Single bonds are different to covalent bonds or ionic bonds
Keith S. Taber
Annie was a participant in the Understanding Chemical Bonding project. She was interviewed near the start of her college 'A level' course (equivalent to Y12 of the English school system). Annie was shown, and asked about, a sequence of images representing atoms, molecules and other sub-microscopic structures of the kinds commonl y used in chemistry teaching. She was shown a representation of the resonance between three canonical forms of BF3, sometimes used as away of reflection polar bonding. She had just seen another image representing resonance in the ethanoate ion, and had suggested that it contained a double bond. She had earlier in the interview referred to covalent bonding and ionic bonding, and after introducing the ideas of double bond, suggested that a double bond is different to a covalent bond.
Focal figure (14) presented to Annie
What about diagram 14?…
Oh.
(pause, c.13s)
Seems to be different arrangements. Of the three, or two elements.
Uh hm.
(pause, c.3s)
Which are joined by single bonds.
What, where, what single, what sorry are joined by single bonds?
However, as I checked what she was telling me, Annie's account seemed to shift.
They're different to double bonds?
Yeah.
And are they different to covalent bonds?
No 'cause you probably get covalent bonds which are single bonds.
So single bonds, just moments before said to different to covalent bonds, were now 'probably' capable of being covalent. As she continued to answer questions, Annie decided these were 'probably' just alternative terms.
So covalent bonds and single bonds, is that another word for the same thing?
Yeah, probably. But they can probably occur in different, things like in organic you talk about single bonds more than you talk about covalent, and then like in inorganic you talk about covalent bond, more than you talk about single bonding or double bonding.
So you think that maybe inorganic things, like sort of, >> copper iodide or something like that, that would tend to be more concerned with covalent bonds?
< Yeah. < Yeah.
But if you were doing organic things like, I don't know, erm, ethane, >> that's more likely to have single bonds in.
< Yeah. < Yeah.
So single bonds are more likely to occur in carbon compounds.
Yeah.
And covalent bonds are more likely to occur in some other type of compound?
Yeah. Sort of you've got different terminology, like you could probably use single bonds to refer to something in inorganic, but when you are talking about the structures and that, it's easier to talk about single bonds and double bonds, rather than saying that's got a covalent bond or that's got an ionic bond.
It seems likely that in the context of the research interview, where being asked directly about these points, Annie was forced to make explicit the reasons she tended to label particular bonds in specific ways. The interview questions may have acted like Socratic questioning, a kind of scaffolding, leading to new insights. Only in this context did she realise that the single and double bonds her organic chemistry lecturer talked about might actually be referring to the same entities as the covalent bonds her inorganic chemistry lecturer talked about.
It would probably not have occurred to Annie's lecturers (of which, I was one) that she would not realise that single and double bonds were covalent bonds. It may well have been that if she had been taught by the same lecturer in both areas, the tendency to refer to single and multiple bonds in organic compounds (where most bonds were primarily covalent) and to focus on the covalent-ionic dissension in inorganic compounds (where degree of polarity in bonds was a main theme of teaching) would still have lead to the same confusion. Later in the interview, Annie commented that:
if I use ionic or covalent I'm talking about, sort of like a general, bond, but if I use double or single bonds, that's mainly organic, because sort of it represents, sort of the sharing, 'cause like you draw all the molecules out more.
This might be considered an example of fragmentation learning impediment, where a student does not make a link that the teacher is likely to assume is obvious.
"It also became clear that although the process was meant to select on the basis of academic ability, to a large extent the outcomes reflected the socio-economic family background of the children.
Where the independent schools largely served the more wealthy in society, the grammar schools admitted disproportionate numbers of children from so called 'middle-class' families (i.e., parents being lower professional and white-collar workers) rather than so-called working class (e.g., children of unskilled labourers). It was found that scholastic achievement at age 11 was strongly linked to social capital deriving from the home background.
If schools are expected to be agents of social change, rather than a means to reproduce existing social differences (and that of course is an ideological choice), then determining a person's educational, and so possibly professional, future at age eleven, based on an examination that did not compensate for levels of educational opportunity and advantage in the home environment, was clearly inappropriate.."
I was checking some proofs for something I had written today* [Taber, 2017], and was struck by an ironic parallel between one of the challenges for teaching about the scientific theory of evolution by natural selection and one of the arguments put forward by those who deny the theory. The issue concerns the value of having only part of an integrated system.
The challenge of evolutionary change
One of the arguments that has long been made about the feasibility of evolution is that if it occurs by many small random events, it could not lead to progressive increases in complexity – unless it was guided by some sense of design to drive the many small changes towards some substantive new feature of ability. So, for example, birds have adaptations such as feathers that allow them to fly, even though they are thought to have evolved from creatures that could not fly. The argument goes that for a land animal to evolve into a bird there need to be a great many coordinated changes. Feathers would not appear due to a single mutation, but rather must be the result of a long series of small changes. Moreover, simply growing features would not allow an animal to fly without other coordinated changes such as evolving very light bones and changes in anatomy to support the musculature needed to power the wings.
The same argument can be made about something like the mammalian eye, which can hardly be one random mutation away from an eyeless creature. The eye requires retinal cells, linked to the optic nerve, a lens, the iris, and so on. The eye is an impressive piece of equipment which is as likely to be the result of a handful of random events, as would be – say, a pocket watch found walking on the heath (to use a famous example). A person finding a watch would not assume its mechanism was the result of a chance accumulation of parts that had somehow fallen together. Rather, the precise mechanism surely implies a designer who planned the constructions of the overall object. In 'Intelligent Design' similar arguments are made at the biochemical level, about the complex systems of proteins which only function after they have independently come into existence and become coordinated into a 'machine' such as a flagellum.
The challenge of conceptual change
The parallel concerns the nature of conceptual changes between different conceptual frameworks. Paul Thagard (e.g., 1992) has looked at historical cases and argued that such shifts depend upon judgements of 'explanatory coherence'. For example, the phlogiston theory explained a good many phenomena in chemistry, but also had well-recognised problems.
The very different conceptual framework developed by Lavoisier [the Lavoisiers? **] (before he was introduced to Madame Guillotine) saw combustion as a chemical reaction with oxygen (rather than a release of phlogiston), and with the merits of hindsight clearly makes sense of chemistry much more systematically and thoroughly. It seems hard now to understand why all other contemporary chemists did not readily switch their conceptual frameworks immediately. Thagard's argument was that those who were very familiar with phlogiston theory and had spent many years working with it genuinely found it had more explanatory coherence than the new unfamiliar oxygen theory that they had had less opportunity to work with across a wide range of examples. So chemists who history suggests were reactionary in rejecting the progressive new theory were actually acting perfectly rationally in terms of their own understanding at the time. ***
Evolution is counter-intuitive
Evolution is not an obvious idea. Our experience of the world is of very distinct types of creatures that seldom offer intermediate uncertain individuals. (That may not be true for expert naturalists, but is the common experience.) Types give rise to more of their own: young children know that pups come from dogs and grow to be adult dogs that will have pups, and not kittens, of their own. The fossil record may offer clues, but the extant biological world that children grow up in only offers a single static frame from the on-going movie of evolving life-forms. [That is, everyday 'lifeworld' knowledge can act as substantial learning impediment – we think we already know how things are.]
Natural selection is an exceptionally powerful and insightful theory – but it is not easy to grasp. Those who have become so familiar with it may forget that – but even Darwin took many years to be convinced about his theory.
Understanding natural selection means coordinating a range of different ideas about inheritance, and fitness, and random mutations, and environmental change, and geographical separation of populations, and so forth. Put it all together and the conceptual system seems elegant – perhaps even simple, and perhaps with the advantage of hindsight even obvious. It is said that when Huxley read the Origin of Species his response was "How extremely stupid not to have thought of that!" That perhaps owes as much to the pedagogic and rhetorical qualities of Darwin's writing in his "one long argument". However, Huxley had not thought of it. Alfred Russel Wallace had independently arrived at much the same scheme and it may be no coincidence that Darwin and Wallace had both spent years immersing themselves in the natural history of several continents.
Evolution is counter-intuitive, and only makes sense once we can construct a coherent theoretical structure that coordinates a range of different components. Natural selection is something like a shed that will act as a perfectly stable building once we have put it together, but which it is very difficult to hold in place whilst still under construction. Good scaffolding may be needed.
Incremental change
The response to those arguments about design in evolution is that the many generations between the land animal and the bird, or the blind animal and the mammal, get benefits from the individual mutations that will collectively, ultimately lead to the wing or mammalian eye. So a simple eye is better than no eye, and even a simple light sensitive spot may give its owner some advantage. Wings that are good enough to glide are useful even if their owners cannot actually fly. Nature is not too proud to make use of available materials that may have previously had different functions (whether at the level of proteins or anatomical structures). So perhaps features started out as useful insulation, before they were made use of for a new function. From the human scale it is hard not to see purpose – but the movie of life has an enormous number of frames and, like some art house movies, the observer might have to watch for some time to see any substantive changes.
A pedagogical suggestion – incremental teaching?
So there is the irony. Scientists counter the arguments about design by showing how parts of (what will later be recognised as) an adaptation actually function as smaller or different advantageous adaptations in their own right. Learning about natural selection presents a situation where the theory is only likely to offer greater explanatory coherence than a student's intuitive ideas about the absolute nature of species after the edifice has been fully constructed and regularly applied to a range of examples.
Perhaps we might take the parallel further. It might be worth exploring if we can scaffold learning about natural selection by finding ways to show students that each component of the theory offers some individual conceptual advantages in thinking about aspects of the natural world. That might be an idea worth exploring.
(Note. 'Representing evolution in science education: The challenge of teaching about natural selection' is published in B. Akpan (Ed.), Science Education: A Global Perspective. The International Edition is due to be published by Springer at the end of June 2016.)
Notes:
* First published 30th April 2016 at http://people.ds.cam.ac.uk/kst24/
** "as Madame Lavoisier, Marie-Anne Pierrette Paulze, was his coworker as well as his wife, and it is not clear how much credit she deserves for 'his' ideas" (Taber, 2019: 90). Due to the times in which they works it was for a long time generally assumed that Mme Lavoisier 'assisted' Antoine Lavoisier in his work, but that he was 'the' scientist. The extent of her role and contribution was very likely under-estimated and there has been some of a re-evaluation. It is known that Paulze contributed original diagrams of scientific apparatus, translated original scientific works, and after Antoine was executed by the French State she did much to ensure his work would be disseminated. It will likely never be know how much she contributed to the conceptualisation of Lavoisier's theories.
*** It has also been argued (in the work of Hasok Chang, for example) both that when the chemical revolution is considered, little weight is usually given to the less successful aspects of Lavoisier's theory, and that phlogiston theory had much greater merits and coherence than is usually now suggested.
Sources cited:
Taber, K. S. (2017). Representing evolution in science education: The challenge of teaching about natural selection. In B. Akpan (Ed.), Science Education: A Global Perspective (pp. 71-96). Switzerland: Springer International Publishing
Cause and effect?: People go to different places because of what they are wearing
Keith S. Taber
Image by anwo00 from Pixabay
Annie was a participant in the Understanding Chemical Bonding project. She was a second year 'A level' student (c.18 years of age) when she was talking to me about atoms and electrons, but I was struck with the way she used the word 'because'.
Technically this conjunction is linked with causality, something of importance in science. To say that X occurred because of Y is to claim that Y was a cause of X.
I wanted to clarify if Annie's use of 'because' in that chemical context actually implied that she was describing what she considered a cause, or whether she was using the word more loosely. To probe this I presented what I considered an obviously inappropriate use of 'because': that football fans following different teams in the same city would go to different matches BECAUSE of the colour of the clothes they wore (i.e., hats and scarves traditionally worn to show support to a particular team).
Because the sky is blue, it makes me cry
I expected Annie to point out that this was not the reason, and so 'because' should not be used – which would have then allowed me to return to her earlier use of 'because' in the context of atoms. However, Annie seemed quite happy with my supposedly 'straw-man' or 'Aunt Sally' example:
So we're talking about what you might call cause and effect, that something is caused by something else. We do a lot of talking about cause and effect in science – "this causes that to happen."
If you think about people in Liverpool, only because this is the first analogy that comes to mind, if you actually go to Liverpool on Saturday [*] and wander round, you'll probably find quite a few people wandering around wearing red, and quite a few people wandering around wearing blue, and sometime after lunch you'll find that all the people wearing red, a lot of the people wearing red, tend to move off to one particular place.[**] And the people wearing blue tend to move to a different sort of place, as though they are repelled, you know, similar colours attracted together.
Uh hm.
Agreed?
Yes.
And we could say therefore, that the reason that some people go towards the Liverpool ground, is because they're wearing red, and the reason some people go towards the Everton ground, is because they're wearing blue. Now would that be a fair description?
Yeah.
And do you agree with the sense of cause and effect there – that people go to watch Liverpool because they're wearing red hats and red scarves? And people go to look at Everton because they're wearing blue hats and blue scarves?
Yes.
So would you say the cause of which football team you go to see, the cause of that, is what clothes you happen to be wearing?
(Pause, c.4s)
Unless you're a rambler. {Laughs}…
No, no, well yes, if you're wearing, you're obviously supporting that colour, so, that team, so so you'd assume, that they were going to watch, the team they favoured.
Right, okay, erm, I'll think of a different example, I think.
Because the world is round, it turns me on
Annie did not seem to 'get' what I had thought would be an obvious flaw in the argument. Fans wear the colours of their team to show support and affiliation; and go to the place where their team is playing: but they do not go to the particular stadium because they happen to be wearing red or blue.
This is linked to the difference between causation and correlation. Often two correlated variables do not have a direct causal relationship, but have a relationship mediated by some other factor.
Height of children in a primary school will be correlated with their grade number (on average, the children in the first year are shorter than those in the second year, who are shorter than…). But children are not organised into grades according to height, and height is not caused by grade. Both are independently related to the child's age.
Colour of football scarves is correlated with destination on match day, but one does not cause the other – rather both colour choice and destination are actually due to something else: affiliation to a club. [***]
I switched to a another example I hoped would be familiar, based on a swimming pool. I though the idea that changing rooms are (usually) designated by gender would make it obvious that where people went to change on leaving the pool correlated to, but was not because of, what they were wearing. Again, however, Annie did not seem to consider it inappropriate to describe this in terms of the the different types of swimming costume causing the behaviour.
If you go to the swimming pool, and watch people swimming, you'll find out that some people when they're swimming at a swimming pool, tend to wear a swimming costume that only covers, the hips basically, and other people either a swimming costume that covers most of the trunk, or two separate parts to it. And if you observe them very closely, which is always a bit suspicious at a swimming pool, you'll notice that when they get out of the pool, they're attracted towards different rooms, these changing rooms…
But all the people who just have the one part of the costume, are attracted towards one room, and the others are attracted towards the other room, the ones with sort of either very long costumes or two part costumes. So is it fair to say that it's caused by what clothes they are wearing, that determines which room they go and get changed in?
Yes.
It is?
(Pause, c.4s)
Yes.
That's the cause of it?
(Pause, c5s)
Yeah. It's also conventional as well.
So in both cases Annie was happy to talk in terms of the clothing causing behaviour. After some further discussion Annie seemed to appreciate the distinction I was making, but even if she did not have a flawed notion of causality, it certainly appeared she have developed non-canonical ways of talking about cause and effect.
Because the wind is high, it blows my mind
Annie was a clever person, and I am sure that the issue here was primarily about use of language rather than an inability to understand causation. However, even if our thinking is not entirely verbal, the major role of verbal language in human thought means that when one does not have the language, one may not have the related explicit concepts.
It is very easy to assume that students, especially those we recognise as capable and having been academically successful, share common 'non-technical' language – but there is plenty of research that suggests that many students do not have a clear appreciation of how such terms are canonically used. These are terms we might think people generally would know, such as adjacent, efficient, maximum, initial, omit, abundant, proportion… (Johnstone & Selepeng, 2001). As always, a useful guide to the teacher is 'never assume'.
* At the time of the interview, it was general practice for most English football league matches to be played at 15.00 on a Saturday.
** One constraint on the scheduling of football matches is that, as far as possible, two local rival ('paired') teams should not play home matches on the same day, to avoid potential clashes between large crowds of rival fans. However, such 'paired clashes', as they are technically called (Kendall et al., 2013), are not always avoided.
*** Of course, this is not a direct cause. A person could support one team, yet choose to wear the colours of another for some reason, but their support for a team usually motivates the choice. Social patterns are messier than natural laws.
Sources cited:
Johnstone, A. H., & Selepeng, D. (2001). A language problem revisited. Chemistry Education: Research & Practice in Europe, 2(1), 19-29.
Kendall G., McCollum B., Cruz F.R.B., McMullan P., While L. (2013) Scheduling English Football Fixtures: Consideration of Two Conflicting Objectives. In: Talbi EG. (eds) Hybrid Metaheuristics. Studies in Computational Intelligence, vol 434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30671-6_14
You have to learn it at a greater depth and a more detailed level in order to be able to teach it
Keith S. Taber
I have listened to a lot of Professor Jim Al-Khalili's interviews with scientists for the BBC's 'The Life Scientific' programme.
I enjoy hearing about the science and the scientific lives, but Professor Al-Khalili's recent interview with Professor Alice Roberts particularly struck me in terms of her comments on teaching.
[Note: the material discussed in this posting is copyright of third parties, i.e., the BBC (the broadcast and website) and the scientists (the text produced in the interview). It is used here with acknowledgement for purposes of critique and review.]
I have made a rough transcription of that part of the conversation, below, starting at about 6' 24" into the podcast 'Alice Roberts on Bones', which is freely available on the BBC website – and the whole programme is highly recommended.
I found myself nodding along to Prof. Robert's comments about teaching.
There has been much talk in education of pedagogic knowledge being important alongside subject knowledge (one needs to now how to teach as well as what to teach), which is clearly so. Perhaps it is less recognised, however, that a specialist teacher's subject knowledge, whilst clearly different from that of a cutting edge researcher in the subject, is also a form of specialised expertise – 'subject knowledge for teaching' is subject matter extensively infused with pedagogic expertise.
Teachers are specialist experts
I would argue that an experienced school teacher's subject knowledge will often be more advanced in some areas than an academic/researcher in the same discipline.
The researcher has very detailed and advanced knowledge in their specialist area, but the teacher will have been repeatedly revisiting the 'foundation bricks' (in Prof. Robert's terms) in the light of students' varied learning difficulties and (sometimes highly creative) questions. The 'building a wall' metaphor, a wall that needs sound foundations, reflects a constructivist perspective on learning that has been widely adopted in science education.
A lust for learning
Prof. Roberts has the healthy attitude that the teacher never knows everything, without being complacent. Being challenged ("I really love that") is an opportunity to spot the limitations in your own knowledge, and to do something about it – to "advance your own understanding". The good teacher never stops learning, and seeks to understand better, and so sets an example to her students of valuing life-long learning .
Did teaching anatomy [at the University of Bristol] enhance your understanding of the subject?
Oh my goodness, yeah, I mean I think it's the same with teaching anything, isn't it?
Mm.
Er, you, you have to learn it at a greater depth and a more detailed level in order to be able to teach it.
And, also, I think as soon as you start teaching, you, you realise where the gaps in your own understanding are. You start probing how well you know a subject, and you think 'oh actually, I thought I know that, and I didn't', and you, and you start to go back to kind of foundation levels.
I always think of it as a wall that you are building up and you get to a certain level of knowledge and then you think 'oh I had better just go and test those bricks at the bottom and make sure they are secure as I though they were',
Yeah {laughing}
and you inevitably find little chinks and you think 'oh I am going to have to work a bit harder than that', > but then > > {laughing} >
<The worst thing is < for me,< you know <, when, teaching, and then, a student, after teaching a course for many years will say 'actually that's not quite right', or 'how can you explain that?' and I'll realise, you know, generations of students, I've been giving them some wrong information, somewhere, and sent them out into the world. Very embarrassing. > Hasn't happened very often >.
< But, I – < But, I really love that. I, you know, when you go, when someone asks you a question and you go 'oh hang on a minute, I think I should know the answer to that'.
I mean some questions you go, 'I'm never going to know the answer to that, but I will go and find out', or you can send your students to go away and find out.
But sometimes you do get asked questions where you think 'actually, I, I would have thought I knew the answer to that, and I don't'.
Yeah, it's never occurred to me.
And so it helps you advance your own understanding. I really appreciate that.
The higher resistance is when there is less current flowing around the circuit when you have the same voltage – but how does that relate to the formula?
There were two apparent alternative conceptions there. One was that 'Resistance is current over voltage', but as Adrian believed that he was not good at remembering formulae, this would be a conception to which he did not have a high level of commitment. Indeed, on another occasion perhaps he would have offered a different relationship between R, I, and V. I felt that if Adrian had a decent feel for the concepts of electrical resistance, current and voltage then he should be able to appreciate that 'resistance is current over voltage' did not reflect the correct relationship. Adrian was not confident about formulae, but with some suitable leading questioning he might be able to think this through. I describe my attempts to offer this 'scaffolding' below.
The other alternative conception was to conflate two things that were conceptually different: the defining equation for resistance (that R=V/I, by definition so must be true) and Ohm's law that suggests for certain materials under certain conditions, V/I will be found to be constant (that is an empirical relationship that is only true in certain cases). (This is discussed in another post: When is V=IR the formula for Ohm’s law?)
So, I then proceeded to ask Adrian how he would explain resistance to a younger person, and he suggested that resistance is how much something is being slowed down or is stopped going round. After we had talked about that for a while, I brought the discussion back to the formula and the relationship between R, V and I.
Linking qualitative understanding of relating concepts and the mathematical formula
As Adrian considered resistance as slowing down or stopping current I thought he might be able to rationalise how a higher resistance would lead to less current for a particular potential difference ('voltage').
Okay. Let’s say we had, erm, two circuits, and they both have resistance and you wanted to get one amp of current to flow through the circuits, and you had a variable power supply.
Okay.
And the first circuit in order to get one (amp) of current to flow through the circuit.
Yes.
You have to adjust the power supply, until you had 10 volts.
Okay.
So it took 10 volts to get one amp to flow through the circuit. And the second (unclear) the circuit, when you got up to 10 volts, (there is) still a lot less than one amp flowing. You can turn it up to 25 volts, and only when it got to 25 volts did you get one amp to flow through the circuit.
Yes, okay.
In mathematical terms, the resistance of the first circuit is (R = V/I = 10/1 =) 10Ω, and the second is (25/1 =) 25Ω, so the second – the one that requires greater potential difference to drive the same current, has more resistance.
Do you think those two circuits would have resistance?
Erm, (pause, three seconds) Probably yeah.
This was not very convincing, as it should have been clear that as an infinite current was not produced there must be some resistance. However, I continued:
Same resistance?
No because they are not the same circuit, but – it would depend what components you had in your circuit, if you had different resistors in your circuit.
Yeah, I've got different resistors in these two circuits.
Then yes each would have a different resistance.
Can you tell me which one had the bigger resistance? Or can’t you tell me?
No, I can’t do that.
You can’t do it?
No I don’t think so. No.
Adrian's first response, that the circuits would 'probably' have resistance, seemed a little lacking in conviction. His subsequent responses suggested that although he knew there was a formula he did not seem to recognise that if different p.d.s were required to give the same current, this must suggest there was different resistance. Rather he argued from a common sense position that different circuits would be likely to have different components which would lead to them having different resistances. This was a weaker argument, as in principle two different circuits could have the same resistance.
We might say Adrian was applying a reasonable heuristic principle: a rule of thumb to use when definite information was not available: if two circuits have different components, then they likely they have different resistance. But this was not a definitive argument. Here, then, Adrian seemed to be applying general practical knowledge of circuits, but he was not displaying a qualitative feel for what resistance in a circuit was about in term of p.d. and current.
I shifted my approach from discussing different voltages needed to produce the same current, to asking about circuits where the same potential difference would lead to different current flowing:
Okay, let me, let me think of doing it a different way. For the same two circuits, erm, but you got one let's say for example it’s got 10 volts across it to get an amp to flow.
Yeah. So yes okay so the power supply is 10 volts.
Yeah. And the other one also set on 10 volts,
Okay.
but we don’t get an amp flow, we only get about point 4 [0.4] of an amp, something like that, to flow.
Yeah, yeah.
Any idea which has got the high resistance now?
The second would have the higher resistance.
Why do you say that?
Because less erm – There’s less current amps flowing around the circuit erm when you have the same voltage being put into each circuit.
Okay?
Yes.
This time Adrian adopted the kind of logic one would hope a physics student would apply. It was possible that this outcome was less about the different format of the two questions, and simply that Adrian had had time to adjust to thinking about how resistance might be linked to current and voltage. [It is also possible too much information was packed close together in the first attempt, challenging Adrian's working memory capacity, whereas the second attempt fed the information in a way Adrian could better manage.]
You seem pretty sure about that, does that make sense to you?
Yes, it makes sense when you put it like that.
Right, but when I had it the other way, the same current through both, and one required 10 volts and one required 25 volts to get the same current.
Yes.
You did not seem to be too convinced about that way of looking at it.
No. I suppose I have just thought about it more.
Having made progress with the fixed p.d. example, I set Adrian another with constant current:
Yes. So if I get you a different example like that then…let’s say we have two different circuits and they both had a tenth of an amp flowing,
Okay. Yes.
and one of them had 1.5 volt power supply
Okay yes.
and the other one had a two volt power supply
Yeah.
but they have both got point one [0.1] of an amp flowing. Which one has got the high resistance?
Currents the same, I would say they have got different voltages, yeah, so erm (pause, c.6s) probably the (pause, c.2s) the second one. Yeah.
Because?
Because there is more voltage being put in, if you like, to the circuit, and you are getting less current flowing in and therefore resistance must be more to stop the rest of that.
Yes?
I think so, yes.
Does that make sense to you?
Yeah.
So this time, having successfully thought through a constant p.d. example, Adrian successfully worked out that a circuit that needed more p.d. to drive a certain level of current had greater resistance (here 2.0/0.1 = 20Ω) than one that needed a smaller p.d. (i.e. 1.5/0.1 = 15Ω). However, his language revealed a lack of fluency in using the concepts of electricity. He referred to voltage being "put in" to the circuits rather than across them. Perhaps more significantly he referred to their being "less current flowing in" where there was the same current in both hypothetical circuits. It would have been more appropriate to think of there being proportionally less current. He also referred to the greater resistance stopping "the rest" of the current, which seemed to reflect his earlier suggestion that resistance is how much something is being slowed down or is stopped going round.
My purpose in offering Adrian hypothetical examples, each a little 'thought experiment', was to see if they allowed him to reconstruct the formula he could not confidently recall. As he had now established that
greater p.d. is needed when resistance is higher (for a fixed current)
and that
less current flows when resistance is higher (for a fixed p.d.)
he might (perhaps should) have been able to recognise that his suggestion that "resistance is current over, voltage" was inconsistent with these relationships.
Okay and how does that relate to the formula you were just telling me before?
Erm, No idea.
No idea?
Erm (pause, c.2s) once you know the resistance of a circuit you can work out, or once you know any of the, two of the components you can work out, the other one, so.
Yeah, providing you know the equation, when you know which way round the equation is.
Yes providing you can remember the equation.
So can you relate the equation to the explanations you have just given me about which would have the higher resistance?
So if something has got a higher resistance, so (pause, c.2s) so the current flowing round it would be – the resistance times the voltage (pause, c.2s) Is that right? No?
Erm, so the current is resistance time voltage? Are you sure?
No.
So Adrian suggested the formula was "the current flowing round it would be the resistance times the voltage", i.e., I = R × V (rather than I = V /R ), which did not reflect the qualitative relationships he had been telling me about. I had one more attempt at leading him through the logic that might have allowed him to deduce the general form of the formula.
Go back to thinking in terms of resistance.
Okay.
So you reckoned you can work out the resistance in terms of the current and the voltage?
Yes, I think.
Okay, now if we keep, if we keep the voltage the same and we get different currents,
Yes.
Which has, Which has got the higher resistance, the one with more current or the one with less current?
Erm (Pause, c.6s) So, so, if they keep the same voltage.
That’s the way we liked it the first time so.
Okay.
Let’s say we have got the same voltage across two circuits.
Yes.
Different amounts of current.
Yes.
Which one’s got the higher resistance? The one with more current or the one with less current?
The one with less current.
So less current means it must be more resistance?
Yes.
Ok, so if we had to have an equation R=.
Yes.
What’s it going to be, do you think?
Erm
(pause, c.7s)
R=
(pause, c.3s)
I don’t know. It's too hard.
Whether it really was too hard for Adrian, or simply something he lacked confidence to do, or something he found too difficult being put 'on the spot' in an interview, is difficult to say. However it seems fair to suggest that the kind of shift between qualitative relationships and algebraic representation – that is ubiquitous in studying physics at this level – did not come readily to this advanced level physics student.
I had expected my use of leading (Socratic) questioning would provide a 'scaffold' to help Adrian appreciate he had misremembered "resistance is current over, voltage, I think", and was somewhat disappointed that I had failed.
Adrian was a participant in the Understanding Science Project. When I interviewed him in Y12 when he was studying Advanced level physics he told me that "We have looked at resistance and conductance and the formulas that go with them". So I asked him was resistance was:
So what exactly is resistance?
Resistance is, erm (pause, c.3s) Resistance is current over, voltage, I think. (Pause, c.3s) Yeah. No.
Not sure?
I can’t remember formulas.
So Adrian's first impulse was to define resistance using a formula, although he did not feel he was able to remember formulae. He correctly knew that the formula involved resistance, current and voltage, but could not recall the relationship. Of course if he understood qualitatively how these influenced each other, then he should have been able to work out which way the formula had to go, as the formula represents the relationship between resistance, voltage and current.
So, I then proceeded to ask Adrian how he would explain resistance to a younger person, and he suggested that resistance is how much something is being slowed down or is stopped going round. After we had talked about that for a while, I brought the discussion back to the formula and the relationship between R, V and I:
And what about this resistance in electricity then, do you measure that in some kind of unit?
Yes, in, erm, (pause, c.2s) In ohms.
So what is an ohm?
Erm, an ohm is, the unit that resistance is measured in.
Fair enough.
It comes from ohm's law which is the, erm, formula that gives you resistance.
V=IR is the formula that gives you resistance, but it is a common misconception, that Ohm's law is V=IR.
Actually, Ohm's law suggests that the current through a metallic conductor (kept at constant conditions, e.g., temperature) is directly proportional to the potential difference across its ends.
So, in such a case (a metal that is not changing temperature, etc.)
I ∝ V
which is equivalent to
V ∝ I
which is equivalent to
V = kI
where k is a constant of proportionality. If we use the symbol R for the constant in this case then
V= RI
which is equivalent to
V = IR
So, it may seem I have just contradicted myself, as I denied that V=IR was a representation of Ohm's law, yet seem to have derived V=IR from the law.
There is no contradiction as long as we keep in mind what the symbols are representing in the equation. I represented the current flowing through a metallic conductor being held at constant conditions (temperature, tension etc.), and V represented the potential difference across the ends of that metallic conductor. If we restrict V and I to this meaning then the formula could be seen as a way of representing Ohm's law.
Over-generalising
However, that is not how we usually understand these symbols in electrical work: V generally represents the potential difference across some resistive component or other, and I represents the current flowing through that component: a resistor, a graphite rod, a salt bridge, a diode, a tungsten filament in a lamp…
In this general case
V = IR
or
R = V/I
is the defining equation for resistance. If R is defined as V/I then it will always be the case, not because there is a physical law that suggests this, but simply because that is the meaning we have given to R.
This is a bit like bachelors being unmarried men (an example that seems to be a favourite of some philosophers): bachelors are not unmarried men because there is some rule or law decreeing that bachelors are not able to get married, but simply because of our definition. A bachelor who gets married and so becomes a married man ceases to be a bachelor at the moment they become a married man – in a similar way to how a butterfly is no longer a caterpillar. Not because of some law of nature, but by our conventions regarding how words are used. If V and I are going to be used as general symbols (and not restricted to our carefully controlled metallic conductor) then V = IR simply because R is defined as V/I and the formula, used in the general case, should not be confused with Ohm's law.
In Ohm's law, V=IR where R will be constant.
In general, V=IR and R will vary, as Ohm's law does not generally apply.
It would perhaps be better for helping students see this had there been a convention that the p.d. across, and the current through, a piece of metal being kept in constant conditions were represented by, say Vⓜand Iⓜ, so Ohm's law could be represented as, say
Vⓜ = k Iⓜ
but, as this is not the usual convention, students need to keep in mind when they are dealing with the special case to which Ohm's law refers.
A flawed teaching model?
The interesting question is whether:
teachers are being very careful to make this distinction, but students still get confused;
teachers are using language carefully, but not making the discrimination explicit for students, so they miss the distinction;
some teachers are actually teaching that V=IR is Ohm's law.
If the latter option is the case , then it would be good to know if the teachers teaching this:
have the alternative conception themselves;
appreciate the distinction, but think it does not matter;
consider identifying the general formula V=IR with Ohm's law is a suitable simplification, a kind of teaching model, suitable for students who are not ready to have the distinction explained.
It would be useful to know the answers to these questions, not to blame teachers, but because we need to diagnose a problem to suggest the best cure.
Wood (cork coaster captured with Veho Discovery USB microscope)
Bill was a participant in the Understanding Science Project. Bill (Y7) was explaining that he had been learning about the states of matter, and introduced the notion of there being particles:
So how do you know if something is a solid, a liquid or a gas?
Well, solids they stay same shape and their particles only move a tiny bit
So what are these particles then?
Erm, they're the bits that make it what it is, I think.
Ah. So are there any solids round here?:
Yeah, this table. [The wooden table Bill was sitting at.]
That's a solid, is it?:
Yeah
Technically the terms solid, liquid and gas refer to samples of substances and not objects. From a chemical perspective a table is not solid. A wooden table (such as those in the school laboratory where I talked to Bill) is made of a complex composite material that includes various different substances such as a lignin and cellulose in its structure.
Wood contains some water, and has air pockets, so technically wood is not a solid to a chemist. However, in everyday life we do thing of objects such as tables as being solid.
Yet if wood is heated, water can be driven off. Timber can be mostly water by weight, and is 'seasoned' to remove much of the water content before being used as a construction material. Under the microscope the complex structure of woods can be seen, including spaces containing air.
I think teaching may be a problem here, as when the states of matter are taught it is often not made clear these distinctions only apply clearly to fairly pure samples of substances. In effect the teaching model is that materials occur as solids, liquids and gases – when a good many materials (emulsions, gels, aerosols, etc.) do not fit this model at all well.
Well there's three groups, solids, liquids and gases.
So how do you know if something is a solid, a liquid or a gas?
Well, solids they stay same shape and their particles only move a tiny bit.
This point was followed up later in the interview.
So, you said that solids contain particles,
Yeah.
They don't move very much?
No.
And you've told me that ice is a solid?
Yeah.
So if I put those two things together, that tells me that ice should contain particles?
Yeah.
Yeah, and you said that liquids contain particles? Did you say they move, what did you say about the particles in liquids?
Er, they're quite, they're further apart, than the ones in erm solids, so they erm, they try and take the shape, they move away, but the volume of the water doesn't change. It just moves.
Bill reports that the particles in liquids are "further apart, than the ones in … solids". This is generally true* when comparing the same substance, but this is something that tends to be exaggerated in the basic teaching model often used in school science. Often figures in basic school texts show much greater spacing between the particles in a liquid than in the solid phase of the same material. This misrepresents the modest difference generally found in practice – as can be appreciated from the observations that volume increases on melting are usually modest.
Although generally the particles in a liquid are considered further apart than in the corresponding solid*, this need not always be so.
Indeed it is not so for water – so ice floats in cold water. The partial disruption of the hydrogen bonds in the solid that occurs on melting allows water molecules to be, on average, closer* in the liquid phase at 0˚C.
As ice float in water, it must have a lower density. If the density of some water is higher than that of the ice from which it was produced on melting then (as the mass will not have changed) the volume must have decreased. As the number of water molecules has not changed, then the smaller volume means the particles are on average taking up less space: that is, they seem to be closer together in the water, not further apart*.
Bill was no doubt aware that ice floats in water, but if Bill appreciated the relationship of mass and volume (i.e., density) and how relative density determines whether floatation occurs, he does not seem to have related this to his account here.
That is, he may have had the necessary elements of knowledge to appreciate that as ice floats, the particles in ice were not closer together than they were in water, but had not coordinated these discrete components to from an integrated conceptual framework.
Perhaps this is not surprising when we consider what the explanation would involve:
Coordinating concepts to understand the implication of ice floating
Not only do a range of ideas have to be coordinated, but these involve directly observable phenomena (floating), and abstract concepts (such as density), and conjectured nonobservable submicroscopic/nanoscopic level entities.
* A difficulty for teachers is that the entities being discussed as 'particles', often molecules, are not like familiar particles that have a definitive volume, and a clear surface. Rather these 'particles' (or quanticles) are fuzzy blobs of fields where the field intensity drops off gradually, and there is no surface as such.
Therefore, these quantiles do not actually have definite volumes, in the way a marble or snooker ball has a clear surface and a definite volume. These fields interact with the fields of other quanticles around them (that is, they form 'bonds' – such as dipole-dipole interactions), so in condensed phases (solids and liquids) there are really not any discrete particles with gaps between them. So, it is questionable whether we should describe the particles being further apart in a liquid, rather than just taking up a little more space.
Bill was a participant in the Understanding Science Project. Interviews allow learners to talk about their understanding of science topics, and so to some extent allow the researcher to gauge how well integrated or fragmented a learner's ideas are.
Occasionally there is a sense of 'seeing the cogs turn', where it appears that the interview is not just an opportunity for reporting knowledge, but a genuine site for knowledge construction (on behalf of the students, as well as the researcher) as the learner's ideas seem to change and develop in the interview itself.
One example of this occurred when Bill, a Y7 student, explained what he had learnt about particles in solids, liquids and gases. Bill seemed unsure if the particles in different states of matter were different, or just had different properties. However, when asked about a change of state Bill related heating to changes in the way particles were arranged, and seemed to realise this implied the particles themselves were the same when a substance changes state. Bill seemed to be making a link between particle identity and change of state through the process of answering the researcher's questions.
Bill introduced the idea of particles when talking about what he had learn about the states of matter
Well there's three groups, solids, liquids and gases.
So how do you know if something is a solid, a liquid or a gas?
Well, solids they stay same shape and their particles only move a tiny bit.
This point was followed up later in the interview.
So, you said that solids contain particles,
Yeah.
They don't move very much?
No.
And you've told me that ice is a solid?
Yeah.
So if I put those two things together, that tells me that ice should contain particles?
Yeah.
Yeah, and you said that liquids contain particles? Did you say they move, what did you say about the particles in liquids?
Er, they're quite, they're further apart, than the ones in erm solids, so they erm, they try and take the shape, they move away, but the volume of the water doesn't change. It just moves.
Okay. So the particles in the liquid, they seem to be doing something a bit different to particles in a solid?
Yeah.
What about the particles in the gas?
The gas, they, they're really, they're far apart and they try and expand.
Does that include steam, because you said steam was a gas?
Yeah.
Yeah?
I think.
So, we've got particles in ice?
Yeah.
And they have certain characteristics?
Yeah.
And there are particles in water?
Yeah.
That have different characteristics?
Yeah.
And particles in gas, which have different characteristics again?
Of particular interest here, is that at this point in the interview Bill did not seem to have a clear idea about whether particles kept their identify across changes of state. However, the next interview question seemed to trigger a response which clarified this issue for him:
So have the solid particles, sort of gone away, when we make the liquid, and we've got liquid particles instead?
No {said firmly}, when a solid goes to a liquid, the heat gives the particles energy to spread about, and then when its a liquid, it's got even more energy to spread out into a gas.
So we're talking about the same particles, but behaving differently, in a solid to a liquid to a gas?
Yeah.
That's very clear.
It appears Bill had learnt a model of what happened to the particles when a solid melted, but had not previously appreciated the consequences of this idea for the identity of particles across the different states of matter. Being cued to bring to mind his model of the effect of heating on the particles during melting seemed to make it obvious to him that there were not different particles in the different states (for the same substance), where he had seemed quite uncertain about this a few moments earlier.
Whilst this has to remain something of a speculation, the series of questions used in research interviews can be quite similar in nature to the sequences of questions used in the method of instruction known as Socratic dialogue – a method that Plato reported being used by Socrates to lead someone towards an insight.
It's covalent bonding where the electrons are shared to create a full outer shell
Keith S. Taber
Brian was a participant in the Understanding Chemical Bonding project. He was interviewed during the first year of his college 'A level' course (equivalent to Y12 of the English school system). Brian was shown, and asked about, a sequence of images representing atoms, molecules and other sub-microscopic structures of the kinds commonly used in chemistry teaching. He was shown a simple representation of a covalent molecule:
Focal figure ('2') presented to Brian
Any idea what that's meant to be, number 2?
Hydrogen molecule.
Why, how do you recognise that as being a hydrogen molecule?
Because there's two atoms with one electron in each shell.
Uh hm. Er, what, what's going on here, in this region here, where these lines seem to meet?
Bonding.
That's bonding. So there's some sort of bonding there is there?
Yeah.
Can you tell me anything about that bonding?
It's covalent bonding.
So, so what's covalent bonding, then?
The electrons are shared to create a full outer shell.
Okay, so that's an example of covalent bonding, so can you tell me how many bonds there are there?
One.
There's one covalent bond?
Yeah.
Right, what exactly is a covalent bond?
It's where electrons are shared, almost, roughly equally, between the two atoms.
So that's what we'd call a covalent bond?
Yeah.
So according to Brian, covalent bonding is where "the electrons are shared to create a full outer shell". The idea that a covalent bond is the sharing of electrons to allow atoms to obtain full electron shells is a very common way of discussing covalent bonding, drawing upon the full shells explanatory principle, where a 'need' for completing electron shells is seen as the impetus for bonding, reactions, ion formation etc. This principle is the basis of a common alternative conceptual framework, the octet rule framework.
For some students, such ideas are the extent of their ways of discussing bonding phenomena. However, despite Brian defining the covalent bond in this way, continued questioning revealed that he was able to think about the bond in terms of physical interactions
Okay. And why do they, why do these two atoms stay stuck together like that? Why don't they just pull apart?
Because of the bond.
So how does the bond do that?
(Pause, c.13s)
Is it by electrostatic forces?
Is it – so how do you think that works then?
I'm not sure.
The long pause suggests that Brian did not have a ready formed response for such a question. It seems here that 'electrostatic forces' is little more than a guess, if perhaps an informed guess because charges and forces had features in chemistry. A pause of about 13 seconds is quite a lacuna in a conversation. In a classroom context teachers are advised to give students thinking time rather than expecting (or accepting) immediate responses. Yet, in many classrooms, 13 seconds of 'dead air' (to borrow a phrase from broadcasting) from the teacher night be taken as an invitation to retune attention to another station.
Even in an interview situation the interviewer's instinct may be to move on to a another question, but in situations where a researcher is confident that waiting is not stressful to the participant, it is sometimes productive to give thinking time.
Another issue relating to interviewing is the use of 'leading questions'. Teachers as interviewers sometimes slip between researcher and teacher roles, and may be tempted to teach rather than explore thinking.
Yet, the very act of interviewing is an intervention in the learners' thinking, in that whatever an interviewer tells us is in the context of the conversation set up by the interviewer, and the participant may have ideas they would not have done without that particular context. In any case, learning is not generally a once off event, as school learning relies on physiological process long after the initial teaching event to consolidate learning, and this is supported by 'revision'. Each time a memory is reactivated it is strengthened (and potentially changed).
So the research interview is a learning experience no matter how careful the researcher is. Therefore the idea of leading questions is much more nuanced that a binary distinction between those questions which are leading and those that are not. So rather than completely avoiding leading questions, the researcher should (a) use open-ended questions initially to best understand the ideas the learner most easily beings to mind; (b) be aware of the degree of 'scaffolding' that Socratic questioning can contribute to the construction of a learners' answer. [Read about the idea of scaffolding learning here.] The interview continued:
Can you see anything there that would give rise to electrostatic forces?
The electrons.
Right so the electrons, they're charged are they?
Yeah. Negatively.
Negatively charged – anything else?
(Pause, c.8s)
The protons in the nucleus are positively charged.
Uh hm. And so would that give rise to any electronic interactions?
Yeah.
So where would there be, sort of any kind of, any kind of force involved here is there?
By the bond.
So where would there be force, can you show me where there would be force?
By the, in the bond, down here.
So the force is localised in there, is it?
The erm, protons would be repelling each other, they'd be attracted by the electrons, so they're keep them at a set distance.
It seemed that Brian could discuss the bond as due to electrical interactions, although his initial ('instinctive') response was to explain the bond in terms of electrons shared to fill electron shells. Although the researcher channelled Brian to think about the potential source of any electrical interactions, this was only after Brian had himself conjectured the role of 'electrostatic forces.'
Often students learn to 'explain' bonds as electron sharing in school science (although arguably this is a rather limited form of explanation), and this becomes a habitual way of talking and thinking by the time they progress to college level study.
I've just seen* an article in Chemistry: Bulgarian Journal of Science Education describing how students intending to be teachers were introduced to ideas about intermolecular bonding by analogy with attraction between people (Karakaş, 2012). In this analogy nuclei are seen as female and electrons as male, and so sometimes the electrons may take an interest in nuclei other than their own, so to speak: hydrogen bonding is seen as a "form of dipole-dipole interactions, caused by highly electronegative atoms (caused by couples with highly attractive females)", occurring between hydrogen and
"oxygen (couple where the nucleus is Maria Sharapova), fluorine (couple where the nucleus is Kim Kardashian) or nitrogen (couple where the nucleus is Beyonce)" (p.345).
This seems to be a variation on an approach that has been around at least since I started teaching (I remember comparing displacement reactions to interactions between couples at parties), and is clearly meant to be a fun idea, as well as having a motivation in terms of making abstract chemical ideas relevant by comparison with something familiar. The study reported was undertaken in Turkey, and I wondered about the cultural acceptability of this approach these days in different contexts. So Karakaş reports that
"the instructor said in a patriarchal society such as Turkey, the male is supposed to take care of the female. Then the instructor said that basically, the male has to revolve around the female like an electron revolving around a nucleus" (p.343).
I suspect that in many countries it might be considered quite inappropriate to make such a comment about gender roles, at least not without a clear sense of intended satire. More significantly, I wonder how acceptable it is to talk about the relative sexual attractiveness of different people – is that politically correct? Especially if the idea was used with adolescent students, many of whom may well be suffering issues relating to their perceptions of their own attractiveness.
Finally, of course, the basic premise, that sexual orientation matches the principle found with electrical charge – opposite charges attract, similar charges repel – would certainly be suspect in the context where I work (where a current issue of public debate is whether same sex couples should be allowed to marry rather than just register civil partnerships). In some ways these complications are a shame, as the analogy will be seen as fun by many learners, and it certainly is something most learners will relate to. This example reminds us that even if chemistry itself can be seen as largely culture-free, teaching and learning of science always takes place in a cultural context that also influences what can be considered good teaching.
Reference: Karakaş, M. (2012). Teaching Intermolecular Forces with Love Analogy: A Case Study. Chemistry: Bulgarian Journal of Science Education, 21(3), 341-348.
* Previously published at http://people.ds.cam.ac.uk/kst24/science-education-research: 9th May 2015
