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 conveyor 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 conveyor 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 conveyor 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 conveyor 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 conveyor 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 conveyor 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.
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.
