Concrete preparation: fast or slow?

Written by Sarah Seleznyov

I’ve often felt in my work with teachers, that concrete preparation was the least well understood of the Let’s Think principles. Social construction has experienced a recent boom in popularity, aligning with work on dialogic teaching (Alexander, 2008) and supporting the move towards partner and group work in classrooms. Metacognition is now a buzz word in the education world, since being flagged up by the Education Endowment Foundation Toolkit for Teachers (https://educationendowmentfoundation.org.uk/resources/teaching-learning-toolkit/meta-cognition-and-self-regulation/) and John Hattie’s Visible Learning (2008) as one of the top hitters for adding value to pupil learning. Cognitive conflict has a large body of research behind it, including studies flagging up the importance of ‘productive failure’ (Kapur, 2008), and increasingly popular approaches like Singapore maths push problem solving as a key strategy to improve reasoning.

Concrete preparation on the other hand, does not have a body of popular interest behind it, nor a vast body of corroborative research, and yet, when watching teachers teach Let’s Think maths lessons with primary pupils, it’s crucial to the development of mathematical thinking.

The essential principle behind the concept of concrete preparation is that pupils need to be given a starter experience for the task that is accessible to them all, even though the task itself may be aimed at a more advanced Piagetian stage. So, it is an early activity in a Let’s Think lesson in which, in the context of the challenge to come, the majority of pupils can be engaged without the need for accommodation. Perhaps we could describe it as accessible preparation. The lesson presents a context that allows a range of levels of cognitive demand AND successful performance by all the pupils in the class (given the expected range of cognitive levels for the relevant age group).

Exploring the concept of concrete preparation with teachers draws their attention to important precursors necessary for the pupils’ future response to the cognitive conflict. Firstly, concrete preparation presents a context for the learning with which pupils can engage and in which they will be motivated to solve the problem (what we sometimes call the ‘hook’). This may be a real life context, or an imaginary context but its role is largely to engage the pupils and so that the cognitive conflict that will emerge is not one of unfamiliarity, but of conceptual demand. So, when exploring decimal notation with Year 4 pupils, we talk about a giant and pixies building a castle using their feet as units of measure (the pixie feet conveniently being 1/10 of a giant’s foot). When sorting and classifying pictures of types of adult and baby animals in different colours, we talk about the need to tidy up a mess created by a naughty group of pupils.

Concrete preparation also involves some activity that serves to activate the pupil’s ideas about an emerging problem, giving them something to ‘get a grip on’ when, as is usually the case, the problem becomes ‘slippy’. Pupils need to ‘see’ some of the problem in a concrete way. So, when exploring measures, pupils look at at a series of rulers with missing or duplicate numbers, which do not all start on zero. When exploring ratio, pupils begin by creating multiple written descriptions of visual images of ratios in the form of jelly babies with differently proportioned heads and bodies.

The words that later may be useful thinking tools begin to emerge, both agreed terminology and schema-specific vocabulary. When working with very young pupils this largely involves handling and describing the equipment, checking the pupils have the necessary vocabulary as a group, and agreeing the ‘rules for the game’. This cues pupils in to the nature of the task and helps them create a bridge with current ideas and terms that may be useful for the challenge to come. When we say ‘big’, do we mean length, breadth, height, volume or weight? Do we all know the names of the colours or the vehicles?

Planning for concrete preparation requires the teacher to consider how the pupil and the problem can be prepared to engage with each other. It is here that the teacher is also making their early diagnosis about the gulf between the reasoning currently available to students currently and the reasoning that will be required as the lesson unfolds. So, when introducing a simple block graph, do the pupils understand that the blocks should be coloured in to represent each item in the picture, or does that need to be discussed in order for them to begin the task?

When watching primary teachers new to Let’s Think Maths, there are a couple of common pitfalls we observe in the concrete preparation section of the lesson:

Teachers sometimes dwell on the ‘hook’ or story that frames the concrete preparation, because it is often very motivating for the pupils and all pupils in the class can access it easily. However, spending 20 minutes on the concrete preparation means the teacher is unlikely to have enough time in the lesson to really challenge pupils’ thinking, especially that of the highest attainers.
When teachers try to counter this by rushing through the concrete preparation the shared vocabulary required for the task is not agreed and pupils’ understanding of the ‘rules for the game’ is too shallow. This limits the depth with which pupils can tackle the cognitive conflict. When pupils are not given sufficient time to explore and physically handle the lesson resources (and this is especially the case with very young pupils), their understanding of the task is reduced and they often focus on grabbing attractive equipment for themselves instead of engaging in social construction to use it to solve the cognitive conflict .

It’s a tricky balance to get right – go too fast and solutions to the cognitive conflict remain out of reach; go too slow and you never get to the cognitive conflict that really pushes the thinking of your class. The only way to get it right is to teach the lessons repeatedly, and to continuously reflect on the way you approached the concrete preparation. I always say, you never really feel like you have got a lesson licked until you have taught it four times!

References

Alexnder, R., 2008. Culture, dialogue and learning: Notes on an emerging pedagogy. In Barnes, D., Mercer, N. and Hodgkinson, S., 2008. Exploring talk in schools.

Hattie, J., 2008. Visible learning: A synthesis of over 800 meta-analyses relating to achievement. Routledge.

Kapur, M., 2008. Productive failure. Cognition and instruction, 26(3), pp.379-424.