I touched on this topic in a previous post. I’d like to explore it in more detail here.
I recently met the COO of Memrise, Ben Whately. He gave me a good analogy for how memory works by suggesting it’s like a party. If someone new enters the party and they don’t know anyone there they might stand by the peanuts for a little while, have a few sips of their drink, and then leave. On the other hand if you welcome them in and introduce them to a few other guests, maybe they’ll stay a while longer.
The more connected a piece of knowledge is to other pieces of knowledge, the greater its storage strength, and the more likely it is going to be possible to still retrieve the memory in the future. This isn’t the only way to build storage strength, but it is one, and it is important.
To understand what I mean when I talk about ‘storage strength’ and ‘ability to retrieve’ take a look at the image below, and consider the green curve to be storage strength, and the orange curve to be ability to retrieve.
This image was really designed – over 100 years ago – to show how forgetting lessened with repeated testing, but it still serves as a good visualisation for the interplay between memory storage strength and ability to retrieve a memory.
It’s this facet of memory – connected knowledge -> improved storage strength – that leads people down the ‘if you understand something you are more likely to remember it’ route. That phrase is the result of an incomplete understanding of how memory works, based on intuition and experience, but without theoretical underpinning or research. There is obviously some sort of truth to it, but the phrase as it is on its own just isn’t quite representative of reality.
If you do ‘fully understand’ something, then chances are it is connected to lots of other ideas. In some cases this will aid future retrieval. However, it’s actually entirely possible to understand something and then completely fail to recall it at a later date, just consider every documentary you ever watched for a plethora of easy examples. For me, proof that Root(2) is irrational is one that I saw again and again, understood every time, and still couldn’t recall from memory. Understanding does not equal memorised (just as memorised does not equate with understood.)
What is a framework?
A framework, in the context that I’m using it, is a web of connected knowledge, mostly simplistic, factual.
Countries and capitals is one for geography, but there are other possibilities, rivers for example, or mountain ranges.
In any given domain it would make sense to have more than one framework, so all three of the above might be possible frameworks for facilitating geographical understanding.
Why might they be important?
These are the guests at the party; you’re going to introduce the new knowledge to them. Without the party guests, you’re inviting someone to be all alone in an empty room – sounds a bit dull, maybe they’ll just leave now.
Taking the times tables as an example framework for mathematics, they can be memorised, requiring zero working memory space to process the results of, say, 7 x 8. There are other benefits beyond this, however. Because they are memorised all those numbers are connected together in long-term memory, easily retrieved when needed, and they will be accessed when meeting something else that might connect to them. For example, when learning to simplify fractions, you might quickly spot that both numbers in 49/63 are in the 7 times table and therefore be able to easily recognise this as a fraction that can be simplified, and how to simplify it. If you were able to procedurally calculate that 7 x 7 = 49 an 7 x 9 = 63, but you hadn’t memorised those facts, you would struggle to find a number that went into both 49 and 63, struggle to recognise it as a fraction not in simplest form, and might fail with it completely.
Other examples might include square numbers up to 144, cube numbers up to 125, and prime numbers up to 100.
Why only up to these limits? Well it’s enough that a child in school has sufficient numbers facts to work with to practice other procedural skills and spot the patterns they reveal, but not so many as to become overwhelming and a bit of a waste of time.
Considering the countries and capitals, you can rest assured that you’ll have some means of spatially interpreting almost anything that takes place anywhere in the world. As you go through life beyond school perhaps this will also aid the chances of that ‘organic learning’ mentioned before; the Matthew Effect comes into play once again, the more you know, the more you learn, the more your understanding of the world deepens and develops.
Frameworks are broad but shallow groups of ideas that help us make some sense of new information, new knowledge in a domain, and help us to make sense of the world around us, all while making it easier to hold on to new information with less effort.
...to the real. 
Kris, does a knowledge framework approximate in any way to a piagetian schema?
I want to say ‘maybe?’ – probably?
I think it’s probably my interpretation of what a ‘schema’ is, and to some extent, and attempt to couch it in terms that are then instantly accessible to the broadest audience.
I haven’t read enough of Piaget’s original writings, though, to comment on how closely the idea I’m espousing would relate to his notion of a schema.
What do you think?
Probably your concept of a schema. Either way we need schemas to think with. We currently hear much about memory, very little about mental schemas, so frames welcome. And this helps to create a useful theory of mind.
Piaget’s concept of schema was broader than Kris’s knowledge frameworks. Schema theory has since been expanded enormously by those working in information theory, cognitive psychology and psycholinguistics. A schema can be tiny e.g. for a dog or cat, or vast e.g. the overall structure of chemistry or biology.
Reblogged this on The Echo Chamber.
Totally and utterly agree Kris – another brilliant post. I am working on something right now that makes the connections in maths every single time a new idea is introduced and allows a student to see those connections so if “when they enter the room they don’t know anybody” they can “look up the people’s names”. I love reading your stuff. Colin
Thanks Colin, that’s nice to hear. =)
This series of blog posts is turning into a classic.
To start with, I fully recognise the Ebbinghaus Forgetting Curve. As you get older, there are more and more people to remember, and I often have a problem matching names to faces. About 10 years ago I had difficulty remembering the names of 2 people I had known 5 years previously. When I eventually remembered their names, I undertook to not forget them again, and have periodically deliberately dredged up their names, with the result that I can now recall them at will. Now, this example is pretty trivial (and a little mad), but it is clearly true that pieces of information that we need to use frequently are remembered more thoroughly. For example, PIN numbers for debit cards. Times tables. Car registration numbers (there was a time when it was widely believed the Police might stop you whilst driving and ask what your registration number was; failure to get it right implied you had stolen the car). Equally, when we no longer need to use these pieces of information then they are very much harder to recall; I can’t remember any of the previous PIN numbers.
Equally, I consciously remember very little of what I learnt at University. That knowledge was a stepping stone, and helped to build up my frameworks of knowledge. These are not just facts, or pieces of information, but ways of seeing and understanding the domain area, and intellectual structures on which new knowledge can be hung. In Chemistry it is possible to map out the important concepts of the subject, and determine the most suitable order in which to study them. More complex areas build on more foundational ones, and it helps to study them in that order. Careful laying of the foundation (the foundations for the framework of knowledge) greatly aids studying the subject at a higher level. In Chemistry, it helps to have automaticity in some pieces of information, but it isn’t necessary for some others. What is important, though, is to grasp the concepts (e.g. atoms, electrons, bonding), and these are the backbone of the framework of knowledge.
Do we really organise our knowledge in this fashion (frameworks of knowledge)? I don’t know…it certainly feels like it. But, it is a very useful model to help understand memory, and understand what information/knowledge needs to be studied, and in what order.
[I’m still not convinced that learning all 195 capitals and countries is necessary. The more relevant question appears to be, what should the framework of knowledge in Geography look like?]
Maybe? I feel I’ve taken a lot from having all 195 in a way that would never have been predictable for me in advance. For that reason – and the many I noted in all those posts – I suppose I’m fairly wedded to the idea.
That said, if someone were to restructure the geography curriculum so that only 100 were learnt, I wouldn’t be overly despondent at that, giving that currently it seems close to zero!
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Hi Kris
You asked me to comment on this post, so here goes;
Representing a knowledge framework as nodes and branches makes sense because it maps well onto the networks of interconnected neurons that carry information in the brain. You’re quite right about the importance of multiple connections. If a piece of knowledge is connected to several other pieces of knowledge it has higher redundancy – the more connections, the less it will matter if one of them fails and the more likely it is that the piece of knowledge will be recalled.
I completely agree that understanding and recall are not synonymous. An important point. However, the claim about understanding isn’t ‘if you understand something you *always* remember it’ it’s that you are *more likely* to remember it. This is true whether you base that claim on intuition and experience or on how understanding aka semantic memory works. There’s a fair bit of theory and research about semantic memory.
A simplistic framework – lists of country names, mountain ranges or times tables – is likely to aid recall, but because of the redundancy of information principle, understanding/semantic memory is likely to improve recall even more. So I might have learned that there’s a country called Tonga, but where does that get me, apart from knowing it’s the name of a country? If I know a bit about Pacific islands; how they formed, how they became populated, the issues all island populations face etc, if I come across Tonga in later life I will have a pre-existing framework of connected pieces of information that I can add to.
I’m still not convinced about the value of learning lists of names. As far as I can see, learning a list of names of countries doesn’t give you ‘some means of spatially interpreting almost anything that takes place anywhere in the world’ because it doesn’t give you any information about those places. Checking out where Tonga is is the easy bit. Understanding why a particular political situation has arisen in Tonga requires a knowledge framework that is much wider than just the name of the country.
Knowledge frameworks can be tiny – or vast since ultimately all knowledge is connected to all other knowledge.
Great comment Sue. Thanks for this.
Re: “However, the claim about understanding isn’t ‘if you understand something you *always* remember it’ it’s that you are *more likely* to remember it.”
You are right, of course, and I hope I acknowledge that in the post. If my language seems to suggest otherwise, though, it is probably because the manner in which I have heard interpreted (many times) by classroom teachers *is* “if you understand something you will always remember it.”
But also, you have to admit, there is surely even more nuance to this. How about:
If you understand something when you hear about it, then you are more likely to be able to recall it later than if you didn’t understand it. But, if you undergo an series of spaced recall activities over the next few weeks, you are more likely to be able to recall it now even if you didn’t (and still don’t) fully understand whatever it is.
Is that not possible?
With the geography stuff, what if I said that I’d intended for it to be ‘countries, capitals and locations (of the countries’), so that there is an explicit spatial dimension to it?
I agree with you when you say understanding why a political situation might have arisen in Tonga requires more than just it’s name and location, but what I have in mind here is what happens when reading about places in the news, or hearing about them in conversation. Imagine you hear about some series of events suddenly occurring in the Republic of Kundu, you might just read over that article without giving it any thought, since you’ve never even heard of Kundu, have no idea where it is, and don’t have the time or inclination to go look it up – you’re a busy person with other things on your mind. Kundu is just a blank space in your mind, holding zero interest (unless perhaps it was to start appearing in the media on a frequent basis.)
If you read a similar article taking place in Somalia on the other hand, it might carry more meaning for you, and you may choose to take greater interest in it, since you at least know where that it and what surrounds it.
I suppose I’m suggesting that knowledge of this kind lowers the barrier for entry in learning *more* about the world, and being able to therefore interact with global politics.
In school, we need to find the knowledge that has the highest impact for the time spent. If we were to spend all of what little geography time exists dedicated to looking in great detail at a few tiny pockets of the world, we wouldn’t get far. If we try to cast a wide net over the world, however, at a very shallow level, then hopefully we could at least cover everything in some minor detail, while still allowing time to explore some parts of the world in real depth.
There is also an additional argument around the idea of ‘what activities really require teacher time?’ Teacher time is the most precious resource, and something like ‘learning names and locations of countries’ could actually be outsourced to computer based quizzes, thus further liberating classroom time…
You’re quite right. What people say isn’t always what they mean.
I agree that knowing the name of a country, its capital city and its location is better than knowing nothing about it at all, but why not teach that information and the impact of geographical features and flora and fauna as well? Geography teachers would do the latter anyway. Or at least they used to. There’s no reason why students shouldn’t learn lists of country names – I just don’t see how much it would help with their understanding of those countries.
If you’re too busy to look up where Kundu is, the chances of you digging down into why it’s in the news are pretty slim too. I know where Somalia is not because I learned its name and the capital city in school, it’s because it’s been in the news headlines for as long as I can remember. Somalia as such didn’t exist when I was at school.
I agree that only ‘looking in great detail at a few tiny pockets of the world’ won’t get us very far on its own. I think where we differ is on what should be included in the ‘wide net’. Personally, I think if there isn’t time to teach the essential principles of geography (or history or any other subject), then we are in trouble and no amount of outsourcing to computer based quizzes is likely to remedy that.
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