Students commonly think that resistance in a circuit has local effects, and in part that is because forming a mental model of what is going on in circuits is very difficult. Often models and analogies can be useful. However when analogies are used in teaching there is also the potential for them to mislead.

For example, Amy (when in Y10) told me she had been taught to use a water flow analogy for electric current. However, because her visualisation of what happens in water circuits was incorrect, she used the analogy to support her alternative conception about circuits:

No, do you have any kind of imagined sort of idea, any little mental models, about what [the flow of electricity round the circuit] might look like? Do you have a way of imagining that?

Erm, yeah, we’ve been taught the water tank and pipe running round it. … just imagine the water  like flowing through a pipe, and obviously like, if the pipe becomes smaller a one point, erm, the water flow has to slow down, and that’s meant to represent the resistance of something.

So, so if I had my water, er, tank and I had a series of pipes, they’d be water flowing through the pipes, and if I had a narrower pipe at one point, what happens then?

The water would have to slow down.

So would it slow down just as it goes through the narrow pipe, or would it slow down all the way round?

Erm – just through that part. [Amy does not appreciate the implications of conservation of mass here – there cannot be a greater flow after (or before) the constriction]. …

And so how do you imagine that’s got to do with resistance, how does that help you understand resistance?

…well resistance, it slows the current down, but then erm, once it passes a resistor or something it, the current is free to flow through the wire again.

Amy was in her first term of A level biology. One of the things she was studying was proteins:

"because proteins do lots of things…they’re used for growth and repair, and they form different things like apparently [sic] insulin is a protein"

Amy admitted to be surprised that insulin, which was “made in the pancreas which controls blood glucose levels” should be a protein. She had not expected this “just because you were never told”. She has also now learnt that “apparently [sic] haemoglobin is a protein”. Amy explained that

“it’s just cause like, up until GCSE you’re just told that like you know a protein is something which is used for growth and repair, and not that it can be used to make sort of something like insulin”

It seems that at GCSE level Amy learnt a slogan relating to the role of proteins – proteins are needed for growth and repair, but a slogan that only related to a processes, without any suggestion of how this might relate to materials and structures. Insulin is considered to be linked to (processes of) sugar regulation, and haemoglobin to (processes of) supplying cells with oxygen. Neither of these processes are seen as growth or repair. It seems ‘repair’ is primarily understood in terms of damage at the level of tissues, not individual cells or molecules.
This could be considered as an example of a fragmentation learning impediment – the student has not made the link. However, if her school teaching was in terms of the slogan ‘proteins are needed for growth and repair’, then this could also be seen as a pedagogic learning impediment, as that way of teaching gave Amy a way of thinking about the roles of protein in the body which did not make her receptive to learning that molecules such as insulin and haemoglobin might be proteins.

Sandra was in year 8 when she told me that light:

“can travel through air and stuff, and glass which makes it bend… because it is coming in at a speed, and it slows down when it is going through glass, and part of it will slow down first, and then so it will bend.”

She explained that:

“I think if it goes in at a straight line, it will come out straight. [But] if it comes in … sort of at an angle, the part, like, the part that hits it first, will slow down, sort of bend when it comes out.”

This was because:

“say the light’s like that thick, it’s that this bit will slow down first, because it has hit it first, it will start bending that way, and then go straight.”

Sandra had undertaken practical work with ray boxes and glass blocks, so I asked her whether if you change the thickness of the beam of light that would change the effect. She thought it would. She had not tried this, but when I asked if a thicker beam would turn more she thought that it “probably” would. She also agreed that “probably” a very, very thin beam of light would not bend very much, because it would all be hitting the glass at more or less the same time. Sandra would not speculate on what would happen with ‘an infinitely thin beam of light’.

In practice the ‘bending’ (deflection of the direction) of the light does not depend upon the thickness of the beam (that is normally understood by physicists as either progressive wave, or a stream of photons of electromagnetic radiation). The common teaching model of refraction is based on an analogy with very different physical systems (soldiers marching across, or vehicles with their wheels hitting, a change of surface at different points in time). Students often relate to these examples and can visualise how they lead to a change in direction for the soldiers or vehicle. This is therefore a very useful model for getting students to form a mental model of what is going on, and therefore to both make refraction seems less abstract and help them remember the phenomenon.

Unfortunately, this teaching model offers little insights into the mechanism of refraction, and if the learner adopts this as an explanation for how refraction occurs, it soon causes problems. Sandra used her mental model of light refraction, based upon this teaching model, and used this to predict how the degree of defection should be different for beams of different thickness. She drew appropriate conclusions in terms of the model, but unfortunately her predictions do not match what actually happens when light is refracted because the model used does not represent the actual physical system.

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It is quite common for students at secodnary level to claim that the smallest particle or thing tat you can have is a single atom…but often the same students can go on to report sub-atomic particles. So, for example, when Amy (Y10) told me that elements were made up of one type of atom, I asked her about atoms:

So what do you mean by an atom, what’s an atom?
An atom is er the smallest particle, in something, and everything is made up of atoms.
Smallest particle?
Yeah.
So you can’t get a smaller particle than that?
Well, you can within an atom.
Oh can you?
Yeah {laughing}
So what can you get within an atom that’s smaller than an atom then?
Oh, proton and neutrons, which are in the nucleus, or, and electrons which orbit the atom.
So everything’s made up of atoms, and atoms are the smallest particles you can get, apart from those particles that are even smaller?:
Within the atom.
Within the atom?
Yeah I think so.
So why don’t we just say that everything’s made up of protons, neutrons and electrons?
Erm,  {laughs} because [pause] I don’t know.

Amy had learnt, by rote, that an atom is the smallest particle, and that it was composed of even smaller particles. Furthermore, she did not appear to have questioned, or even spotted, any inconsistency here. We might argue that there is a sense in which an atom is a type of smallest possible particle (perhaps the smallest particle of an element which is substantially [given isotopes] the same as all the other particles at its scale?) However, the notion that the atom is the smallest particle is commonly presented without such qualification, and may be learnt as a mantra without any real meaning, as seems to be the case here.

There are two related issues here. One is the value of learning by rote without any real understanding of the concepts. This is not what any science teacher really wants. The second is that convenient 'catch-phrases' such as 'an atom is the smallest thing you can get' can actually impede further learning by offering a superficial notion that stands in the place of real understanding. Amy was a very clever girl, but accepted what she had been taught and failed to question whether it really had any meaning for her.

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