Teaching for understanding: Schema-building and generative learning.

I’ve had the privilege of observing a lot of lessons already this term – with huge thanks to the teachers concerned for their warm welcome. As I’ve been doing this, I realise I’m applying a continually evolving mental model of the learning process to what I’m seeing – and this is what influences the dialogues I’m having afterwards. What I’m always interested in is the challenge of getting everyone to engage with successful learning – including the less confident kids in the corners, trying hard to grasp the ideas but finding it hard.

More and more I feel that it’s really helpful and important for teachers to think in terms of the concept of schema-building: that every student is piecing together ideas, information, experiences and concepts to form a coherent web that constitutes their understanding and fluency with the material in hand.

A key element in the learning process as viewed through this model, is that students need to build on prior knowledge. This has a few implications:

• prior knowledge needs to be activated deliberately – so, before introducing new ideas, time needs to be spent enabling all students to revisit the foundational knowledge to which new ideas will connect.
• different students have different arrays of prior knowledge – so the teaching processes need to engage all students in tasks that allow them all to think about what they already know and the teacher needs to get some sense of the range in the class in order to provide the most appropriate form of instruction. This doesn’t happen if most of the talk is between the teacher and a small sample of students who answer most of the questions.
• these processes need to be generative – which means they need to involve students in retrieving their existing schema, exploring their mental models consciously, making as many connections as they can to new information. This doesn’t happen if lessons are too task dominated – getting things written down neatly in books that aren’t properly understood.
• the richer the array that is engaged, the more ways there are for new knowledge to be made sense of and assimilated into the overall schema; because students have different arrays of prior knowledge, it’s not possible to map a neat linear path that all students will follow successfully
• new knowledge needs to be consolidated into the schema by all students in ways that they themselves understand; this needs a degree of rehearsal and evaluation so that what is being stored is complete and accurate; this means we need to think about how we’re engaging all students as much of the time as possible. The simple act of getting students thinking or talking through what they know and understand, with guidance and structure, is important – but isn’t always offered to everyone.
• in many subjects, all of this needs to happen before engaging in retrieval activities primarily designed to strengthen recall and fluency. The knowledge often needs to make sense first at some basic level, connected to prior knowledge in a meaningful way, before you worry about forgetting it.

Before this all sounds too generic, let’s look at a couple of examples.

States of Matter

What is going on in these images? How do we make sense of melting, freezing, condensation, evaporation, solid/liquid/gas, temperature, heat?

Some of understanding is based on experiences:

• e.g. feeling an ice cube melt in your hand – thinking about the sense that ‘cold’ is coming into your hand from the ice when it’s actually heat leaving your hand; that the molecules of liquid water are the same ones that were once solid in the ice, now moving more freely.
• feeling the wet exterior of a beaker of icy water – considering where that water came from. Not from inside the beaker – no! From the air – the invisible water vapour cooling and condensing on the cold surface.

Some is based on knowing the words to use: condensation, molecule, heat, temperature, melting: these have specific meaning that I can apply to the experiences and observations. They also have a grammar that I need. The water condenses; the process is condensation. Water is made of molecules; its structure is molecular.

Some of it is based on mental models of invisible processes: the particle model allows us to envisage how molecular forces and structures and particle energies explain the macro changes we observe:

Embedded in this is the related knowledge that water is made of molecules: i.e particles with two or more atoms joined together. It is also a compound: made of more than one type of atom. H₂O is the symbolic representation telling us that two atoms of the element hydrogen join with one atom of the element oxygen in every water molecule. Terminology is King here!

So – imagine your goal is for every student to be able understand and explain a range of phenomena related to states of matter. What is needed? Most importantly, they all need to form some mental model for what is happening during these processes that makes sense in their heads – ideally in terms of a particle model because that will be very powerful. In order to communicate these ideas, they all need to connect a list of words to the real-world phenomena they’ve experienced, observed, witnessed or (at the very least) imagined. The model will always be a simplification – it will have representational elements that serve an explanatory purpose whilst not being ‘true’ – nobody can really visualise the sheer number of molecules in a drop of water; the scale at which evaporation or condensation happens at a molecular level is beyond imagining.

How do we do this? Well, for a start, let me suggest that it won’t be enough to explain and demonstrate, ask a few students some questions and then to get everyone to draw a diagram in their book, followed by a few word-definition quiz questions. There are a number of things students often do that only create an illusion of learning:

• Adding the label solid, liquid, gas to the simple particle diagrams. This is trivial.
• Reproducing the definitions on cue: Condensation? Ah that’s “Condensation is the conversion of a vapour or gas to a liquid“

These cued-up fact retrieval exercises don’t represent real understanding of the phenomena. It’s possible to go through the motions with all of this and still not really understand it.

What is needed is for all students to blend information from instructional inputs, demonstrations and hands-on experiences with the ideas they already had in much more rounded, holistic ways. They need to engage in a varied series of generative processes that allow them to reconstruct their models; to review their fluency with the terminology; to test their understanding by applying it to various scenarios to explain what is happening. Before we start quizzing, how about some of the following:

• In pairs (so that everyone is doing it), explain how the outside of the beaker gets wet, using both of the terms ‘molecules’, ‘condense’, ‘condensation’ and ‘energy’.
• You’ve seen the model example but now, books shut, on your own, draw a diagram and use it to explain why your hand feels cold and gets wet when holding an ice cube – as if you were explaining it to a younger sibling. Again, use the terminology; say the words out loud.
• Use the labelled diagram from the knowledge booklet in your pair to take turns to ask each other probing questions about the process. Ask ‘why?’ questions as well as ‘what does it mean?’ questions.
• Write out a summary of the key steps that happen from having a solid block of ice to a puddle of water and then, on a warm day, a dry patch where the ice once was. Explain it to yourself first, then try to write it down.

Each of these processes requires students to rehearse using the terminology, to create connections between new ideas and existing ideas; to make sense of the phenomena in a real-world physical space and link them to an underlying mental model for the changes that are happening. It requires thinking, thinking, thinking. Hard thinking. Ultimately, this is what will secure the learning in long-term memory.

Cold Calling, Pair Share and Check for Understanding used in combination allow the teacher to probe, sample and re-teach as needed as well as creating an ongoing level of accountability that makes sure all students are switched on, focused on the material in hand.

Once students have engaged in generative processes teachers have to engineer activities that allow them to check for accuracy and errors, misconceptions and omissions. This should include accurate use of the terminology – molecule, particle, atom, heat, temperature etc. If you’re not practising using words, you don’t know if you can use them properly. The more often you use them accurately, the more fluent you become. (A simple reflection: did you ensure all of your students used all of the terminology you were teaching them in the lesson enough times for it to stick?)

After an evaluation/feedback cycle, students can then have another go to re-explain, deepen, elaborate, extend – and apply reasoning using their new understanding to new scenarios. Thinking in terms of molecules of water, why do my glasses steam up over my Covid mask the whole time? Why do sheets dry on the line on a windy day even if it’s cold?

This is schema-building at work. All students are doing it. It requires high quality highly interactive instructional inputs, lots of structured thinking and talking and, ideally, some specific hands-on experiences and tasks that are highly generative in nature.

Fracking

Here’s another, shorter example. I saw a really good lesson that included fracking and I realised I didn’t really know as much about it as I thought! What do you know about fracking? If you really know about it, ideally you should be able to give a short talk without notes explaining a) how it works and b) what the main advantages and disadvantages are and why it is controversial. You’d be able to compare it to other energy sources in terms of human and environmental impact.

Imagine you’d never heard of fracking. Where would you begin? You might read an article: https://www.theweek.co.uk/62121/what-are-the-pros-and-cons-of-fracking. This has the benefit of placing the ideas in context, linking them together. There are neat lists of advantages and disadvantages. However, to visualise what’s going on, you need a diagram too:

Now, I could copy this out and make a list of advantages and disadvantages in my book, whilst reading the article. Would that mean I’ve formed a secure schema for fracking? It could… but only if I already know and understanding quite a lot of the basic terms and references; if I have a sense of the scale distortions implicit in the schematic diagram.

Before I do any writing on this, I think it would help if I actually just process my understanding for a few minutes. Book shut, what is fracking? What’s happening? Where does it happen? How does it work? What’s the extent of this activity? Why is it any good to anyone? Why is it a problem? If I’m unsure, I’ll go back to my notes and check for the things I still don’t know yet. Then I can try to re-explain it, adding more detail. If I have a partner we can do this together in turns, so we can verbalise the terminology and check if we’re getting our facts right. We can deepen our understanding by asking each other hard questions – following the model, our teacher uses.

Once I’ve got the general idea – I don’t want to forget, so I’ll write out a list of key points; I’ll make a summary diagram and a summary table, maybe some kind of flow diagram – from memory. Then I’ll check back to see what I’ve missed out. This is now a list of things I know, rather than a list of things I don’t know. I can use it to test my recall and fill in some gaps. It would help if my teacher could check my efforts – or showed me what they would have done – to provide some corrective feedback – but I still need to be able to do it myself after that. I don’t need a complete table so it looks nice; I need it so I can check that I’ve got it in my head so I know I understand it.

Ok – now, I’m about ready to give that talk from memory – because I’ve got a good idea about what fracking is and what the pros and cons are. I understand it; I know it.

Hopefully this captures the essence of what I’m saying. There are two key challenges:

• Making learning sufficiently broad and generative to allow secure schema-building at a conceptual level to take place, building on prior knowledge, linking elements of knowledge into a coherent whole, before engaging in too much retrieval practice for individual elements.
• Constructing activities so that all students can do this at the same time, including opportunities for all students to run through what they know and understand.

Top tip: Check out Zoe and Mark Enser’s Generative Learning in Action. It’s full of ideas for doing this.