Tag Archives: big ideas

Strategic curriculum leadership phase 2: the detail

This post, the second of three, details the process carried out to reform the curriculum upon taking up my Headship back in July 2018.  Every school’s needs are different so it is important to set the process I carried out into context.  The school I took over was judged as requires improvement in March 2017.  Between then and my appointment, there was a time of leadership instability.  Initial visits to the school revealed that there was a lack of any curriculum leadership – no subject overviews, no progression across the key stage and no shared understanding of how any subject should be taught.

In the first part of this series, I set out the thinking about the big picture of curriculum design and this can be summarised with three key insights:

  1. Subject leaders need to do the thinking themselves.  The value is in leaders enacting the process and learning along the way, not in buying in a commercial curriculum that is not tailored the school’s needs.
  2. The curriculum is the progress model.  If children are keeping pace with a curriculum that increases in complexity, then they are making progress.
  3. Clarify the desired outcome for each unit of work.  With periodic outcomes in mind for each unit of work, it is far easier to set children up for success in producing purposeful high quality work.

Once the big picture had been set out, it was time to focus on the details.


Strategic curriculum leadership 

Phase 2: The details


In researching other schools’ curricula, it seemed that many stopped at the big picture and handed over responsibility to teachers to create medium term plans.  This bothered me for two reasons.  The first is the workload associated with writing medium term plans because doing this well requires significant expertise and plenty of time.  If neither are afforded, then we are left with teachers trawling search engines for tasks to do which are then thrown together.  Doing the work to a high enough standard to enact the intended curriculum is not something that a typical primary subject leader, not remunerated specifically for the responsibility nor usually with the knowledge and experience necessary, can be morally expected to do.  The second reason that handing over subject overviews for subject leaders to write medium term plans from bothered me was because of the inevitable breakdown in cohesion.  All the care invested in the content and sequencing choices for each subject could easily be lost.

The resultant decision was to provide detailed medium term plans for teachers for every unit of work in order to increase the likelihood that the intended curriculum became the enacted curriculum as well as to eliminate unnecessary workload.  With so many plans to write and now beginning to train others with the right expertise, a number of criteria were needed to ensure that there was sufficient detail for teachers.

Components that build to the composite end piece of work

Medium term plans are not divided into lessons, they are divided in to components – chunks of understanding that accumulate to enable children to produce that high quality end piece.  Some components may take a couple of lessons for children to master, while some lessons could provide children with the chance to develop more than one component.  The important idea here is that lessons are the wrong unit of measurement.  Teachers need to exercise autonomy in how much time they spend developing each component because splitting the sequence up into lessons can encourage coverage rather than learning.

Each unit of work has a sequence of learning that builds towards a high quality end result.  We frame these as questions that children should be able to answer once the work has been completed.  By setting out what exactly children need to be able to articulate, it allows those writing the plans to consider different ways in which that can be achieved.

Deliberate vocabulary development

With a good overview of the content of a unit of work and where it fits in to the overall curriculum, choosing target vocabulary that children simply must understand serves two purposes.  The first is to ensure that teachers focus vocabulary instruction on that which will contribute most to understanding the key concepts of that unit.  Those with well developed subject knowledge are far better placed to make those decisions than if teachers needed to get to grips with the content and do this themselves.  The second purpose is to give leaders a simple way of monitoring the extent to which the curriculum has been learned and understood.  Sampling children’s understanding of the identified key vocabulary is a great starting point for assessment.  This can be picked up from looking at the quality of articulation of vocabulary in children’s work as well as some good old fashioned questioning.  More on this in part 3.

Identification of necessary prior knowledge

Ideally, each unit of work builds on what children have been taught at some point in the past but it is inevitable that children will forget some of what is necessary to understand the more complex ideas that come later on.  Time at the beginning of a unit of work needs to be set aside to assess and reteach what children should have remembered from those previous units.  Many schools will experience children joining school at different times of the year and at different points in the key stage and so deliberately checking and reteaching required prior knowledge helps those children to succeed too.

A thread of key concepts

Early on in the first phase of strategic curriculum leadership, I used the national curriculum and the work of the subject associations to clarify the key concepts for each subject – the big ideas that often recur at increasing levels of complexity in most year groups.  Examples of key concepts are:

  • position on a number line in maths
  • the effect of writing on a reader in English
  • the idea that a force is required to change an object’s movement in science
  • cause, effect and legacy in history
  • scale in geography
  • worship in RE
  • identity in PSHE
  • performance in music
  • invasion strategy in PE
  • depth in art
  • accent and pronunciation in French
  • debugging in computing

These concepts should be regularly revisited and developed iteratively over the span of a curriculum and drawing explicit attention to them in medium term plans helped to focus the plans on addressing them as well as drawing attention to high level curriculum thinking for teachers reading and using them.

What teachers need to know

Teachers’ subject knowledge is vital to them explaining clearly and enthusing children in each subject.  Proper research into the topics being taught takes time but this burden can be eased by the inclusion of key subject knowledge for teachers on each medium term plan.  Experts compiled extracts, links and videos for teachers to access as a bare minimum to teach the unit well.  This has now become a significant strand of our CPD offer.  The experts writing the medium term plans will occasionally come across some content that clearly requires some high quality face to face training too.  When developing our art plans and talking to the teachers that would be teaching each topic, it became clear that a unit on perspective drawing and a unit on op art would never be successful without structured training because the teachers had no experience at all of them.  Working with a local artist, they showed our teachers how execute certain artistic techniques and as a result, we had far more confident teachers and excellent pieces of art.

Skeleton presentations for teachers

Teachers would need to take the medium term plans that have been written and turn them into what children will see in each lesson.  However this is another example of a key moment when all the careful thinking about curriculum design can go wrong.  It is very easy now to find published presentations, some free and some needing subscription, with a quick online search.  The quality is variable and so is the relevance.  Choosing the right models, images pictures and video clips to show children can be time consuming when done properly.  For this reason, the plan is for those with the time and expertise to source these visuals and compile them for teachers into presentations.  Teachers will be free to use these if they wish and welcome to add to or improve them.

A key consideration throughout all this work is striking the right balance between prescription and autonomy.  Leaning too far towards prescription may ease workload but remove a lot of teacher choice about what is covered and when.  Leaning too far towards autonomy may give teachers more choice but increase their workload and result in a loss of cohesion.  For this reason, the medium term plans that we wrote detail what children need to know, understand and remember.  Ideas are provided for how teachers might achieve that but it is here that teachers have autonomy to do different things.  These decisions are guided by our teaching and learning guidance about what makes great teaching.

In the third part of this series, I describe the information that we gather that informs us of how well the curriculum is being learned and then what we do with that information.

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Maths — the big ideas

The beauty of maths lies in the interconnectedness of ideas and concepts yet this concept of relationships is often lacking in children who struggle with maths.  Mike Askew, Professor of Education at Monash University, Melbourne, has written about what he calls the big ideas of maths. These help children to connect different areas of mathematical understanding, yet are small enough to understand in their own right.  

Read the rest of the article here.

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A place for everything and everything in its place

Place value is very often one of the first units of work for maths in most year groups and is absolutely fundamental to a good understanding of number.  By getting this right and giving children the opportunity for deep conceptual understanding, we can lay solid foundations for the year.

For the purpose of this blog I’m going to assume that children can count reliably and read and write numbers without error. If these things are not yet developed to the appropriate standard then targeted intervention needs to happen without the child missing out on good modelling and explanations of place value.

Children need plenty of practice constructing and deconstructing numbers, first using concrete manipulatives like base ten blocks or Numicon.  This is to show that 10 ones is equivalent to 1 ten etc.  While they’re making these numbers they should be supported to talk articulately about what they are doing, perhaps with speaking frames: ‘This number is 45.  It has 4 tens and 5 ones.  45 is equal to 40 add 5.’

Read the rest of the article on the Rising Stars Blog.

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What I think about…maths

Moving schools and with more than an eye on headship is sure to get you reflecting.  The following posts are what I think about various things, in no particular order.  Previous posts were about displays and learning.  Next up – maths.

Any unit of work should be planned with end points in mind.  Teachers should start with the relevant National Curriculum statements but more importantly, the types of questions that children will be expected to be able to solve.  Teachers in Y2 and Y6, with their experience of end of key stage testing, may well have internalised the type of questions that would be appropriate for children to solve but resources like the Rising Stars Assessment Bank are invaluable for teachers.  Our expectations of what children will learn are vital. All children are capable of achieving age related expectations given the right support and sufficient time. If we begin a unit with lowered expectations for some children based on perceived ability then we are failing them.

Once the expectations of what children will be able to do at the end of the unit are clarified, teachers should then plan backwards, thinking carefully about what children will need to know and be able to do in order to solve those problems as well as figuring out a sensible conceptual sequence of those things.  For me, these include fluency with number, learning the underlying structure of the problems to be solved, the deliberate teaching of mathematical language and opportunities to reason.  The more I think about this, the more I’m settling on a sequence of development that units of work should be structured around, key parts of the sequence are developed and consolidated over time:
Stages of a unit of work

This model may not work for all topics but I’d suggest that units of work start with pure number.  Contexts can be stripped away to reduce load on working memory and children can get on with learning and practising fluency so that as soon as possible, they are able to recall necessary factual knowledge and manipulate numbers in calculations with little mental effort.  This is by no means rote learning – it should be carefully thought out so that children develop sound conceptual understanding, starting with concrete representations, progressing to more efficient pictorial representations and then on to even more efficient abstract representations.  It is important that teachers remember that the abstract representations are not the maths itself, merely the most efficient way of recording or communicating the thinking.

Fluency

If children can recall number facts and other basic mathematical knowledge within a few seconds, if children can calculate reliably without expending too much mental effort, and if children can recall varied mathematical knowledge, switching between topics, then they will be considerably more able to commit precious working memory capacity to problems that require deeper thinking.  It is for this reason that fluency must come first and continue to be practised in order for that recall to become increasingly accurate and efficient.  Flash cards are very useful here – they provide the opportunity for self-testing and, with a little training, can help the child to become more aware of the what they know and do not know, enabling them to focus their own study.  Teachers figure out what basics are required and deliberately teach those basics if they are not sufficiently internalised already.  If some children are already fluent, they can work on speed and efficiency, for children may well have fluent but inflexible strategies.

Underlying structure

Stories can be said to be a variation or combination of just seven basic plots and expert writers have a sound knowledge of these, enabling them to see stories at a deeper level.  I’d argue that there is a significant similarity in maths; that there are five basic problem structures.  These five structures are aspects of either additive or multiplicative reasoning and are classified based on what is unknown in a problem:

Maths structures

Knowing the structures is not sufficient.  Children must be able to identify the underlying structure from a given problem.  This is no mean feat so sticking to just number problems and avoiding distracting contexts for the time being is important.  Take a problem like this:

Empty box

Hattie and Yates, in Visible Learning and the Science of How We Learn, said that experts see and represent problems at a deeper level.  A novice will only see the surface features in this problem: two numbers and an addition sign.  Consequently, they’ll solve this by adding the two numbers together.  Of course, this is a mistake.  An expert, on the other hand, will know that the whole is made up of parts and that you add the parts together to make the whole.  They may even ignore the numbers at first and read it as part + part = whole, realising that it is a problem where one of the parts is unknown.  They may see it or draw it like this:

Bar model

They’ll use their knowledge of the relationship between the whole and its parts, plus the idea that to find a missing part, you subtract the known part from the whole, therefore calculating 564 – 327 to find the unknown.

It is this kind of thinking that we must get children to do.  Maths lessons should be planned with a sole priority – what will the children be thinking about?  In this first stage of a unit of work, children develop their fluency and then begin to reason about what is unknown in a numerical problem and how to figure out that unknown.

Deliberate teaching of language

The second stage of my model involves building on the number work by adding layers of mathematical language that enable children to talk like mathematicians and understand problems involving ambiguous language. We need to embrace ambiguity because it is in that grey area of language that we can really get children to think hard.  The image below is one I’ve seen many times in many schools and even had up in my classroom in a previous life:

Language.jpg

What this kind of display tells children is that a word equates to an operation.  This is misleading at best and more likely disastrous for understanding.  Words like this only carry meaning in context, for example look at the phrase ‘more than’:

More than

It does not mean that you have to add the numbers together.  It can mean that, but it could also mean finding the difference.  And what of the word difference?

Difference

The ambiguity of language must be deliberately taught and linked back to the underlying structures that children will have been working on.  Teachers model the thinking and ask: In the first  question, is the whole unknown or a part unknown?  What about the second sentence? Draw it…

Wider problem solving

Remembering Hattie and Yates’ assertion that novices see surface features of problems and experts see the same problems at a deeper level, consider this:

Anum and Jay have saved up their pocket money.  Altogether they have £35 and Anum has saved £18.50.  How much has Jay saved?

A novice would read that question and would say it’s a problem about pocket money – the surface feature.  An expert would look at the same problem and say that it’s one where the whole is known and so is one of the parts, but that the other part is unknown.

Once teachers know how experts think, it is perhaps a mistake to simply try and get novices to think like that.  Experts have a vast store of knowledge from which they draw on when analysing problems and so to get novices to eventually think like experts, we must first teach them the underlying patterns.

With this in mind, take a look at this common practice:

Subtraction problems

If we teach children how to subtract, then give them problems that only require subtraction, what are children really thinking about?  Not structure.  Not language.  And yet we can still mislead ourselves when children ‘get the right answers’ that they truly understand what they’re doing.  They may well do but we can’t be sure with tasks like this.  The tasks that we set show what we value.  Perhaps a better task is to ensure that children are thinking like mathematicians, sorting then solving problems based on their underlying structure:

Sorting 1

Sorting 2

Throughout the entire unit

Other considerations during a unit of work include the big ideas in maths.  Coined by Mike Askew, these are concepts that children develop throughout their time at school and are built on year on year:

  • position on a number line
  • estimation
  • equivalence
  • place value
  • numerical reasoning
  • the meaning of symbols
  • classifying
  • sequences

Opportunities should be created throughout a unit for children to think about content in these ways so that they can make connections between ways of thinking and different representations.

Finally, but by no means of least value, teachers must pay careful attention to success criteria. Before this though, objectives need to be sound. Shirley Clarke’s work on formative assessment is important here and there should be clarity between closed and open objectives. Closed objectives are absolute. They have either been achieved or they have not. Procedural success criteria are most appropriate here – steps to follow in order to be successful. Open objectives on the other hand are subjective in that they can be achieved to varying degrees of quality. A selection of tools is most appropriate for success criteria in this instance – strategies to choose from with the goal of efficiency, for example. Year 5 children could be given the calculation 5023 – 3786 and they should be able to, following great teaching, choose a subtraction strategy to solve that calculation in the most efficient way possible. All the procedural work, such as deliberately learning to count up, count back, round and adjust, or carry out column subtraction comes together and all those strategies form a toolkit from which children choose he best tool for the  job.

This model for teaching maths certainly covers National Curriculum aims but more importantly, it strives to get children to think and communicate like mathematicians.

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Multiplying fractions and integers

This is an account of a particularly successful topic from Y5 on multiplying fractions and integers. It’s fast becoming one of my favourite concepts to teach.
I showed multiple representations of a calculation, showing how to make it with cubes:

  
In this example, it was important to make four lots of two thirds first before rearranging the coloured cubes: later when they draw it on a number line, they’ll need to be thinking of four jumps of two thirds. The language of number of parts, size of each part and whole was supported by the bar model and came in handy for the empty box problems later.
Children needed to make other examples of calculations, talking about it with a partner:

  
Most children were fine with this and ready to move on to pictorial representation on a number line. Some needed a bit more consolidation with how the cubes represent a calculation. This is of a set of scaffolded questions where children made the calculation with cubes, then drew it:

  
For those ready for a number line, I explained a worked example before modelling how to do one from scratch:

  
The explanation had to be clear on how to construct the number line accurately, which involved making decisions about how many squares to leave between each whole number (using the denominator of the ‘size of each part’), and how many squares each jump needed to be (using the numerator of the ‘size of each part’). The final decision to make was how many jumps to draw, using the number of equal parts. The whole, and the answer to this particular calculation, was where the last jump ended up in the number line.

When children practised doing this, they chose from using a scaffold of minimally different questions or tackling varied questions:
  
Some children needed a few lessons to keep practising this and each time we returned to it, I started by showing multiple representations of the same calculation:

   

 Some children grasped this concept quickly and needed to work on deeper tasks. I made some subtle changes to the language I used to describe what was happening (bottom right corner of the above image) and used the same bar model to introduce inverse operations with aim of learning to solve empty box multiplication of fractions:

  
Bar models helped to explain what was known and what was unknown, using the language of whole, number of parts and size of each part. I showed how it looked on a number line too:

  
Some managed to get on to dividing fractions and whole numbers, using bar models (which they were familiar with for integer multiplication and division) and number lines to show what was happening:

   
 All the while, more children began to move from basic multiplication of fractions to some deeper thinking about multiplicative reasoning and fractions.

A few weeks later, children worked out the area of rectangles involving fractions and had internalised much of the language to be able to represent questions like this:

  

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