Understanding or Memorising?


Herbert A Simon (1916-2001)

One of the most damaging myths in education is that there is a conflict between memorisation and understanding, when in fact, they go together, and are both essential. This is one of the ideas demolished by Daisy Christodoulou in Seven Myths, under the heading of ‘facts prevent understanding’. The classic piece of research by Nobel laureate Herbert Simon on chess players shows how memorising and understanding are not in conflict; rather, they are intertwined and interdependent. Chess grand masters can look briefly at a chess board and then remember the positions of the pieces far better than those not skilled in chess. But they could only do this when the pieces were arranged as they would be in a game scenario. When they were randomly arranged, the chess players performed no better than the average.

The chess grand master’s supreme skill is based largely on memorising tens of thousands of game scenarios. Most of the time, most of what a grand master is doing in a chess game is remembering. This is not in conflict with understanding. Obviously the grand master understands the rules of chess, but then so does someone who is only a beginner. What distinguishes the grand master from the beginner is the difference between their long term memories. One is well-stocked with chess moves and scenarios, while the other isn’t. If the beginner wants to advance, she needs to put in the effort and get memorising. She needs to be drilled, or drill herself. She needs to study hard.

This applies to every academic subject. Understanding and memorisation are both essential, but the majority of the effort must go into memorising, because a pupil can grasp a concept readily in a lesson, but quickly forget it, because she has not been drilled in class, nor has she been required to self-quiz for homework to consolidate the knowledge, nor has she been tested at intervals to make sure it does not fade. Drilling, self-quizzing, testing at intervals: these are the foundations of teaching which enable everyone to make progress, because memorisation is absolutely essential, and it strengthens and consolidates understanding. Without the knowledge in your mind, how can you think about it? It is the lack of these foundations which leads to the lament which I have heard so often in so many staff rooms: “I taught them that material. Why can’t they remember it? Why did so many fail the end of term exam?”

It is because of the false distinction between understanding and memorisation that teachers do not focus anywhere near enough time on making sure the foundations are in place. The bulk of class and homework time needs to be dedicated to making sure that core knowledge is thoroughly mastered. If this is not done, then only the most able and motivated will make much progress. The most able and motivated may well then go on to become education professors, and because they were not required to memorise, they’ll think that everyone else can just blithely sail along without the hard work of deliberately committing key facts and procedures to memory.

This is known as expert blindness, and the more gifted a person is, the more likely they are to suffer from it. But all teachers suffer from it to some extent, and to overcome it, we need good programmes of instruction which emphasise drill and repeated practice. We can’t depend upon our gut feeling, or even our ‘professional judgement’, to know when something has been practised enough.

(Image from Wikimedia).



Liberation from Levels


This man wrote ‘effectively’. But was his writing ‘sophisticated’?

Since national curriculum levels were abandoned, schools have had to build their own systems for describing and assessing progress. Unfortunately, as with many of their new found freedoms, few schools are making the most of this opportunity to transform curriculum and assessment, and make them more specific, reliable and meaningful. Instead, they are producing schemes of work and assessment filled with recycled versions of the old national curriculum level descriptors.

It’s understandable that schools do not want to leave level descriptors behind. They were statutory for many years, and they are still used by examination boards to describe grades. The only problem is, they are nonsense, and educationally harmful nonsense, too.

For writing, they typically involve statements like ‘wide vocabulary’ or writing ‘effectively’, or writing with ‘sophistication’. What do these words actually mean? How ‘wide’ is ‘wide’? What does ‘sophisticated’ look like? Such statements do not provide an objective standard of measurement, because they are open to multiple interpretations.

A far better method of assessing writing is by ranking it. Systematised comparative judgement looks like an excellent way of harnessing the reliability of ranking. Teachers cannot agree consistently on a mark for any given piece of writing, but they can agree very consistently, when shown two pieces of writing, on which one is better.

Even in the absence of the more systematised comparative judgement, teachers can mark by ranking. When they have a set of essays or stories to mark, they can put them in a rank order, and if they have to assign a grade, they can do so according to that rank order.

An experienced marker is doing some kind of comparative judgement in any case. He will say ‘I know what an A looks like’. What this means, is that he has marked hundreds or even thousands of pieces of work and compared them mentally, placing A grade work at the top of the rank order. An experienced marker will never be thinking to himself, as he gazes at a mark scheme, ‘Now is this sophisticated, or is this effective?’ Even if he uses those words because the mark scheme tells him to, what he will really be thinking is, ‘Is this top, middle or bottom? How does this compare to the best writing I’ve seen?’ and similar questions.

As well as being hopeless for accurate assessment, level descriptors undermine efforts to build a knowledge curriculum. They tend to be generic. In the study of literature, they will contain statements like ‘Can analyse the author’s use of language’. If we’re measuring progress against vague, general statements like this, we will not be thinking in terms of content that must be mastered, but in terms of general skills that can supposedly be demonstrated with any content. The content becomes indifferent.

Level descriptors take us away from specific content, because they never say clear, specific things like ‘Knows in what century Chaucer lived’, or ‘Knows Chaucer’s attitude towards late medieval society’. In fact, it’s rare to see the word ‘knows’ in a level descriptor. They tend to be about what you can do, not what you know, and thus they perpetuate the myth of general skills divorced from specific domains of knowledge.

If we want to assess attainment meaningfully, and if we want to build a knowledge-rich curriculum focused on specific content, we need to consign level descriptors to educational oblivion. Once we’ve left them behind, we will be able to focus our attention on specific content that should be mastered, and measure attainment against exemplar work.

Specific content and exemplar work give teachers and pupils something clear and definite to aim for. Pupils will be relieved and pleased to be shown a definite way forward, instead of wandering in the vague territory of the difference between ‘effective’ and ‘sophisticated’. And teachers will be able to say to pupils, ‘I want you to know this’ and ‘I want you to be able to write like this’, instead of muddling around with grade boundaries and tick boxes.

The Experience of Mastery Learning

A major component of traditional teaching has always been memorisation. Core knowledge must be stored in long term memory, because unless you remember something, you can’t think with it, and you can’t even be said to have learned it. Learning means changes in long term memory.

To this end, I’ve put together ‘memory points’ for my pupils to learn, which consist of questions and answers. Here are a few examples from the year seven literature course:

When is Beowulf set? Beowulf is probably set in the sixth century, before the Germanic peoples converted to Christianity.

Who is Beowulf? Beowulf is a Geat warrior who crosses the sea to aid the Danes and later returns to Sweden to succeed his uncle Higlac as king.

Who is Grendel? Grendel is an evil monster descended from Cain, who brings death and destruction to Herot.

Of course, these do not stand in isolation. We read Beowulf, we discuss it, we analyse it, and we also enjoy memorising and reciting a part of the poem itself. The section we memorise is taken from the speech of Wiglaf, Beowulf’s cousin, when Wiglaf is attempting to persuade his fellow warriors to stand by Beowulf in his hour of need, as he takes on a mighty dragon in his final battle:

And we must go to him, while angry
Flames burn at his flesh, help
Our glorious king! By Almighty God,
I’d rather burn myself than see
Flames swirling around my lord.
And who are we, to carry home
Our shields, before we’ve slain his enemy
And ours, to run back to our homes with Beowulf
So hard-pressed here? I swear that nothing
He ever did deserved an end
Like this, dying miserably and alone,
Butchered by this savage beast: we swore
That these swords and armour were each for us all!

I never studied Beowulf before I decided to teach it. It was one of the many holes in my knowledge of classic literature. I have therefore been through the process of learning about it myself over the last year, as I have been introducing a more traditional, chronological curriculum. I have been learning the memory points myself, as well as the passages from the texts which I set for memorisation.

Going through the process of memorisation is highly instructive. I wrote the memory points myself, but that certainly did not mean they were thereby stored in my memory. If engaging with ideas and synthesising knowledge were enough for mastery, then I would have known them after having written them. But my knowledge was hazy at best after having studied the material and written the memory points. And if it was hazy for me, someone who is adept at literary analysis and already has a large store of literary knowledge, how hazy would it be for year seven pupils with far less prior knowledge and experience?

The haziness of the material as I have struggled to commit it to memory has helped me understand the process of mastering new knowledge. I have learned it with the classes. When we begin tackling a new set of memory points, we chant them together, gradually looking less and less at the page on which they are written. We tend to do this at the start and the end of a lesson, so there is time for forgetting in between. And because I am going through the process myself, I can see how much I have forgotten in that twenty or thirty minutes.

The continued haziness even after many practice sessions also helps me to see how we tend severely to underestimate the amount of practice required. When I am teaching something I have already mastered, I soon start to think, ‘Oh, that must be enough practice now’, but then I recall how much practice I did when I didn’t yet thoroughly know the material, and how it still hadn’t sunk in. Expert blindness is a very real and very misleading phenomenon. Our pupils really do need far more practice than we think they do. Putting oneself through the process of memorisation is an excellent way of convincing ourselves of this.

There has been no getting around it. Engaging, analysing, thinking, have not been enough. If I have wanted clarity of thought, if I have wanted real mastery, I have had to hammer the knowledge into my head, and that takes a lot of hard work. I really enjoyed writing the memory points, but actually mastering the knowledge they contain has been more about gritting my teeth and getting on with it, and suffering many mistakes and failures along the way.

Still, it has had its pleasures, and these are part of what Doug Lemov calls the ‘joy of schooling’. A class full of children is the most enjoyable environment imaginable for committing material to memory, because you can chant it enthusiastically together. It becomes a shared experience. Everyone is learning exactly the same thing, including me. How often I have been corrected by year seven pupils who have mastered the material more quickly than I have! It’s a great equaliser, because, as I explain to them frequently, and as I exemplify through my own struggle, everyone can memorise, but it’s not effortless for anyone. It just takes hard work and repeated, spaced out practice. That’s true whether you are eleven or thirty eight, whether you have three university degrees or none.

Are General Ideas Superior to Specific Detail?

Michael Fordham and Greg Ashman have recently blogged about the distinction between knowledge and understanding, a distinction which has often been used to denigrate what is referred to as ‘mere’ knowledge.

Michael Fordham points out that the supposedly ‘higher’ cognitive phenomenon which is labelled understanding actually means more detailed and more complex knowledge, as well as the knowledge of how one fact links to another. At the highest level, this detailed and complex knowledge, along with the knowledge of relevant connections, is achieved by experts over many years of study.

In contrast, the type of abstract of conceptual knowledge which is often labelled ‘understanding’ is low on detail. It might be termed generalised knowledge, and it is actually much quicker to master than the large amounts of detail which a genuine expert has at his fingertips. It’s so short on content that you might even learn it through group work, with a few prods to point you in the right direction.

Even at a basic level, we can see this in operation. If we consider arithmetic, we can say that mastering the concept of addition requires very little specific knowledge. On the other hand, it takes lots of laborious practice to make number bonds truly automatic, because there are so many, and automaticity takes so long to build.

The idea of addition, the concept that by combining two numbers you end up with a higher number that is the sum of the numbers added, is quite abstract, and it might seem more sophisticated to articulate this concept than to memorise number bonds. But a general definition is much less valuable than the ability to return an answer to a number bond automatically, without thinking. And as Michael Fordham points out, these are not two fundamentally different things, knowledge and understanding: they are just two different types of knowledge, one generalised and abstract, the other much more concrete and applicable to specific situations.

The idea that generalised concepts are somehow higher than specific applications, and that general knowledge is more valuable than large amounts of detail, is an idea which privileges managerial over technical ability. It is not an idea which encourages hard work and application; instead, it elevates those who present smooth and credible vagueness and generalisation and leave the hard work of the details to others.

Ultimately, praising so-called conceptual knowledge over hard, specific information encourages us to live in a fantasy world, in which the boring details can always be left to somebody else. In fact, it is the world of television and film, which always edit out the tedious effort of piecing together details in a criminal investigation, or piecing together evidence in scientific research. Instead, a fictional Stephen Hawking gazes into glowing coals and the next day has a eureka moment and comes up with his theory of everything.

This is the fantasy of the individual Romantic hero, questing for the transcendent and the sublime, or the revolutionary guerrilla, transforming society with just a Kalashnikov, a colourful bandanna and a few glamorous slogans; it is dangerous nonsense.

As Hannah Arendt does, we should ask the deeper question about why these ideas are so popular. Why should a culture embrace concepts that undermine hard work and the mastering of objective knowledge? Could it be that we have privileged the subjective over the objective, and ceased to believe that there is any definite and certain knowledge to master?