Analogies are thinking tools as well as communication tools.
Keith S. Taber
Analogy is very familiar to science teachers as a tool for communicating ideas (one way to help 'make the unfamiliar familiar'), but analogies have also been important to research scientists themselves. Analogy can be a useful thinking tool for scientists, as well as a means of getting across novel ideas.
Indeed we might suggests that analogies have roles that might be described as exploratory, autodidactic, and pedagogic:
- I wonder if it is like this? A creative source of ideas generating hypothesis to test out;
- Ah, I see, it is like this! A tool for making sense of something that seems unfamiliar to us;
- You see, it is somewhat like this… A tool for helping others to make sense of some novel or unfamiliar notion.
On this site, I have given quite a lot of attention to the pedagogic, communicative role of analogies as used by teachers – and also by other communicators of science such as journalists, and indeed sometimes also scientists themselves when writing for their colleagues. As well as discussing some teaching analogies in detail in blog postings, I've also compiled some examples I have come across from my reading and other sources (such as radio items).
I was recently using an analogy myself to communicate an idea as part of a talk I had been asked to give. I set up an analogy to illustrate four categories in a model of 'bugs' that can occur in teaching-learning when students either do not understand, or misunderstand (misinterpret), teaching. I was trying to explain an educational model to science teachers, so used some science (that I assumed would be familiar to the audience) as the analogue.
An analogy involves a comparison between the structures of two systems where there is an explicit mapping to show similar structural features between the two systems – the analogue being used to explain and the target being explained. (If that sounds a bit obscure, there is an example presented in the table below).
Analogy as a thinking tool
I readily found 'mappings' for my four categories, so my analogy 'worked' (for me!) But, in working out the analogy, I realised that there was an additional option, a variation on one of the categories, that I had not fully appreciated. That is, by thinking about an analogy, I discovered a potential mapping back to my model that I had not expected, so the act of developing an analogy (meant to communicate the idea) actually deepened my own understanding of the model.
This is just the kind of thinking that analogy as an exploratory tool can offer (even if that was not how I was intending to use the analogy). This did not lead to a drastic rethinking of my model, but I thought it was interesting how working with the analogy could offer a slightly different insight into the original model.
Accommodating concepts
This puts me in mind of how concepts can both grow and then be modified by analogical thinking in science. For example, when (the substance that was to be named as) potassium was first discovered it had a combination of properties quite unlike any previously known substances. It seemed to share some – but not all – properties with the group of known substances referred to as metals, so it could be considered a metal by analogy with them. But for potassium (and then sodium) to be accepted as actual metals (not just partial analogies of metal) it was necessary to modify the set of properties considered essential to a substance that was classed as a metal (Taber, 2019).
Read about the Origin of a Chemical Concept: The Ongoing Discovery of Potassium
(Of course, it seems 'obvious' to us now that potassium and sodium are metals – but that is with the benefit of hindsight, as the metal concept we learnt about in chemistry had long since been adapted to 'accommodate' the alkali metals.)
Types of learning blocks
The 'target' material in my talk was the typology of learning impediments which is meant to set out the types of 'bugs' that can occur in a 'teaching learning system'. That is, when
"there is a teacher who wishes to teach some curriculum material that has been prepared for the class; and a learner, who is present; willing, and in a fit state, to learn; who is paying attention in class; and where there is a good communication channel, which will normally mean that the learner and teacher can see and hear each other clearly… even when this system exists, we cannot be confident the learner will always understand what is being taught in the manner intended"
Taber, 2023
The teacher-learner system – a learner, motivated to study, able to see and hear the teacher, and paying attention to the teacher's clear explanation of a scientific idea: "even when this system exists, we cannot be confident the learner will always understand what is being taught in the manner intended"
The model has four main categories of system 'bugs', organised in two overarching classes:
A null learning impediment meant the student failed to associate teaching with prior learning – that the teaching did not lead to the learning bringing to mind something that helped them make sense of the teaching. This could be because the expected prior learning had never happened, called a deficiency learning impediment; or because the relevance of prior learning was not appreciated (i.e., not associated), a so-called fragmentation learning impediment.
The two main types of substantive learning impediments involve the learner making sense of teaching in a way that does not match that intended, either because the relevant prior learning includes alternative conceptions, and so the learning is distorted by being understood within a conceptual framework that does not match the science; or through the teaching being understood in the context of some other prior learning that seemed relevant to the learner, but which, from the teacher's perspective, was not pertinent. These are referred to in the model as grounded learning impediments and associative learning impediments, respectively.
Taber, 2023
A typology of learning impediments: things that go wrong even when the teacher explains the concepts clearly, and the learner wants to learn and is paying attention.
Read about the typology of learning impediments
The analogy
The analogy that came to mind was from biochemistry (perhaps because I had recently been thinking about the metaphors and analogies in a book on that subject?) As meaningful learning requires teaching to be related to (fit into, anchor in, make sense of in terms of) some prior learning available to the learner, I envisaged learning as being analogous to some small molecule that in metabolism became bound to a protein (an enzyme perhaps) which was only possible because there was a good fit between the molecular configurations of the protein (a component of the learners' existing conceptual structure) and the metabolite (the information provided in teaching).
An analogy for learning – a metabolite will only bind to a protein if there is a good 'fit' between the structures.
So in my analogy, the mapping was:
| analogue | maps to | target concept |
| binding of a metabolite to a protein | ⟷ | conceptual learning |
| protein | ⟷ | an aspect of the learner's existing conceptual structure |
| metabolite | ⟷ | a 'quantum' of information presented in teaching |
| metabolite-protein complex | ⟷ | new information understood in terms of prior learning – new information assimilated to develop conceptual understanding |
So, in my talk I represented learning, and the possible 'bugs' in learning, through simple animations, using the following signs:
Dramatis personae for the analogue…
These signs were somewhat arbitrary symbols, except that they had an iconic feature – a complicated shape representing the molecular conformation that could indicate the presence or absence of a binding site capable of leading to complex formation.
Learning was modelled as the binding of the metabolite (information presented in teaching) with the protein (an existing feature of conceptual structure) into a new complex (new information from teaching assimilated into prior learning).
Learning was seen as analogous to the binding of a metabolite to a protein…
Each of my four main types of learning block seemed to have a parallel in scenarios where the metabolite would not become tightly bound to the protein in the molecular analogue.
Impediments to assimilating the metabolite
The learner can only relate new information to prior learning if they have indeed learnt that material. If the teacher assumes that students have already learnt some prerequisite material but the learner has not (perhaps a previous teacher ran out of time and missed the topic; or the learner was off-school ill at the time; or the learner attended a lesson on the material, but made no sense of it; or the student attended a lesson on the material which made sense at the time, but the material was never reinforced in later lessons, so was never consolidated into long-term memory…) then this will be as if the target protein is missing from the cytosol, so there is no target structure for the metabolite to bind to:
…and the binding could not occur if the protein was not present…
Then, even if a student has the expected prior learning, they will only interpret new information in terms of it if they realise its relevance. Teachers may assume it is obvious what prior leaning is being relied upon to make sense of new teaching, but sometimes this prior learning is not triggered as pertinent and so 'brought to mind' by the learner. (Or, to be fair to the teacher, they may have even deliberately reminded students of the relevant prior learning just before introducing the new material, but without the learner realising this was meant to be linked in any way!)
So, this is as if the two molecules are both present in a cell's cytosol, but they never come close enough to interact and bind:
…and binding could not occur if the metabolite molecule did not come into contact with the protein…
Now students often have alternative conceptions ('misconceptions') of science topics. So, even if they do know about the topic that the new teaching is expected to develop for them, if they have a different understanding of the topic, then – although they may interpret the new information in terms of their existing understanding of the topic – they will likely understand the new teaching in a distorted way so it fits with their alternative take on the topic.
I thought that, in my analogy, an alternative conception was like a protein that was 'mis-structured' (as may happen if there are genetic mutations). If a mutation only subtly changes the shape of the binding site on the protein it is possible that the complex may form, but with a different, more strained, conformation. So, the new complex structure will not match the usual canonical structure.
…and a mutation may change the conformation of the binding site so that the metabolite does not bind as effectively * …
It was at that point that I realised there was another possibility here. I will return to that in a moment.
My fourth class of system bug, or learning impediment, involved a learner understanding teaching in terms of some material which (from the teacher's perspective) was unrelated. These creative links are sometimes made, and can be misleading (e.g., sleeping is like putting a battery on change, so it gives us energy).
So, this was like our metabolite colliding with a completely different protein, but one to which it could bind, before it reached our target protein. There is a fit, but within the 'wrong' overall structure – teaching is (subjectively) understood, but in a completely idiosyncratic and non-canonical way:
…intended binding may not occur if the metabolite first comes into contact with another molecule with which it can bind to form a different complex…
It was when I was drawing out my mutated protein, such that binding was strained to distort the complex (like a student interpreting teaching through an alternative understanding of the right topic, so the meaning of teaching gets distorted) that I realised a mutation could also lead to the protein lacking a viable binding site at all.
In this case the protein is present, but there was no way to bind the metabolite with it to form a complex. The learner has prior learning of the topic, but it is not possible to link the new information presented in teaching with it, as it would simply not fit with the learners' alternative understanding of the topic (as when for many years it was assumed by chemists that no noble gas compounds could be made because the inert gases had inherently stable electronic configurations which could not be disrupted by chemical processes).
So here the 'cause' of the lack of complex formation (a mutated protein / an alternative conceptual framework) could lead to two different outcomes – new information being distorted to fit in the alternative structure (like a protein with a slightly altered binding site) or new information not being linked with the prior topic learning at all (akin to a mutation meaning a protein had no viable binding site for forming a complex with the metabolite).
…* and I realised that a mutated protein may have no functioning binding site (rather than just a slightly distorted one) which leads to a different outcome.
So, consideration of my analogy brought home to me that the presence of an alternative conception may have different impacts depending on the extent of the differences between the students' thinking and the canonical scientific account.
Two types of 'mutated' prior learning?
What might these two possibilities, these different extents of mutated conceptions, mean in practice?
Consider a learner who is taught that 'plants do not need to be given food as they can manufacture their own food by photosynthesis'. If the learner has a notion of plants that includes fungi such as mushrooms and toadstools then the new information can 'bind' to the existing conceptual structure, but the learning will be 'strained' in the sense that the intended meaning is distorted (because the learner now thinks mushrooms and toadstool photosynthesise). This was the kind of example I had had in mind as a grounded learning impediment caused by a prior alternative conception.
By contrast, a deficiency learning impediment had reflected the absence of prerequisite learning needed to make sense of teaching (such as teaching that the bonds in methane are formed by the overlap of sp3 hybrid orbitals with the hydrogen 1s atomic orbitals to a student who had not previously been introduced to atomic orbitals).
However, the absence of prerequisite knowledge need not be due to having missed prior teaching, but could instead be having formed alternative conceptions so that the topic is represented in the learner's conceptual structure, but in a distorted ('mutated') version.
Consider the example of a teacher explaining properties of substances in terms of quanticle (nanoscopic particle) models. The teacher may explain that ionic salts tend to have high melting temperatures because the solids comprise of a lattice of strongly bonded ions which therefore takes a good deal of energy to disrupt.
A very common alternative conception of ionic bonding is based on the (false) idea that ionic bonds are formed by electron transfer from a metal atom to a non-metal atom. Often when a student acquires this alternative conception they understand the ionic solid to be composed of small units held together by ionic bonds (e.g., Na+-Cl–), but held to each other by weaker forces. For a student holding this alternative conceptual framework ionic bonds are not easily disrupted by heating an ionic solid, but the weaker forces between the bonded units will easily be disrupted so that melting will occur. The student assumes the small units (such as NaCl ion pairs) are like molecules (or actually are molecules) that continue to exist in the liquid phase when a solid like ice melts.
This learner had existing prior learning of the ionic bonding concept, but because this was not canonical, but involved alternative conceptions, the new information did not fit with the prior learning (it could not 'bind' with the 'mutated' conceptual structure) so the intended learning did not occur – a kind of deficiency learning impediment.
So, a deficiency learning impediment is due to a lack of existing conceptual learning that the new information can bind to – but this may be either because there is no prior learning on the topic, or because alternative conceptions of aspects of the topic mean the conceptual structure has the wrong 'conformation' to be perceived as relating to the new information presented in teaching.
It is just a model
The model of kinds of learning impediments is just that – a model of conceptual learning. It is one that I found helpful in my own work, especially when researching student thinking. I hope it may offer some insights to others, including teachers. Any value it has is in informing our thinking about learning and the teaching that can promote it. The analogy discussed above is just a(nother) kind of model of that model – a teaching analogy to introduce an abstract idea
Here, I wanted to just share how I found my own use of the analogy as a teaching aid helped develop my own thinking about the target domain of student learning. Analogies are just models, but like all models they can be useful thinking tools as long as we remember that they only somewhat resemble, and are not the same as, the targets they are compared with.
Work cited
- Taber, K. S. (1997) Student understanding of ionic bonding: molecular versus electrostatic thinking?, School Science Review, 78 (285), pp.85-95. [Download a copy]
- Taber, K. S. (2019). The Nature of the Chemical Concept: Constructing chemical knowledge in teaching and learning. Cambridge: Royal Society of Chemistry.
- Taber, K. S. (2023, 14th August). Debugging teaching. Improving the teacher's mental model of the learners' mental models. The Keynote Address given at the Science Teachers Association of Nigeria Annual Conference. In, Suleiman Sa'adu Matazu (Ed..) The Learning Sciences and STEM Education: 63rd Annual Conference Proceedings, 2023: Science Teachers Association of Nigeria, pp.7-49. [Download the paper.]
The book Student Thinking and Learning in Science: Perspectives on the Nature and Development of Learners' Ideas gives an account of the nature of learners' conceptions, and how they develop, and how teachers can plan teaching accordingly.
It includes many examples of student alternative conceptions in science topics.
