Does memorisation get in the way of learning? – Part 2

Inflexible knowledge is a necessary first step towards understanding.

Following on from my previous post, I’d like to take a look at this post by Ben Orlin, and use it as a lens to focus the discussion.  Orlin echoes, I think, the sentiments of many a teacher out there, so this should serve as a good opportunity to discuss many of the common worries around memorisation in education, as well as some misconceptions about how memory works.

First, just to be clear, Orlin defines memorisation as ‘learning an isolated fact through deliberate effort.’  This is quite different from the way I used the word in my previous post.  I’m not sure whether I would personally agree with that definition, and I won’t be able to stick to it here because I want to be able to talk about the idea of knowledge being ‘memorised’ to refer to the state of that knowledge in the mind.  I would refer to something as memorised if it can be easily recalled, ideally with that recall ability being retained over a lengthy period of time, regardless of the method or process used to achieve this state.  I should note that, according to Bjork’s theory (The New Theory of Disuse), memory is more complex than a simple dichotomy between ‘memorised’ and ‘not memorised,’ but without going into that in more detail I will have to stick with the language I have available.

There is much in the post that rings true I imagine for any teacher.  Orlin says many things I agree with.  He is obviously not opposed to the idea that knowing something by heart, or being able to recall something, is a bad thing; he challenges certain methods of achieving what I am calling the state of ‘memorised,’ and how he see them being used to achieve high exam scores at the expense of any real understanding.

As I say though, this is a rather ‘old hat’ topic.  Any layperson can step into the educational arena and note that cramming rote facts is not desirable, no matter how high the grade achieved as a result.  Coming from a background of top exam grades, but not a clue really as to what any of the mathematics meant, this is an issue I take very seriously.  My mathematical ability suffered as a result of this lack of deeper understanding, and certain opportunities were consequently closed to me – GCSE results alone clearly not enough.  I don’t believe in Orlin’s solutions though; I think there is much here that sounds like something that is true… but isn’t quite.

Old Hat

Blaming ‘memorisation’ for a lack of understanding is becoming old hat

Before I entered the world of teaching, before I read anything about human cognition, I might have agreed with everything Orlin says – as I mentioned before, his arguments sound completely valid when read with a colloquial understanding of human memory.  It’s when we dig a little deeper that they start to come apart; and when Orlin’s ideas influence Meyer, and Meyer influences so many others, then I feel we need to challenge those ideas.

So what are his main points?

    • Some things are worth memorising, but others are not.
    • Knowledge matters – “even a head full of memorized facts is better than an empty one.”
    • Raw rehearsal is a memorisation technique, but not a very effective one.
    • Mnemonics are a better memorisation technique, but they still promote the memorisation of meaningless facts.
    • ‘Repeated use’ is a better route to memorisation, and one that he advocates.
    • ‘Building on already known facts’ is a second route to memorisation that he strongly advocates.

Let’s look at each point in turn, starting with the first two today.

Only some things are worth memorising

Well of course this is true.  Not much profundity to the statement, but no harm in stating it either.  Before computers, still no-one would bother memorising trig tables or log tables!  …but we do ask that people memorise some multiplication and division tables, and I reckon most mathematicians would agree that there’s value to be had in having memorised some of the more fundamental trigonometry and log facts.  In MFL, surely vocabulary must be memorised; no-one wants to wait for you while you look up every word!  In English and the humanities, Daisy Christodoulou has written at length as to why you can’t ‘just look it up.’

Some things must be memorised.  I suppose the question is what’s important to memorise, and here Orlin and I are going to disagree.

 Google it

What do we really need to know?

Here’s what Orlin takes issue with:

“What’s the sine of π/2?” I asked my first-ever trigonometry class.

 “One!” they replied in unison. “We learned that last year.”

 So I skipped ahead, later to realize that they didn’t really know what “sine” even meant. They’d simply memorized that fact. To them, math wasn’t a process of logical discovery and thoughtful exploration. It was a call-and-response game. Trigonometry was just a collection of non-rhyming lyrics to the lamest sing-along ever.

Some things are worth memorizing–addresses, PINs, your parents’ birthdays. The sine of π/2 is not among them.

(Emphasis added)

That sine π/2 = 1 is not worth knowing… What ‘sine’ means, is worth knowing…  No.

Why not?

That sine π/2 = 1 is very easy to learn, that is to say, very easy to memorise, with just a little time and practice.  Also, it is one of the more fundamental trigonometric facts, very important to understanding the nature of Sine… ironically, and then being able to manipulate it effectively.

Understanding what Sine is, what it means… this is not easy!  This will take a great deal of time, and patience.  How much?  Well I didn’t get it at all until about three years ago, and I reckon there’s still a great deal more about it that I could learn.  In the meantime, knowing sine π, π/2, 3 π/2 and 2 π, are important fundamental facts, easy to know.

 Sine

Got it?

I suppose the counter-argument is that if you really understand Sine, then you can use it to derive all the facts you’d ever need.  I’d argue that if you know the facts, you can piece them together to form an understanding or conceptualisation of Sine.  Without them, holding on to that conceptualisation is all the more difficult.

Herein lays the old implicit assumption that I hear many people make: if you understand something, you will remember it.  This is easy to challenge, and so when challenged people slip back into: if you understand something, it’s easier to remember.  It just doesn’t work that way.  ‘Meaning,’ is what we find easier to remember.  When things are meaningful, we are more likely to recall them.  This is not always the same thing as ‘understanding.’  Also, ‘meaning’ doesn’t guarantee anything – if the ‘meaning’ is complex, it may do very little to aid the recall of an idea.  More on this in the next post, though.

Do I agree with Orlin that there’s a problem when your class can repeat facts like this, but have no deeper understanding?  Absolutely.  Does it follow, therefore, that knowing these facts is a bad thing?  Absolutely not.  They are a part of the journey; the problem these pupils had, that most of us have had, is that the journey stopped short before getting to the interesting part.

Knowledge matters – “Even a head full of memorized facts is better than an empty one.”

To start with, Orlin and I are using a different understanding of the word ‘memorised.’  What he really means here is ‘rote facts.’  By contrast I am saying that any knowledge you have has been necessarily memorised, one way or another, including facts that you ‘understand.’

Here, yes, there’s a tip of the hat to the importance of knowledge; this is again, though, a little self-evident.  It boils down to ‘something is better than nothing.’  This tack is often used by people who, by design or by accident, downplay the importance of knowledge in human cognition: ‘Sure, it’s better than nothing, but it isn’t a high priority.’

Actually when it comes to things like this, I might even disagree, since I would look at opportunity cost.  If you’ve spent time memorising things that are purely rote in nature, and then stopped… you might not get much from it; it’s time that may have been better spent elsewhere.

What we lack for here is language – Orlin is assuming a conceptualisation of knowledge that allows only for ‘rote’ or ‘meaningful’ knowledge, established as a dichotomy – ‘not understood,’ or ‘understood.’

Rote or Meaningful

Either you get it, or you don’t

 An alternative conceptualisation is offered by Daniel Willingham, that of rote, inflexible and flexible knowledge.

“What is Pythagoras’ Theorem?”

“Why, it’s a2 + b2 = c2

“Jolly good.  Now can you use it to find the length of the hypotenuse in this triangle?”

                “Can I… what?”

“Well, can you start by at labelling the sides of the triangle with ‘a, b and c’?”

                “…no?”

Can repeat the formula on cue – no idea what to use it for.  Rote knowledge is pointless, unless it’s going to be transformed into something more later.

Alternatively:

“What is Pythagoras’ Theorem?”

“Why, it’s a2 + b2 = c2

“Jolly good.  Now can you use it to find the length of the hypotenuse in this triangle?”

                “Yes of course.”

“Excellent.  Now, how about finding the shorter side of this triangle?”

                “…no?”

Here, they have some applicable knowledge of the theorem, but it is fixed to only one context – Willingham calls this inflexible knowledge, and it is useful, though not the end goal.  It is a necessary first step.

Eventually, as a person’s conceptualisation of the theorem builds, they can apply it to a myriad of contexts, and Willingham now calls the knowledge ‘flexible,’ and defines it as being akin to ‘expertise.’

Inflexible Flexible

Flexible knowledge takes time and hard work to build

My point here is that, well actually no, a head full of utterly vacuous and disconnected facts is not a good thing, but that deep, expert understanding is not our only alternative!  We have another alternative, which is knowledge that has some connection to other ideas, albeit perhaps still at a rudimentary level.  This knowledge are not only desirable, it is the essential starting point.  Taking the day to memorise the first 50 dinosaur names, in alphabetical order, and then nothing more… probably a waste of time.  On the other hand if your pupils have all memorised key values for Sine, Cosine and Tangent, do not lament this!  This is brilliant!  Now use it, and take them forward.

****

These first two ideas were ‘some knowledge is worth memorising’ and ‘knowledge is important.’  Those statements on their own are almost tautologically correct.  Combined, they point at the shadow of a more profound truth of cognition, one which Orlin’s articulation here suggests he missed:

Inflexible knowledge is a necessary first step towards understanding.

Or meaning, or flexible knowledge, or expertise, or relational understanding – whatever you want to call it.  Either way, it’s where we all begin in our ‘learning journeys’ of anything novel, regardless of our age.

I’ll be coming back to this point in the next post.

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About Kris Boulton

Teach First 2011 maths teacher, focussed on curriculum design.
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2 Responses to Does memorisation get in the way of learning? – Part 2

  1. Pingback: Does memorisation get in the way of learning? – Part 4 | …to the real.

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