Former school and college science teacher, teacher educator, research supervisor, and research methods lecturer. Emeritus Professor of Science Education at the University of Cambridge.
Physicists see electromagnetism as one of the fundamental forces in the universe, and physics often includes a topic or module on 'electricity and magnetism'. Magnetism can be considered an electrodynamic effect (i.e., due to the movement of charges), but this will not be obvious to students.
Sophia was a participant in the Understanding Science Project. I spoke to here in Y7 (of the English school system) when she told me about the things she had been learning in the topic of electricity. I asked her,
Anything else you've done on electricity?
The er, I don't know what, it's not that much to do with electricity but, yesterday or the day (before) we done magnets.
Oh right. So that's a new topic, is it, not to do with electricity, or?
Well, I think we're still doing electricity. I don't know if it was just something – so we know what might, er, so we know what, what electricity will flow through, and maybe it's something to do with – 'cause magnets like stick to other things, they might be – I'm not sure, I think we might just have had a break from it, I don't know, but.
So, Sophia came up with some suggestions for why magnets might be featured in the electricity topic, but she was not very convinced about this rationale, and considered it was quite possible that the teacher was just interspersing other material to give a 'break' from the main topic. So, instead, they "done magnets".
It is interesting that one of Sophia's suggestions was "what electricity will flow through". The constructivist theory of learning ( read about constructivism here) suggests that meaningful learning involves learners making sense of what they are taught by linking it to their existing ideas and wealth of past experiences. This is a creative process, and sometimes students make unhelpful associations, that can act as learning impediments. Although ceramic magnets are increasingly common, iron, a good conductor, and its alloys, are still used for bar and horseshoe magnets that children will often be familiar with – so this association has potential to be built on constructively.
Of course electricity and magnetism were at one time considered quite distinct phenomena by scientists – and James Clerk Maxwell is rightly remembered for his synthesising theoretical work showing that electricity, magnetism and light could all be understood as manifestations of a single underlying 'phenomenon' of electromagnetism. (Indeed it seems stretching then notion of phenomena to refer to electromagnetism as a single phenomenon, as no one would intuitively perceive its manifestations as being observations of the same phenomenon!) We can hardly expect students to appreciate why electricity and magnetism might be considered a unitary physics topic in school science.
To the science teacher, magnetism is an electrical effect, and electromagnetism is one of the fundamental forces in nature. The unification of electricity, magnetism, and electromagnetic radiation is seen as a major integrative step forwards in science–but our students are not going to see the connections without some help.
When I asked her to tell me what she learnt about magnets she told me that the north pole and the south poles go together because one of them is coming out and one is going in.
One aspect of academic life that has never sat easily with me, is having to be a publicity officer and marketing manager for oneself as a scholar. Not only does this involve keeping good records of everything one has contributed that might conceivably count in seeking a post or promotion and so forth, but making a case for just how important one's work is – its supposedly seminal status, and its inconceivably incredible impact – by seeking out and reporting various indicators. Perhaps it is something about being British, but it is one aspect of the role that I am pleased to be leaving behind.
Presentation is important. Yet, of course, one must retain one's integrity. One might need to display one's contributions in the best possible light, but lying is clearly not acceptable. Unlike on TV's 'The Apprentice' where hopeful future entrepreneurs making up achievements or exaggerating beyond any possible justification in their applications is presented as entertainment – a little naughty, but it shows they are committed and enthusiastic – this would (I assume) clearly be unacceptable in the real world of work. If that is idealistic, it is certainly not okay in the Academy.
A confession
Yet I must confess that for some years it seems I have been padding my publications list with an article that, I now find, may never have been published. Inadvertently, obviously.
But how can a scholar seriously claim they thought they had been published, when, actually, they never were? What possible defence can there be?
But ('your honour') it is true: I found out some days ago that one of my 2012 publications [sic] may not have actually been a publication at all – as it may never have been published. So my publications list may have misrepresented the status of this possibly previously* unpublished work. (*I've just 'published' it myself on the website – but of course that would not count for much in the hiring-and-tenure-and-promotions game.)
So how did this situation develop?
The invitation
On the 8th September 2009 I was invited by an esteemed colleague
As Editor-in-Chief of the Encyclopledia of the Sciences of Learning (to be published in 2011 by Springer Publ.) and in accordance with strong recommendations of the editorial advisory board I am wondering if you would be interested in joining the Encyclopedia's list of contributors…If you have the time and inclination, the Editorial Advisory Board and I would very much appreciate your support. If you agree to serve as an author on the topic(s) on molecular conceptions of research into learning
The deadline was in January 21st 2010, and I got the submission completed just before Christmas 2009. I was sent reviewer comments, and completed a revision in June 2010. I assumed all was well.
The article is shown as coded green: Manuscript accepted
However, when I saw in May 2012 that the book was published, my article did not seem to be listed. So I contacted the publisher:
Would you be able to give me an update on the current status of this project. On the project website the contribution I was invited to provide is shown as green (manuscript accepted) [see image above], and according to the Springer site the Encyclopedia is now published. However, I cannot see how to access the material (perhaps my institution does not have access (yet?), or pehraps the on-line version is not yet available?), and I cannot see my contribution (Molecular conceptions of research into learning Regular Entry 00394 894/894) in the downloadable contents. Please could you advise?
The publisher responded: "I can´t find the entry either. This is very strange as it should be there. I will check with the production team and the company that runs the website for us."
The next day came the bad news. Well, given the kinds of things that happen in the world it was only slightly bad, but as publications are seen as so important for academics, and given that I'd done the work, it was pretty disappointing!
I´m terribly sorry to tell you that your article was the only one that has not been received by the production vendor team although we sent it to them. That means that we didn't even had a proof of your article. We didn´t notice that before for which we apologize deeply. For the current printed book Encyclopedia of the Sciences of Learning it is much too late to get your article in. Please accept my apologies.
A second invitation
But I was offered a partial corrective:
We have developed a new publication platform for our Reference Works that launched in August last year. As the Encyclopedia is part of the Springer Reference Works series it is also published as Online Version …The Encyclopedia on that platform can be seen as a living book as authors and editors can add articles or update old ones at any time….Would you be interested to write/update your article on SpringerReference as part of the electronic/online version of the Encyclopedia of the Sciences of Learning?
Yes, I would. The next day I was formally invited to write my article, once more:
Thank you very much for taking part in Encyclopedia of the Sciences of Learning…With this e-mail we invite you to SpringerReference.com as author of the following topic(s): Molecular Conceptions of Research into Learning…
At SpringerReference.com, we offer an extremely innovative way of publishing that allows authors to keep articles constantly updated and make their writing efforts immediately visible online. … When the article is complete, simply click 'Submit' to submit your content. By doing so, your contribution will become immediately visible on the site for other users to read and cite–you do not need to wait until the deadline is reached should you have been given one.
The article was (now) due on July 17th, 2012. There were some technical issues using the on-line submission system, but an assistant at the publisher helped sort the problems relating to an image file and cross-links with other contributions. Finally, by the 9th July, the files were uploaded and some formatting issues were sorted, and I was told by the publisher's assistant: "You can confirm it and click on the ACCEPT button".
I did not have access to an accept button, but was able to reply "Thank you – I have clicked the submit button."
Looking back now, I am wondering if perhaps I did need to click on the accept button – except I did not have such a button on my screen. Perhaps the publisher did have an accept button at their end, and the production assistant did not realise that I did not, or had intended to accept the article later and for some reason…
However, as I could see the article on line (see below), I assumed all was well. After all, I had been told that "When the article is complete, simply click 'Submit' to submit your content. By doing so, your contribution will become immediately visible on the site for other users to read and cite…"
The article showed as being part of the on-line Reference collection, with its own DOI
As I am retiring from teaching, I have been building up this website as a central point for various things I've worked on, and have been reviewing the publications I've written over the years (some of which I have no files for, as the manuscripts were typed and submitted in hard copy in those days). When I came to check the current location of this reference article, I could not find it on line, nor indeed any reference to it in a search. Well, that is not absolutely true: I found it was referred to in a list of my publications, but nowhere else. So I reached out to the publisher:
The files were lost (again) in a migration
The publisher could not find my article, nor indeed any record of it.
I'm sorry to say that after scouring our repositories and email we've failed to find your entry "Molecular conceptions of research into learning". Encyclopedia of the Sciences of Learning was developed on older platforms we decommissioned years ago, and email archives go back only so many years, I am sorry to say. (16th June 2020)
It seems the publisher had decided the original system, a wiki-based platform, did not fully meet their needs, and that something more sophisticated was needed, a "a file- and book-based publishing workflow" that worked better for academic publishing. That is perfectly understandable.
I can also understand that if the publisher had never accepted the submission at their end, then it might be quite possible that the files would be missed completely when the published materials were transferred to a new platform. It seems the files were lost in that process.
A Schrödinger publication?
On the other hand, if it was true that "by [clicking submit], your contribution will become immediately visible on the site for other users to read and cite" then it is not obvious to me why the files were not transferred – unless the transfer was based on a list of the files at the time of the original publication. If that is the case then the "living book [where] authors and editors can add articles or update old ones at any time" died, and reverted to the state of the initial 2012 publication, when the transfer took place.
I am not sure what the moral of this story is. After writing, submitting, and revising an invited article, having the publisher lose it; resubmitting it, a lot of back and forth sorting format issues…it is disappointing to know all that effort may have came to nought.
In retrospect, perhaps when I emailed to say "I have clicked the submit button" I should have written "I have clicked the submit button as I do not have an ACCEPT button, so if an ACCEPT button needs to be clicked please advise, or otherwise confirm no further action is needed at my end". Usually I tend to be pedantic and explicit – and so, I suspect, annoying. Annoyingly, on one of the few occasions I let my guard down, being my usual annoyingly pedantic might have stopped the article being lost a second time.
On the other hand, perhaps my article WAS published on-line in 2012 (when I could access it), but then lost some years later when the resource was transferred to a new platform. That would be a bit like having a chapter in an edited book that has gone out of print (which would not stop an academic including it on a publications list) – except that the only copies of my article which would have survived would have been any downloaded onto individual computers whilst the original platform was live.
Perhaps I should label this a Schrödinger publication – and consider it as an entanglement of two states – ⎮published but no longer available ⎮ / ⎮ accepted for publication but never published ⎮ – as there does not seem to be any observation I can make now which would collapse the wave function.
So I am not not entirely sure if my entry in the encyclopaedia actually never was a real publication (given the publisher has no record of it), or is just not a currently available publication (given that it was submitted according to the instructions that were supposed to make it live immediately). That makes keeping an accurate publications list quite challenging.
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.
It's covalent bonding where the electrons are shared to create a full outer shell
Keith S. Taber
Brian was a participant in the Understanding Chemical Bonding project. He was interviewed during the first year of his college 'A level' course (equivalent to Y12 of the English school system). Brian was shown, and asked about, a sequence of images representing atoms, molecules and other sub-microscopic structures of the kinds commonly used in chemistry teaching. He was shown a simple representation of a covalent molecule:
Focal figure ('2') presented to Brian
Any idea what that's meant to be, number 2?
Hydrogen molecule.
Why, how do you recognise that as being a hydrogen molecule?
Because there's two atoms with one electron in each shell.
Uh hm. Er, what, what's going on here, in this region here, where these lines seem to meet?
Bonding.
That's bonding. So there's some sort of bonding there is there?
Yeah.
Can you tell me anything about that bonding?
It's covalent bonding.
So, so what's covalent bonding, then?
The electrons are shared to create a full outer shell.
Okay, so that's an example of covalent bonding, so can you tell me how many bonds there are there?
One.
There's one covalent bond?
Yeah.
Right, what exactly is a covalent bond?
It's where electrons are shared, almost, roughly equally, between the two atoms.
So that's what we'd call a covalent bond?
Yeah.
So according to Brian, covalent bonding is where "the electrons are shared to create a full outer shell". The idea that a covalent bond is the sharing of electrons to allow atoms to obtain full electron shells is a very common way of discussing covalent bonding, drawing upon the full shells explanatory principle, where a 'need' for completing electron shells is seen as the impetus for bonding, reactions, ion formation etc. This principle is the basis of a common alternative conceptual framework, the octet rule framework.
For some students, such ideas are the extent of their ways of discussing bonding phenomena. However, despite Brian defining the covalent bond in this way, continued questioning revealed that he was able to think about the bond in terms of physical interactions
Okay. And why do they, why do these two atoms stay stuck together like that? Why don't they just pull apart?
Because of the bond.
So how does the bond do that?
(Pause, c.13s)
Is it by electrostatic forces?
Is it – so how do you think that works then?
I'm not sure.
The long pause suggests that Brian did not have a ready formed response for such a question. It seems here that 'electrostatic forces' is little more than a guess, if perhaps an informed guess because charges and forces had features in chemistry. A pause of about 13 seconds is quite a lacuna in a conversation. In a classroom context teachers are advised to give students thinking time rather than expecting (or accepting) immediate responses. Yet, in many classrooms, 13 seconds of 'dead air' (to borrow a phrase from broadcasting) from the teacher night be taken as an invitation to retune attention to another station.
Even in an interview situation the interviewer's instinct may be to move on to a another question, but in situations where a researcher is confident that waiting is not stressful to the participant, it is sometimes productive to give thinking time.
Another issue relating to interviewing is the use of 'leading questions'. Teachers as interviewers sometimes slip between researcher and teacher roles, and may be tempted to teach rather than explore thinking.
Yet, the very act of interviewing is an intervention in the learners' thinking, in that whatever an interviewer tells us is in the context of the conversation set up by the interviewer, and the participant may have ideas they would not have done without that particular context. In any case, learning is not generally a once off event, as school learning relies on physiological process long after the initial teaching event to consolidate learning, and this is supported by 'revision'. Each time a memory is reactivated it is strengthened (and potentially changed).
So the research interview is a learning experience no matter how careful the researcher is. Therefore the idea of leading questions is much more nuanced that a binary distinction between those questions which are leading and those that are not. So rather than completely avoiding leading questions, the researcher should (a) use open-ended questions initially to best understand the ideas the learner most easily beings to mind; (b) be aware of the degree of 'scaffolding' that Socratic questioning can contribute to the construction of a learners' answer. [Read about the idea of scaffolding learning here.] The interview continued:
Can you see anything there that would give rise to electrostatic forces?
The electrons.
Right so the electrons, they're charged are they?
Yeah. Negatively.
Negatively charged – anything else?
(Pause, c.8s)
The protons in the nucleus are positively charged.
Uh hm. And so would that give rise to any electronic interactions?
Yeah.
So where would there be, sort of any kind of, any kind of force involved here is there?
By the bond.
So where would there be force, can you show me where there would be force?
By the, in the bond, down here.
So the force is localised in there, is it?
The erm, protons would be repelling each other, they'd be attracted by the electrons, so they're keep them at a set distance.
It seemed that Brian could discuss the bond as due to electrical interactions, although his initial ('instinctive') response was to explain the bond in terms of electrons shared to fill electron shells. Although the researcher channelled Brian to think about the potential source of any electrical interactions, this was only after Brian had himself conjectured the role of 'electrostatic forces.'
Often students learn to 'explain' bonds as electron sharing in school science (although arguably this is a rather limited form of explanation), and this becomes a habitual way of talking and thinking by the time they progress to college level study.
I've just seen* an article in Chemistry: Bulgarian Journal of Science Education describing how students intending to be teachers were introduced to ideas about intermolecular bonding by analogy with attraction between people (Karakaş, 2012). In this analogy nuclei are seen as female and electrons as male, and so sometimes the electrons may take an interest in nuclei other than their own, so to speak: hydrogen bonding is seen as a "form of dipole-dipole interactions, caused by highly electronegative atoms (caused by couples with highly attractive females)", occurring between hydrogen and
"oxygen (couple where the nucleus is Maria Sharapova), fluorine (couple where the nucleus is Kim Kardashian) or nitrogen (couple where the nucleus is Beyonce)" (p.345).
This seems to be a variation on an approach that has been around at least since I started teaching (I remember comparing displacement reactions to interactions between couples at parties), and is clearly meant to be a fun idea, as well as having a motivation in terms of making abstract chemical ideas relevant by comparison with something familiar. The study reported was undertaken in Turkey, and I wondered about the cultural acceptability of this approach these days in different contexts. So Karakaş reports that
"the instructor said in a patriarchal society such as Turkey, the male is supposed to take care of the female. Then the instructor said that basically, the male has to revolve around the female like an electron revolving around a nucleus" (p.343).
I suspect that in many countries it might be considered quite inappropriate to make such a comment about gender roles, at least not without a clear sense of intended satire. More significantly, I wonder how acceptable it is to talk about the relative sexual attractiveness of different people – is that politically correct? Especially if the idea was used with adolescent students, many of whom may well be suffering issues relating to their perceptions of their own attractiveness.
Finally, of course, the basic premise, that sexual orientation matches the principle found with electrical charge – opposite charges attract, similar charges repel – would certainly be suspect in the context where I work (where a current issue of public debate is whether same sex couples should be allowed to marry rather than just register civil partnerships). In some ways these complications are a shame, as the analogy will be seen as fun by many learners, and it certainly is something most learners will relate to. This example reminds us that even if chemistry itself can be seen as largely culture-free, teaching and learning of science always takes place in a cultural context that also influences what can be considered good teaching.
Reference: Karakaş, M. (2012). Teaching Intermolecular Forces with Love Analogy: A Case Study. Chemistry: Bulgarian Journal of Science Education, 21(3), 341-348.
* Previously published at http://people.ds.cam.ac.uk/kst24/science-education-research: 9th May 2015
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.)
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.
Focal figure presented to Annie
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.
I just heard the UK Prime Minister introduce a public information message about what would be considered when deciding to ease current measures to tackle the COVID-19 pandemic.
Two particular statements in the clip played gained my attention:
"All viruses, like normal 'flu, have a rate of infection. Scientists call this R. R is the average number of people one infected person passes the virus onto."
"In March, at its peak, R was around 3, which seems to be the natural rate for this virus."
Neither of these statements seemed strictly correct to me.
To make things clearer, let's call a spade, a fork
Surely the rate of infection is the number of people who are infected in a unit time period – say per day. R is something else – the reproduction number. Now, those working in the public understanding of science, just as in science education, have to seek an optimum level of simplification when communicating with non-experts. There is no point using complex language that will be unclear to people, and so likely lead to them disengage with the message. So, simplification may indeed be needed. But not such a degree of simplification that what we say no longer adequately represents the ideas we are trying to convey.
But the term 'reproduction number' is not some really obscure and inaccessible jargon – it uses words that most people are quite familiar and comfortable with.It does not seem any more technical and frightening that the term 'rate of infection'. Now I accept that perhaps the compound phrase 'reproduction number' is itself unfamiliar, whereas 'rate of infection' is more commonly heard. BUT rate of infection already has a meaning, a different one – so is it sensible to confuse matters by defining rate of infection with a new meaning inconsistent with the existing common usage?
This seems an odd way to promote public understanding of science to me. This is a bit like deciding that the term 'electrical field' may seem a bit too technical for an audience, so it will be a good idea to instead start calling it 'gravity' from now on, because people are used to that term. Or thinking that 'water of crystallisation' sounds obscure, so deciding to refer to the copper sulphate crystal incorporating 'ice cubes' when talking to non-experts because they know what ice cubes are (i.e., something other than molecules of water of crystallisation!).
So what is natural about rates of viral infection?
I was not sure precisely what a normal 'flu was (in relation to an abnormal 'flu, presumably?), but was more surprised to the reference to a virus having a natural rate of infection – even if this actually meant a natural reproduction number.
Will this not depend on the conditions in which the virus exists?* R will surely be very different in a population that is sparsely spread with small social group sizes than in a population that is largely living in extended family groups in overcrowded slums – so what is the natural environment for that virus?
We have reduced R by social distancing and increased hygiene measures. Are we to assume what is natural is the work and social (and hygiene) habits of the UK population as it was in February 2020, rather than now? If so, were the social conditions in the UK in 1920 or 1820 'unnatural'? So, I think the reference to the rate (actually R) being 3 is not a natural rate, but the R value contingent on the specific conditions of UK social and economic activity at a particular historical moment. To believe that the way WE live NOW (or, actually, two months ago) reflects what is natural seems a very anthropocentric notion of 'natural'.
I guess I am being pedantic (one of the few things I tend to be good at – and we all need to work to our strengths) but it seems to me that if you are going to commission a public health message at a time when the public understanding of science is actually a matter of life and death, then it is worth trying to get the science right.
* This seemed intuitively obvious, but I thought I ought to check. A quick web-search led to lots of different estimates of R (or R0, that is R whilst a population is all susceptible) presented as if there was a single right value (even if we do not know it precisely) that applied across different contexts globally. Hm. So, I was reassured to come across: "Firstly, R0 is not an intrinsic variable of the infectious agent, but it is calculated through at least three parameters: the duration of contagiousness; the likelihood of infection per contact between; and the contact rate, along with economical, social and environmental factors, that may vary among studies aimed to estimate the R0", Viceconte and Petrosillo, 2020, COVID-19 R0: Magic number or conundrum?, Infectious Disease Reports, 12(1).
Adrian was a participant in the Understanding Science Project. When I spoke to him during the his first year (Y12) of his 'A level' course he told me he had been studying quantum theory, and I asked him about the name 'quantum theory'. He suggested that a theory is an idea that can be proven, but struggled to suggest any other scientific theories.
What about the theory of evolution? Would you count that as a theory?
Yes, but I am not familiar with it. Was it e=mc²?
That's relativity.
Relativity.
I was thinking evolution?
I don't know that one.
Not sure about evolution at all?
No.
Of course there is more than one theory of evolution, but natural selection was a compulsory topic in the school curriculum, and widely referred to as 'the theory of evolution'. Adrian, however, seemed to have no recollection of hearing about evolution at all. It is inconceivable that he had not met the term in school or elsewhere, but it was not something he was bringing to mind in response to my questioning.
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 *.
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"*.
Some learners have been found to see the electron transfer process described by Mohammed (which is purely a way of conceptualising ion formation, and has little connection with what actually happens when ionic substances form) as being the bond, and sufficient to hold species together. However, Mohammed did recognise the role of electrical forces in holding the species together:
And did you say that if you take a sodium atom and a chlorine atom, you get salt?
Yeah… Sodium chloride. And the way they bond together, is because now one, the sodium has lost an electron. And they start off neutral because the protons and electrons balance each other out, because the same number of them, but when you lose one you get plus one in the sodium, and like when you have a chlorine, you add an electron so you get minus one. In the end the whole compound is neutral, but because erm, like they, they're differently charged they attract together, and they bond together. I think.
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.
So here Mohammed is clear (if somewhat tentative) that a bond has been formed. Yet his focus is on the iteration of two atoms, forming ions, whereas ionic bonding needs to be understood as the various interactions at work in a lattice. The process of ion formation described by Mohammed:
would not actually be energetically viable for two atoms (as the electron affinity of chlorine is 364 kJ mol-1, whereas the first ionisation energy of sodium is 494 kJ mol-1, so the electron capture of a chlorine atom would not release enough energy to remove the electron from the sodium atom);
neither sodium nor chlorine atoms are stable under normal chemical conditions: neither sodium nor chlorine used in a binary synthesis would be in the form of discrete atoms; and sodium chloride is more likely to be formed by neutralisation using substances where the sodium and chloride ions are already present, e.g. sodium hydroxide and hydrochloric acid.)
Mohammed's explanation conflates two levels – the macroscopic level of bench phenomena (such as the substance sodium chloride – common salt) and the level of models at the submicroscopic scale of molecules, ions and atoms. Even if one atom of sodium could interact ('react' is better kept as a term for what occurs at the level of substances) with one atom of chlorine in the manner Mohammed envisages, to give the "two atoms joined together", that entity could not meaningfully be identified as salt as many of the properties of salts emerge from the ionic lattice of myriad ions.
[If sodium-chloride ion pairs could be formed then we might consider these as the component quanticles of a form of sodium chloride, but this would need to be considered a different allotrope to table salt, just as ozone molecules are not the basis of the oxygen in air that supports respiration.]
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.
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:
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).
