Creating the conditions for mastery (1)

With thanks to Nick Hart, Deputy Head at Penn Wood Primary and Nursery School in Slough, for this fascinating article on scaffolding.

In one episode of the Simpsons, Bart moves school and is immediately put into a remedial class. He joins a lesson where they are continuing their work from the previous day – the letter ‘a’. Bart’s observation is: ‘Let me get this straight. We’re going to catch up to the other kids by going slower than them?’

Our expectations are a self-fulfilling prophecy so if we differentiate work by giving lower level tasks, it limits what children could possibly achieve. Of course, if children are weak on the basics, time must be found to work on them outside of maths lessons where possible but if we scaffold work so that all children think about the same concept, and allow appropriate time, then we expose them to the full spectrum of fascinating, beautiful maths. The metaphor of scaffolding is useful in that it allows buildings to be erected that would otherwise be impossible.

What do you want children to think about? Learning happens when people have to think hard about something and memory is the residue to thought. These two insights from Rob Coe and Daniel Willingham make the link between thinking and learning. By focusing first on what children will be thinking about rather than what they will be doing, we can have more influence on what they remember. For example, a Year 3 objective is: ‘Add and subtract two two-digit numbers mentally’. A quick trawl online would yield a number of (questionable) worksheets that may not get children thinking in a way that is best for conceptual development. For this objective, and for children to understand an efficient mental strategy, children will need to be thinking about partitioning the second number, adding the tens, then the ones.

What will their task look like? Having clarified what children will think about, their tasks should be designed to prompt this thinking. If we opt for published or previously used tasks, it is well worth analysing them – will this task get children to think about the right content or think in an appropriate way? All children should find work difficult, but not too difficult. That difficulty needs to be the right kind of difficulty too. When designing or adapting tasks, it is important to reduce any distractions for novice learners and the load on their working memories so that they can focus on the necessary thinking. Using the Year 3 objective above, any task would need to ensure that children are thinking ‘Add the tens, add the ones’. Base ten blocks are perfect for questions like 63 + 32. Children make the first part (63) and then the second part (32). They’d partition the 32 into tens and ones before keeping 63 in mind and moving the tens, one at a time over to the 63 and counting ’73, 83, 93’. They’d manipulate the ones in the same way: ‘94, 95’. Children might record this on a number line or simply record the addition statement that they have modelled.

How will the task be scaffolded? The use of concrete manipulatives is a scaffold to help children work mentally. The intention is not to make work easier, or for some children to be doing different work, but to get all children to think with clarity and increasing expertise about the concept in hand. Getting the scaffold right is important and there are a number of choices to make:

Scaffolding before the lesson

Some scaffolding can be provided in advance of the lesson(s). If there is any fundamental prior knowledge or skill that certain children have been identified as lacking, spending some time working on this would make their success more likely. They would need to practise recalling that knowledge or performing that skill before-hand. In the Year 3 example, children need to be fluent in counting in 10s from any number and partitioning 2 digit numbers.

Scaffolding tasks

Partially completed examples are those in which part of the process is already completed and the children finish them off. This type of scaffold can reduce load on working memory and when it is gradually removed (children do more and more themselves), they can eventually be completing tasks that may otherwise have been out of reach. With the two-digit addition example, a partially completed scaffold might be a number line that has been started for the child and which they need to finish off.

Minimally different examples can reduce load on working memory because only one or a small number of things change from one example to the next. This can lead to children doing more work than they otherwise might and in turn thinking more about the content. If examples are increasingly different, the scaffold is gradually removed and children would experience varied examples. For adding two digit numbers, a series of questions might look like this:

56 + 21

56 + 22

56 + 32

46 + 32

46 + 34

45 + 34

Isolating decisions can reduce workload on working memory because children have a small number of decisions to make. Multiple choice questions can be designed well with misconceptions in mind and if we slowly increase the number choices or the similarity between choices, the scaffold can be removed. For adding two-digit numbers, children could be presented with a calculation and two or more number line representations of it (where one is a correct representation and the others are not). The child would then select the accurate representation and talk about why they chose it, using the same language of adding the tens then adding the ones.

Working collaboratively with a peer or with adult support can help to focus children’s thinking on the required content. The peer or adult can model their thought processes, and provide feedback on the child’s work.

How will children know what to do? The modelling of a concept (and the supporting explanation) needs to be concrete and clear. For many children, this will be enough of a scaffold. A worked example where the teacher shows children what to do whilst verbalising the thinking behind it is powerful. Discussion about what the teacher did can lead to the co-construction of success criteria, which children will have access to when they work themselves. Good success criteria, again, may be enough of a scaffold for many children. It is important to consider what kind of success criteria is appropriate:

Procedural steps, for example the process of written division.
A toolkit, for example choosing a mental strategy based on the calculation.
A fundamental principle, for example when you subtract, you always do so from the whole and not one of the parts.

In the ongoing example from Year 3, procedural steps are the most appropriate form of success criteria:

Partition the second number
Count on the tens
Count on the ones

Which children get the scaffold and when should it be removed? In her book, Outstanding Formative Assessment: Principles and Practice, Shirley Clarke says that: ‘Deciding how much children know and what they need next is a minute by minute necessity in the class.’ If all children are going to be working on the same concept, we have important decisions to make about which children are given a scaffold and what type of scaffold is most appropriate. This goes beyond having fixed ability groups or sets. We must judge when and how to remove a scaffold so that in the end, children are working on appropriate content without it.

An approach to lesson design such as this over time allows children to be successful at age appropriate content. If this is combined with intelligent curriculum design and sharp formative assessment, children rely less and less on the scaffolds as the year progresses and the conditions are created in which the vast majority can master the content.

Creating the conditions for mastery (1)

Scaffolding before the lesson

Scaffolding tasks

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