TL;DR

There are at least 3 uses of metaphor in the educational process: 1. Invitation to enter; 2. An instrument to grasp knowledge with; 3. Catalyst to transform understanding. Many educators assume that 1 is enough but it rarely leads to any useful understanding.

Explanation is a salient part of the educational process to such an extent that it is often allowed to stand for all of it even though it is only one step.

Explanation often helps the person doing the explaining more than the person being explained at.

Metaphors and explanations have been misused by educators from Socrates to Rousseau.

A metaphor can only be successful if the student already has some knowledge of the target domain. Knowledge of the source domain is often less important.

Metaphor only makes sense if it is a part of a process. A process of learning. It doesn’t do much good on its own.

How metaphors work in helping us understand things

Teachers love explaining things. Students love understanding things. On the rare occasions that the two coincide, the feeling of joy shines like a beacon for the power of explanation. Teachers tell stories of seeing the “lightbulbs come on” in their students’ eyes. Students remember fondly the ecstatic moments of sudden illumination as their teacher’s words suddenly lit up the darkness within them. Thus the myth of teaching as explaining and learning as understanding those explanations was born.

Most of the more powerful explanations rely on metaphor in the broadest possible sense. In fact, all explanation is to some extent metaphorical in that it provides a projection from one domain of understanding onto another. Metaphor brings out the familiar – or ex plains it – in the unfamiliar. Or so the story goes.

We can think of metaphoric projection as putting two thin sheets of paper over each other and looking at them against a bright light. What can be on these sheets? Sketches, images, words or even just smudges of color. The projection then obscures certain things and shows others in new contexts. Sometimes, with more complex slides we may see completely new shapes and color hues. The process of making sense of the metaphor then involves slight adjustments in how those two sheets align against one another. This can be described as the metaphor giving a new structure to the target domain.

Another way to think about metaphoric projection is as two sets of items which are mapped onto each other. We can put the sets side by side and draw lines between items we think match. Or we can take them out and place them side by side in a new set. We often see them displayed in this way.

Note: This way of thinking about metaphor started with Lakoff and Johnson’s ‘Metaphors we live by’ from 1980. This led to the formulation of the Conceptual Metaphor Theory. It was later developed into a more general theory of frames or mental models by Turner and Fauconnier (2002) known as the theory of conceptual integration or blending. But it can also be found in Donald A Schön’s ‘Displacement of Concepts’ from 1963 which indirectly inspired Lakoff and Johnson.

But despite all this, it is easy to overlook that in order to form a projection from one mental space into another, we have to have some structure in both. In fact, metaphor often assumes equal knowledge of both domains, and in the process of making a projection from one another, a new previously unimagined structure emerges that is a blend of both domains. Because of the complexity, it is hard to give brief examples, but Turner’s and Fauconnier’s ‘The Way We Think’ is full of very illuminating case studies.

But it is also not at all uncommon for metaphor to borrow from a domain we know much less about to elucidate a domain we know a lot about. For example, if I hear, ‘don’t go into that office, the boss is on a warpath’, I understand a lot more about the boss’s behaviour than I do about any warpaths. Here, only the general feeling of ferocity is transferred with none of the possible association of weaponry or military supply lines.

Metaphor is also always partial. It would make no sense to project every aspect of both domains onto one another. But the ability to understand which bits it makes sense to project and which must be left out also requires at least some understanding of both domains. To understand what we mean when we call a piece of software a ‘virus’ we must know enough about computers to know that the infection cannot be transmitted through simple touch.

Metaphor at its most powerful helps us understand both domains better. It also often results in the creation of new understanding of both domains as we strive to find the limits of possible cross-domain mappings. Often, this happens with honest historical explanations of the present. By comparing the Iraq war to Vietnam, we may only choose to transfer the feeling of emotion and loss associated with the former. But we may also choose to explore both in their own right to find the best way in which they project on to one another. And this gives us new understanding of both.

Three uses of metaphor in explanation

There are many ways to classify the uses of metaphors, I’ve outlined some in an early paper. But for the purposes of metaphor in explanation, I’d like to offer three broad types: 1. Metaphor as invitation; 2. Metaphor as instrument; 3. Metaphor as catalyst. I fear that the first type may be most common while only the second two play any real role in building understanding. These three types could also be viewed as forming a sort of process but this is not inherent in the definition.

As we will see, sometimes the same metaphor can serve all three roles, providing a certain thread through the process of learning. But most often, we need new metaphors for each type or stage.

1. Metaphor as invitation

Novice students often come to a new subject with no knowledge and a healthy dose of fear of the unknown. To help them feel more comfortable, teachers like to reach for metaphors relying on the familiar. This gives the learner a chance to grasp onto something while they build up sufficient mental representations of the new domain.

But this use of metaphor usually does not help understanding. It just provides emotional support along the arduous journey towards that understanding. It can also backfire. Teachers often spin up these kinds of metaphors in such a way that they assume an understanding of the unfamiliar. And it is only once students have bootstrapped themselves into some understanding of the subject that the metaphor starts to make any sense to them.

For instance (to use a famous example), we can teach students that the electrical current is like a flow of water. This certainly takes some fear out of the invisible world of electrons. But unless students have at least some prior understanding of electricity, they may ask questions like ‘how do you get the water into the wires?’

This type of metaphor can only be used for a fleeting moment and it must be followed by hard work of accumulating understanding of the new domain on its own terms. Perhaps with the use of more metaphors, this time of the instrumental kind.

2. Metaphor as an instrument

The instrumental use of metaphor for explanation is where real understanding starts to happen. But not all teachers are as good at it. In this case, the metaphor provides a way for the student to grasp the new subject. A lens to see it through, or a mental instrument to manipulate it with. Such metaphors are essential to the learning process. However, they do not rely on the moment of instant insight, which they can sometimes trigger, but rather on continuing exploration of the projection between the two domains. Their usefulness is less in the feeling of illumination than in their availability to be used over and over again.

For instance, electrical engineers may be able to make better judgments about certain properties of electrical circuits when they think of electrons as a flow of water. But in other instances, they may be better off when they think about electrons as lots of tiny balls rubbing against one another, generating heat. This metaphor can come up over and over to help them mentally manipulate the two domains.

Here, as with all metaphors, it is essential that we know when to let go. Or even better, when to switch to a different or even a contradictory metaphor. These instrumental metaphors can be local or global but it is rare that one will be enough.

3. Metaphor as catalyst

In the third use, the metaphor plays the role of a catalyst. Like a powder dissolved into a liquid, it makes a new substance in which both domains are transformed into one unified understanding. This is when the student transforms into a scholar. Making independent judgments, challenging the teacher’s own understanding, and ultimately becoming her own teacher. To work as a catalyst, the metaphor may be very rich and detailed or just a quick sketch resulting in a slight shift of perspective. But it always requires solid knowledge of the target domain.

Let’s continue with our electrical current example. Here, the student comes not only to understand that sometimes electricity behaves like a liquid and sometimes like a collection of particles, they also come to see the complexity of liquids and particles. They start making predictions both ways and ask questions like ‘What if we thought of the flow of water as a collection of particles?’, etc.

Here the metaphor becomes a process without an end. It spurs new mixtures and remixtures as one finds out more about the two (and often more) domains. Unlike with instrumental and invitational metaphors, it is no longer important that the metaphor be apt. It is just important that it is useful for new understandings or the possibilities of these new understandings. Donald Schön called one subtype of these ‘generative metaphor’.

But as with the other types, it is important that these metaphors come with some sort self-destruct mechanism.

What often happens is that these metaphors are taken up by those who presume that they map fully onto the target domain and that no other understanding of the target domain is necessary. I described how this is a problem with Schroedinger’s cat, or Lorenz’s hurricane-triggering butterflies.

What’s even worse, teachers often use these metaphors far too soon. This either confuses students or, worse, it gives them an illusion of understanding that they do not possess.

How NOT to use metaphor to explain something – two case studies

Case study 1: Metaphor gap in data science

My first case study of a bad use of explanation with metaphor is the podcast Data Skeptic. In fact, listening to the most recent episodes prompted me to write this in the first place.

I must preface this by saying that I like the podcast and recommend it to others who want to understand modern data science. It covers important subjects and there is much to learn from it. Its one unfortunate feature, however, are certain episodes when the host, data scientist Kyle Polich, uses his wife, project manager and English major, Linh Da Tran as co-host and tries to explain concepts from abstract computational theory to her. Or rather at her.

This almost invariably fails. Not because Linh Da does not possess the raw intelligence or aptitude to understand these concepts but because Kyle confuses metaphor with explanation and explanation with understanding.

In two recent episodes, he attempted to explain attention in neural networks and Neural Turing Machines. It was an unmitigated disaster. As the metaphors kept piling up, Linh Da finally cried out “I don’t know what you want me to understand”. That’s exactly the problem with a metaphor that only relies on the understanding of the source domain. It serves as a good invitation to the subject but as a very bad instrument for developing an understanding.

There are several problems with this set up that make it a bad place for too many metaphors. First, Linh Da is clearly just humoring Kyle. She’s vaguely interested in machine learning as a phenomenon but has no real interest in putting much work in to learning about how it works. This forces Kyle into more and more metaphors involving their pet bird Yoshi. These are useful socially and emotionally because they allow Linh Da to contribute to the discussion. But her contributions at every turn show that she cannot use any of the analogies to make useful inferences about the subject. She almost never brings up previous subjects. At the end of the episode on Neural Turing Machines, she asked who owns the Turing Machine. In all the torrent of analogies, Kyle neglected to stress that the Turing Machine is itself a metaphor. This is despite a prior episode where another guest explained why Turing Machines are important very clearly.

The conceit of the episodes is that data science can be explained even to English majors. That is certainly correct. But those majors must be willing to put in some work between episodes or have some prior knowledge. And as the subjects get more technical or abstract, the explanations have to get longer and include some practice time. And the amount of this practice needs to increase as if the practice was filling a funnel and not a test tube. Namely, to get from level B to C requires more work than getting from level A to B. Otherwise, the metaphors have nothing to hold on to. They constantly invite the student in but then offer no tools for going further. At best, they will confuse the learner and at worst, they will give them an illusion of understanding. About as useful as a seat belt made from masking tape.

While it is pleasant learning about these concepts through listening in on a married couple having a light-hearted conversation, at a certain stage, this pedagogic device just gets in the way of learning by the audience. Initially, the listener can just do their own metaphor mapping and ask the right questions in their head. But as the abstractness level increases, the host doing the explaining cannot go into sufficient depth because the co-host can’t keep up. And the increasingly convoluted and unnecessary metaphors just create a mental fog that descends over all.

I was particularly disappointed in the episode on Attention in neural networks which is something I wanted to learn more about. I found the initial metaphor of attention as a sort of memory span very useful but then it got stuck because Linh Da could not use it to go any further. This was because she was not given a chance to integrate the previous episodes where similar things were discussed. It was still useful to me because then I could go read about attention with a renewed perspective. But an opportunity for a deeper exploration of the metaphor was wasted.

This would have been fine if the episode was aimed at general public with no other understanding rather than an interested audience with some prior background. But even then, the general public would have needed more and different information to make any sense of it.

At one point Kyle, raised the possibility that maybe he wasn’t an effective teacher because Linh Da could not understand something he had explained. But in fact, he was not being a teacher at all. In this setting, he’s just a provider of images. Like a documentary from the Serengeti where the audience remembers there are lions, but could not place it on a map.

I can imagine that Kyle would be a very effective teacher with students who are interested in the subject and if he had a chance to take them through it step by step. And his use of metaphors would be a valuable contribution to that. But in the podcast, he’s only playing at being a teacher with Linh Da and she’s only pretending being a student. His only goals are getting her to answer questions within his metaphor that seem like she achieved comprehension. This means she never gets a chance to try out the structures of the source domain on the target domain. And because of this she never gets to develop any understanding that could later be used as a foundation for further metaphors. Without this, adding more to the mix feels like an avalanche of analogies.

Case study 2: The explanation illusion at Wired magazine

But Data Skeptic is not the worst example of this type of pseudo-teaching by explanation. Only the most recent in my mind. A possibly much worse example is the Wired magazine series in which one expert supposedly explains a technical concept at 5 levels of difficulty: 5-7-year old, young teen, college student, graduate student, and another expert. These explanations often involve some level of metaphor, but they are mostly pointless. The conceit is that anybody can understand these concepts at “some level”. But the explanations do not equal understanding as is amply demonstrated in the videos. The people being explained to do not usually develop any new understanding. And it is doubtful whether the people watching do either.

Some of these are because the topic just is not appropriate to be explained to a certain audience. A 5 or 13-year old do not need to understand (nor do they have the background to) things like CRISPR or the Conectome. At best, they may learn which discipline they belong to, but that’s just teaching them a new name. No understanding of the phenomena is necessary.

But even when the understanding is well within reach and might have its use, the ‘expert’ fumbles. Thus the great and inventive musician Jacob Collier failed to explain the concept of ‘harmony’ to any of his charges. First, he tried to convince a five year old that harmony is a way of expressing a feeling with music (as opposed to melody). This is not only too abstract, it is also wrong. Both harmony and melody express feelings. But harmony is different notes played on top of one another rather than in sequence as in a melody (the feelings come from the pitch distance between the tones). This is well within the scope of understanding of a 5-year old when accompanied by some examples. No elaborate metaphors are necessary. But Jacob Collier goes into a very abstract explanation concluding with the most pointless question in any teacher’s arsenal: ‘does this make sense?’ to which he gets a an ‘uhuh’ from the child who clearly has no clue.

But explaining anything to 5-year-olds is hard. So does he do better with a teen? No. He still sticks with the metaphor of harmony as adding emotion to a melody. But then he mixes in the idea of harmony being a journey. To illustrate this, he goes from demonstrating a simple major / minor cord distinction to a jazz chord substitution. Which is wonderful and impresses the student but does not illustrate the concept of harmony to her.

No explanation happens at the higher levels either because all of the others (culminating in jazz giant Herbie Hancock) know the key concepts. So Collier just chats with them about harmonization and reharmonization. Which also reveals that that’s what he had in his mind with the 5-year old and the teen – he was just explaining a much more advanced concept under the label of the simple one.

One of the commenters on the video made an astute observation:

“it’s interesting how in the earlier levels it has to do more with theory and as you get higher up the level it goes back to nature and life experience and emotions. It’s almost as if, as the complexity increases, there’s also a level of fundamental basic understanding of nature and how it goes hand in hand at the most complex level” (emusik97531 [DL fixed small typos])

Essentially, as the level of the underlying understanding grows, the simple metaphor of journey, place and feeling have the most impact. At the lower levels, they just hang in there, not doing much of anything. They may feel like an invitation, but they don’t have any way to be used as a tool for understanding.

At the higher levels, Collier also shows that maybe he could be a great teacher to somebody closer to his level of skill and understanding. But it also reveals the pointlessness of an isolated act of explanation with (or without) metaphor if it is not supported by the hard work of making the connections necessary for the metaphor to become a proper instrument or a catalyst.

This is not a particular critique of Jacob Collier who is a great teacher to students at Berklee but rather of the whole set up of the series by Wired. Nobody could succeed in this setting. The concept is either going to be hard at the low levels or too basic at the higher ones.

The inglorious history of metaphorical explanation in education

Collier and Polich, as well as countless others, are in illustrious company of people who overestimate what explanation can do in the process of learning.

Socrates in a famous scene from ‘Meno’ walks a slave boy through a series of questions “proving” that he already knew the answer to how to ‘double’ the area of the square. B F Skinner (1965) [PDF] called the Socratic method modeled on this example “one of the great frauds in the history of education”. Setting aside the metaphysics of innate transcendental knowledge Socrates was after, the boy clearly did not learn anything through the interaction. He would not even be able to recreate the proof at a later point. He never got a chance to develop an understanding. This is very much reminiscent of the long-suffering Linh Da who simply answers questions without getting the point of them at any stage and clearly not being able to reconstruct the argument later.

Another giant of philosophy, Rousseau, constructed a thought experimental student in Emile (because, by his own admission, he found teaching actual students too ill-suited to his temperament). Rousseau took the imaginary Emile on a similarly Socratic journey to create the perfect ‘natural man’. Rousseau’s Emile always immediately gets the point of his metaphors and learns the right lesson as if by magic. He rarely does anything in the way of practice – although he perhaps has more time to assimilate new knowledge than Socrates’ victim.

There is much of Rousseau and Socrates in all teachers. Explanations and metaphors are heady stuff while boring practice such as that Skinner was hoping to replace by his teaching machines is the embodiment of tedium for all involved. But without some sort of practice-like engagement with the subject, no understanding is possible. Educators often leave this for the spaces ‘in-between’ teaching events – invisible to them other than as returned homework assignments. Students who succeed have somehow figured out how to do that unmentioned task of conceptual practice. This then looks like effortless insight to the students who struggle.

How to actually use metaphors for explanation

So, is there a way to avoid the pitfalls we encountered above? As we saw, the first step should be asking oneself whether this is a time for more explanations and if metaphors are the best way of arriving at a useful understanding.

We must also remember that there is no such thing as a perfect explanation or perfect metaphor. Not everybody finds the conceptual work of cognitively decoupling one domain so that it can be projected on another easy to do or even useful. But at some point a metaphor is the only way to go about explaining something.

So when it comes time to construct the metaphor, we must make sure of two things.

First, we have to find the right source domain for the metaphor that can be projected onto the target domain so that the student can achieve useful understanding of some aspect of the target. This happens pretty much through a process of trial and error. Which means, we’re unlikely to happen on the right metaphor on the first try.

Second, we have to make sure we have a good grasp on the possible projections between the two domains. I broadly described the process in my guide to metaphor hacking. We have to decide on what the purpose of the metaphor is and whether successful mappings can be made between the two domains. But we have to keep exploring both domains to see if there are any mappings that would result in a misunderstanding. These then have to be explicitly cut off from the metaphor.

For example, a virus is a good metaphor for a piece of software that ‘infects’ your computer. But we must also specify that this can only happen by executing the software, not by simple exposure of 2 PCs in the same room.

The teacher must know when to abandon a metaphor as much as when to bring one up. Some metaphors are local and others are global. The global metaphors are particularly dangerous because they can lock out possible alternative sources of understanding.

Switching between metaphors is essential. But it also contains a danger. The biggest mistake teachers (including this one) make when students say don’t understand, is to fill the air with more different explanations. Yes, these may be necessary. But first give the student some space and time to integrate this into their current level of understanding.

The teacher also has to make sure that the student already has sufficient mental representations from both domains to be able to make the projections between them catch onto something. A computer virus metaphor is useless if the student knows nothing about viruses but it also does not help, if the student knows nothing about computers.

Particularly when metaphors are used as catalysts, it is important to investigate the source domain as much as the target domain. For instance, if we use the metaphor ‘education is business’, we may want to look at various aspects of the way businesses work to see if there are unexpected dangers in using this metaphor globally. Then, if we decide that schools should run along the same model as New York restaurants, we should ask what is the equivalent of a restaurant going out of business, or a customer having a bad meal. And what happens if we start thinking of education as a dining experience? Etc.

Finally, it is essential-+ that we pay attention to what happens before and after the metaphor. Each student will bring a slightly different understanding of both the source and the target domains. Can we rely on them coming up with the same mappings on their own? And, if we think of the metaphor as an instrument for dealing with a particular concept, we must make sure we teach the students how it works and give them enough time to practice with it before we leave them to their own devices.

There is no perfect procedure for building a metaphor that explains a new concept. And the metaphor is always only a small part of the process of understanding. We must pay attention to the hard work necessary before a metaphor can be used. And we must think about the work required afterward for the metaphor to continue its usefulness.

Good metaphors are often remembered by students and teacher alike for a long time with emotional salience. But even the best metaphor becomes simply a fond memory of a past moment of enlightenment without any understanding if it is not being continually exercised and stretched. It is far too common for people to just remember the source domain with only the vaguest glimpses of the target domain distorted by time.

Ultimately, any metaphor-based explanation can be but a singular event in the continual process of understanding. Metaphors, when used well, can be great instruments for further exploration. But when used poorly, they are but ornaments on an empty box of the vacant mind.

Post script:

Lest there be any doubt. I have not only seen others make the mistakes I mention here. I have made them all myself. Again and again and again. Deepest apologies to my students.

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