grounded learning impediment - Science-Education-Research

Temperature is measuring the heat of something …

Keith S. Taber

Image by Peter Janssen from Pixabay

Bill was a participant in the Understanding Science Project. Bill, then in Y7, was telling me about work he had done in his science class on the states of matter, and what happened to the particles that made up objects during a change of state. He suggested that "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". Later in the interview I followed up to find out what Bill understood by heat:

Now you mentioned earlier, something about heat. When you were talking about the experiment you did.
Yeah.
Yeah. So tell me about the heat again, what's, how does the heat get involved in this solids, liquids and gases?
When I heat, when heat comes to a solid, it will have, erm, a point where it will go down to a liquid,
Okay,
A melting points of the, the object.
Do you know what heat is? If you had a younger brother or sister, and they said to you, 'you are good at science, what's heat?'
I'm not sure how I can explain it, 'cause it's, it can be measured at different temperature, it can be measured at temperature, erm, by degrees Celsius, degrees Fahrenheit, and – I'm not really sure how I could explain what it is, but, I know it can be measured and changed.
So is it the same thing as temperature, do you think, or is it something different?
Erm, I think temperature is measuring the heat of something.
So they're related, they're to do with each other?
Yeah.
But they are not exactly the same?
No.

Bill appreciated that heat and temperature were not the same, but was not entirely clear on the relationship. Distinguishing between heat and temperature is a recognised challenge in teaching and learning physics.

We commonly introduce temperature as a measure of how hot or cold something is – which relates to phenomena that all students have experienced (even if our actual perception of temperature is pretty crude). Heating is a process, and heat is sometimes considered to be energy being transferred due to a difference of temperature (although energy is a very abstract notion and there is much discussion in science teaching circles about the best language to be used in teaching about energy).

Put simply, it is reasonable to suggest a very hot object would have a high temperature, but not that it contained a lot of heat. So, it is strictly wrong to say that "temperature is measuring the heat of something" (and it would be more correct, if not very technical, to say instead "temperature is measuring the hotness of something – how hot something is"). Perhaps the idea Bill wanted to express was more about the heat that one can feel radiating form a hot object (but likely that is an interpretation suggested by the canonical science use of 'heat'?)

This is one of those situations where a student has an intuition or idea which is basically along the right lines, in the sense of knowing there is an association or link, but strictly not quite right – so, an alternative conception. In a teaching situation it might be useful to know if a student actually has a firm conception that temperature measures the amount of heat, or (as seems to be the case with Bill) this is more a matter of using everyday language – which tends to be less precise and rigid than technical language – to express a vague sense. If a student has a firm notion that hot objects contain heat, and this is not identified and responded to, then this could act as a grounded learning impediment as it will likely distort how teaching is understood.

The teacher is charged with shifting learners away from their current ways of thinking and talking, towards using the abstractions and technical language of the subject, such as the canonical relationship between heat and temperature – and this often means beginning by engaging with the learners' ideas and language. Arguably the use of the term 'heat capacity' (and 'specific heat capacity') which might suggest something about the amount of heat something can hold, is unhelpful here.

Is mass conserved when water gets soaked up?

Setting up a thought experiment on plant growth and mass

Keith S. Taber

Sophia was a participant in the Understanding Science Project.

I was aware that research has suggested that children often do not appreciate how carbon obtained from the carbon dioxide in the air is a key source of matter for plants to build up tissue, so learners may assume that the mass increase during growth of a plant will be balanced by a mass reduction in the soil it is growing in.

"The extra [mass of a growing tree] comes from the things it eats and drinks from the ground. It's just like us eating and getting larger."
Response of 15 year old student in the National science survey carried out the Assessment of Performance Unit of the Department of Education and Science, as reported in Bell and Brook, 1984: 12.

During an interview in her first year of secondary education (Y7), Sophia reported that she had been studying plants in science, and that generally a plant was "a living thing, that takes up things from soil, to help it grow" (although some grew in ponds). Sophia was therefore asked a hypothetical question about weighing a pot of soil in which a seed was planted, with the intention of seeing if she thought that the gain in mas of the seed as it grew into a mature plant would be balanced by a loss of mass from the soil.

Sophia was asked about a pot of soil (mass 400g) in which was planted a seed (1g), and which was then watered (adding 49g of water).

There seemed two likely outcomes of this thought experiment:

A learner considers that the mass of pot, seed and water is collectively 450g, and assumes that as the mass of plant grows, the mass of soil decreases accordingly to conserve total mass at 450g.

A learner is aware that in photosynthesis carbon is 'captured' from carbon dioxide in the air, so the mass of the plant in the soil will exceed 450g once the plant grows.

Of course, a learner might also invoke other considerations – the evaporation of the water, or the acquisition of water due to condensation of water from cold air (e.g., dew); that soil is not inert, but contains micro-organisms that have their own metabolism, etc.

I first wanted to check that Sophia appreciated we had (400 + 1 + 49 =) 450g of material at the point the seed was first watered. That was indeed her initial thought, but she soon 'corrected' herself.

Any idea how much it would weigh now?
[Four] hundred and fifty, no, cause, no cause it will soak it up, wouldn't it, so just over four hundred (400).
So we had four hundred (400) grammes of soil plus pot, didn't we?
Uh hm.
…And we had one (1) gramme of erm, of plant seed. Just one little seed, one (1) gramme. And forty nine (49) grammes of water. But the water gets soaked up into the soil, does it? So when it's soaked up, you reckon it would be, what?
Erm, four hundred and twenty (420).

Sophia's best guess at the mass of the pot with soil (initially 400g) after planting a 1g seed and adding 49g of water was 420g, as the water gets soaked up.

So, Sophia suggests that although 49g of water has been added to a pot (with existing contents) of mass 401g , the new total mass will be less than 450g, as the water is soaking into the soil. Her logic seems to be that some of the water will have soaked into the soil, so it's mass is not registered by the balance.

If you poured the water in, quite quickly, not so quickly that it splashes everywhere, but quite quickly. Before it had a chance to soak up, if you could read what it said on the balance before it had a chance to soak up, do you think it would say four hundred and twenty (420) grammes straight away?
No, it would probably be just under, erm, four hundred and fifty (450).
And it would gradually drop down to about four twenty (420) say, would it?
Yeah.
Might be four hundred and fifteen? (415) Could be four hundred and twenty five (425)?
Yeah.
Not entirely sure,
No
but something like that?
Yeah.

It appears Sophia recognises that in principle there would be a potential mass of 450g when the water is added, but as it soaks up, less mass is registered.

Sophia recognises that mass is initially conserved, at least before the water soaks into the soil.

In other words Sophia in the context of water soaking into soil is not conserving mass.

This is a similar thought experiment to when students are asked about the mass registered during dissolving, where some learners suggest that as a solid dissolves the total mass of the beaker/flask plus its contents decreases, as if the mass of the dissolved material is not registered (Taber, 2002). In that case it has been mooted that ideas about buoyancy may be involved – at least when it is clear that the learners recognise the dissolved material is still present in the solution.

However, that would not explain why Sophia thinks the balance would not register the mass of water soaked into the soil in this case. Rather, it sees more a notion that 'out of sight' is out of mass. Sophia's understanding of what is happening to mass here would be considered an alternative conception or misconception, and is likely based on her intuition about the scenario (acting as a grounded learning impediment) rather than something she has been told.

Sources cited:

Bell, B., & Brook, A. (1984). Aspects of Secondary Students' Understanding of Plant Nutrition. Leeds: : Centre for Studies in Science and Mathematics Education, University of Leeds.
Taber, K. S. (2002). Chemical Misconceptions – Prevention, Diagnosis and Cure. London: Royal Society of Chemistry.

Sleep can give us energy

Sleep, like food, can give us a bit more energy

Keith S. Taber

Jim was a participant in the Understanding Science Project. When I was talking to students on that project I would ask them what they were studying in science, rather than ask them about my own agenda of topics. However, I was interested in the extent to which they integrated and linked their science knowledge, so I would from time to time ask if topics they told me about were linked with other topics they had discussed with me. The following extract is taken from the fourth of a sequence of interviews during Jim's first year in secondary school (Y7 in the English school system).

And earlier in the year, you were doing about dissolving sugar. Do you remember that?
Erm, yeah.
Do you think that's got anything to do with the human body?
Erm, we eat sugar.
Mm. True.
Gives us energy…It powers us.
Ah. And why do we need power do you think?
So we can move.

This seemed a reasonable response, but I was intrigued to know if Jim was yet aware of metabolism and how the tissues require a supply of sugar even when there is no obvious activity.

Ah what if you were a lazy person, say you were a very lazy rich person? And you were able to lie in bed all day, watch telly, whatever you like, didn't have to move, didn't have to budge an eyelid, … you're rich, your servants do everything for you? Would you till need energy?
Yes.
Why?
I dunno, 'cause being in bed's tired, tiring.
Is it?
When I'm ill, I stay off for a day, I just feel tired, and like at the end of the day, even more tired than I do when I come to school some times.

Jim's argument failed to allow for the difference in initial conditions

Staying in bed all day and avoiding exercise could indeed make one feel tired, but there seemed something of a confound here (being ill) and I wondered if the reason he stayed in bed on these days might be a factor in feeling even more tired than usual.

So maybe when you are ill, you should come to school, and then you would feel better?
No.
No, it doesn't work like that?
No.
Okay, so why do you think we get tired, when we are just lying, doing absolutely nothing?
Because, it's using a lot of our energy, doing something.
Hm, so even when we are lying at home ill, not doing anything, somehow we are using energy doing something, are we?
Yes.
What might that be, what might we use energy for?
Thinking.

I thought this was a good response, as I was not sure all students of his age would realise that thinking involved energy – although my own conceptualisation was in terms of cellular metabolism, and how thinking depend on transmitting electrical signals along axons and across synapses. I suspected Jim might not have been thinking in such terms.

Do you think it uses energy to think?
(Pause, c.3s)
Probably.
Why do you think that?
Well cause, like, when you haven't got any energy, you can't think, like the same as TV, when it hasn't got any energy, it can't work. So it's a bit like our brains, when we have not got enough energy we feel really tired, and we just want to go to sleep, which can give us more energy, a bit like food.

So Jim here offered an argument about cause and effect- when you haven't got any energy, you can't think. This would certainly be literally true (without any source of energy, no biological functioning would continue, including thinking) although of course Jim had clearly never experienced that absolute situation (as he was still alive to be interviewed), and was presumably referring to experiences of feeling mentally tired and not being able to concentrate.

He offered an analogy, that we are like televisions, in that we do not work without energy. The TV needs to be connected to an electrical supply, and the body needs food (such as sugar, as Jim had suggested) and oxygen. But Jim also used a simile – that sleep was like food. Sleep, like food, according to Jim could give us energy.

So sleeping can give us energy?
Yeah.
How does that work?
Er, it's like putting a battery onto charge, probably, you go to sleep, and then you don't have to do anything, for a little while, and you, then you wake up and you feel – less tired.
Okay so, you think you might need energy to think, because if you have not got any energy, you are very tired, you can't think very well, but somehow if you have a sleep, that might somehow bring the energy back?
Yeah.
So where does that energy come from?
(Pause c.2s)
Erm – dunno.

So here Jim used another analogy, sleeping was like charging a battery. When putting a battery on change, we connect it to a charger, but Jim did not suggest how sleep recharged us, except in that we could rest. When sleeping "you don't have to do anything, for a little while", which might explain a pause in depletion of energy supplies, but would not explain how energy levels were built up again.

[A potentially useful comparison here might have been a television, or a lap top used to watch programmes, with an internal battery, where the there is a buffer between the external supply, and the immediate source for functioning.]

This was an interesting response. At one level it was a deficient answer, as energy is conserved, and Jim's suggestion seemed to require energy to be created or to appear from some unspecified source.

Jim's responses here offered a number of interesting comparisons:

sleep is a bit like food in providing energy
not having energy and not being able to think is like a TV which cannot work without energy
sleeping is like putting a battery on charge

Both science, and science teaching/communication draw a good deal on similes, metaphors and analogies, but they tend to function as interim tools (sources of creative ideas that scientists can then further explore; or means to help someone get a {metaphorical!} foothold on an idea that needs to later be more formally understood).

The idea that sleeping works like recharging a battery could act as an associative learning impediment as there is a flaw in the analogy: putting a battery on charge connects it to an external power source; sleep is incredibility important for various (energy requiring) processes that maintain physical and mental health, and helps us feel rested, but does not in itself source energy. Someone who thought that sleeping works like recharging a battery will not need to wonder how the body accesses energy during sleep as they they seem to have an explanation. (They have access to a pseudo-explanation: sleep restores our energy levels because it is like recharging a battery.)

Jim's discourse reflects what has been called 'the natural attitude' or the 'lifeworld', the way we understand common experiences and talk about them in everyday life. It is common folk knowledge that resting gives you energy (indeed, both exercise and rest are commonly said to give people energy!)

In 'the lifeworld', we run out of energy, we recharge our batteries by resting, and sleep gives us energy. Probably even many science teachers use such expressions when off duty. Each of these notions is strictly incorrect from the scientific perspective. A belief that sleep gives you energy would be an alternative conception, and one that could act as a grounded learning impediment, getting in the way of learning the scientific account.

Yet they each also offer a potential entry point to understanding the scientific accounts. In one respect, Jim has useful 'resources' that can be built on to learn about metabolism, as long as the habitual use of technically incorrect, but common everyday, ways of talking do not act as learning impediments by making it difficult to appreciate how the science teacher is using similar language to express a somewhat different set of ideas.

Learning about natural selection and denying evolution

An ironic parallel

Keith S. Taber

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.

Light bounces off the eye so you can see

Light is actively bounced out of the eye towards objects, so we can see

Keith S. Taber

Sophia was a participant in the Understanding Science Project. Y8 pupil Sophia had been studying sound and light in her school science lessons. Her model of sight involved light entering the eye, but then reflecting out again.

Do you know how you hear and see?
Does the light come in your eye, and it reflects off so you can see. … Just reflects, does it, and bounces on.
So if I've got my eye, some light comes in, some light comes in, what does it do, it bounces where?
About.
Inside the eye?
No around … it bounces out.
And then what?
Then you can see…so you look where you want to see, so it bounces off like in that direction, …you've got to actually look over, …you've got to look that way.

One long-established historical model of sight was based on rays coming from the eyes to detect objects in the outside world. Sophia's model appears to be a hybrid of this historical model, and modern understandings. For Sophia, light does not originate form the eye, but bounds out of it towards the object of sight. The idea that something must come out of the eye for us to see seems to be an intuitive assumption some people make – perhaps because we actually turn out heads and direct out eyes at what we want to focus on. This intuition has potential to act as a grounded learning impediment to learning the scientific model for vision.

Iron turning into a gas sounds weird

Keith S. Taber

Amy was a participant in the Understanding Science Project. She was interviewed when she had just started her 'A level' (i.e. college) chemistry, and one of the topics that the course had started with was mass spectrometry – (see A dusty analogy – a visual demonstration of ionisation in a mass spectrometer). Amy seemed to be unconvinced, or at least surprised by a number of aspects of the material she had learnt about the mass spectrometer.

So, for example, she found it strange that iron could be vaporised:

So which bits of that are you not convinced about then?
(Pause, c.3 seconds)
It just all … I don't, it's not that I'm not convinced about it, it's just sound strange, because it's like…
(Pause, c.2s)
… erm, well this sounds like ridiculous but, like but before today like none of the people in out class had thought about iron being turned into a gas, and it's little things like that which sound weird.
Okay, erm so if you said to people, can you turn water into a gas, most people would say.
Yeah.
Yeah, do it in the kettle all the time, sort of thing.
Yeah.
But if you said to people can you turn iron into a gas? – do people find that a strange idea?
Yeah.
Yeah?
Well we did. (She laughs)

Although Amy and her classmates had studied the states of matter years earlier at the start of secondary school, and would have learnt that substances can commonly be converted between solid, liquid and gaseous phases, their life-world (everyday) experience of iron – the metallic material – made the idea of iron vapour seem 'weird'.

Given the prevalence of grounded learning impediments where prior learning interferes with new learning, this did not seem as "ridiculous" to the interviewer as Amy suspected it may appear.

As science teachers we have spent many years thinking in terms of substances, and the common pattern that a substance can exist as a solid, liquid or gas – yet most people (even when they refer to 'substances') usually think in terms of materials, not substances. Iron, as a material, is a strong solid material suitable for use in building structures – thinking of iron the familiar material as becoming a gas requires a lot of imagination for someone who not habitually think in terms of scientific models.

Although Amy thought her classmates had found the idea of iron as gas as weird, they had not rejected it. Yet, if it is such a counter-intuitive idea, it may not be later readily brought to mind when it might be relevant, unless it is consolidated into memory by reinforcement through being revisited and reiterated. (Indeed the research interview provides one opportunity for rehearsing the idea: research suggests that whenever a memory is activated this strengthens it.)

[Another student I interviewed told me that Iron is too heavy to completely evaporate.]

They're both attracting each other but this one's got a larger force

Iodine's got a larger force that lithium, so it will pull towards the lithium more

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 commonly used in chemistry teaching.

When she was shown an image representing the electron cloud around an iodide ion polarised by an adjacent lithium ion Annie interpreted this as the iodine exerting a greater force on the lithium than vice versa.

What about this, any idea about this?
It's the same sort of thing again – the lithium combines with the iodine – to make a stable outer shell between the two, by sharing electrons, but the lithium has a smaller charge, or smaller pull than the iodine, so the actual shape of it goes in towards. It sort of goes inwards because its attracting the lithium, whereas if the lithium was attracting it, it would be like a reverse picture.
So, so the iodine's attracting what, sorry?
The lithium.
The iodine's attracting the lithium, and the lithium is not attracting the iodine?
Yeah, they're both attracting each other but because this one's got a larger force, then it will pull towards the lithium more.
The iodine's got a larger force,
Yeah.
so it will pull towards the lithium more?
Yeah.

Any image used to represented chemical bonding is necessarily a kind of model, and a partial representation – and there are a range of types of representations students meet. It is perhaps not surprising if students cannot always 'guess what the teacher (or textbook author or researcher) is thinking, and what they intend by a particular type of image.

Annie here demonstrates the common notion that chemical bonding can be based upon 'sharing' electrons (i.e., covalent bonding). At this point in her course Annie would not be expected to appreciate polar bonds or the polarisation of ions, but her prior learning that covalent bonding could be understood as 'sharing' of electrons could potentially act as an impediment to learning that the ionic-covalent bonding distinction should be seen as a spectrum, a continuous dimension, not a dichotomy.

The way forces are understood in physics is that they are interactions between two bodies, and that the same magnitude of force acts of both bodies (i.e., Newton's third law). However, students commonly consider that a 'larger' body (e.g., more massive, more highly charged) exerts a large force on the smaller body. Students do not clearly distinguish the force from its effect, and so this alternative conception seems to draw upon intuitions based on actual experience of the world (i.e., a grounded learning impediment) where larger sources (larger fires, bigger loudspeakers, larger lamps) often seem to have larger effects.

[Read about Newton's third law, and student learning difficulties]

In a molecule, the electron actually slots into spaces

Keith S. Taber

Mohammed was a participant in the Understanding Science Project. When interviewed in the first term of his upper secondary (GCSE) science course (in Y10), he told me he had been learning about ionic bonding in one of his science classes. Mohammed had quite a clear idea about ionic bonding, which he described in terms of the interactions of two atoms where "they both want to get full outer shells", leading to salt which was "like two atoms joined together":

The "two atoms joined together" sounds much like a molecule (and it is very common for students to identify molecule like ion-pairs even in representations of extensive ionic lattices), so I asked Mohammed about this:

Can I see these atoms?
No. They're really small. Because the wavelength of visible light is actually too like large to see the atoms, they just pass over them.
Okay, so I can't see them. But I can imagine them, can I?
Yeah.
So if I could imagine a sodium atom and chlorine atom, and then they form salt, what would it look like afterwards? How could I imagine it afterwards.
Oh it's like two atoms joined together.
That sounds like a molecule to me?
It's not actually, like, joined.
No?
Because I know that whenever things of opposite charge, I know two rods, when they come together, they don't actually touch, so they don't exactly touch, but they are very close, two atoms close to each other
So a molecule would be different to that in some way, would it?
Yeah, a molecule's actually bonded
So how that different?
I think in a molecule, the electron actually slots into spaces.
I see, and it doesn't do that in this case?
No.

So Mohammed thinks that the interaction between the ions will be due to their electrical charges, but, for him, this may not count as a bond, as the forces just hold the ions ("atoms") close together, and do not actually join them. Mohammed's idea of the atoms not actually touching, "they don't actually touch, so they don't exactly touch", is transferring a notion from the familiar world of macroscopic phenomena (where things touch, or they do not touch) to the submicroscopic world of quanticles that do not have definitive size/volume, and do not actually have distinct surfaces, so touching is a matter of degree. There is no more (or less) 'touching' in a covalent bond than in ionic bonding. So according to Mohammed the ions do not form a molecule, as in a molecule there would some kind of more direct joining – he suggests something like an interlocking with electrons from one atom slotting into spaces on another.

Interestingly, Mohammed bases his notion that the ions would not touch on a general principle that he considers to apply whenever considering things of opposite charge – which he justifies on his knowledge that "two [charged] rods, when they come together, they don't actually touch". He may be misremembering something here – or he may have seen a demonstration of suspended charged rods of the same material (so either both negatively or both positively changed) that when one is moved closer to the other the rods repel. Whatever the source, Mohammed seems to feel he has a valid general principle that he can apply here that act as a grounded learning impediment channelling his thinking about the case under discussion along 'the wrong lines'.

Mohammed's notion of the ionic bonding as being just due to forces rather than being a proper bond is very similar to a common alternative conceptions of ionic bonding which sees ions in a lattice only having a limited number of ionic bonds depending upon valency (the valency conjecture) but bonded with other coordination counter-ions by 'just forces' (the just forces conjecture) – although here Mohammed suspected that all ionic bonding fell short of being proper chemical bonds.

This is a very mechanical model of the covalent bond, whereas the scientific model presents bonding as more of a process than a material mechanical link. However teaching models often present bonding this way, and sometimes molecules are modelled in terms of jigsaws with atoms or radicals as pieces to be slotted together. Although such models are only meant to provide a simple analogy for the bonding they may act as learning impediments if learners take them too 'literally' as realistic representations and transfer inappropriate associations from the model to their understanding of the system being modelled.

Mohammed also uses similar language when asked about salt dissolving in water, as the charge of the water forces the sodium and chlorine ions to slot into certain places within the water molecules *.

In ionic bonding, they both want to get full outer shells

Keith S. Taber

And you said in chemistry you've been doing about electron arrangements [electronic configurations], and ionic bonding.
Yeah.
So what's ionic bonding, then?
Ionic bonding is when, like let's say, a sodium atom and take a chlorine atom, which make salt if they react. What happens is – the sodium atom has one electron on its outer shell, and the chlorine atom has seven, now they both want to get full outer shells, so if I er let's say move the electron from the sodium to the chlorine, then the chlorine would have a full outer shell because it would have eight, and because it's lost that shell the sodium will also have eight.

This account of ionic bonding is a common one, although it is inconsistent with the scientific model. A key problem here is that the driving force for bond formation is seen in terms of atoms wanting to complete their electron shells (the 'full shells explanatory principle'). Mohammed's explanation here uses anthropomorphism, as it treats the individual atoms as though they are alive and sentient, acting to meet their own needs – "they both want to get full outer shells".

When Mohammed was probed, he related a full outer shell to atomic stability (a central feature of the full shells explanatory principle).

Okay. How do you know they want full outer shells?
Because it makes them more stable.
Why does it make them more stable?
(pause, c.1 s)
Erm. (Why do electrons?*) (* sotto voce – apparently said to himself)
(pause, c.2s)
Er, because they don't react as much with other elements if they have a full outer shell.
I see.
They don't react.

There is an interesting contrast here between Mohammed's instant response that full shells "makes them more stable", and the long pause as he thought about why this might be so.

His response reflects something quite common in students' explanations n that a student asked why X is the case may respond by explaining why they think X is the case. (That is, as if an appropriate answer to the question "why is it raining so heavily?" would be "because I got soaked through getting here", i.e. actually responding to the question "how do you know that it is raining heavily?")

Such responses seem to be logically flawed, but of course may be a mis-perception of the question being asked (so the learner is answering the question they thought was asked), or (possibly the case here) substituting a response to a related question as a strategy adopted when aware that one cannot provide a satisfactory response to the actual question posed.

The anthropomorphic aspect of his earlier answer was probed:

How do the atoms know that they need to get a full outer shell, they want to get a full outer shell? Do they know about this stability thing?
Not really.
No?
It's just what happens.
Oh, I see, it's just what happens?
Yeah.

So although Mohammed used an anthropomorphic explanation, it seemed he did not mean this literally. (It may seem strange to suggest a 14 year old might consider atoms alive and sentient, but research suggests this is sometimes so!) This has been described as weak anthropomorphism, where the anthropomorphism is only used as a figure of speech. However, such language can act as a grounded learning impediment because if it becomes habitual it can stand in place of a scientific explanation (thus giving no reason to seek a canonical scientific understanding).

I went on to ask Mohammed about the formation of salt in the process he had described.

Liquid iron stays a liquid when heated

Keith S. Taber

Sophia was a participant in the Understanding Science Project. In Y7, Sophia had told me that if molten iron was heated "some of it would evaporate but not all of it, 'cause it's not like water and it's more heavy". She thought only "a little" of the iron would evaporate to give iron vapour: The rest "really just stays as a liquid". [See 'Iron is too heavy to completely evaporate'.]

Just over a year later (in Y8) Sophia had been studying "that different erm substances have different freezing and melting and boiling points, and some aren't like a liquid at room temperatures, some are a solid and some are a gas and things like that".

Give me an example of something else that's a solid at room temperature?
Iron.
Do you think iron would have a melting point?
Yeah.
Yeah, and if I, what would I get if I, if I heated iron to its melting point?
It would become a liquid.
And why would it do that?
Because it's got so hot that particles – they have spread out or something?
So what do you think would happen if I heated the iron liquid?
It would stay a liquid.
No matter how much I heated it?
It might, I don't know if it would become a vapour.
Can you get iron vapour?
No, I don't think so.
You don't think so?
No.

So it seems that Sophia had shifted from accepting that iron would partially evaporate (when learning about the particle model of the different states), to considering that iron (probably) can not become a vapour. The notion of iron as a gas is not something we can readily imagine, and apparently did not seem very feasible. In part this might be because we think of iron the material (a metal, which cannot exist in in the vapour phase) rather than as a substance that can take different material forms.

It seems Sophia's prior knowledge of iron the material was working against her learning about iron the substance, an examples of a grounded learning impediment where prior knowledge impedes new learning.

In Y7 Sophia had seemed to have a hybrid conception where having been taught a general model of the states of matter and changes of state, she accepted the counter-intuitive idea that iron could evaporate, but thought that (unlike in the case of water) it could not completely evaporate . This might have been a 'stepping stone' between not accepting iron could be in the gaseous state and fitting it within the general model that all substances will when progressively heated first melt and then evaporate (or boil) as long as they did not decompose first.

However, it seems that a year later Sophia was actually more resistant to the idea that iron could exist as vapour and so now she thought molten iron would remain liquid no matter how much it was heated. If anything, she had reverted to a more intuitive understanding. This is not that strange: it has been shown that apparent conceptual gains which are counter to strongly held intuitions that are brought about by teaching episodes that are not regularly reinforced can drop away as the time since teaching increases. Conceptual change does not always involve shifts towards the scientific accounts.

[Sophia was in lower secondary school when I talked to her about this: but I was also told by a much older student that the idea of iron turning into a gas sounds weird.]

Iron is too heavy to completely evaporate

Some molten iron would evaporate but not all of it, 'cause it's not like water and it's more heavy

Keith S. Taber

Sophia was a participant in the Understanding Science Project. In her first interview near the start of Y7, Sophia told me that she had learnt "about the particles…all the things that make – the actual thing, make them a solid, and make them a gas and make them a liquid" (i.e. the states of matter). All solids had particles, including (as examples) ice and an iron clamp stand. There would be the same particles in the ice as the iron.

"because they are a solid, but they can change , 'cause if erm they melted they would be a liquid so they would have different particles in…Well they are still the same particles but they are just changing the way they act".

Sophia's suggestion that particles in ice and the iron were the same types of particles as both were solid seems to be 'carving nature' at the wrong joints – that is in this model the particles in ice and (solid) iron would be of one type, whilst those of water and liquid iron would be of another type (that is she had an alternative ontology). Sophia quickly corrected this, so it is not clear if this reflected some intuitive idea or was just 'a slip of tongue'.

According to Sophia the ice could be melted "with something that's hot, like a candle" but for the iron "you need more heat, 'cause it's more, it's a lot more stronger…because it's got more particles pushed together".

Sophia's explanation suggested a causal path (right-hand side) quite different from a canonical causal path (left-hand side)

Strictly the difference is more about the strength of the interactions between particles, than how many were pushed together – although strong bonding forces would tend (all other factors being equal) to lead to particles being bound more tightly and being closer. We might argue here that Sophia seemed to confuse cause and effect – that a higher density of particles was an effect of strong bonding, which would also mean more energy was needed to overcome that bonding. (However, we should also be aware that when students use 'because' (which formally implies causality) they sometimes mean little more than 'is associated with'.)

If the water obtained from melting ice was heated more "it will evaporate into the sky". However, if the molten iron was heated Sophia thought that "some of it would evaporate but not all of it, 'cause it's not like water and it's more heavy". She thought only "a little" of the iron would evaporate to give iron vapour:

"No, I think that water all of it goes, but other material, other liquids some of it will go, not all of it". The rest "if it's cold enough, it will go back into a solid, but if not it really just stays as a liquid".

Sophia's idea that no matter how much liquid iron was heated it would not completely evaporate so some would remain liquid, which seemed to be linked in her mind to its density, seems to be evidence of an alternative conception. Students may not expect that something as (apparently) inherently solid as iron could evaporate (everyday experience may act as a grounded learning impediment), and so may not readily accept that the basic model of the states of matter and changes of state (i.e., a heated liquid will evaporate or boil) can apply to something like iron. Sophia seemed to have formed a hybrid conception – applying the taught model, but with a modification reflecting the counter-intuitive notion that iron could become a vapour.

Conceptual change can be a slow progress, although hybrid conceptions may be 'stepping stones' towards more scientific understandings. However, when I spoke to Sophia in Y8 she did not seem to have progressed further. [See 'Liquid iron stays a liquid when heated'.]

In a sponge, the particles are spread out…

In a sponge, the particles are spread out more, so it can absorb more water

Keith S. Taber

Morag was a participant in the Understanding Science Project. In her first term of secondary school, she told me that he had learnt about particles. Morag had explained, and simulated through role play for me, the arrangements of particles in the different states of matter (See: So if someone was stood here, we'd be a solid.) She had also emphasised just how tiny the particles were, "little, little-little-little things", and so how many there were in a small object: "millions and millions and millions". This suggested she had accepted and understood the gist of the scientific model of submicroscopic particles.

Yet as the conversation proceeded, Morag suggested the macroscopic behaviour of sponge in absorbing water could be explained by the arrangement of particles leaving space for the water. This is perhaps a reasonably, indeed quite imaginative, suggestion at one level, except that the material of a sponge is basically solid (where, as Morag recognised, that the particles would be very close together). A sponge as whole is more like a foam, with a great volume of space between the solid structure (where air can be displaced by liquid) and an extensive surface area.

Do you think it is important to know that everything is made of particles?
No.
It's not important?
Well it could be important, but it's not that important. Well, you see, like that [indicating the voice recorder used to record the interview] has got like lots and lots of particles pushed together this [Morag gestures]…But a sponge, the particles are like, the particles are more kind of like, they're still the same, but it's just spread out more, so it can absorb more water.
Oh I see, so are you saying that the same particles are in my little recorder, as in the sponge.
Yeah, they're the same, but there's just more of them in one than there would be in the other.

The failure here is perhaps less Morag's inappropriate explanation, than the tendency to teach about the ideals of solids, liquids and gases, which strictly apply only to single substances, where most real materials students come across in everyday life are actually mixtures or composites where the labels 'solid', liquid' and 'gas' are – at best – approximations.

Teaching has to simplify complex scientific ideas to make them accessible to students of different ages, so often teaching models are used. But sometimes simplifications can cause misunderstandings, and so the development of alternative conceptions. If 'everything is a solid, liquid or gas' is used as a kind of teaching model, or even presented as a slogan or motto for students to echo back to the teacher, when lots of things students come across in everyday life (e.g., butter, clouds, the pet cat – a bathroom sponge) do not easily fit these categories, and this is likely to lead to students overgeneralising.

Although it is often not possible to assign a single simple cause to a student's flawed thinking, this could be considered likely to be an example of a pedagogic learning impediment (a type of grounded learning impediment) in chemistry: a case where an approach to teaching can lead students' thinking in unhelpful directions.