leading questions - Science-Education-Research

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

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:

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.