5 books on knowledge and expertise: Reading list for exploring the role of knowledge and deliberate practice in the development of expert performance

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Recently, I’ve been exploring the notion of explanation and understanding. I was (partly implicitly) relying on the notion of ‘mental representations’ as built through deliberate practice. My plan was to write next about how I think we can reconceptualize deliberate practice in such a way that it draws on a richer conception of ‘mental representations’. But that is turning out to be a much longer project.

Meanwhile, in a recent conversation about teaching practitioners, somebody mentioned reading Kahneman’s ‘Thinking Fast and Slow’ as being relevant to the problem and we discussed maybe starting a reading group. This got me thinking about what should such a reading group have on its reading list.

The literature on expertise is vast (just look at the Cambridge Handbook of Expertise and Expert Performance). In my proposed reading list, I would focus on identifying different perspectives on how our mental representations of the world are structured, how we develop them (or how we can help others develop them), how we solve problems with them, and how they are embedded in the social environment in which we function.

1. Thinking Fast and Slow by Daniel Kahneman (2011)

Kahneman’s famous book is not really focused on experts but rather on the limitations of our thought – summarised under the heuristics and biases banner. But Kahneman’s notion of ‘System 1’ (fast) and ‘System 2’ (slow) thinking is directly relevant to the question of expertise. Expertise means that one can think about complex issues quickly but also that one can analyze that same issue with deliberate attention to detail. Exactly how this applies to the question of educating experts is a matter of discussion that I think the other books on my list can help elucidate.

2. Peak: Secrets from the new science of expertise by Anders Ericsson with Robert Pool (2016)

In this book, Ericsson (helped by journalist Pool) provides an outline of a cognitive mechanism by which fast thinking is acquired without the sacrifice of deliberation in the concept of ‘delibrate practice’. I propose that the key to understanding deliberate practice is not the process of practice but rather on Ericsson’s rethinking of the target that the practice should help us achieve. According to Ercisson, what delibrate practice leads is not knowledge or skill but rather ‘mental representations’. Mental representations are best thought of as chunks of knowledge (frames, scripts, schemas, etc. – which makes this approach overlap with Kahneman and Tversky’s work even though Ericsson does not mention this). This allows experts to perform complex mental operations on very rich subject domains which would be beyond the computational powers of anyone’s pure raw intelligence. The best analogy is being able to play chess or speaking a language – this is impossible by simply knowing the rules – we need a rich complex of mental representations to compete at chess or to speak with any fluency.

3. The Way We Think: Conceptual Blending and the Mind’s Hidden Complexities by Gilles Fauconnier and Mark Turner (2002)

Where Kahneman provides the framework and Ericsson the mechanism of acquisition, Fauconnier and Turner offer us a much more detailed description of the actual structure of ‘mental representation’ and how it is used during live processing of information. Building on work in cognitive linguistics and semantics, they develop the notion of ‘conceptual integration’ (or ‘blending’ as it’s more popularly referred to in the field) that explains how multiple ‘mental spaces’ or ‘domains’ can be merged seemingly without any conscious effort into new domains (blends) that we can then build further understanding on.

In this context, I’d also recommend reading the parts of Lakoff’s ‘Women, Fire, and Dangerous Things’ that describe what he then called ‘Idealized Cognitive Models’ and now calls ‘frames’. The book is quite vast and not all of it relevant to this question, which is why I wrote a guide to it.

4. Rethinking Expertise by Harry Collins and Robert Evans (2008)

What’s missing in all the works I’ve looked at so far is any awareness of the social embeddedness of expert performance. There is little discussion of types or levels of expertise and barely any mention of how experts interact with one another. In ‘Rethinking Expertise‘, Collins and Evans propose what they call a ‘periodic table of expertise’ (which happens to overlap quite nicely with my 5 types of understanding). They think not just about the specialist expert knowledge but also about what they call ‘ubiquitous expertise’ – all the underlying skills and knowledge required to even get started (such as languages, basic social skills, metacognition, etc.). Most importantly, they also pay attention to ‘meta-expertise’, i.e. how non-experts evaluate experts and experts judge other experts.

Their notion of expertise relies on the concept of ‘tacit knowledge’ (later developed by Collins in a separate book) which is reminiscent of Ericsson’s ‘mental representations’ and echoes Kahneman, as well.

5. Reflective Practitioner: How professionals think in action by Donald A. Schön (1983)

While Schön’s book has had a profound impact in terms of citation and ways of thinking, I suggest that it has been largely under-appreciated for its depth of epistemological insight. Despite being more than 2 decades older than any of the other books on this list, it is very much still relevant. It considers the very nature of ‘practical knowledge’ as opposed to ‘academic knowledge’. Schön, more than any of the others thinks about the practical needs of a person needing to achieve practical tasks with their knowledge in a complex situation. He highlights the tensions between the technical preparation of experts that focuses on knowledge about a subject and the practical needs of a practitioner who needs to act in such a way that simply recalling information would not be sufficient. His concept of ‘reflection-in-action’ could be seen as a precursor or better still a companion to the notion of ‘deliberate practice’.

Schön followed this up with Educating The Reflective Practitioner which focuses on the practical question of structuring a training course. Another reason to include Schön on this list is that he focuses more directly on ‘professional’ expertise.

Bringing it all together

What these books have in common is an underlying conception of knowledge and its processing. But what they lack is almost any awareness of each other. This makes them add up to more than just the sum of their parts.

Kahneman mentions Ericsson in a footnote and Ericsson and Collins appear jointly in the Cambridge Handbook I mentioned at the start. But they largely travel in separate spheres. Bizarrely, none of them refers to Schön. And all of them are completely unaware of Fauconnier and Turner, who in turn ignore the work done outside their field of cognition (even though we can trace the lineage of their work on cognitive domains directly to Schön’s earlier work on metaphor).

All these approaches are clearly converging on the same thing but they don’t do it using the same terminology, methods or even a shared conceptual framework. Which is why reading just any one of them would probably not be enough to get at the full scope of the issues involved.

I’m not certain that this selection is the most representative of the field. It is certainly not exhaustive and it is definitely shaped by my idiosyncratic intellectual journey and personal interests. But my hope is that it does triangulate the problem domain in a way that a more narrowly focused selection would not.

Writing as translation and translation as commitment: Why is (academic) writing so hard?

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This book will perhaps only be understood by those who have themselves already thought the thoughts which are expressed in it—or similar thoughts. It is therefore not a text-book. Its object would be attained if there were one person who read it with understanding and to whom it afforded pleasure.
(opening sentence of the preface to Tractatus Logico Philosophicus by Lugwig Wittgenstein, 1918)

Background

I’ve recently been commenting quite a lot on the excellent academic writing blog (which I mostly read for the epistemology) Inframethodology by Thomas Basbøll. Thomas and I disagree on a lot of details but we have a very similar approach to formulating questions about knowledge and its expression.

The recent discussion was around the problem of ‘writing as expressing what you know’. While I find it very useful to distinguish between writing to describe what you know and writing to explore and discover new ideas (something I first reflected on after reading Inframethodology), I commented:

I still find that no matter how well I think I know my subject, I discover new things by trying to write it down (at least with anything worth writing).

Thomas responded in a separate blogpost, first picking up on my parenthetical:

Can it really be true that the straightforward representation of a known fact is not “worth writing”? Is the value of writing always to be discovered (by way of discovering something new in the moment of writing)? I think Dominik is thinking of kinds of writing that are indeed very valuable because they present ideas that move our own thinking forward and, ideally, contribute positively to the thinking of our peers. But I also think there is value is writing that doesn’t do this, writing that is, for lack of a better word, boring.

With this, I agree wholeheartedly. 110% coach! Yes, this was a throwaway line I wasn’t comfortable with even as I was writing it. The majority of my writing is mundane: emails, instruction manuals, project proposals, etc. They may or may not be “worthy” but they certainly have a worth. And people who do nothing but that sort of writing certainly do not do anything I would find ‘beneath me’ or not worthy. I might have been better served by the term ‘quotidian’ or even ‘instrumental’ writing.

I agree even more with Thomas’s elaboration (my emphasis):

In fact, I think it’s the primary of value of academic writing and one of the reasons that so many people (and even academics themselves) almost equate “academic” (adj.) with “boring”.The business of scholarship is not to bring new ideas into the world, indeed, the function of distinctively academic work (in contrast to, say, scientific or philosophical or literary work) is not to innovate or discover but to critique, to expose ideas to criticism. In order for this happen efficiently and regularly, academics must spend some of their time representing ideas that are not especially exciting to them along with their grounds for entertaining them. They must present their beliefs to their peers along with their justification for thinking they’re true. And they must do this honestly, which is to say, they must not invent new beliefs or new reasons for holding them in the moment of writing. They must write down, not what they’re thinking right now, but what they’ve been thinking all along.

I find this an incredibly valuable perspective and when I think of my own writing, I think this is precisely where I’ve often been going wrong. This is partly because academic writing is more of a hobby than a job, so I don’t have the time to do more than write to discover. But it is partly because of my temperament. I don’t enjoy the boring duties of writing things I know down and then formatting them for the submission to a journal. I prefer to work with editors which is why the bulk of my published writing is in journalism or book chapters.

But there is still another aspect that needs to be explored. And that is, why do most people find it so difficult to write down what they know even while taking into account all of the above.

Writing as translation

I propose that a good way to think about the difficulty of writing to describe our thoughts is to use the metaphor of translation. We can then think of the content of our thoughts in our head as a series of propositions expressed in some kind of ‘mentalese’. And when we come to write them down, we are essentially translating them into ‘writtenese’ or in this case, one of its dialects ‘academic writtenese’.

This is made more complicated by the existence of a third language – let’s call it ‘spokenese’. We are all natively bilingual in ‘mentalese’ and ‘spokenese’ even if not everybody is very good at translating between these two languages. In fact, children find it very difficult until quite late ages (10 and up) to coherently express what they think and even many adults never achieve great facility with this. Just like many natively bilingual speakers are not very good at translating between their two languages.

But nobody is a native speaker of ‘writtenese’. Everybody had to learn it in school with all its weird conventions and specific processing requirements. It is not too outlandish to say (and I owe this to the linguist Jim Miller) that writing is like a foreign language. (Note: see some important qualifications below).

When we are translating from mentalese to academic writtenese, we are facing many of the same problems translators of very different languages faces. The one I want to focus on is ‘making commitments’.

Translation as commitment: Making the implicit explicit

Perhaps the most difficult problem for a translator (I speak as someone who has translated hundreds of thousands of words) is the issue of being forced by the way the target language operates to commit to meanings in the translation where the structure of the source language left more options for interpretation.

Let’s take a simple paragraph consisting of three sentences (Note: this is a paraphrase of an example given by Czech-Finnish translator at a conference I attended some years ago):

The prime minister committed to pursue a dialogue with the opposition. This was after the opposition leader complained about not being involved. She confirmed that he would have a seat at the table in the upcoming negotiations.

The first commitments I have to make at some point is to the gender of the participants in the actions I write about. In English, I can leave the gender ambiguous until the third sentence. In Finnish, which does not have gendered third-person-singular pronouns, I don’t have to express the gender at all.

In Czech (and many other languages), on the other hand, I have to know the gender of the prime minister from the very first word. Like actor and actress in English, all nouns describing professions have built-in genders (this is not optional as in English because all Czech nouns have assigned some grammatical gender). I also need to express gender as part of the past tense morphology of all verbs. So even if I could skirt the gender of the ‘leader’ (there are some gender-ambiguous nouns in Czech), I would have to immediately commit to it with the verb ‘complained’. Which is why knowledge of their subject is essential to simultaneous translators.

But this is a relatively simple problem that can be solved by reference to known facts about the world. A much more significant issue is the differential completion of certain schemas associated with types of expressions. Let’s take the phrase ‘committed to pursue’. The closest translation to the word ‘commit’ is ‘zavázat se’ which unfortunately has the root ‘bind’. It is therefore ever so slightly more ‘binding’ than ‘commit’. I can also look into something like ‘promise’ which of course is precisely what the prime minister did not do.

Then, there is the word ‘pursue’. One way to translate it is ‘usilovat o’ which has connotations of ‘struggle to’. So ‘usilovat o dialog’ is in the neighborhood of ‘pursue a dialog’ but lacks the sense of forward motion making it seem slightly less like the dialog is going to happen. So here each language is making subtly different commitments.

When you’re translating academic writing, there are hundreds of similar examples, where you have to fill in blanks and make some claims seem stronger and others weaker. And even if you know the subject intimately (which I did in most cases), you often have to insert your judgement and interpretation. And the more you do that, the less certain you feel that you got the meaning of the original exactly right. This is even when while reading the original, I had no sense of something being left unexpressed. The only way to get this right is to ask the author. But even that may not always work because they may not remember their exact mental disposition at the time of writing.

Writing as filling in holes in our mind

I believe that this is exactly the experience we have when we write about something that only exists in our head or something we’ve only previously talked about. Even when I’ve given talks at conferences and had many conversations with colleagues, writing my ideas down remains a difficult task.

When writing, the structure of ‘writtenese’ (as well as the demands of its particular medium) forces me to make certain commitments I never had to make in ‘mentalese’ (or even ‘spokenese’). I have to fill out schemas with detail that never seemed necessary. I have to make more commitments to the linearity of arguments, that could previously run parallel in my head. So when I write it is not clear what should come first and what last.

When I just write down what’s in my head (or as close to it as it is possible), it is unlikely to make any sense to anybody. Often including myself after some time. I need to translate it in such a way that all the necessary background is filled out. I also need to use the instruments of cohesion to restore coherence to the written text that I felt in my mind without any formal mental structure.

But during this process, I often become less certain. The act of writing things down triggers other associations and all of a sudden I literally see things from a different perspective. And this is often not a comfortable experience. Many writers find this a source of great stress.

This is, of course, true even of writing instructions and directions. Often, when describing a process, we find there are gaps in it. And when writing down directions, we come to realise that we may not know all aspects of the familiar sufficiently well to mediate the experience to someone else.

Teaching writing as translation

Translation is a skill that requires a lot of training and practice. In many ways, a translator needs to know more about both languages than a native speaker of either. And then they need to know about different ways of finding equivalent expressions between the two languages in such a way that the content expressed in the source language produces similar mental effects when reading in the target language. This is not easy. In fact, it is frequently impossible to achieve perfectly.

When I translate I often refer to a dictionary (such as slovnik.cz) that lists as many possible alternatives of words even if I know exactly what the original ‘means’. This is because I want to see multiple options of expressing something which may not be immediately triggered by my understanding of the whole.

But for this to work, I need to have done a lot of deliberate reading in both languages to know how they tend to express similar things. At the early stages, I may approach this more simply as learning to speak a language. I may learn that ‘commit to pursue’ is best translated as ‘zavázat se usilovat o’. But I have to back that up by a lot of reading in both languages, studying other translators’ work and making hypotheses about both languages and the differences between them. Eventually, this becomes second nature and to translate fluently, we need to ‘forget’ the rules and ‘just do it’.

So how could we apply this to teaching (academic) writing? We need to start by ensuring that students have enough facility in both the source and the target languages. We usually assume greater fluency in the source language (most translators work primarily in the direction of native to non-native). So in this case, we need to focus on the structures and ways of ‘academic writtenese’.

We can very much approach this as teaching a foreign language. Our first aim should be to help students acquire fluency in the language of academic writing. We need to give them some target structures to learn. This should ideally be based on an actual analysis of that writing rather than focusing on random salient features. But ultimately, the key element here is practice.

Then we also need to focus on helping the students develop better awareness of their native mentalese and how to best map its structures onto the structures of writtenese. We can do this by helping them write outlines, create mind maps, come up with relevant key words, and of course, read a lot of other people’s writing, think about it, and then write summaries in similar ways.

None of these are particularly revolutionary ideas and they are being used by writing teachers all over the world. What I’m hoping to do here is to provide a metaphor to help focus the efforts on particular aspects of what makes the translation from thought to writing difficult.

Writing as playing a musical instrument

One final analogy that can help us here is the idea of writing as playing a musical instrument. This analogy is in many ways even more apt. When we play a musical instrument, we are initially translating relatively vague musical ideas into actual notes (melodies and harmonies) by way of the structures given to us by the musical instrument.

We may start by learning some chords to accompany a song we hear but later we will progress into more details of musical theory which will allow us to express more elaborate ideas. But, in fact, this also allows us to have more those more elaborate ideas in the first place.

Initially, our ability to express musical ideas via an instrument (such as piano or guitar) will be limited by our skill. We may not even realize what exactly the idea in our head was until we’ve played it. And often, what we can play limits the ideas we have. Jazz teachers often say something like ‘sing your solos first and then play’ (others call it ‘audiation’). But this is not trivial and requires extensive training. Which is why one common advice for jazz musicians is to transcribe (or at least copy) famous songs and solos. But as you’re transcribing and copying, you’re supposed to notice patterns in how musical ideas are expressed. You can then recombine them to express what is in your ‘musical mind’.

But it seems that the musical ideas and their form of expression are never completely separate. They are not a pure translation but rather a co-creation. And this is true of any good translation and probably also ultimately true about any act of writing. We are using a different medium to express an existing idea but in the process, we are filling gaps in the ideas, creating new connections until we ultimately cannot be completely certain which came first.

As we get better at translation, music or writing, there are some levels about which the last part does not hold true. There are some ideas we can truly and faithfully translate from our head to paper, musical instrument or from one language to another. This is why practice is so important. But at the highest levels of difficulty, writing, translation and music making will always be acts of co-creation between the medium and the message.

Teaching writing as music

So finally, could we teach writing in the same way as we teach music? We certainly could. Just like teaching a foreign language, teaching music is mostly dependent on a lot of practice.

But perhaps there are some techniques that music teachers use that could be useful for both language teachers, translators and writing coaches.

One is the emphasis on patterns. The idea of practicing scales, licks, or chords relentlessly (up to hours a day) holds a lot of appeal. Perhaps we start teaching self-expression with writing too soon. Maybe we should give students some practice patterns to repeat in different combinations. Then we could tell them to just copy and then dissect parts of good texts. The idea of ‘mindless’ copying will probably stick in many teachers’ craws. But just analysing reading will never be enough. Students need the experience of writing some good writing. If only to develop some muscle memory. And while it should never be completely mindless, it should also perhaps not be completely meaningful from the very start. Of course, we could invent numerous variations on this approach to transform the texts in various fun ways while still making sure, students are writing extended chunks and developing fluency. The point is that we would not be focusing on self-expression but developing a language for self-expression.

Music teachers and students use what has been described by Anders Ericsson as ‘deliberate practice’. Ericsson gives the example of Benjamin Franklin who used similar techniques to improve his writing:

He first set out to see how closely he could reproduce the sentences in an article once he had forgotten their exact wording. So he chose several of the articles whose writing he admired and wrote down short descriptions of the content of each sentence—just enough to remind him what the sentence was about. After several days he tried to reproduce the articles from the hints he had written down. His goal was not so much to produce a word-for-word replica of the articles as to create his own articles that were as detailed and well written as the original. Having written his reproductions, he went back to the original articles, compared them with his own efforts, and corrected his versions where necessary. This taught him to express ideas clearly and cogently.

Obviously, this was not all there was to it, but it is very much reminiscent of what music students do. It seems to me that most beginner writers are often asked to do too much at the very start and they never get a chance to improve because they essentially give up too soon.

Writing is NOT foreign language, translation or music: The Unmetaphor

Writing is writing! It has its specific properties that we need to attend to if we want to see all of its complexities. We must use metaphors to help us do this but always by remembering that metaphors hide as much as they reveal. One useful way of understanding something is to create a sort of unmetaphor: a listing of similar things that are different from it in various respects. This is something that, while not uncommon, is done much less than it should be when using analogies.

Written language is not a foreign language

Some of the fundamental mental orientations of a language are shared between the written and spoken forms. This includes tense, aspect, modality, definiteness, case morphology, word categories, meanings of most function words, the shape of words, etc. These present some of the most significant difficulties to learners of foreign languages making it very difficult to acquire a second language by exposure alone after a certain age for most adults.

Writing, on the other hand, can be acquired predominantly by exposure alone for many (if not most) adults. There are many people who acquire native-like competence in the written code in the same way they acquired their spoken language competence (even if there are just as many who never do). And we must also be mindful (as Douglas Biber’s research revealed) that there is a bigger difference between some written genres then there is between writing and speech overall. So we should perhaps attend to that.

Writing is not translation

That writing is not actually translation is contained in the fact that written language is not actually a foreign language. There are many genres and registers in any language with their specific codes. And we could call going from one code to another translation much more easily than going from what I called ‘mentalese’ and ‘writtenese’. (Again, the work of Douglas Biber should be the first port of call for anyone interested in this aspect of writing.)

But most importantly, what I called ‘mentalese’ does not actually have the form of a language. Individuals differ in how they represent thoughts that end up being represented by very similar sentences. Some people rely on images, others on words. For some, the mental images more schematic and for others, they have more filled in details. For instance, Lakoff asked how different people imagine the ‘hand’ in ‘Keep somebody’s at arm’s length’. And the responses he got were that for some the hand is oriented with the palm out, others with the palm in.  For some, it includes a sleeve, for others it does not. Etc.

Writing is not music

I’ve already written about the 8 ways in which language is not like music. And they all apply to writing, as well. The key difference for us here is that music cannot express propositions. This means that musical expression can be a lot freer than expressing ideas through writing.

We could argue that writing is more like music than spoken language because it requires some kind of an instrument. Pen, paper, computer, etc. But we usually learn these independently of the skill of expressing ourselves through writing. My ability to play the piano is much more closely tied to my ability to express my musical meanings. However, people write just as expressive prose by the hunt and peck method as when they touch type. One can even dictate a ‘written text’ – that’s how independent it is of the method of production.

Of course, improving one’s facility with the tools of production can improve the writing output just by removing barriers. This is why students are well-advised to learn to touch type or to use a speech-to-text method if they struggle for other reasons (e.g. visual impairment or dyslexia). But when it comes down to it, this is just writing down words and as we established, writing in most senses is more than that.

Conclusions and limitations

Ultimately, writing and translation are not the same. Just as writing and music are not the same. But there are enough similarities to make it worthwhile learning from each other.

Many writers have developed great skills by the ‘tried and tested’ approach of ‘just doing it’. But we also know that even many people who do write a lot never become very ‘good’ at it. They struggle with the mechanics, ability to express cogently what’s in their minds, or just hate everything about it.

For some beginner writers, the worst thing we could do is give them a lot of mindless exercises. These people will want to do it first and would hate to be held back. Just like many students of languages or music like dive off the deep end. But equally, for many others, telling them to ‘just do it’ is the perfect recipe for developing an inferiority complex or downright phobias of writing.

But all of these writers will need lots of practice – regardless of whether we provide lots of ladders and scaffolding or just put a trampoline next to the edifice of their skill. In this, writing is exactly like music, language and translation. You can only get better at it by doing it. A lot!

I started with a quote from Wittgenstein. But he also famously said in summarising his book:

What can be said at all can be said clearly; and whereof one cannot speak thereof one must be silent.

I think we saw here that this is not necessarily how the act of writing presents itself to most people.

He then continued:

The book will, therefore, draw a limit to thinking, or rather—not to thinking, but to the expression of thoughts; for, in order to draw a limit to thinking we should have to be able to think both sides of this limit (we should therefore have to be able to think what cannot be thought). The limit can, therefore, only be drawn in language and what lies on the other side of the limit will be simply nonsense.

This is was the so-called “early Wittgenstein” before the language games and family resemblances. He spent the rest of his career unpicking this boundary of sense and non-sense. Coming to terms with the fact that what is thought and what is its expression are not straightforward matters.

So all the metaphors notwithstanding, we should be mindful of the constant tensions involved in the writing process and be compassionate with those who struggle to navigate them.

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.