In 2010 Big Maths introduced the idea that the bulk of a cohort (any child without a genuine learning difficulty for maths, or what looks like a genuine gift for maths) should be brought to the same point in the numeracy learning journey. This ‘pre-managed spread’ allows the teacher to guide them forward together, as one large group. In 2014 the English government ‘introduced’ this idea as an Asian approach called ‘mastery’, elements of which have since made their way into Wales and Scotland. Most schemes and approaches that existed before the word ‘mastery’ agenda took hold were adapted to tick the boxes of the education authorities. Big Maths wasn’t changed, therefore appearing to some that it wasn’t a mastery curriculum, yet, in reality, it is the original UK maths mastery curriculum!
The principles of Big Maths prioritise the following features:
A curriculum that recognises a Basic Skills journey and a Wider Maths journey to provide clear progression and expectations. Children’s progress on their Basic Skills journey should always inform (and be prioritised over) the Wider Maths skills that they can be introduced to.
We believe that all children can attain the expected journey being outlined. Indeed, with any curriculum this shouldn’t just be a ‘belief’, but rather the rationale that should be evidenced in the curriculum design. In Big Maths you can always see why all children can attain the progression in fluency being described.
For this to work, then the early stages of the journey must be light and ‘doable’ for all. Big Maths advocates a relatively low age-related expectation in the early years. This allows children who start school with relatively low attainment to be quickly brought into the expected journey for fluency with number. This is achieved by having a strong focus (i.e. intensity and consistency) on the teacher-modelling and the child copying, with explicit instruction of doing and understanding from expert to novice. We advocate the ‘I do’, ‘We do’, ‘You do’ model of teaching.
Again, for all this to work, then children who have mastered the expectations of fluency ahead of the rest of their cohort (or ahead of the fluency journey expectations) are stretched with their mathematical thinking into other areas of the maths curriculum (for example, problem-solving, maths investigations and connecting their number fluency to shapes, fractions, etc.). These children do not simply press on with the fluency journey.
However, there may be a small group of genuinely elite mathematicians (and it may well look as if they are gifted) who are ahead of the expected fluency journey. This small group provides a management challenge to the teacher (as do those with a genuine special need) and may well need different input to the main group.
The outcome of the successful implementation of this curriculum is that the teacher can give input on fluency journey progression to one large group. A common error of a mastery curriculum implementation is that the teacher gives input to one large group where there is a spread of number ability. The teacher then attempts to differentiate through group work after the main input. A successful mastery curriculum provides the teacher with a ‘pre-managed spread’ (due to the reasons described above), not an unmanaged spread. In a well-implemented mastery curriculum, the teacher should have a reduction in workload in this regard (preparing fewer inputs and managing less group work).
In 2017 Dylan Wiliam tweeted to the education world that he had “come to the conclusion Sweller’s Cognitive Load Theory (CLT) is the single most important thing for teachers to know“. Back came a tweet, “shouldn’t they know their students?“. I’m not sure if that was a wisecrack or a serious challenge to CLT. Either way, it shows how easy it is to misunderstand the offering that CLT provides to teachers. The great thing about CLT is that it is a lens through which to view learning before teaching. CLT provides the door into a new age of teaching that allows us to leave behind any teaching strategies that weren’t in alignment with the research into how the human brain learns.
For too long teachers have been blind to the architecture of the human brain… the only place where learning actually happens! According to CLT, when it comes to providing a productive and yet manageable cognitive challenge to students, then we need to know students’ brains. Indeed, it is CLT that invites us to really know our students. CLT invites us all to consider the brain first, learning second, and teaching third.
Further to this, the CLT door isn’t just the end of the ‘teaching-blind journey’, it’s also the beginning of a new journey. If you’re just stepping through this door and you wish to know what CLT is, then you might find it useful to read what I consider to be the 10 things you need to know about CLT. I’ve written a short ‘start-up’ booklet that unpacks these 10 things. It can be found here. My aim is that on reading this document you will quickly grasp the key principles of CLT. There is more to be said for each aspect of CLT, and there is a wealth of research to read, so, enjoy! It’s a wonderful journey and, by traveling with intellectual humility, we can all travel it together!
The 10 things you need to know are:
The working memory of the brain is very limited.
Use explicit instruction for new content.
New knowledge needs to then be stored in long-term memory, ready for retrieval and transfer.
Learning happens through schema extension and connection.
Break the curriculum down into very small chronological parts.
Know the learners’ background knowledge.
Focus the attention of learners on the new content…only!
Teaching becomes redefined as ‘focussing, guiding and responding’
Identify the key schemas operating across the bigger learning journey.
Systemise CLT across the school to maintain CLT principles and reduce workload.
Download your FREE Cognitive Load Theory booklet here:
‘Big Maths Beat That!’ isn’t like any other assessment and tracking system. It is at the very centre of the school’s entire maths curriculum. It is the engine room of the pedagogy, as opposed to ‘bolt-on tracking’. Yes, you can also say goodbye to marking! If you were told to throw out all your tracking systems (unless you desperately wanted to keep them for your own purpose), then BMBT would remain. When the curriculum, pedagogy, and tracking are one, then you have an easy and natural response to the question, ‘What impact is our curriculum having on our children’s learning?’
Simple Assessment of Progress
The BMBT challenges are at one with the curriculum design and learning journey that children enjoy, whilst also allowing adults to assess progress and attainment in relation to age-related expectations. This means that at any moment in time, we can see if a child is ‘on-track’, ‘off-track’, or ‘ahead of track’. Perhaps most importantly, however, the challenges inform us of each child’s reality, where they have learning gaps, so we can precisely address their needs, irrespective of their age!
Cognitive Learning tells us to clean up our ‘Explicit Instruction Act’
You may already be familiar with the three inner dimensions of the brain’s working memory; the intrinsic load, the extraneous load, and the germane load. Of them all, the extraneous load appears to be the simplest one to ‘get right’. It is to do with the instructional design of the learning episode, i.e. what you (as a teacher) choose to present to learners. In that sense, you have more control over it than the actual content/nature/subject of the ‘curriculum moment’ and the wiring already present in the learner’s brain as they walk through the door. Generally, the extraneous load is thought of in terms of the medium you use to present your input.
The most basic message is ‘don’t provide busy PowerPoint slides’, but the overarching CLT truth is that anything that occupies the brain’s working memory (that is not an integral part of the teaching/learning process) is taking away precious focus. If we look particularly at explicit instruction for primary school mathematics we see that there are more extraneous load factors to consider than just busy slides and making sure the window cleaner doesn’t suddenly appear just as the kids are hanging on your every word and are about to ‘get it’!
The implications of CLT (Cognitive Load Theory) for teachers are becoming well-established. However, the end result for busy teachers can end up looking like a list of ‘tips for teachers’:
‘remember not to have unnecessary animations in your powerpoint slides’,
‘remember to wait in silence while learners are processing new information before talking again’ etc.
This would be a serious watering down of the extensive research that has gone into CLT and the profound implications for teachers that have come out of that research. So, can CLT actually transform teaching in the way that it promises, and, if so, how?
In the CLT post, we suggested that exploring adaptive teaching can lead schools to advancements in their curriculum design, quality of teaching, and, crucially, the joining of the two. Here, we present 2 basic features of curriculum design that spring out of adaptive teaching, 3 broad modes for approaching adapting teaching, and finally 3 classic implementation errors.
Curriculum Design: 2 Basic Features
There are two basic requirements of a curriculum designed for adaptive teaching (i.e. one that empowers the teacher to be constantly responding to learners in a purposeful way).
I was an NQT in 1993. I can still recall the mixture of emotions in the last week of the summer holidays, preparing to launch into my teaching career proper. The usual format was to spend the day excitedly cutting out giant letters for display and writing names on books/pegs/trays etc. only to be followed by a night of waking up in a cold sweat, having dreamt – yet again – that I’d lost control of the class. Except, one night I slept really well; I was so happy because I’d had the brilliant idea to call my higher-ability group ‘Smarties’! Of course, this meant calling my middle ability group ‘Skittles’ and my low ability group ‘M&Ms’. By definition, I had already told two of my groups that I didn’t consider them ‘smart’. I shudder to think of the long-term damage being a member of ‘The M&Ms Group’ had on those poor children (now aged 34), but that was the way of it at that time. Every primary teacher had fixed ability groups, notwithstanding the occasional battle for individual promotion/relegation from group to group.
This is the last of three posts exploring how you use CLT to Crack Addition, and how this can transform your teaching! We suggest you read Part 1 & Part 2 before this post.
We are picking up on children learning to add two 2-digit numbers together for the very first time in their life, and in Part 2 we looked at using Cognitive Load Theory to ensure that the child’s Working Memory (WM) is prepared for this moment. Here is a step-by-step guide to what this episode of explicit teaching looks like:
If you haven’t read Part 1 of this thread regarding Using CLT to Crack Addition, please do so before reading this post. There is a day in a child’s life when they first learn to solve ‘2-digit add 2-digit’ addition questions. Every child has this day! The child’s teacher wakes with great excitement. This is what it’s all about. Within this day there is an actual moment when the teacher starts their explicit instruction. This will be a beautiful moment since the child’s life is about to change…well, mathematically anyway! There are a lot of steps to teach in a child’s mathematical learning journey and they don’t all have equal weighting; some are more important than others and some are just crucial. This one is one of those crucial ones; tying shoelaces, riding a bike, and ‘2-digit add 2-digit’.
Cognitive Load Theory is a ginormous beast of a pedagogical concept! At times it’s mightily complex and far from being visible in a moment, yet at other times it couldn’t be more simple, more clear, and more beautiful. It is CLT that gets us to this beautiful moment!
Rocking up to teach 30 seven/eight year-old children in an area of high social deprivation where children have been taught Big Maths using CLT to crack addition, the teacher walks straight in and presents a ‘3 digit add 3 digit’ question on screen:
Five seconds later, every single student holds up a little whiteboard displaying the correct answer; having processed the calculation entirely mentally.