What Rote Knowledge Isn’t – A short introduction to inflexible and flexible knowledge

Almost inevitably, when talking about memory and memorisation, the notion of ‘rote knowledge’ came up more than once, but I’ve tended to find that what is meant by ‘rote knowledge’ is rarely well-defined.  I’ve found that people generally have a notion of what rote knowledge might be, and that it’s bad… but that’s about it.

Daniel Willingham put together an article on the idea of ‘inflexible knowledge’ that’s been hugely influential on me.  In it he describes very clearly the distinction between inflexible knowledge and flexible knowledge, and separates them from rote knowledge.  I would strongly, strongly advocate that everyone read it now, before going any further.  If you haven’t read it before, it is essential reading.

Transferring his ideas to this context, it is almost impossible for what I am describing to be rote knowledge.  This is in no small part because there is a distinction to be made between facts and concepts.

What is a concept?

In Willingham’s article he gives an example whereby a pupil learns what the equator is ‘by rote,’ and because they do not understand the concept, they ‘learn’ and regurgitate that it is:

‘A menagerie lion running around the Earth through Africa.’

Equator Lion

The Equator, before he sets off

The equator is an example of a concept.  Concepts are frequently conflated with facts.

As another example, a triangle is also a concept.  We could try to communicate the idea of a triangle by describing facts about it e.g.

  • It is a three sided shape and all the sides must be straight lines.

We can try to communicate more and more facts about triangles to flesh out the concept and develop a more complex understanding/conceptualisation, such as:

  • it having three angles that always sum to 180 degrees,
  • or that no one side can be longer than the sum of the other two side lengths.

If you really want to get to know triangles, then you can yet take this further and further, looking at:

  • special cases such as the equilateral,
  • or the isosceles triangles,
  • or right-angle triangles,
  • and the relationship between the side lengths described by Pythagoras’ Theorem.

If you start delving into trigonometry then the complex mesh of interrelated facts that fully describe triangles explodes, and that’s all before you think to bring in their relationship to circles, squares, the congruence ‘rules’ or non-Euclidean and fractal geometry.

But really, all we mostly want to absolutely guarantee is that every citizen can see a triangular shape and identify it as a triangle.  This is an exercise in categorisation, and for this the best course of action is usually to show a sequence of examples of the triangle shape, and non-examples as well.


Well what is a fact then?

Facts are different.  Unlike concepts which are very difficult to communicate by description, facts can be directly communicated.  For example, it is a fact that:

  • 2 is the smallest prime number, or that
  • the angle sum of a triangle is 180 degrees.

The highlighted words are all examples of concepts; in order for the fact to be understood, those concepts must first be known.

So to understand Fact 1 a person will first need to learn the concept of ‘the number 2,’ ‘small, smaller and smallest,’ and ‘prime number,’ but assuming those three concepts are known then the fact can be communicated directly.

It may or may not be immediately accepted, and a demonstration or opportunity to challenge the fact may be required before it is accepted, but it can be communicated that directly.  A common demonstration for the triangle angle sum is given here, though I have to stress that despite the video title this is not a proof (also remarkable that this girl had to wait until she was 19 and in her second year of university before seeing this!)

As for 2 being the smallest prime number, it doesn’t take much thinking to realise and accept that this must be true.

What’s this got to do with countries and capitals?

Tuvalu is a country, and its capital is Funafuti.

In the statement above there are two concepts, ‘country’ and ‘capital.’  If someone were to learn/memorise all of the countries and capitals then they must first have some conceptual understanding of what a country is and what a capital city is; without that they would be learning to repeat sounds without any meaning, such as in the menagerie lion example.  i.e. their knowledge would be rote.

Most everyone I’ve ever met, though, has developed some understanding of countries and capital cities early in their life.

With that known, being told that Tuvalu is a country cannot be rote knowledge.

It is an exercise in categorisation.

There is no doubt much more that can be learnt about Tuvalu, and this is where my earlier triangle example becomes so important.  Learning all that there is to learn, know and understand about triangles takes, frankly, a degree in mathematics, and probably beyond that.  It is never-ending, and so it falls on us to define an end point for state education somewhere.

For triangles we start with simple categorisation.  We then seek to communicate a great deal more about them by the time pupils leave school, and with good reason.  There are many other shapes where we do not do this, however.  We mandate that they be known, perhaps occasionally some limited knowledge of how to calculate their areas, but nothing more.

For ‘countries‘ and ‘capitals‘ as concepts, I’ve no doubt that, as suggested in this comment:

Countries, maybe, capitals, not so much. I would put the focus on teaching people what makes something qualify as a country to be able to discuss issues like Taiwan, Palestine, Greenland, Antarctica …

There is a substantial amount to be learnt about ‘What makes a country, or a capital city?’  I expect, again, that in fact it’s probably a degree’s worth of study.  As with triangles, I’m more than happy for some of that to be happening in schools.

For Tuvalu the country, I’m sure there’s much more to learn about it than just its name, location and capital.  For one, just take a look at how much you need to zoom in before you can even see it on Google maps! How does a country so small still get to be considered a country, while Greenland doesn’t…?  Why doesn’t size matter?  What does matter?

However, while learning just the names, locations and capitals of all 195 countries is so feasible as to make suggestions to the contrary a bit obtuse, learning all there is to learn about 195 is similarly unfeasible.

So we can learn;

  • a little something about everywhere in the world, and ‘much more’ about a few places,
  • or ‘much more’ about a few places, and have all others stamped out of public consciousness.

I found it ironic that there were two commentators who accused an exercise of this sort, one which valued knowledge and awareness of the existence of all countries, as being imperialist, fascist or nationalist, when it is the alternative that sweeps vast swathes of the globe and its population out of our society’s mind.

Most importantly, though – provided the concepts of country and capital city are understood – memorising facts such as these is by very definition not, and can never be, rote knowledge.

About Kris Boulton

Teach First 2011 maths teacher, focussed on curriculum design.
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6 Responses to What Rote Knowledge Isn’t – A short introduction to inflexible and flexible knowledge

  1. In my experience, when you require pupils to memorise something, discussions naturally emerge which clarify concepts. Understandably, if there is anything in a fact which they are memorising which they do not grasp, they want to know about it. For example, I recently set pupils to memorise that Shakespeare’s ‘Julius Caesar’ is set during the era of the Roman Republic, and it led to an interesting discussion of what exactly a republic is, and how the ancient ones differed from modern versions. The memory point is a kind of peg on which a deeper conceptual understanding hangs.

    • Kris Boulton says:

      Yes! That has been *exactly* my first hand experience. When I memorised poems I found I started to actually really consider their meaning for the first time, as a simple example.

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