"Resistance is how much something is being slowed down or is stopped going round"
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". However, when asked about the formula, he suggested, without conviction, that "resistance is current over voltage". So, I asked him how he might go about explaining resistance to a younger student:
We will come back to the formula in a minute then, so let us say you had a younger brother or sister who hasn’t done much physics.
Yes.
And doesn’t do, doesn’t like maths, doesn’t like formulas.
Okay.
So what does it mean though? Why is it important? What’s resistance about?
Erm – I would say it was how much something is being slowed down, or erm how much it is being stopped going round. If it is in electric¬… electricity then it is in a circuit. If it’s in like the wide open range of things it's like erm how resistant is something if you push it? How much force does it give back?
So Adrian was aware of electrical resistance, and also aware of resistance in the context of mechanics.
Oh I see, so, erm if I asked you to push that table over there
Yes.
There might be resistance to that?
Yes.
And that’s different to if we were talking about meters and wires and things?
Yes.
Are they similar in some way?
They have got the same name. {laughs}
Got the same name, okay.
They probably are similar. I've never really thought about it.
So although Adrian associated electrical resistance with 'resistance' in mechanical situations, the similarity between the two types of resistance seemed primarily due to the use of the same linguistic label. This was despite him describing the two forms of resistance in similar terms – "how much something is being slowed down… how much it is being stopped going round" cf. "how resistant is something if you push it".
To a physicist, a property such as resistance should be defined precisely, and therefore preferably mathematically – and so operationally in the sense that there is no ambiguity in how it would be measured. However when students are learning, definitions and formulae may be abstract and have little meaning or connection to experience, so qualitative understanding is important. Students' initial suggestions of what technical terms mean when they first learn about them may be vague and flawed, but if this is linked to a feeling for the concept this may ultimately be a better starting point than a formula which cannot be interpreted meaningfully – as seemed to be the case with Adrian.
Arguably, understanding a relationship in qualitative terms can support later formalising the relationship in mathematical terms, whereas trying to learn a formulae by rote may lead to misremembering and algorithmic application (and so, for example, not noticing when non-feasible results are calculated).
Adrian's suggestion that resistance might be"how resistant is something if you push it? How much force does it give back?" presumably linked to his own experiences of pushing and pulling objects around. However, it seemed to confuse notions of inertia and reaction force (as well as possibly frictional forces). If Adrian were to push with a force of 100N on the wall of a building, a puck on an ice rink, or on a sledge on gravel the reaction force would be 100N in each case (cf. Newton's third law) – although the subjective experience of resistance would be very different in the different situations – as would the outcome on the object pushed.
In these situations it may be difficult for a teacher to know if a vague or confused description reflects conceptual confusion (and/)or limited expression. Yet, students need time and opportunities to be able to explore concepts in their own terms to link the abstract scientific ideas with the 'spontaneous conceptions' they have developed based on their own experiences of acting in the world.
The teacher should offer feedback, and model clear language, but needs to recognise that understanding abstract scientific ideas takes time. After all, Aristotle would be considered to have alternative conceptions of mechanics by comparison with today's science, but Aristotle was clearly highly intelligent and gave the matter a lot of thought!
After this there was extended discussion on the way resistance related to current and voltage, following Arian's comment that resistance is current over voltage. As part of this he was asked about ⚗︎ an example where different voltages were needed in different circuits to allow the same current to flow. ⚗︎ He suggested that the circuit with the higher resistance would be the one where "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".
Adrian's way of talking about the current in the circuits did not seem to reflect a view of current as driven by a given p.d. across a circuit and limited by a certain resistance, but almost as a fixed potential flow, some of which would be permitted to pass, but some of which would be stopped by the resistance ("how much it is being stopped going round", "resistance … to stop the rest of that"). Yet, as suggested above, it can take time, and opportunities for exploration and discussion, for students' concepts and ways of talking about them to mature towards canonical science.
That Adrian could talk of "more voltage…less current…therefore resistance must be more" seemed promising, although ⚗︎ Adrian could not relate his qualitative description to the mathematical representation of the formula. ⚗︎
