What is Rote Knowledge? (Teaching Facts)

Facts Connect Concepts

Podcast is AI generated, and will make mistakes. Interactive transcript available in the podcast post.

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Read the following passage, and then answer the questions underneath:

’Twas brillig, and the slithy toves

Did gyre and gimble in the wabe:

All mimsy were the borogoves,

And the mome raths outgrabe.’

Questions

(1) Who were all mimsy?

(2) What did the slithy toves do?

(3) When did this all happen?

Chances are you answered correctly that it was the borogroves who were all mimsy.

So you can read the series of facts given, and you can respond to questioning that would suggest you understood what you were reading… but did you?

We all know something is off here. We feel it.

So, surely teaching facts can’t be as simple as ‘just tell them.’

But it is.

And it isn’t.

What are facts?

Here’s the key to understanding what a fact is, and what we’re teaching when we teach facts:

It was brillig, and the slithy toves

Each word in bold above is a concept.

The reason you can read the lines above and even respond to questions about them is that they follow regular rules of English grammar.

The reason you can’t fully make sense of them is that you have no knowledge of the concepts referred to.

If you answer question (3) by saying ‘brillig,’ you’re still left wondering ‘but what sort of time is brillig? Is it morning, noon, night? Is it a month, a season? A moment that occurs only once every hundred years, when the moon shines black?’

You will look at slithy toves and instantly know that either slithy toves are ‘something,’ probably an animal since they’re ‘gyring and gimbling,’ whatever that means (you know they’re doing something, and that usually, but not necessarily, implies life, and it sounds a bit like ‘toad';’) or, you will understand that ‘toves’ are something, and these particular toves happen to be ‘slithy.’ More likely you picked the former, since you also know implicitly that if ‘slithy’ were intended as an adjective, then the word ‘the’ probably wouldn’t have been placed in front of them. But it could be… so this is all guesswork right now, all happening instantly in your mind, happening implicitly, subconsciously, with you barely aware of it beyond an uncomfortable feeling of ‘I get it… but I don’t get it. Why don’t I get it; why is this so hard to understand?’

Welcome to life as a maths student in the K-12 classroom.

They sort of understand us, sort of understand that we’re saying English words, arranged using the implicit rules of English grammar… but also they don’t really understand us, and can’t quite understand why they don’t.

‘Sir, I don’t get it!’

‘Okay, well, which part don’t you get?’

‘I don’t know… all of it!’

‘Just telling you’ that ‘the borogroves were all mimsy’ doesn’t communicate everything you need to know, because you don’t have any knowledge of the concepts borogrove, and mimsy.

But what if you did?

What if instead I told you that the ‘rabbits were all nervous’?

This time, there was no issue with ‘just telling you.’

You readily understood everything about that sentence, and might have even started to subconsciously picture reasons for their nervousness; a nearby fox sighting, perhaps, or humans roaming the fields in the distance… but not quite distant enough.

The issue with trying to ‘just tell you’ came from me using words that referred to concepts of which you have no prior knowledge or understanding.

Facts Connect Concepts

If the concepts are known and understood, the fact will be understood

Conversely, if any concepts in your factual statement are not already known and understood, then the fact will not be understood.

In this case you cannot ‘just tell them.’

Or, you can, it just won’t convey any meaning.

Instead, you will only provide someone with rote knowledge.

This! This, is what rote knowledge is. This is what we should act to mostly avoid.

You can learn things that are true, but rote.

You can learn for example that Paris is the capital of France.

But if you have no wider knowledge or understanding of the concepts France, Paris, and capital, then your knowledge will be rote. You could utter it, you could respond correctly to questions such as ‘What is the capital city of France?’ But your words would have no meaning to you.

You can learn that Palikir is the capital of The Federated States of Micronesia, and provided you have a concept of ‘capital city,’ which you probably do, you have learnt something meaningful, but that idea probably feels a little blank in your mind.

What separates learning the fact above from learning the fact that Tarawa is the capital of Kiribati?

Assuming you don’t already know both pairs of country and capital, each of these new facts is probably ‘equivalent’ in your mind. You can’t place them on the map, know nothing of their relative size, ethnic makeup, religious demography, economic power, technological infrastructure, and so forth. You could consciously make some reasonable guesses based on how unfamiliar they are and the sounds of the names, you will probably make some unconscious assumptions as your mind tries to fill the blanks, but both could be way off.

So we have rote knowledge, where you know a fact, but have no knowledge of the concepts it connects.

Then we can move increasingly towards something ‘not rote’ but on its own still ‘not very helpful,’ like the two examples above.

And then you can imagine knowing a great deal about Micronesia and Kiribati…

Once again we end up with something that looks an awful lot more like Willingham’s continuum of inflexible to flexible knowledge.

Rote knowledge is a real risk in school education.

You can easily imagine a child answering the question:

‘What is the smallest prime number?’ with:

‘Two is the smallest prime number.’

If they don’t know what you mean by ‘two’ and ‘prime number,’ then they have acquired rote knowledge.

If they know what you mean by ‘two,’ but still don’t know ‘prime number,’ then that isn’t quite rote, but it’s certainly not very meaningful; it almost might as well be rote.

So, there is a real risk that we communicate rote knowledge in schools.

On the other hand, there is an equally grave risk that we confuse ‘learning facts’ with ‘rote learning.’

For example, we have been told in the past that students learning times tables is ‘rote learning,’ but there is nothing rote about it. Times tables facts are not rote knowledge. Assuming you have knowledge of the concepts seven, eight, fifty-six, and times, then learning ‘seven times eight is fifty-six’ is entirely meaningful.

The antidote to each of these risks, and the solution to understanding why something like times table facts are not rote knowledge, is factual atomisation.

We’ll look at factual atomisation next time.

First, one further, more extended example of how exams can push us - probably unintentionally - in the direction of asking students to accumulate rote knowledge: