5 kinds of understanding and metaphors: Missing pieces in pedagogical taxonomies

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TL;DR

This post outlines 5 levels or types of understanding to help us better to think about the role of metaphor in explanation:

  1. Associative understanding: Place a concept in context without any understanding.
  2. Dictionary understanding: Repeat definitions, give examples, and make basic connections.
  3. Inferential understanding: Make useful inferences based on knowledge about – but without ability to use the understanding in practice. Requires more than just one concept.
  4. Instrumental understanding: Use the understanding as part of work in a field of expertise. Impossible to acquire for an isolated concept.
  5. Creative understanding: Transform understanding of one domain by importing elements from another. Requires instrumental understanding – goes beyond hints and hunches.

Introduction

In a previous post, I proposed three uses of metaphor leading to different levels of understanding.

  1. Metaphor as invitation
  2. Metaphor as an tool
  3. Metaphor as catalyst

Only 2 and 3 led to any meaningful understanding and that could only be achieved by acquiring some ‘native’ structure of the target domain. But I was rather loose with how I used the word ‘understanding’. I was using notions like ‘meaningful understanding’ or ‘useful understanding’ but never went into any detail. That is the purpose of this post.

In what follows, I provide a sketch for one way of classifying different kinds of understanding. They are not meant to be descriptions or even discovery of some sort of ‘natural kinds’. Instead, I find them to be a useful way of looking at understanding from the perspective of metaphoric cognition.

Associative understanding

Associative understanding is the ability to place something in a context or category without necessarily knowing almost anything about it. So, we may know that an emu is a flightless bird without knowing anything else about it. We could also think of this kind of understanding as a vague notion.

This is the kind of understanding the vast majority of education leaves us with after a few years. Watching a documentary, a TV quiz show, or reading a popular news article fosters this kind of understanding.

Many people can get very far with displaying this kind of understanding – such as con artists impersonating doctors – by successfully imitating experts. The famous Sokal hoax was based on the same principle – making plausible sounding noises can get you published in a prestigious publication. But it is even possible to pass a poorly constructed multiple choice knowledge test with just this understanding by being able to eliminate the wrong options rather than by knowing the correct ones.

The associations can be of various kinds. They can be in the form of basic-category labels (such as – this is an animal). They could place the thing into a discipline – such as ‘something they do in chemistry’. And they could simply be in the form of ‘this is the thing that my friend always talks about’. Or they could also just be parts of the cultural vocabulary without a proper object of understanding.

For example, in the 1960s there was a famous pop song called ‘Pták Rosomák’ (The Bird Wolverine). The band simply liked the sound of the Czech word for ‘wolverine’ and its rhyme with the word for ‘bird’. Wolverines are not native to Europe or well known outside of this song. I did not find out what the word meant until I learned it in English (I also knew what the word wolverine meant long before I looked it up in a Czech dictionary). When I presented this at a conference on cognition in Prague, most Czech academics present were surprised by the meaning. Yet, if you asked them – do you understand the word ‘rosomák’, they would have said ‘of course, I do’. But it was just an associative understanding.

My claim is that the vast majority of what passes for understanding and knowledge in ‘polite society’ is of the associative kind. People feel comfortable when concepts like evolution or philosophy are mentioned but have only the vaguest idea of where they belong.

My favourite example of this is Monty Python’s ‘Philosopher’s song‘. All the audience needs to know to appreciate the jokes is that there is a philosopher stereotype and that certain names are of philosophers. In fact, by their own admission (citation needed but I did hear it in an interview), the authors of these sketches also did not know much more than the names. Even the little nod to knowledge in ‘John Stuart Mill of his own free will’ is just a glimmer of something deeper.

Associative understanding is pretty much only useful for social signalling. It can also play a role in making a new field appear more familiar in later stages. I have had that experience several times when vague memories from school made me feel more confident I was on the right track when I set about studying a subject in depth even if I had very little more than a vague feeling about something. But on its own, this kind of understanding has little practical value.

In formal instruction, we generally start with the next step but over time, without practice, this is the kind of understanding, we’re left with. But in literature on pedagogy, it is mostly unaddressed. It is the kind of understanding below the bottom rung of Bloom’s taxonomy. But many teachers encounter it when at the end of classes students come and ask questions that barely show a hint of an understanding that makes it seem like they may not have even been in the same room.

Lexical understanding

At this level, we can repeat a definition as we might find it in a dictionary and give a few examples. We can look at a picture and say, this is an emu. It lives in Australia and it is a kind of ostrich. For something like an emu, it may well be enough for most of us.

This is the kind of understanding we may be able to take away from a quick explanation of something. It is the sort of understanding most tests check for. It is also often used as a proxy for intelligence or ‘being smart’. Lexical understanding is what is required of successful quiz show panellists. UK shows such as ‘Mastermind’, ‘Brain of Britain’ or ‘University Challenge’ are great examples of these.

Conversely, lack of lexical (and sometimes even associative) understanding is also often given as an example of educational decline or lack of intelligence.

This would be roughly equivalent to the ‘Knowledge’ and ‘Comprehension’ levels on the Bloom’s taxonomy. It is the minimum target for instruction but it is very unstable. Unless it has been recently used, it often reverts to associative kind of understanding.

This kind of understanding is generally not very useful outside the educational context. This is the kind of understanding that is the result of ‘teaching to the test’. It can be leveraged into something more but only with practice and application.

In terms, of frames or mental representations, we could say that the only mental representations developed as part of this understanding are propositional or rich imagery. Meaning, we have sentences or images in our head that we can draw on but we would find it very hard to combine them into larger wholes.

This level and the transition from this level to the next are where what we call pedagogy plays the most important role.

Inferential understanding

This kind of understanding lets us make useful inferences about the concept in context. It requires some knowledge of a whole domain or several domains. You can never understand a solitary concept at this level. But it does not necessarily require deep ability or skill. I know nothing about emus, so I cannot think of an example that would not be misleadingly trivial.

But I have a personal example from when I was recently catching up on the latest developments in machine learning. I was reading about different types of neural nets. And when I was reading about CNNs (Convolutional Neural Networks) which are usually used for images, I had an idea for using the similar approach to process language by representing text in a way similar to the way images are represented. And it turned out there are already papers and models out there that do just that.

Inferential understanding is the kind of understanding that good students develop about favorite subjects that they pursue later. The kind of understanding that collaborators develop about each others’ discipline in interdisciplinary projects. The kind of understanding good generalist managers develop about the domains in which they supervise subject experts. Or really good journalists develop about areas on which they report. This is also the kind of understanding experts have about related fields or that teachers have about some of the more advanced areas of their field.

The sociologist of science Harry Collins described in one of his books (I think it was ‘Rethinking Expertise’) how he could pass some knowledge tests in gravitational wave physics better than professional physicists from adjacent specialisations. This was after many years of observing these physicists but without any real ability to the actual calculations or research required.

It may not always be easy to tell the boundary between this and lexical or even associative understanding. This is the kind of understanding potentially displayed by an audience member at a lecture who asks a question that is then described as ‘a good question’ by the presenter. But often this is just a fluke. A random hit based on superficial resemblance of words in a definition.

This is the kind of understanding that sort of ‘does not count’ in the terms of Bloom’s hierarchy. We feel it is insufficient because it is not something people consciously aim at in instruction. But it is in many ways the best we can hope for. It is the first kind of any useful knowledge.

It requires more developed mental representations. Representations where the definitions and rich images are replaced by schemas and scenarios. These are a sort of useful compressions that can be blended (or integrated) with others. What it means that when reasoning with these concepts, we can use them as whole units (mental chunks) rather than laboriously compute them from first principles.

It may also derive from some basic level of instrumental understanding. The humour in XKCD cartoons can be understood with a combination of inferential and instrumental understanding. I immediately understood this comic famous among programmers without being a programmer myself but having some skills with databases and knowledge of common problems with security.

But for the most part, we cannot use this understanding for actual work. This is where the humanities and sciences often diverge. It is possible to pretend (even to oneself) that this understanding lets us do real useful work in history or sociology. Whereas with mathematics, engineering, medicine, or biology, the barrier between this and instrumental understanding is much more clearly defined by specialised tools such as mathematics and chemistry. But if we look at the many former physicists or biologists who have tried their hand at philosophy, sociology or even literary criticism, we see that even here, this kind of understanding is not enough.

You really need more to have a chance of doing something useful.

Instrumental understanding

This is the kind of understanding experts and practitioners have. It requires being able to use the concepts or tools in practice. I don’t have any instrumental understanding of convolutional neural networks. I couldn’t build one and possibly couldn’t even reconstruct the exact way in which it works.

This level of understanding or ability or skills requires more than just reading or learning about. It requires practice and building of mental representations which only comes from long-term engagement with a subject. For example, I don’t have that kind of understanding of neural nets, but I do have it of metaphor.

I can create metaphors, identify them in text, speak to the controversies around them, compare and contrast the various theories of metaphor. I can teach somebody how metaphors work. I can write a successful paper or give a conference presentation in the field. If somebody wants to know about metaphor they can come to me. Other people with good instrumental understanding of metaphor may disagree with some of what I have to say, but they won’t do it (I hope) as they would with somebody who has just an associative, lexical or even inferential level of understanding – e.g. knowing that metaphor has something to do with poetry. You have to put in the work.

This work may require actual repetitive practice (such as working out math problems or analysing text). It absolutely requires extensive engagement with other experts in the field. Taking classes, going to conferences, reading latest research, writing papers, blogs, etc. That’s why loner autodidacts almost never reach this level of understanding.

Here the distinction between understanding and ability or skill becomes blurred. Mental representations develop at the highest levels of schematicity. This means that an expert can look at a very complex situation and treat it as one unit that can be blended with other complex units in a way that only the relevant parts are engaged.

For instance, I can read a complex argument about metaphor and immediately compare with three other complex arguments about metaphor – not because I have a large mental capacity for abstract concepts but because I have developed a number of highly schematic mental representations about the shapes of arguments people make about metaphor. This way, I can project these schemas onto the argument as one big chunk.

Perhaps an even better analogy is learning a foreign language. I may know all the rules and words but I cannot speak the language with any level of fluency until I have developed larger chunks I can just slightly modify. It is simply impossible for even the most highly mentally endowed human to dredge up individual words, apply rules to them and combine them into a sentence quickly enough to speak with any level of coherence. It’s even worse for understanding. Just reading a text with a dictionary is such a slow affair that we forget what a sentence was about before we get to the end.

In other words, we can then define instrumental understanding as developing a basic fluency in the language of the discipline. And this takes time, targetted practice, and active ‘communicative’ engagement across a whole field.

In the ‘hard sciences,’ it requires a good facility with formalisms or even equipment and in the ‘softer’ disciplines it relies on extensive reading, talking, and writing.

Here we are at a much wider aperture of our knowledge funnel. It is therefore impossible to exactly compare 2 people’s levels of instrumental understanding. Everybody will have a slightly different set of mental representations. Also, many people will only be able to ‘perform’ at this level some of the time or only for small chunks of their discipline.

At this level, pedagogy is much less relevant. This is where it makes a lot less sense to talk about teaching and learning if only because it is impossible to acquire this level of understanding purely in the classroom. Training, coaching or even an apprenticeship are much better models.

Creative understanding

Creative understanding is instrumental understanding with a transformative element. This requires knowledge of several domains and their creative intermingling. It is the sort of understanding innovators in their field have. This can lead us to a complete rejection of the thing we understand as an independent concept.

For example, I have long argued that metaphor is only one place in language where domain projection occurs and that we should not think of it as something special but rather as a shortcut for thinking about broader phenomena of framing or cognitive models. I found this a useful way of extending the concept. So, I can make a serious statement such as ‘metaphor and metonymy are the same thing’ that can be productive in the study of metaphor. But it only makes sense because I can actually distinguish between metaphors, similies, synechdoches or metonymies, and I can also reproduce arguments that maintain that the difference between metaphor and metonymy is crucial for understanding figurative language.

It is hard to say whether this type of understanding is even a part of the funnel hierarchy. Perhaps it is just an ingredient (catalyst) to instrumental understanding. But I do want to stress that it only works as a catalyst to instrumental understanding. As I showed in my post on types of metaphors, creativity needs to start from somewhere.

We may often confuse almost accidental insights by people with inferential or even just lexical understanding for creativity. But this is like recognising a melody in the sounds a child makes by randomly banging on the piano keyboard.

We often valorise the outsider perspective in a field. And it certainly can act as a catalyst for creativity but only if it has proper instrumental understanding to lean on.

Conclusions and limitations

I cannot stress enough that this classification is just a useful heuristics. I am not claiming that this kind of classification of understanding is exhaustive or even that it represents some sort of a natural category. But I found it useful when thinking about explanations and pedagogy.

Approaches to classifying understanding

It is quite common to distinguish between shallow and deep understanding. This is intuitively obvious but not very helpful because it assumes the existence of some sort of objective scale of a depth of understanding.

We can also distinguish understanding from knowledge for example by differentiating between explicit and tacit knowledge. Understanding and explicit knowledge intuitively overlap even if we don’t have a firm definition of either. If we understand something, we can mentally manipulate it and, most importantly, pass it along.

But the boundaries between tacit and explicit knowledge are not firm. All explicit knowledge depends on some tacit knowledge – or in other words, all understanding depends on knowledge. We could even say that deep learning is the process of transforming understanding into knowledge. In the sense, that we need to build up schematic mental representations to be able to manipulate ever more complex combinations of concepts.

Another way to try to get at understanding is to investigate how to achieve it. Bloom’s taxonomy of educational objectives is one famous example. There are many tweaks and elaborations – some as extreme as Jack Koumi’s 33 pedagogic roles. But they are ultimately not very satisfying because they already assume we know what the understanding is.

Understandings as a process revisited: The wave and the funnel

Even though these different types of understanding are ‘broadly hierarchical’, I want the emphasis to be on ‘broadly’. It would make no sense to think of these as a straightforward linear hierarchy measurable on a scale of discrete and comparable units. They are more like overlapping waves. Layers of water covering the beach in successive bursts as the tide is coming in.

But that metaphor does not make it easy to visualise the differences and mutual interdependence. It only evokes how hard and unreliable it is to do so. But for the purposes of this comparison, I’d like to offer something more like a funnel (which I also brought up in the context of the metaphor explanation hierarchy) or inverted cone.

The substance that fills the funnel might be a mixture of effort and coverage of material. This makes it easy to visualise the fact that it takes much more effort, time and background knowledge to get from level 3 to level 4 than it does to get from level 1 to level 2. Also, at the higher levels, the concepts themselves transform and interconnect. So it is not possible to understand them in isolation.

This truly takes into account the processual nature of understanding. The funnel also needs to be constantly topped up to maintain certain levels. But it can also underscore the fact that we can never perfectly compare 2 people’s levels of understanding. Because at the higher levels, the funnel is so broad, not everybody will have filled it in the same way with exactly the same substance.

I got this idea from ACTFL language competency levels and I think it is one of the most underappreciated metaphors in education.

Another really useful thing ACTFL does is that it defines low, mid and high sublevels for each competency levels. And a part of the definition of the ‘high’ sublevel is that the person can function at the ‘low’ sublevel of the next level about half the time. (E.g. a Novice-Low can function as Intermediate-Low about 50% of the time). During the test (most often an interview), the examiner establishes a floor and a ceiling rather than pinpointing an exact point on a scale.

This very much applies to the levels in my metaphor. There are no clear boundaries between these levels of understandings. In as much as they are levels in the first place.