Iconic chemical triangles
Keith S. Taber
Derek was a participant in the Understanding Science Project. When I interviewed Derek soon after the start of his secondary schooling, he told me he liked science, and was currently studying 'burning'.
So, I asked him what that was:
What is burning?
[pause, c.2s]
When [pause, c.2s] a fuel, oxygen and heat gets – in, erm, I'm not quite sure how to explain, but it's like – you get the triangle of fire, and then, burning is just when you've got fire and you're burning something with it.
Okay, so you'd recognise it if you saw it, would you?
Yeah.
Yeah, but maybe it's not that easy to explain?
Yeah.
The notion that 'burning is just when you've got fire and you're burning something with it' – might be considered tautological:
- burning is when you are burning something
Scientists look to explain natural phenomena with theories, principles, models, and so forth. But for most people, phenomena that they have been familiar with since very young (such as a dropped object falling) do not seem to need explanation – as they are seen as just natural events (Watts & Taber, 1996).
Derek knew about the fire triangle, but his response reminded me of another triangle that is often referred to by science educators.
Johnstone's triangle
For many years Prof. Alex Johnstone (1930-2017) worked at the Centre for Science Education that he founded at the University of Glasgow; where he undertook, supervised, and collaborated on, a good many projects in science education – especially, but not only, relating to the teaching and learning of chemistry and physics in higher education.
However, one of Johnstone's most influential publications must be the short article he published in the School Science Review (Johnstone, 1982) – the secondary science journal of the Association for Science Education. In this short piece he argued that in each of biology, chemistry, and physics, learning difficulties in part derived from how the subject was taught at several 'levels' at once, asking young learners to think simultaneously on different planes as it were. In each of these science subjects, this could be represented by a triangle. In many lessons students would be asked to think about, and inter-relate, considerations from the viewpoints of several vertices.
Johnston's chemistry triangle distinguished between three levels:
- the macroscopic (the scale at which people observe and handle materials);
- the submicroscopic (molecular) scale at which many chemical explanations are developed;
- the symbolic level – where abstract symbols are used to represent the chemistry
"Those of us who are academic chemists can view our subject on at least three levels.
There is the level at which which we can see and handle materials, and describe their properties in terms of density, flammability, colour and so on. We are also interested in the possibility of conversion of one material into another with consequent changes in properties.
A second level is the representational one in which we try to represent chemical substances by formulae and their changes by equations. This is part of the sophisticated language of the subject.
The third level is atomic and molecular, a level at which we attempt to explain why chemical substances behave the way they do. We invoke atoms, molecules, ions, structures, isomers, polymers etc to give us a mental picture by which to direct our thinking and rationalize the descriptive level mentioned above.
These levels could be called (a) descriptive and functional, (b) representational, (c) explanatory. Trained chemists jump freely from level to level in a series of mental gymnastics. It is eventually very hard to separate these levels."
Johnstone, 1982 (added emphasis)
Over the years there have been many attempts to apply, elaborate, and refine Johnston's triangle, and it has been an idea that has proved very productive in thinking about learning difficulties in the subject.
"Chemistry seeks to provide qualitative and quantitative explanations for the observed behaviour of elements and their compounds. Doing so involves making use of three types of representation: the macro (the empirical properties of substances); the sub-micro (the natures of the entities giving rise to those properties); and the symbolic (the number of entities involved in any changes that take place). Although understanding this triplet relationship is a key aspect of chemical education, there is considerable evidence that students find great difficulty in achieving mastery of the ideas involved…" (Publisher's description)
One well-respected, edited, scholarly book ('Multiple Representations in Chemical Education' – Gilbert & Treagust, 2009) consisted of contributions exploring implications of the idea. Indeed, now, there is even a book entitled 'The Johnstone Triangle' (Reid, 2021) with the telling subtitle: 'the key to understanding chemistry'!
Reconceptualisation
Derek was just being introduced to burning as a science topic, and for him it was still just a familiar phenomenon rather than a theoretical construct. We have all seen fires, and can recognise when something is burning – but how many people really know what fire is?1 Burning and fire are everyday concepts – fire is an impressive phenomenon to a young child: one that is salient enough to be noticed. The child's brain then recognises different instances of fire as being similar and it abstracts a spontaneous concept – that there is a category of events in the world that appear like this.
Of course, the brain of the young child does this without using language (it forms a category of events in the sense that it readily recognises new instances – it does not yet have access to have technical notions of 'category', 'concept', 'abstraction' of course.) And the child does not instinctively know this is called 'fire' or 'el incendio' or 'l' incendie' or whatever, until someone who is a more mature member of the child's natural language community shares this label.2
School science will involve learning that there is a formal scientific concept3 called 'combustion' that is basically the chemist's name for burning. However, 'combustion' is a technical term, so combustion will be defined in terms of other concepts. So, whereas in everyday life we recognise what counts as a fire or burning using the brain's inherent pattern-recognition mechanism (a spontaneous conception), in chemistry we have a technical definition (a scientific concept defined in relation to to other scientific concepts, and so 'theoretical').
That is, in everyday life, if you told someone you saw something on fire, it is unlikely anyone (leaving aside science teachers) would ask you which criteria you used to know this: you did not deliberate on the matter, you simply saw, and instantly recognised, a fire. When you refer to a fire, the other person recognises what you mean because they have learnt 'fire' to be the label for their own spontaneously formed conception that allows their perceptual-cognitive system to instantly recognise a fire.
But, for a chemist, combustion is one class of chemical reaction (so the learner can only understand combustion in chemical terms if they have an appreciation of what a chemical reaction is), which only makes sense to someone who has reasonable idea what a scientist means by a substance, as chemical reactions are changes resulting in different substances. Here we have shifted from everyday notions to the theoretical descriptions of science.
The invisible nanoscopic world
But chemists are seldom satisfied with macroscopic accounts – even when posed in technical language. Rather, students will be taught to explain the observable macroscopic phenomena in terms of invisible entities which have unfamiliar properties. Imagined entities such as molecules4, nanoscopic systems which are best understood as fuzzy balls of fields – that have no actual surface, and are mostly tenuous 'clouds' of charge. (Molecules are sometimes modelled as if billiard balls, or sets of balls connected by sticks, but this is just an attempt to represent entities quite unlike the familiar referents available to learners in ways they can make sense of.)
That is, combustion will be explained as a rearrangement of electrons and atomic cores that changes one set of molecules (of the reactants in the reaction) into another (the products). This process will involve energy changes, due to differences in stability of different sets of molecules, and will progress through the breaking and making of chemical bonds.
If the learner is able to form a mental image of (i.e., imagine) chemical reactions at the nanoscopic level, and see how this can be used to explain an actual observable phenomenon (such as a fire), they then also have to learn how chemists often represent these ideas in what is in effect a specialist language – involving chemical formulae, and reaction equations, and the like.
So, when Derek was using a Bunsen burner to set fire to pasta and (not quite set fire to) raisins as he reported to me, he was using a chemical reaction that might be summarised by the chemist or science teacher as:
CH4 + 2O2 ➞ CO2 + 2H2O
Johnstone suggested that the symbolic representation was the third level, alongside the macroscopic and submicroscopic. He was absolutely right that it added to the 'learning demand'. However, there is another complication in that many of these key representations (the formulae and equations) are ambiguous as they can represent either the macroscopic level of substances weighed out in grammes (2O2 would represent 64 g of the substance oxygen, although as it is a gas it would normally be measured by volume) or the individual imagined entities of the molecular world (where 2O2 would mean two molecules of oxygen).
Useful ambiguity
This is useful ambiguity for the chemist – but an added complication for the learner who has to follow the teacher's transitions where one moment a symbol reflects a test tube of stuff, and the next some molecule. Because of its role in bridging between the two very different scales at which we explain chemistry I prefer to see these symbols as being along one side of the triangle (whilst separating out the everyday phenomenological level from the technical, theoretical descriptions used by science). However, whatever version of Johnstone's triangle is applied, it has become something of an iconic image in chemistry education.
Another iconic triangle
Derek had not yet been introduced to all this, and he was still operating with burning as a phenomenon:
And why is this important, do you think? Why do you think we study burning?
[pause, c.2s]
I'm not sure.
No one's told you that?
No.
Is it fun, is it a fun topic?
Yeah.
What Derek did seem to have learned well was the fire triangle.
But you have this 'triangle of fire'. So does that mean that fire is always a triangular shape?
No.
So, what's a triangle of fire?
You need three things to make a fire, which is oxygen, heat and fuel.
Okay, so what if I had erm some fuel and some heat, but I didn't have any oxygen, but maybe I've got lots of fuel?
No – wouldn't have fire.
I can't have extra fuel instead?
No.
No?
You need the three things.
What if I've got lots and lots of fuel, and lots and lots of oxygen, but it's very, very cold?
No.
No, that won't work either. So I always have to have the three things?
Yeah.
Derek stuck to his claim – you always needed all three. This is a useful heuristic (useful if ever one is faced with a fire as it tells you can act by just removing one of the three essentials) even if (like most heuristics) it will sometimes fail, e.g.
- some materials will continue burning in the absence of an external supply of oxygen as they have an internal source;
- chlorine will support combustion in place of oxygen (but that's seldom a practical issue in everyday situations) ;
- substances have an auto-ignition temperature (where they can spontaneously ignite), and for a few substances this is around or below room temperature;
These exceptions do not undermine the general utility of the' 'triangle'.
Some useful learning had gone on here – and potentially not just about fire, because the idea that one factor may be limiting on a process is a generally useful principle (e.g., plants grown in a soil depleted in potassium will not thrive, no matter how much sunlight, water, nitrate and phosphate is present).
But the fire triangle, even if it is not supported by a deep understanding of chemical principles, is worth teaching because of its practical value. It seems to offer a heuristic that people accept and recall. And rather like Johnston's triangle, it seems to have become rather iconic. At least, I assume that is why when COVID-19 infection rates were high, the fire triangle was used as a familiar analogy to persuade people to avoid the 'oxygen' of social mixing…
Read 'COVID is like a fire because…'
Work cited
- Gilbert, J. K., & Treagust, D. F. (Eds.). (2009). Multiple Representations in Chemical Education. Springer.
- Johnstone, A. H. (1982). Macro- and microchemistry [Notes and correspondence]. School Science Review, 64(227), 377-379.
- Reid, N. (2021). The Johnstone Triangle: The Key to Understanding Chemistry. Royal Society of Chemistry.
- Taber, K. S. (2013). Revisiting the chemistry triplet: drawing upon the nature of chemical knowledge and the psychology of learning to inform chemistry education. Chemistry Education Research and Practice, 14(2), 156-168. https://doi.org/10.1039/C3RP00012E (This article is free to download from the publisher's website)
- Watts, M. and Taber, K. S. (1996) An explanatory gestalt of essence: students' conceptions of the 'natural' in physical phenomena, International Journal of Science Education, 18 (8), pp.939-954.
Notes
1 It has been mooted that fire should be understood as an example the 'fourth' phase of matter, plasma – that is an ionised gas.5 But actually fire is more complicated than this as it contains a mixture of reactant and product molecules and the molecular fragments that form intermediate and/or transition states. Some chemical reactions, when studied at the molecular level, largely follow a single reaction path. But combustion tends to be much more complex with multiple pathways involving many different ions and molecular fragments.
Read: The states of (don't) matter? Which state of matter is fire?
So, fire is a multiphase mixture, more akin to a solution, aerosol, or suspension, than to a gas or plasma.
2 The child does not know this is called fire, and when she is told this she may not realise that such names are social conventions – according to Jean Piaget's research young children may assume that things in the world have (that is, have always had) a name that people have had to learn.
This childish idea reflects superstitious notions about names that are part of some magical systems of knowledge – 'the law of names': the idea that if you know a person or thing's real name this gives you over over them/it.
3 A very influential theory due to Lev Vygotsky takes the distinction between spontaneous concepts formed automatically, and formal taught concepts that are shared through social interaction (such as teaching). These latter kinds of concepts are usually translated from Vygotsky's Russian as 'scientific' though this is meant in the broad sense of any formal field of study. A key point emphasised by Vygotsky was that, assuming the learners could relate a taught concept to existing spontaneous concepts (that is, 'meaningful learning' occurred), they would actually come to operate with a concept which was a hybrid developed from the interaction of the intuitive understanding and the learned technically defined notion – a melded conception.
4 By referring to molecules and ions and electrons as imagined entities, I am not suggesting they are only imaginary. Most (if not all) scientists today see them as real things (even if strictly our evidence is indirect, and they arguably remain theoretical constructs). But a teacher cannot directly show the class a molecule or an electron, even if some types of imaging equipment do now produce representations of individual atoms. For the learners (and I would suggest even the teacher) these are only ever imagined entities. Yet, we expect students to do a good deal of thinking about, and with, these imagined entities.
5 If we are expanding the three states of matter, then there is an argument for making plasma the 5th phase:
- Bose-Einstein condensates
- solids
- liquids
- gases
- plasma
- (quark 'soups'?)
