Category: conceptual integration

Are physics teachers unaware of the applications of physics to other sciences?

Confounding conceptual integration

Keith S. Taber

Tuysuz and colleagues seem to have found chemistry and physics teachers have a different attitude to the importance of integrating concepts from across the subjects.

Conceptual integration?

Conceptual integration is very important in science. That is, science doesn't consist of a large set of unrelated facts, but rather the ability to subsume a great many phenomena under a limited number of ideas is valued. James Clerk Maxwell is widely remembered for showing that electricity, magnetism and radiation such as light (that is, what we now call electromagnetic radiation) were intimately related, and today theoretical physicists seek a 'Grand Unified Theory' that would account of all the forces in nature. Equally, the apparent incompatibility of the two major scientific ideas of the early twentieth century – general relativity and quantum mechanics – is widely recognised as suggesting a fundamental problem in our current best understanding of the world.

So, conceptual integration can be seen as a scientific value: something scientists expect to find in nature 1 and something they seek through their research.

Learners may not appreciate this. When I was teaching physics and chemistry I was quite surprised to see how little some students who studied both subjects would notice, or indeed expect, ideas taught in one course to link to those in another (e.g., Taber, 1998).

A demarcation criterion?

I have even, only partially tongue-in-cheek, suggested that a criterion for identifying an authentic science education would be that it emphasises the connections within science, both within and across disciplines (Taber, 2006). 2

Sadly, there has been limited attention to this theme within science education, and very little research. I was therefore pleased to find a references to a Turkish study on the topic. 3

A study with teachers-in-preparation

Tuysuz, Bektas, Geban, Ozturk and Yalvac (2016) undertook an interview study with students preparing for school science teaching. One of their findings was:

"Generally speaking, while the pre-service chemistry teachers think that physics concepts should be used in the chemistry lessons, the pre-service physics teachers believe that these two subjects' concepts generally are not related to each other."

Tuysuz, Bektas, Geban, Ozturk & Yalvac, 2016

Reading this in isolation might seem to suggest that those preparing for chemistry teaching (and therefore, likely, chemistry teachers) saw more value in emphasising conceptual integration in teaching than those preparing for physics teaching (and therefore, likely, physics teachers).

Why might physics teachers give less value to conceptual integration?

It is easy to try to think of possible reasons for this:

  • Conjecture 1: chemistry teachers are aware of how chemistry draws upon physical concepts, and so are more minded to emphasise links between the subjects than physics teachers. 4
  • Conjecture 2: physicists, and so physics teachers, are more arrogant about their discipline than other scientists (cf. "All science is either physics or stamp collecting" – as Ernest Rutherford supposedly claimed!)
  • Conjecture 3: chemists are more likely to have also studied other science disciplines at a high level (and so are well placed to appreciate conceptual integration across sciences), whereas physics specialists are more likely to have mainly focussed on mathematics as a subsidiary subject rather than other sciences.

I imagine other possibilities will have occurred to readers, but before spending too much time on explaining Tuysuz and colleagues' findings, it is worth considering how they came to this conclusion.

Not an experiment

Tuysuz and colleagues do not claim to have undertaken an experimental study, but rather claim their work is phenomenology. It did not use a large, randomly selected (and, so, likely to be representative) sample of populations of pre-service science teachers (as would be needed for an experiment), but rather used a convenience sample of six students who were accessible and willing to help: three pre-service physics teachers and three pre-service chemistry teachers.

Read about sampling populations in research

It is not unusual for educational studies to be based on very small samples, as this allows for in-depth work. If you want to know what a person really thinks about a topic, you need to establish rapport and trust with them, and encourage them to talk in some detail – not just offer a rating to some item on a questionnaire. Small samples are perfectly proper in such studies.

What is questionable, is whether it is really meaningful to tease out differences between two identified groups (e.g., pre-service chemistry teachers; pre-service physics teachers) based on such samples. We cannot generalise without representative samples, so, when Tuysuz, Bektas, Geban, Ozturk and Yalvac write "Generally speaking…", their study does not really support such generalisation. The authors are only reporting what they found in their particular sample, and so the reader needs to contextualise their claim in terms of further details of the study, i.e., the reader needs to read the claim as

"Generally speaking, while the three pre-service chemistry teachers who volunteered to talk to us from this one teacher preparation programme think that physics concepts should be used in the chemistry lessons, the three pre- service physics teachers who volunteered to talk to us from this one programme believe that these two subjects' concepts generally are not related to each other."

Put in those terms, this is a very localised and limited kind of 'generally'.

This does not undermine the potential value of the study. That any future school science teachers might think that "these two subjects' concepts generally are not related to each other" is a worrying finding.

A confounded design

Another reason why it is important not to read Tuysuz's study as suggesting a general difference between teacher candidates in physics and chemistry, is because of a major confound in the study design. If the research had been intended as an experiment, where the investigators have to control variables so that there is only one differences between the different conditions, this would have been a critical flaw in the design.

The pre-service physics teachers and the pre-service chemistry teachers were taking parallel, but distinct, courses during the study. The authors report that the teaching approaches were different in the two subject areas. In particular, the paper reports that in the case of the pre-service chemistry teachers conceptual integration was explicitly discussed. The chemists – but not the physicists – were taught that conceptual integration was important. When interviewed, the chemists (who had been taught about conceptual integration) suggested conceptual integration was more important than the physicists (who had not been taught about conceptual integration) did!

  • This might have been because of their different subject specialisms;
  • It might have been because of the differences in the practice teaching courses taken by the two groups, such as perhaps the specific engagement of the chemists (but not the physicists) with ideas about conceptual integration during their course;
  • It might have been due to an interaction between these two factors (that is, perhaps neither difference by itself would have led to this finding);
  • And it might have simply reflected the ideas and past experiences of the particular three students in the chemists group, and the particular three students in the physicists group.

Tuysuz and colleagues found that, 'generally speaking', three students (who were chemistry specialists and had been taught about conceptual integration) had a different attitude to the importance of conceptual integration in teaching science to three other students (who were physics specialists and had not been taught about conceptual integration)

Read about confounding variables in research

The researchers might have just as readily reported that:

"Generally speaking, while the pre-service science teachers who had discussed conceptual integration in their course think that physics concepts should be used in the chemistry lessons, the pre-service science teachers who had not been taught about this believe that these two subjects' concepts generally are not related to each other."

Of course, such a conclusion would be equally misleading as both factors (subject specialism and presence/absence of explicit teaching input) vary simultaneously between the two groups of students, so it is inappropriate to suggest a general difference due to either factor in isolation.

Work cited:
Notes

1 Although science is meant to be based on objective observations of the natural world, scientists approach their work with certain fundamental assumptions about nature. These might include beliefs that

  • an objective account of nature is in principle possible (that different observers can observe the same things), and
  • that there is at some level a consistent nature to the universe (there are fixed laws which continue to apply over time)

assumptions that are needed for science to be meaningful. As these things are assumed prior to undertaking any scientific observations they can be considered metaphysical commitments (Taber, 2013).

[Download 'Conceptual frameworks, metaphysical commitments and worldviews']

Another metaphysical commitment generally shared by scientists as a common worldview is that the complex and diverse phenomena we experience can be explained by a limited number of underlying principles and laws. From this perspective, progress in science leads to increased integration between topics.

2 The term 'demarcation criterion' is often used in relation to deciding what should be considered a science (e.g., usually, astronomy is considered a science, and so is biochemistry; but not astrology or psychoanalysis). A famous example of a demarcation criterion, due to Karl Popper, is that a scientific conjecture is one which is in principle capable of being refuted.

Astronomers can use their theories and data to predict the date of the next solar eclipse, for example. If the eclipse did not occur when predicted, that would be considered a falsification.

By contrast, if a psychotherapist suggested a person had personality issues due to repressed, unresolved, feelings about their parents, then this cannot be refuted. (The client may claim having positive and untroubled relationships with the parents, but the therapist does not consider this a refutation as the feelings have been repressed, so they are not consciously available to the client. The problem can only be detected indirectly by signs which the therapist knows how to interpret.).

3 I became aware of the study discussed here when reading the work in progress of Louise Vong, who has been doing some research in this important topic.

4 Physics concepts are widely applied in chemistry, but not vice versa. So, this is suggesting that chemistry teachers have more need to refer to physics in teaching their subject than the converse.

However, we could also have looked to explain the opposite finding (had it been reported that pre-service physics teachers paid more attention to conceptual integration than pre-service chemistry teachers) by suggesting physics teachers have more reason to refer to chemistry topics when discussing examples of applications of concepts being taught, than chemistry teachers have to refer to physics topics.

Sandstone looks like it is made out of sand

Keith S. Taber

Image by Norman Bosworth from Pixabay 

Sandstone looks like it's made out of a load of sand stuck together

Sophia was a participant in the Understanding Science Project. Sophia (when a Y8 pupil) had been learning in class about different kinds of rocks, including

  • rocks that erupt from volcanoes,
  • rocks that are formed underground, and
  • rocks that 'come from mountains' that 'get worn away':

When rocks … come from mountains, they like get worn away.

Mm, so what happens when you wear away the rock then?

 Does it go like into a river, like a spring, and then gets carried – down, and gets smaller….when it gets tiny, tiny would it turns into sand?

And then what happens to the sand, it just stays as sand does it?

Prob¬ [Probably]… Yeah. …

Have you heard of a kind of rock called sandstone?

Yeah.

Any idea, what sandstone is?

It's sand like, on the rock, it just looks like it's made out of a load of sand stuck together.

Despite having been taught about the three categories of rock formed in different ways, Sophia had apparently only remembered the erosion stage in formation of the sedimentary rocks.

Erosion leads to rocks being broken down into sand. And sandstone 'looked like' it was made of a lot of 'sand stuck together', but for Sophia this seemed to be little more than a coincidence. She did not make the expected connection.

This seems to be an example of a fragmentation learning impediment, where the learner does not perceive the relevance of prior learning, and so does not use it to interpret teaching in the way intended by the teacher. So, here there was a lack of conceptual integration with material that was meant to be related being learnt as discrete facts.

Some stars are closer than the planets

Stars look so little because they are a long way away, but some stars are closer than the planets

Keith S. Taber

Sophia was a participant in the Understanding Science Project. When I interviewed her in her first year of secondary school (Y7 in the English school system). I asked her about what she remembered about the science she had studied in primary school. She told me about she had studied the topic of space, and had learnt about the nine planets. When I asked her if she could name the planets she produced a list of planets including both the moon and sun: "Pluto, Jupiter, Venus, Uranus, Earth, the Sun, the Moon".

[Read 'The sun is the closest of the eleven planets']

As Sophia thought the sun might be a planet, I asked her what a planet was:

Do you know what a planet is?

Erm, it's like – a round – a sphere, in space, kind of. Though we don't know if people live, animals live there or not.

…If I say someone was going through space, in a spaceship, and they are a long, long way away from earth, they've gone a long way across space, and they came across something in space…And er one of the crew said 'oh that's a planet'. And another one of the crew said 'no, that's not a planet'. And you were in charge, you were the captain. How would you decide who was right, whether that was a planet or not in space?

Er

(pause, c.5s)

I'd look if it was all the things that you thought a planet was.

Good, and what would that be?

If it was round, if it was a bit lumpy, a bit – if it was quite big, not like a little star, well there's no stars that little…

It seemed that Sophia (reasonably) thought stars would be larger than planets, which invited an obvious question, that I assumed would have an almost-as-obvious answer.

Why do they [the stars] look so little?

Because they are a long way away.

Oh, I see. So they are big really?

Yeah.

Okay. What's the difference between a star and a planet then?

A star's made up of different things, but planets – can't – cause you don't really see a planet, so you just see stars quite lot.

That's true, there is lots and lots of stars up there, isn't there? So how can you see the stars and not the planets, do you think?

I think the stars, some stars are closer, maybe, than planets.

There seemed to be something of a contradiction here. Sophia thought that 

  • stars were not as 'little' as planets
  • but they seemed little because they were a long way away.
  • but the stars were easier to see than planets
  • so they might be closer to us than the planets.

Both these arguments are logical enough suggestions (things seem smaller, and may be harder to see, if they are a long way off), but there was a lack of integration of ideas as her two explanations relied on seemingly inconsistent premises (that the stars are "are a long way away" but could be "closer, maybe, than planets").

It seemed that Sophia was not aware, or was not bringing to mind, that stars were self-luminous whereas planets were only seen by reflected light. Lacking (or not considering) that particular piece of information acted as a 'deficiency learning impediment' and led to her explaining why the planets could be more difficult to see by suggesting they might not be as close as some stars.

Not considering luminosity as a criterion also seemed to explain why she was not clear that the (self-luminous) sun was not a planet.

[Read 'The sun is the closest of the eleven planets']

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.

How plants get their food to grow and make energy

Respiration produces energy, but photosynthesis produces glucose which produces energy

Keith S. Taber

Image by Frauke Riether from Pixabay 

Mandy was a participant in the Understanding Science Project. When I spoke to her in Y10 (i.e. when she was c.14 year old) she told me that photosynthesis was one of the topics she was studying in science. So I asked her about photosynthesis:

So, photosynthesis. If I knew nothing at all about photosynthesis, how would you explain that to me?

It's how plants get their food to grow and – stuff, and make energy

So how do they make their energy, then?

Well, they make glucose, which has energy in it.

How does the energy get in the glucose?

Erm, I don't know.

It's just there is it?

Yeah, it's just stored energy

I was particularly interested to see if Mandy understood about the role of photosynthesis in plant nutrition and energy metabolism.

Why do you think it is called photosynthesis, because that's a kind of complicated name?

Isn't photo, something to do with light, and they use light to – get the energy.

So how do they do that then?

In the plant they've got chlorophyll which absorbs the light, hm, that sort of thing.

What does it do once it absorbs the light?

Erm.

Does that mean it shines brightly?

No, I , erm – I don't know

Mandy explained that the chlorophyll was in the cells, especially in the plant's leaves. But I was not very clear on whether she had a good understanding of photosynthesis in terms of energy.

Do you make your food?

Not the way plants do.

…

So where does the energy come from in your food then?

It's stored energy.

How did it get in to the food? How was it stored there?

Erm.

[c. 2s pause]

I don't know.

At this point it seemed Mandy was not connecting the energy 'in' food either directly or indirectly with photosynthesis.

Okay. What kind of thing do you like to eat?

Erm, pasta.

Do you think there is any energy value in pasta? Any energy stored in the pasta?

Has lots of carbohydrates, which is energy.

…

So do you think there is energy within the carbohydrate then?

Yeah.

Stored energy.

Yeah.

So how do you think that got there, who stored it?

(laughs) I don't know.

Again, the impression was that Mandy was not linking the energy value of food with photosynthesis. The reference to carbohydrates being energy seemed (given the wider context of the interview) to be imprecise use of language, rather than a genuine alternative conception.

So do you go to like the Co-op and buy a packet of pasta. Or mum does I expect?

Yeah.

Yeah. So do you think, sort of, the Co-op are sort of putting energy in the other end, before they send it down to the shop?

No, it comes from 'cause pasta's made from like flour, and that comes from wheat, and then that uses photosynthesis.

Now it seemed that it was quite clear to Mandy that photosynthesis was responsible for the energy stored in the pasta. It was not clear why she had not suggested this before, but it seemed she could make the connection between the food people eat and photosynthesis. Perhaps (it seems quite likely) she had previously been aware of this and it initially did not 'come to mind', and then at some point during this sequences of questions there was a 'bringing to mind' of the link. Alternatively, it may have been a new insight reached when challenged to respond to the interview questions.

So you don't need to photosynthesise to get energy?

No.

No, how do you get your energy then?

We respire.

Is that different then?

Yeah.

So what's respire then, what do you do when you respire?

We use oxygen to, and glucose to release energy.

Do plants respire?

Yes.

So when do you respire, when you are going to go for a run or something, is that when you respire, when you need the energy?

No, you are respiring all the time.

Mandy suggested that plants mainly respire at night because they are photosynthesising during the day. (Read 'Plants mainly respire at night'.)

So is there any relationship do you think between photosynthesis and respiration?

Erm respiration uses oxygen – and glucose and it produces er carbon dioxide and water, whereas photosynthesis uses carbon dioxide and water, and produces oxygen and glucose.

So it's quite a, quite a strong relationship then?

Yeah.

Yeah, and did you say that energy was involved in that somewhere?

Yeah, in respiration, they produce energy.

What about in photosynthesis, does that produce energy?

That produces glucose, which produces the energy.

I see, so there is no energy involved in the photosynthesis equation, but there is in the glucose?

Yeah.

Respiration does not 'produce' energy of course, but if it had the question about whether photosynthesis also produced energy might have been expected to elicit a response about photosynthesis 'using' energy or something similar, to give the kind of symmetry that would be consistent with conservation of energy (a process and its reverse can not both 'produce' energy). 'Produce' energy might have meant 'release' energy in which case it might be expected the reverse process should 'capture' or 'store' it.

Mandy appreciated the relationship between photosynthetic and respiration in terms of substances, but had an asymmetric notion of how energy was involved.

Mandy appeared to be having difficult appreciating the symmetrical arrangement between photosynthesis and respiration because she was not clear how energy was transformed in photosynthesis and respiration. Although she seemed to have the components of the scientific narrative, she did not seem to fully appreciate how the absorption of light was in effect 'capturing' energy that could be 'stored' in glucose till needed. At this stage in her learning she seemed to have grasped quite a lot of the relevant ideas, but not quite integrated them all coherently.

Particles are further apart in water than ice

Keith S. Taber

Image from Pixabay 

Bill was a participant in the Understanding Science Project. Bill, a Y7 student, explained what he had learnt about particles in solids, liquids and gases. Bill introduced the idea of particles when talking about what he had learn about the states of matter.

Well there's three groups, solids, liquids and gases.

So how do you know if something is a solid, a liquid or a gas?

Well, solids they stay same shape and their particles only move a tiny bit.

This point was followed up later in the interview.

So, you said that solids contain particles,

Yeah.

They don't move very much?

No.

And you've told me that ice is a solid?

Yeah.

So if I put those two things together, that tells me that ice should contain particles?

Yeah.

Yeah, and you said that liquids contain particles? Did you say they move, what did you say about the particles in liquids?

Er, they're quite, they're further apart, than the ones in erm solids, so they erm, they try and take the shape, they move away, but the volume of the water doesn't change. It just moves.

Bill reports that the particles in liquids are "further apart, than the ones in … solids". This is generally true* when comparing the same substance, but this is something that tends to be exaggerated in the basic teaching model often used in school science. Often figures in basic school texts show much greater spacing between the particles in a liquid than in the solid phase of the same material. This misrepresents the modest difference generally found in practice – as can be appreciated from the observations that volume increases on melting are usually modest.

Although generally the particles in a liquid are considered further apart than in the corresponding solid*, this need not always be so.

Indeed it is not so for water – so ice floats in cold water. The partial disruption of the hydrogen bonds in the solid that occurs on melting allows water molecules to be, on average, closer* in the liquid phase at 0˚C.

As ice float in water, it must have a lower density. If the density of some water is higher than that of the ice from which it was produced on melting then (as the mass will not have changed) the volume must have decreased. As the number of water molecules has not changed, then the smaller volume means the particles are on average taking up less space: that is, they seem to be closer together in the water, not further apart*.

Bill was no doubt aware that ice floats in water, but if Bill appreciated the relationship of mass and volume (i.e., density) and how relative density determines whether floatation occurs, he does not seem to have related this to his account here.

That is, he may have had the necessary elements of knowledge to appreciate that as ice floats, the particles in ice were not closer together than they were in water, but had not coordinated these discrete components to from an integrated conceptual framework.

Perhaps this is not surprising when we consider what the explanation would involve:

Coordinating concepts to understand the implication of ice floating

Not only do a range of ideas have to be coordinated, but these involve directly observable phenomena (floating), and abstract concepts (such as density), and conjectured nonobservable submicroscopic/nanoscopic level entities.

* A difficulty for teachers is that the entities being discussed as 'particles', often molecules, are not like familiar particles that have a definitive volume, and a clear surface. Rather these 'particles' (or quanticles) are fuzzy blobs of fields where the field intensity drops off gradually, and there is no surface as such.

Therefore, these quantiles do not actually have definite volumes, in the way a marble or snooker ball has a clear surface and a definite volume. These fields interact with the fields of other quanticles around them (that is, they form 'bonds' – such as dipole-dipole interactions), so in condensed phases (solids and liquids) there are really not any discrete particles with gaps between them. So, it is questionable whether we should describe the particles being further apart in a liquid, rather than just taking up a little more space.

Energy cannot be made or destroyed (except in biology)

Keith S. Taber

Energy can be made, but only in biology: Amy had learnt that respiration was converting glucose and oxygen into energy – but had learnt in physics that energy cannot be made

Amy was a participant in the Understanding Science Project. Amy was a Y10 (14-15 year old) student who had separate lessons in biology, chemistry and physics. When I spoke to her (see here), she had told me that respiration was "converting glucose into energy and either carbon dioxide and lactic acid, or just carbon dioxide". When I spoke to her again, some weeks later, Amy repeated that respiration was "converting oxygen and glucose into energy and carbon dioxide…it produces energy" ; that trees "need to produce energy and when they photosynthesise they produce like energy"and that food is "broken down and converted into energy".

Later in the same interview I asked her about her physics lessons, where she had been told that "there's like different types of energy" and that it "cannot be made or destroyed, only converted". Amy did not seen to have recognised any conflict between how she understood the role of energy in biology, and what she was taught in physics.

However, on further questioning, she seemed able to recast her biology knowledge to fit what she had been taught in physics:

So in physics, they tell you (that) you cannot make or destroy energy.

Yeah.

And in biology, they tell you that you can make energy from oxygen and glucose?

(No response – Pause of c.2 seconds)

But only in biology, not in physics?

Oh, erm, I suppose the energy, erm well in respiration, erm the energy must be converted from stored energy in food.

So in an interview context, once the linkage was explicitly pointed out, Amy seemed to recognise that the principle learnt in physics should be applied in biology. However, she did not spontaneously make this link, without which the nature of respiration was misunderstood (in terms of energy being created from matter). This would appear to be an example of a fragmentation learning impediment, as although Amy had learnt about the conservation of energy she did not immediately how this related to what she had studied in biology, about respiration.

She'd never thought about whether ionic bonding is the same thing as chemical bonding

Keith S. Taber

Amy was a participant in the Understanding Science Project. When I talked to her near the start of her GCSE 'triple science' course in Y10 she told me that ionic bonding was "atoms which have either lost or gained electrons so they are either positively or negatively charged" and that chemical bonding was "like in a compound, where two or more elements are joined together", but she seemed unsure how the two concepts were related.

I followed up on Amy's use of the term 'compound' to explore how she understood the term:

How would you define a compound?

Erm …Something which has erm two or more elements chemically bonded.

… So you give me an example of that, compound?

Erm, sodium oxide.

Sodium oxide, okay, so there are two or more elements chemically bonded in sodium oxide are there?

Uh hm

And what would those two or more elements be?

Sodium and oxygen.

Okay. Erm, so when we say sodium oxide is chemically bonded, what we are saying there is?

[pause, c 2s]

Erm – a sodium atom has been bonded with a oxygen atom to form erm a new substance.

So Amy's example of a compound was sodium oxide, which would normally be considered essentially an ionic compound, that is a compound with ionic bonding. So this gave me an opportunity to test out whether Amy saw the bonding in sodium chloride and sodium oxide as similar.


Okay, so that was chemical bonding,

Mm.

and that occurs with compounds?

Yeah.

And what did you say about ionic bonding?

Erm, it's the outer electrons they are transferred from one element to another.

Now what does that occur in? You gave me one example, didn't you?

Uh huh

Sodium chloride?

Yeah
…

Erm. Would sodium chloride be er an element?

[pause, c.2s]

Sodium chloride, no.

No?

It would be a compound.

You think that would be a compound?

Yeah.

And a compound is two or more elements joined together by chemical bonding?

Yeah.

So Amy had told me that sodium chloride, which had ionic bonding, was (like sodium oxide) a compound, and she had already told me that a compound comprised of "two or more elements chemically bonded", so it should be follow that sodium chloride (which had ionic bonding) had chemical bonding.

Do you think sodium chloride has chemical bonding?

Er – I think so

And it also has ionic bonding, or is that the same thing?

Erm,

[pause, c.2s]

I dunno, I've never thought about it that way, erm,

[pause c.3s]

I'm not sure, erm

[pause, c.2s]

I dunno, it might be.

Clearly, whatever Amy had been taught (and interviewing students reveals they often only recall partial and distorted versions of what was presented in class) she had learnt

  • (1) that ionic bonding was transfer of electrons (an alternative conception) as in the example of sodium transferring an electron to chlorine; and that
  • (2) a compounds was where two or more elements chemically bonded together, and an example was sodium oxide where the elements sodium and oxygen were chemical bonded.

Yet these two pieces of learning seemed to have been acquired as isolated ideas without any attempt to link them. Initially Amy seemed to feel ionic bonding and chemical bonding were quite separate concepts.

When taken through an argument that led to her telling me that sodium chloride, that she thought had ionic bonding, was a compound, which therefore had chemical bonding, there should have been a logical imperative to see that ionic bonding was chemical bonding (actually, a kind of chemical bonding – as the logic did not imply that chemical bonding was necessarily ionic bonding). Despite the implied syllogism:

  • sodium chloride has ionic bonding
  • sodium chloride is a compound
  • compounds have elements chemically bonded together
  • therefore ionic bonding …

Amy was unsure what to deduce, presumably because she had seen the two concepts of ionic bonding and chemical bonding as discrete notions and had had given no thought to a possible relationship between them. However explicit teaching had been on this point, it is very likely that the teacher had expected students to appreciate that ionic bonding was a type of chemical bonding – but Amy had not integrated these ideas into a connected conceptual structure (i.e., there was a learning bug that could be called a fragmentation learning impediment).

There are particles in everything – but maybe not chlorophyll

Keith S. Taber

Bill was a participant in the Understanding Science Project. Bill (a Year 7 pupil) told me that "solids they stay same shape and their particles only move a tiny bit". He explained that the 'particles' were "the bits that make it what it is", although "you can't see them" as "they're very, very tiny". Later he commented that "they are microscopic".

Although it is very common for such particles to be said to be 'microscopic', a better term would be 'nanoscopic'. Microscopic suggests visible under a microscope, and the particles referred to here ('quanticles') are actually submicroscopic." The term microscopic could therefore be misleading, and it is known that often when students first learn about particles in science they often have in mind small grains of powder or dust.

Bill explained that "there is particles in everything". Bill was able to talk a lot about particles in solids, liquid and gases and explain what happened during melting.

Later in the same interview Bill talked about how in his primary school he had studied "a lot about plants, and – inside them, how they produce their own food", and how "inside, it has leaves, inside it, there is chlorophyll, which stores [sic] sunlight, and then it uses that sunlight to produce its food."

I asked Bill if plants had anything to do with particles:

Well in the plant, there is particles….'cause it's a solid…. inside the stem is, 'cause going up the stem there would be water, so that's a liquid. And, it also uses oxygen, which is a gas, to make its food, so. I think so.

Bill explained that "…in the leaves it is chlorophyll which is a green substance, so that would make, give it its colour".

Do you think chlorophyll is made of particles?

Hm, don't know.

So it seemed that although 'there is particles in everything', Bill did not seem to feel this meant that he could apply the particle idea to all substances. This could be an example of a fragmentation learning impediment: that is, where learning in one area is not recognised as relevant in studying other subjects or topics.

Plants store sunlight

Keith S. Taber

Bill was a Y7 student participating in the Understanding Science project. He used the idea of energy in talking about some aspects of his science. So when considering melting "the particles in (a solid), would have the energy, to move about more, and then it would melt down, because of its melting point, and go into a liquid". Although he could not explain what energy was, he knew "it gives something – the energy to move, it will make something else move or something". He remembered having done some work "where we had to make elastic band powered, 'cause the elastic band stored the energy to make it move", so energy could be stored.

Bill also told me about how in his previous school "we did a lot about plants, and – inside them, how they produce their own food". He explained that "inside, it has leaves, inside it, there is chlorophyll, which stores sunlight, and then it goes, then it uses that sunlight to produce its food. It also uses water from the roots, and the soil, and oxygen in the air. So it needs sunlight, oxygen and water to make its food and live."

However, Bill did not relate this process to the notion of energy, and see that the 'storing sunlight' might have been like the energy stored in an elastic band:

Interviewer: We were talking about energy just now.

Bill: Yeah

I: Do you think that's got anything to do with energy? That process you just talked about?

B: Hm, erm, (pause, c.3 seconds) I'm not sure

So Bill did not make the connection between storing energy, and what he interpreted from his science lesson as 'storing sunlight'. This appears to be an example of a fragmentation learning impediment.

With science it will always be the same

Keith S. Taber

Ralph was a participant in the Understanding Science project. When I interviewed him in his first term of upper secondary science he told me he was studying a range of topics in science, so I asked him what was common to these topics that made these different lessons all science.

I: So what makes that science, then, because it all seems so varied?

R: Well (Exhales) – physics is kind of like just like, distinguishing it from like, like forces and the things that we can't really see, so it's like, whereas chemistry is like big bangs and things so you can like, very visual one, and biology is like understanding the human body and things, so, I've completely forgotten what the original question was.

I: So what makes physics, chemistry and biology science, why don't we just call them three separate subjects, have they got anything in common?

R: Mm, erm. Er (Pause, c.2s, then Ralph exhales) … Erm, it's more because they're kind of like, they are laws so they kind of like effect, so these things have to be true. Whereas kind of in English and things, yeah that's fine, but they can be changed with different places, depending where you are, whereas, with science, it will always be the same. It's like maths because maths is kind of like physics and physics uses maths, because maths will always be the same wherever you go, 'cause the, you can't like, you can't say like in one place that two will equal two and in another place two will equal three or something. They've always got to be the same.

So for Ralph, a distinguishing criterion for science (and maths) was the universal nature of science: that it offered laws which "will always be the same". This is an interesting observation about the nature of science, with Ralph rejecting any relativistic notions of science, which might apply to some other subjects ("they can be changed with different places, depending where you are"). The need for scientific laws to apply regardless of context would be widely accepted, although Ralph's comments could also be seen to ignore the provisional nature of science (e.g. if laws are seen as  human constructions to interpret patterns in nature, rather than understood as given in nature).

(Although Ralph observed that because they are laws these things have to be true, when he attempted to exemplify this in physics, chemistry and biology, he was not able to suggest clear examples of universal laws in science.)