Category: scaffolding

Catalysis as an analogy for scaffolding

Keith S. Taber

Image by Gerd Altmann from Pixabay

A key part of teaching or communicating science, is about 'making the unfamiliar familiar'.

(Read about 'Making the unfamiliar familiar')

Analogies can be used as pedagogic devices to make the unfamiliar familiar' – that is by suggesting that something (the unfamiliar thing being explained) is somehow like something else (that is already familiar), the unfamiliar can start to become familiar. The analogy functions like a bridge between the known and the unknown. (Note: the idea of a bridge is being used as simile there – another device that can be used to help make the unfamiliar familiar.)

(Read about 'analogies in science')

(Read about 'similes in science')

For an analogy (or simile) to work, the person being taught or communicated with has to already be familiar with the 'source' that act as an analogue for the 'target' being communicated. (If someone did not know what a bridge was, what it is used for, then it would be no help to them to be told that an analogy can function like one! Indeed it would probably just confuse matters.)

An analogy is based on some mapping of structure between two different systems. For example, at one time a common teaching analogy was that the atom was like a tiny solar system. For that to be useful to a learner, they would need to be more familiar with the solar system than the atom. To be used as an effective teaching analogy, the learner would have to understand the relevant parts of the conceptual structure of the solar system idea that were being mapped across to the atom (perhaps a relatively large central mass, the idea of a number of less massive bodies orbiting in some way, a force between the central and peripheral bodies responsible for the centripetal acceleration of the orbiting bodies…).

A person might easily map across irrelevant aspects of the source to the target, perhaps as all the planets are different then all electrons must be different! This might explain why some students assume the force holding the atom together is gravitational!

(Read about 'Understanding Analogous Atomic and Solar Systems')

In teaching science, it is common to use everyday sources as analogues for scientific ideas. But, of course, it is also possible to use scientific ideas as the source to try to explain other target ideas.

Below I reproduce an extract from a recent publication (Taber & Li, 2001). I developed an analogy between enzymatic catalysis (a scientific concept) and scaffolding of learning (an educational or psychological concept), to use is a chapter I co-wrote with Xinyue Li .

(Read about 'Scaffolding learning')

The mapping I had in mind was something like this:

AspectSource (Enzymatic catalysis)Target (Scaffolding)
ProcessChemical reactionDevelopment of new knowledge/skills
ImpedimentLarge activation energy – barrier far greater than energy available to reactant species Large learning demand – gap between current capability and mastery of new knowledge/skill exceeds manageable 'learning quantum'
InterventionAddition of enzymeMediation by 'teacher'
MechanismProvides alternative reaction pathway with small energy barriersStructures learning by modelling activity, and leads learner through small manageable steps
MatchingThe enzyme 'fits' the reactant molecule and readily bindsA good scaffold matches the learners' current capacity to progress in learning (in the so-called 'ZPD')
Degrees of freedomThe binding of the enzyme to a substrate 'guides' the subsequent molecular reconfigurationThe scaffolding guides the steps in the learning process taken by the learner
Mapping between two analogous conceptual structures

Scaffolding Learning as Akin to Enzymatic Catalysis

"Metaphors and analogies should always be considered critically, as the aspects that do not map onto the target they are being used to illustrate can often be as salient and as relevant as the aspects that map positively. Given that, and in the spirit of offering a way to imagine scaffolding (rather than an objective description) we suggest it may be useful to think of scaffolding learning as like the enzymatic catalysis of a chemical process in the body (see Figure 3).

Figure 3. Scaffolding learning can be seen as analogous to enzymatic catalysis (b) which facilitates a reaction with a substantive energy barrier (a).

Some chemical reactions are energetically viable (in chemical terms, exothermic) and so in thermodynamic terms, occur spontaneously. However, sometimes even theoretically viable (so spontaneous) reactions occur at such a slow rate that for all practical purposes there is no reaction. For example, imagine a wooden dining table in a room at 293 K (20˚C) with an atmosphere containing about 21% oxygen – a situation found in many people's homes. The combustion of the table is a viable chemical process [1] and indeed the wood will (theoretically) spontaneously burn in the air. Yet, of course, that does not actually happen. Despite being a thermodynamically viable process, the rate is so slow that an observer would die of old age long before seeing the table burst into flames, unless some external agent actively initiated the process. If parents returned home from an evening out to be told by their teenage children that the smouldering dining table caught alight spontaneously, the parents would be advised to suspect that actually this was not strictly true. Although the process would be energetically favourable, there is a large energy barrier to its initiation (cf. Figure 3, top image). Should sufficient energy be provided to ignite the table, then it is likely to continue to burn vigorously, but without such 'initiation energy' it would be inert.

The process of catalysis allows reactions which are energetically favourable, but which would normally occur at a slow or even negligible (and in the case of our wooden table, effectively zero) rate to occur much more quickly – by offering a new reaction pathway that has a much lower energy barrier (such that this is more readily breached by the normal distribution of particles at the ambient temperature).

In living organisms, a class of catalysts known as enzymes, catalyse reactions. Enzymes tend to be specific to particular reactions and very effective catalysts, so reactions akin to the burning of organic materials (as found in our wooden table) can occur as part of metabolism at body temperature. The second image in Figure 3 represents the same chemical reaction as in the top image (note the same start and finish points) reflecting how an enzyme changes the reaction pathway, but not the overall reaction. Two particular features of this graphical metaphor are that the overall process is broken down into a number of discrete steps, and the 'initiation energy' needed to get the process underway is very much smaller.

This is similar to the mediation of learning trough scaffolding, where a task that is currently beyond the capacity of the learner is broken down into a sequence of smaller steps, more manageable 'learning quanta', and the learner is guided along a learning pathway. The parallels go beyond this. Part of the way that an enzyme functions is that the enzyme molecule's shape is extremely well matched to bind to a target reactant molecule (something reflected in the teaching analogy of the 'lock and key' mechanism of enzymatic action: the enzyme and substrate molecules are said to fit together like a lock and key). This is analogous to how effective scaffolding requires a teacher to design a scaffold that fits the learner's current level of development: that is, her current thinking and skills. Once the substrate molecule is bound to the enzyme molecule, this then triggers a specific reconfiguration: just as a good scaffolding tool suggests to the learner a particular perspective on the subject matter.

Moreover, whereas a free substrate molecule could potentially follow a good many different pathways, once it is bound to the enzyme molecule its 'degrees of freedom' are reduced, so there are then significant constraints on which potential changes are still viable. Most organic chemistry carried out in vitro (in laboratory glassware) is inefficient as there are often many 'side reactions' that lead to unintended products, just as students may readily take away very different interpretations from the same teaching, so the yield of desired product can be low. However in vivo reactions (in living cells), being enzyme-catalysed, tend to give high yields.

The process of enzymatic catalysis therefore makes the preferred pathway much 'easier', offers a guide along the intended route, and channels change to rule out alternative pathways. Digital tools that support teaching to meet curricular aims, such as apps intended to be used by learners to support study, therefore need to offer similar affordances (structuring student learning) and constraints (reducing the degrees of freedom to go 'off track'). Clearly this will rely on design features built into the tool. Here we very briefly discuss two examples."

[1] We avoid the term 'reaction' here, as strictly a chemical reaction occurs between specific substances. Wood is a material composed of a wide range of different compounds, and so the combustion of wood is a process encompassing a medley of concurrent reactions.

(Taber & Li, 2001, pp.55-58)
Work cited:

Single bonds are different to covalent bonds

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?

All the F to the B to the F. Are single bonds they are not double like before. [i.e., a figure discussed earlier in the interview]

So are they covalent bonds? Or ionic bonds, or? Or are single bonds something different again?

Single bonds are different.

This reflected her earlier comment to the effect that a double bond is different to a covalent bond, suggesting that she did not appreciate how covalent bonds are considered to be singular or multiple.

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.

Annie's explanation did not seem to be a fully thought-out position. It was not consistent with the way she had earlier reported there being five covalent bonds and one double bond in an ethanoate ion.

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.

Learning about natural selection and denying evolution

An ironic parallel

Keith S. Taber

Image by Free-Photos from Pixabay 

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
  • Taber, K. S. (2019). The Nature of the Chemical Concept: Constructing chemical knowledge in teaching and learning. Cambridge: Royal Society of Chemistry.
  • Thagard, P. (1992). Conceptual Revolutions. Oxford: Princeton University Press.

Higher resistance means less current for the same voltage – but how does that relate to the formula?

Image by Gerd Altmann from Pixabay 

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?

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" and told me that "Resistance is current over, voltage, I think" although he did not think he could remember formulae. He thought that an ohm was the unit that resistance is measured in, which he suggested "comes from ohm's law which is the…formula that gives you resistance".

Two alternative conceptions

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.

Covalent bonding is sharing electrons

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.