these journeys already exist and there is a moral imperative to act as a true profession, in which we use the professional body of knowledge that the workforce has created over time. We do, of course, build on this body of knowledge and continue to learn as a profession, but it is unwise for a school or group of schools or country to try to exist in a silo, ignorant of what has gone before.
With curricula defined in a way that ensures each new idea rests on top of the necessary foundations of pre-requisite ideas, a unitised approach can then be plotted out and the correct starting point for any group of students diagnosed and defined. There are no hard and fast rules regarding how long each of these units might last – after all, time is the key variable – but work carried out by Bloom, Guskey, Kulik and others repeatedly points to units of between one and three weeks as being typical and impactful.
The reason for this unitised approach is to carefully build new schema in students’ minds as the map of the subject is gradually revealed to them and they can make new connections, revisit ideas and build on their previous understanding, and to ensure that both factual and procedural knowledge are gained in the correct order to allow students to grip new ideas, ask questions and follow lines of enquiry and, in the broadest sense of the phrase, solve problems.
Turning to my own subject, mathematics, for a moment: I often describe the subject as being like one massive Jenga tower. Each brick in the tower representing an idea, concept, skill or leap in knowledge. It is glaringly evident that the main reason that students fail to acquire all of the knowledge expected of them by the end of schooling is not because the bricks at the top of the tower are somehow beyond them, but because the bricks lower down are loose, wobbly or missing entirely. Attempting to learn a new mathematical idea without the necessary foundations in place is pointless.
Carleton noted that not only did student attainment rise in the mastery model, but so too did student satisfaction and engagement. It feels good to be successful and human beings love to overcome, love to solve, love to learn something new.
However, although curiosity seems universal in humans and the brain rewards us when a problem is solved (a quick hit of dopamine), thinking can be incredibly frustrating if the problem cannot be solved because the student does not have the toolkit to overcome it.
When students are learning a new idea, teachers must therefore ensure that the challenge is just right. There is no point whatsoever in asking students to carry out tasks if they have no way of becoming successful in time. The layers of the Jenga tower must be firm and secure before building on top, otherwise students will only become frustrated and damaged.
This too is true of problem solving. There is little point in asking students to engage in critical thinking if they have nothing to think about! The unitised approach that Carleton, Burk, Morrison, Bloom and others plotted out is designed to ensure that students have access to the background information required before engaging with a problem. They will draw on their long-term memory to engage with problems in a meaningful manner, which in turn will enable them to become more expert.
Becoming More Expert
Carleton recognised that the study of an idea is, in practical terms, infinitely broad. One does not end learning, rather an idea can grow and develop, make new connections and make new meaning as it is set in new schema as a child acquires new knowledge of interrelated ideas.
For each idea or leap in understanding that a child is required to make by a curriculum, there is a never ending journey of extension and enrichment that they can pursue. An idea is not ‘mastered’, but one does become more expert (and sometimes less expert – learning is not a linear process!)
Becoming more expert can be defined in terms of attention: as one becomes more expert, one does not have to attend to the idea as much. That is to say that a student can stop thinking so much about what they are doing with an idea that they have become expert in.
This is true of all learning. Rather than having to think, the brain uses the much less demanding process of using memory. Because the student does not then have to attend to the new idea as strongly, they can turn that attention elsewhere and this allows the student to make new connections or take the idea way beyond the demands of a school curriculum document.
Take, for example, the process of commuting to work. Suppose this involves a drive through a city. When one first takes the drive, there is a lot of new information to take in – which way to go, what lane to be in, how the traffic flows, and so on – so the brain is engaged in thinking and the journey seems long and tiring. But, of course, as any regular commuter will know, it soon becomes the case that the journey seems to happen almost on autopilot. How many times have you arrived at work with almost no memory of the journey!
This is because the brain is now using long-term memory, rather than thinking about the journey. Memory is a much easier process for the brain. The driver now no longer has to attend to the journey and so, as we all do, the brain can attend to other things; what’s for supper this evening, making plans for the weekend, planning today’s lessons!
The journey has been practised repeatedly and so no longer poses the brain with any significant challenge.
As another example, consider a child learning to play the piano. She will spend a lot of time learning about the structure of the keyboard, the relationship between the keys, perhaps learning the scales and some simple melodies. At first, hammering out even the simplest of tunes seems an impossible task. The child must think incredibly hard to make their hands move in the correct way, to strike the correct notes, to keep in time. I guess most of us remember this feeling; learning to play Frère Jacques as a child and the concentration is takes.
She will knock out an awful rendition, thumping the correct keys eventually but barely recognisable as the famous ditty. However, with practice and repetition, she gradually becomes more expert. Rather than thinking hard about where the fingers should land, she uses memory. This allows our fictional child to attend to other things, such as timing, perhaps using the foot pedal, and eventually even composing. And so the journey towards expert continues.
Becoming more expert means the student is able to attend less to the idea and can progress in learning new ideas. They are committing factual and procedural knowledge to long-term memory, which can be retrieved with far less effort from the brain, meaning the expert appears to be able to carry out a task with very little effort. Committing knowledge to the long-term memory is vital if one is to be able to learn well.
Carleton knew that students arrived at school with differing levels of knowledge. The experience he had at the school in La Punete shook him to the core – he had never before witnessed such poverty, both financially and educationally. The students he met there were fundamentally different human beings to the ones he had grown up with. Here, the children had experienced a great deal less by the time they arrived into the school system. They knew fewer words, had visited fewer places, understood less about the world, did not have access to books, never visited a museum or attended the theatre. He knew that his mastery model would, therefore, need to take careful account of the student’s individual starting point and build from there.
This becomes the key challenge of the teacher in a mastery model: identifying the starting point and filling in the gaps. Carleton believed, and John B Carroll later proved, that all students could learn well. All have the ability to commit to long-term memory the factual and procedural knowledge that is needed to unlock learning new ideas and concepts.
Figuring out how to get students to commit knowledge to the long-term memory then became a key question and the answer forms a key component of the teaching profession’s body of knowledge. It can be shown that knowledge and the ability to retrieve if from the long-term memory is a result of a student attending to a task. This seems obvious, but its importance is profound. Only by ensuring that a student pays attention to a task will they actually think about the meaning of the concept, idea, problem or material. Ward and Burk were interested in getting students to really think: forcing the student to bring consideration of the facts or ideas to be learnt to their conscious thinking (generally referred to today as the ‘working memory’). Carleton suggested that tasks must therefore be varied to promote as many thinking opportunities as possible. Repetition is also important, which is why Carleton built in the need for sustained, regular and deliberate practice.
A key characteristic of the expert is, therefore, that they no longer have to think about a task, rather they rely on the ability to retrieve the relevant knowledge and procedures from their long-term memory.
The unitised approach ensures that students have to think about ideas repeatedly over the years, so giving additional practice and opportunities to learn more about the original concept in the framework of new schema. This also gives new opportunities to commit ideas to the long-term memory, since it is very difficult to guarantee knowledge is stored following a single attempt.
Laying out the journey through a discipline in this unitised manner gives the teacher more opportunities to spot and act, filling in the gaps and creating new connections in subject matter for further depth of understanding.
Using the Journey
So, subject leaders will now have at their disposal an entire journey through their subject and multiple approaches to tackling each concept, backed up with the relevant course and assessment materials (probably taking a couple of years to collate and refine). A head teacher taking a long-term strategy towards a mastery model for schooling can now begin the process of implementing the model in the classroom.
Later, I will outline what implementation looks like for my own subject of mathematics, but for now the commentary is generalisable.
In parallel with subject leaders and their teams producing the journeys and materials, a head teacher will ensure that all staff are engaged with sustained, high-quality professional development targeted to their own subject specific knowledge and subject specific pedagogies and didactics. Much of this knowledge will already lie within the staff – individual teachers will have refined different approaches for teaching the same concepts, which they can share with each other, test (preferably through lesson study) and accept or reject from the canon. Of course, it is crucial to engage with other outside sources, such as research books, debates, conferences, subject experts and associations. This CPD must be long-term and focused on the impact it has in the classroom.
As these two parallel tasks begin to intertwine and mature, a head teacher finds himself positioned to begin implementation of a new model of schooling. Reaching this point takes a great deal of time, but the head teacher now has:
- Subject departments equipped with detailed course, assessment and corrective materials
- Subject teachers equipped with the subject knowledge and pedagogical insight such that each teacher knows multiple ways of teaching every concept
Only when this point is reached can implementation begin.
It is obvious that the work involved here is great. For the initiative to be successful, a school or group of schools must have constant leadership from a driving force who is relentless in ensuring both strands are achieved. The Winnetka Plan was only possible because Carleton, as Superintendent, was able to provide long-term vision and see it through with long-term leadership and delivery. Having these two strands in place is just the start of the journey. Carleton knew that not only would he need to create courses with the transferable ideas of one-to-one tutoring, but that it would also require students to have the dispositions of those who succeed in group based models. These dispositions include being self-directed, seeking out new opportunities to learn, following up on misconceptions, determination and being open to trying again and again. In other words, for the model to work, the onus is not just on the adults in the school but also on the students: they must work really hard.
As schools move through the process of designing courses and training or re-training teachers, they must also develop students into, in many cases, quite different people. The student needs to know, understand and, crucially, believe that they can learn all things given the right amount of time as long as the conditions are appropriate. They need to be clear that these appropriate conditions include effort on their part. During the period of planning and development, head teachers can work carefully with all teachers, students and parents to shift the perceptions of those who believe that being able to learn well is somehow the result of luck of the draw. Learning is simply a result of appropriately thinking – so all students need to know that they must engage and think if they are to be successful.
Carleton noticed a huge change in the attitude of the students in Winnetka when they were exposed to this revelation. It might seem obvious, but students really do respond better to being told they will always get there in the end rather than being labelled as someone who cannot learn well.
The pre-implementation process described so far is likely to take at least 2-3 years.
For many head teachers, the leap of faith is just too much. With perceived pressure on school leaders to focused on annual high-stake test results and their position in league tables or comparison against largely arbitrary nationally set targets, many head teachers do not feel it is within their ability to take a sustained, long-term view. Without this, however, implementation is never successful.
In Part 3 of this blog, I will explore some of the key logistical challenges to consider and overcome when implementing a mastery approach and the known pedagogical choices that must be present if we are to ensure pupils commit mathematical ideas to the long term memory.
In later parts, I will showcase some examples of teaching for mastery in practice, giving several vignettes of lessons that you can use in your own school.
In later parts, I will showcase some examples of teaching for mastery in practice, giving several vignettes of lessons that you can use in your own school.