Former school and college science teacher, teacher educator, research supervisor, and research methods lecturer. Emeritus Professor of Science Education at the University of Cambridge.
Plants mainly respire at night because they are photosynthesising during the day
Keith S. Taber
Image by Konevi 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. She suggested that "respiration produces energy, but photosynthesis produces glucose which produces energy". (See 'How plants get their food to grow and make energy'). She told me that she respired to get energy.
How do you get your energy then?
We respire.
Is that different then [from photosynthesis]?
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.
… What about plants? Do they respire all the time?
They mainly do it at night.
Why's that?
'cause they're photosynthesising during the day, cause they need the light.
I was not clear why Mandy thought that plants should respire less when they were photosynthesising.
So why do you need to respire all the time?
'cause you're making energy and you need energy to do everything.
So are you respiring at the same rate all the time, do you think?
No.
So sometimes more than others?
Yeah.
So when might you need to respire more?
When you are doing exercise. Running around a lot.
So are there time when you do not need to respire as much?
Yeah.
So when might you not need to respire very much?
When you 're sleeping or just sitting watching tele [television].
…Do you have to respire at all during the night – you are not doing anything are you?
You need a little bit of energy.
What for?
Erm, I don't [indistinct], well I suppose it's just to keep everything, cause if you did not have energy then your heart would not beat, and you need it to keep breathing, and your heart pumping.
Mandy recognised the need for people to respire continuously, although she associated this with functioning at the organism level (breathing, blood circulation) and did not seem to be thinking about cellular level metabolism.
Why do plants need to respire? What do they use it, the energy for?
Erm, to grow, and to fix cells that are – broken.
Oh right, like repair damage?
Yeah.
So, do you think they are like us then, that they sort of sleep sometimes and don't need to respire as much, or?
Not as much, I don't know. I don't know.
Do you think a plant sleeps, a tree has a good sleep?
No.
So when do you think plants need to respire the most, or do you think they respire the same all the time?
They respire more at night, because – they do it then instead of in the day because they do photosynthesis during the day, but they still respire a little bit.
So is it difficult to try and do both at the same time?
Probably.
Or just maybe they are too busy photosynthesising to do much respiration?
Yeah, erm, I don't know.
Not sure?
No.
Mandy was not offering any specific reason why a plant should need to respire less at night (and did not seem to have previously thought about this), but simply seemed to assume that when the plant was photosynthesising a lot it would only respire "a little bit". This seemed to be an intuition rather than a considered proposition. It was almost as if she implicitly assumed that the plant would be fully occupied photosynthesising, and so would put respiration 'on the back burner'.
It seemed Mandy's understanding of the roles of photosynthesis and respiration at that point in her learning was limited by not fully seeing how energy was involved in the two processes (i.e., respiration produces energy, but photosynthesis produces glucose which produces energy), and because she was not considering the need for respiration to support ongoing basic cell functions.
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.
In scholarly circles it is sometimes said "Publish, or be dammed" (a variation on the 'Publish and be dammed" retort to blackmail), and there is no doubt that, generally, success in academia – when judged in such mundane terms as getting academic positions, keeping them, getting promoted – in large part requires academics to build up their publication list.
The value of peer review
Quality should obviously be more important than quantity, but that requires evaluations of the former. The peer review process that is used by most journals is far from perfect, but is said (like democracy) to be, despite its flaws, the best system we have. Quality journals depend upon rigorous peer review to ensure that articles published will be recognised within a field to be robust and significant. Peer review takes time. Some publishers pressure editors and reviewers to work to a short time scale – but there is always a fine balance: the review needs to be done carefully, and by experts – rather than either hastily, or by those who are not really qualified but will have a go because they want the reviewing on their c.v (resumé)
Authors are under pressure to publish, and publish quickly. (Indeed I am aware that recently university employees in one country were put under pressure to get published quickly even if that meant compromising where the work was published).
Peer review not only leads to rejection of substandard work, but also provides feedback on submitted work that could be published, suggesting improvements indicated. Such suggestions inevitably are somewhat subjective – but I think most editors would agree that generally the peer review process improves the quality of the final published article – even if it often delays the process by some months and requires authors to go back and do further work when they might have hoped to have moved on to the next article they want to write.
Ultimately peer review (when done carefully by qualified reviewers) means not only that there is quality control that rejects poor work, but that several people scrutinise published work, point out any mistakes missed by authors, and often suggest changes that will lead to work more likely to impress the readership and have lasting impact. As authors we should welcome rigorous peer review of our work – even if sometimes we do not agree with the criticisms of our precious writing.
Instant gratification – immediate publication
Since the advent of on-line publishing, it has become very easy to start a journal, and the number of journals out there has proliferated. (Read 'Challenges to academic publishing from the demand for instant open access to research'.) This makes it hard sometimes, especially for new scholars, to know which journals are of high quality. Many journal publishers are looking to get a competitive edge by speeding up processes. I know from my own role as an editor that it is now possible, sometimes, to get a paper from submission to publication in around a month – but this is still the exception and a quality journal will never look to speed up the process by deliberately selecting referees who are not thorough or avoiding author revisions that are indicated.
So I was rather surprised to get an invitation from a journal I was not familiar with, International Educational Scientific Research Journal, entitled 'Publish your paper in May issue' on 15th April. The idea that I could submit something and have it published two weeks later seemed unlikely if there was any kind of robust peer review process in place. However, the email suggested that the
"Last date for manuscript submission is 30th April, 2016 for 1st May, 2016 Issue".
Really?
Dubious impact factors
Of course it is quite possible that the 1st May issue may not appear till September (that would not be a first in journal publishing), but otherwise this seemed to shout "we publish anything, quality not an issue". This is a journal which charges fees to authors – and the homepage suggests that the cost depends on the length of the manuscript and (oddly) the number of authors. However the email also claimed an Impact factor of 3.606.
If I was a new scholar I would likely be very impressed by an impact factor of over 3, as I know many quality specialist journals in my field with much lower impact factors. However, visiting the webpage revealed that the impact factor has not be awarded by Thomson Reuters, the organisation used by most quality journals, but rather by 'SJIF'.
The impact factors used by top journals reflect how many times (on average) each of their published papers are cited in articles in the highly ranked journals over a period. I found the webpage of the SJIF and found that it evaluates journals on a wide range of criteria, such as number of papers published, language of papers, quality of graphics and many other things. Some of the criteria used are certainly relevant to journal quality – but this type of evaluation is not comparable to the impact factors that are recognised and used by the top academic publishers.
The academic publishing landscape is very diverse today. The possibility of open publishing, and the easy access to tools to publish internet journals, is to be welcomed – but makes it more difficult for scholars to know which journals are genuinely of quality. There is certainly no intrinsic value in a journal having slow processes and all authors welcome a speedy review and publication process. Ultimately, however, submit today, publish tomorrow is likely to mean ignored thereafter.
Fingerprint image by OpenClipart-Vectors from Pixabay
Dear ***** ****
Thank you for your message, asking me download a paper using the University of Cambridge library subscription, and then send you a copy of the pdf. I am sure you are aware that if I did this I would be breaching the terms of my use of the library subscription. It is unfortunate that your institution does not have a subscription to this journal (and quite incredible if as you suggest "only a person from Cambridge university can access this article….A person from any other institution cannot access this article" – I guess the journal cannot be of very high quality if no other institutions in the world subscribe to it).
As you are an academic (moreover, apparently a well renowned researcher in your field who has been awarded many distinctions nationally and internationally) you must be aware what you are asking is improper. The article is copyright material and the publisher is entitled to charge a fee for access. You are asking me (and many colleagues here) to be complicit in an act of theft. It is poor academic practice for you to make this request. I realise it must be very frustrating for you to not have ready access to an article you wish to read for your work – however, rather than composing emails to people you do not know, and asking them to undertake an underhand and improper act (which could in principle lead to them being disciplined for breaching the legal contract between library user, library and publisher), perhaps you could find a legal way to access the article:
perhaps your library could arrange an inter-library loan;
if the authors are still alive, perhaps they would send you a preprint;
if all else fails, perhaps you could raise the thirty US dollars to enable you to buy a copy of this 'really crucial' article from the publisher.
If this work is so essential for your research, you might consider if it is worth buying rather than asking someone to steal it for you.
I am sorry not to be more helpful, as I am aware many academics see copyright and licensing infringement as very minor matters, but I actually think both that legal agreements should be respected (certainly unless they represent clear violations of higher rights) and that academics, as professional authors themselves, should take intellectual property rights seriously.
Best wishes
Keith
(First published 20th January 2016 at http://people.ds.cam.ac.uk/kst24/)
Thank you for your email asking about review times.
You will appreciate that I was a little confused by your message.
You tell me that you are a "Deputy Head of Foreign Economic Legislation at the Financial Legislation Department" somewhere unspecified (apparently in Ukraine, although you use a hotmail account) and that you "have a PhD degree in Law" and you are eager to get your article (unspecified) published in "the" (unspecified) journal. So immediately I am quite confused as I am not associated with any journals in that field at all. I edit a journal in chemistry education, but that would hardly seem relevant.
Then you suggest you are "just a beginner at it". I assume 'it' here is scholarly research, or writing for publication – in which case perhaps you should be co-writing with a mentor or supervisor – and perhaps not targeting top international journals at this stage. This claim is hardly likely to recommend you to high status research journals.
Even if you were referring to the journal I edit, it is not possible to "specify the approximate time it would take to review the article". Usually authors get a first decision within a matter of weeks – but this depends on the availability of suitable reviewers, and whether the reviewers who first comment offer consistent recommendations. Nearly all articles published pass through two or more rounds of review as authors respond to initial reviewer comments, and the reviewers evaluate the revised manuscript(s). Articles certainly can sometimes be published within a month, but it may take much longer.
I am pleased to hear you have "many good ideas and ongoing projects in different fields of science… connected to further development and promotion of my scientific work and that of my colleagues" – that must be quite time consuming in view of your professional responsibilities as a lawyer. I can certainly understand that you "do not have much free time". However, even if "that is why my assistant will respond to the messages", journal editors tend to only deal with article authors, not their staff.
To be honest, it seems obvious that you do not actually have any work to submit to any journal I am involved with, and that no one undertaking serious scholarly work would send such vague undirected emails asking for this kind of information, so please forgive me if I assume some kind of scam or scheme is behind your message. Perhaps your request was innocent enough, but I wonder how many people you sent this message to? And what you hope to do with any responses?
Likely you will only get responses from journals desperate for authors looking to pay for publication regardless of article quality. As Groucho might have advised, you would not want to be published in the kind of journal that would encourage contributions in response to your kind of approach.
Best wishes
Keith
(First published on 2nd October, 2015 at http://people.ds.cam.ac.uk/kst24/)
Cause and effect?: People go to different places because of what they are wearing
Keith S. Taber
Image by anwo00 from Pixabay
Annie was a participant in the Understanding Chemical Bonding project. She was a second year 'A level' student (c.18 years of age) when she was talking to me about atoms and electrons, but I was struck with the way she used the word 'because'.
Technically this conjunction is linked with causality, something of importance in science. To say that X occurred because of Y is to claim that Y was a cause of X.
I wanted to clarify if Annie's use of 'because' in that chemical context actually implied that she was describing what she considered a cause, or whether she was using the word more loosely. To probe this I presented what I considered an obviously inappropriate use of 'because': that football fans following different teams in the same city would go to different matches BECAUSE of the colour of the clothes they wore (i.e., hats and scarves traditionally worn to show support to a particular team).
Because the sky is blue, it makes me cry
I expected Annie to point out that this was not the reason, and so 'because' should not be used – which would have then allowed me to return to her earlier use of 'because' in the context of atoms. However, Annie seemed quite happy with my supposedly 'straw-man' or 'Aunt Sally' example:
So we're talking about what you might call cause and effect, that something is caused by something else. We do a lot of talking about cause and effect in science – "this causes that to happen."
If you think about people in Liverpool, only because this is the first analogy that comes to mind, if you actually go to Liverpool on Saturday [*] and wander round, you'll probably find quite a few people wandering around wearing red, and quite a few people wandering around wearing blue, and sometime after lunch you'll find that all the people wearing red, a lot of the people wearing red, tend to move off to one particular place.[**] And the people wearing blue tend to move to a different sort of place, as though they are repelled, you know, similar colours attracted together.
Uh hm.
Agreed?
Yes.
And we could say therefore, that the reason that some people go towards the Liverpool ground, is because they're wearing red, and the reason some people go towards the Everton ground, is because they're wearing blue. Now would that be a fair description?
Yeah.
And do you agree with the sense of cause and effect there – that people go to watch Liverpool because they're wearing red hats and red scarves? And people go to look at Everton because they're wearing blue hats and blue scarves?
Yes.
So would you say the cause of which football team you go to see, the cause of that, is what clothes you happen to be wearing?
(Pause, c.4s)
Unless you're a rambler. {Laughs}…
No, no, well yes, if you're wearing, you're obviously supporting that colour, so, that team, so so you'd assume, that they were going to watch, the team they favoured.
Right, okay, erm, I'll think of a different example, I think.
Because the world is round, it turns me on
Annie did not seem to 'get' what I had thought would be an obvious flaw in the argument. Fans wear the colours of their team to show support and affiliation; and go to the place where their team is playing: but they do not go to the particular stadium because they happen to be wearing red or blue.
This is linked to the difference between causation and correlation. Often two correlated variables do not have a direct causal relationship, but have a relationship mediated by some other factor.
Height of children in a primary school will be correlated with their grade number (on average, the children in the first year are shorter than those in the second year, who are shorter than…). But children are not organised into grades according to height, and height is not caused by grade. Both are independently related to the child's age.
Colour of football scarves is correlated with destination on match day, but one does not cause the other – rather both colour choice and destination are actually due to something else: affiliation to a club. [***]
I switched to a another example I hoped would be familiar, based on a swimming pool. I though the idea that changing rooms are (usually) designated by gender would make it obvious that where people went to change on leaving the pool correlated to, but was not because of, what they were wearing. Again, however, Annie did not seem to consider it inappropriate to describe this in terms of the the different types of swimming costume causing the behaviour.
If you go to the swimming pool, and watch people swimming, you'll find out that some people when they're swimming at a swimming pool, tend to wear a swimming costume that only covers, the hips basically, and other people either a swimming costume that covers most of the trunk, or two separate parts to it. And if you observe them very closely, which is always a bit suspicious at a swimming pool, you'll notice that when they get out of the pool, they're attracted towards different rooms, these changing rooms…
But all the people who just have the one part of the costume, are attracted towards one room, and the others are attracted towards the other room, the ones with sort of either very long costumes or two part costumes. So is it fair to say that it's caused by what clothes they are wearing, that determines which room they go and get changed in?
Yes.
It is?
(Pause, c.4s)
Yes.
That's the cause of it?
(Pause, c5s)
Yeah. It's also conventional as well.
So in both cases Annie was happy to talk in terms of the clothing causing behaviour. After some further discussion Annie seemed to appreciate the distinction I was making, but even if she did not have a flawed notion of causality, it certainly appeared she have developed non-canonical ways of talking about cause and effect.
Because the wind is high, it blows my mind
Annie was a clever person, and I am sure that the issue here was primarily about use of language rather than an inability to understand causation. However, even if our thinking is not entirely verbal, the major role of verbal language in human thought means that when one does not have the language, one may not have the related explicit concepts.
It is very easy to assume that students, especially those we recognise as capable and having been academically successful, share common 'non-technical' language – but there is plenty of research that suggests that many students do not have a clear appreciation of how such terms are canonically used. These are terms we might think people generally would know, such as adjacent, efficient, maximum, initial, omit, abundant, proportion… (Johnstone & Selepeng, 2001). As always, a useful guide to the teacher is 'never assume'.
* At the time of the interview, it was general practice for most English football league matches to be played at 15.00 on a Saturday.
** One constraint on the scheduling of football matches is that, as far as possible, two local rival ('paired') teams should not play home matches on the same day, to avoid potential clashes between large crowds of rival fans. However, such 'paired clashes', as they are technically called (Kendall et al., 2013), are not always avoided.
*** Of course, this is not a direct cause. A person could support one team, yet choose to wear the colours of another for some reason, but their support for a team usually motivates the choice. Social patterns are messier than natural laws.
Sources cited:
Johnstone, A. H., & Selepeng, D. (2001). A language problem revisited. Chemistry Education: Research & Practice in Europe, 2(1), 19-29.
Kendall G., McCollum B., Cruz F.R.B., McMullan P., While L. (2013) Scheduling English Football Fixtures: Consideration of Two Conflicting Objectives. In: Talbi EG. (eds) Hybrid Metaheuristics. Studies in Computational Intelligence, vol 434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30671-6_14
And a voice in the wilderness was heard calling out upon the racing wind: our Psychology conference offers publication and an unformed fear!
Keith S. Taber
This week's* most bizarre invitation is to submit a proposal to a Psychology conference:
"The aim objective of CPSY 2016 is to provide a platform for researchers, engineers, academicians as well as industrial professionals from all over the world to present their research results and development activities in Psychology. Submitted conference papers will be reviewed by technical committees of the Conference."
Well that all sounds pretty standard. But then the next paragraph begins:
"Before her eyes as she gazed a smooth plain of snow spread out in the distance. The wind, carrying white, shaggy masses, raced over the plain, piping cold, shrill whistles."
I'm not sure they are really selling the location (in Shanghai, China) as an ideal place for a conference. The paragraph continued….
"Across the snowy expanse moved a girl's figure, dark and solitary, rocking to and fro. The wind fluttered her dress, clogged her footsteps, and drove pricking snowflakes into her face. Walking was difficult; the little feet sank into the snow. Cold and fearful the girl bent forward, like a blade of grass, the sport of the wanton wind. To the right of her on the marsh stood the dark wall of the forest; the bare birches and aspens quivered and rustled with a mournful cry. Yonder in the distance, before her, the lights of the city glimmered dimly."
Perhaps the airport is some way outside the City?
Perhaps the lights 'glimmered dimly' due to air pollution – I've supervised a student from China who told me it can get pretty bad there.
The next paragraph tells me that the conference proceedings will be published by "by DEStech Publications" and will be indexed, for example in Google Scholar. Then I am told:
"'Lord in heaven, have mercy!' the mother muttered again, shuddering with the cold and horror of an unformed fear."
It seems papers are invited in areas including educational psychology and the psychology of learning, so although I am not a psychologist, I can see there might be presentations of interest. But it does sound a bit chilly there, and I think I probably already have enough unformed fears without travelling half way around the world to develop some more.
Perhaps they just wanted to get my attention.
Perhaps it's an experiment with different recipients randomly split into groups getting different messages in their invitations, to see if there is differential uptake?
Perhaps the person who prepared the copy did not have the high level of English skills they claimed when they applied for the job?
Or they had just learnt to 'cut and paste'?
Or perhaps this was prepared on someone's last day in post, and they had not enjoyed their employment there?
If anyone reading this is going to the '2016 International Conference on Psychology' next June, perhaps you'd be kind enough to drop me a line if you find out what that was all about!
* First published 9th September 2015 (at http://people.ds.cam.ac.uk/kst24/) – but I'd still be interested to hear from anyone who went to the conference!
You have to learn it at a greater depth and a more detailed level in order to be able to teach it
Keith S. Taber
I have listened to a lot of Professor Jim Al-Khalili's interviews with scientists for the BBC's 'The Life Scientific' programme.
I enjoy hearing about the science and the scientific lives, but Professor Al-Khalili's recent interview with Professor Alice Roberts particularly struck me in terms of her comments on teaching.
[Note: the material discussed in this posting is copyright of third parties, i.e., the BBC (the broadcast and website) and the scientists (the text produced in the interview). It is used here with acknowledgement for purposes of critique and review.]
I have made a rough transcription of that part of the conversation, below, starting at about 6' 24" into the podcast 'Alice Roberts on Bones', which is freely available on the BBC website – and the whole programme is highly recommended.
I found myself nodding along to Prof. Robert's comments about teaching.
There has been much talk in education of pedagogic knowledge being important alongside subject knowledge (one needs to now how to teach as well as what to teach), which is clearly so. Perhaps it is less recognised, however, that a specialist teacher's subject knowledge, whilst clearly different from that of a cutting edge researcher in the subject, is also a form of specialised expertise – 'subject knowledge for teaching' is subject matter extensively infused with pedagogic expertise.
Teachers are specialist experts
I would argue that an experienced school teacher's subject knowledge will often be more advanced in some areas than an academic/researcher in the same discipline.
The researcher has very detailed and advanced knowledge in their specialist area, but the teacher will have been repeatedly revisiting the 'foundation bricks' (in Prof. Robert's terms) in the light of students' varied learning difficulties and (sometimes highly creative) questions. The 'building a wall' metaphor, a wall that needs sound foundations, reflects a constructivist perspective on learning that has been widely adopted in science education.
A lust for learning
Prof. Roberts has the healthy attitude that the teacher never knows everything, without being complacent. Being challenged ("I really love that") is an opportunity to spot the limitations in your own knowledge, and to do something about it – to "advance your own understanding". The good teacher never stops learning, and seeks to understand better, and so sets an example to her students of valuing life-long learning .
Did teaching anatomy [at the University of Bristol] enhance your understanding of the subject?
Oh my goodness, yeah, I mean I think it's the same with teaching anything, isn't it?
Mm.
Er, you, you have to learn it at a greater depth and a more detailed level in order to be able to teach it.
And, also, I think as soon as you start teaching, you, you realise where the gaps in your own understanding are. You start probing how well you know a subject, and you think 'oh actually, I thought I know that, and I didn't', and you, and you start to go back to kind of foundation levels.
I always think of it as a wall that you are building up and you get to a certain level of knowledge and then you think 'oh I had better just go and test those bricks at the bottom and make sure they are secure as I though they were',
Yeah {laughing}
and you inevitably find little chinks and you think 'oh I am going to have to work a bit harder than that', > but then > > {laughing} >
<The worst thing is < for me,< you know <, when, teaching, and then, a student, after teaching a course for many years will say 'actually that's not quite right', or 'how can you explain that?' and I'll realise, you know, generations of students, I've been giving them some wrong information, somewhere, and sent them out into the world. Very embarrassing. > Hasn't happened very often >.
< But, I – < But, I really love that. I, you know, when you go, when someone asks you a question and you go 'oh hang on a minute, I think I should know the answer to that'.
I mean some questions you go, 'I'm never going to know the answer to that, but I will go and find out', or you can send your students to go away and find out.
But sometimes you do get asked questions where you think 'actually, I, I would have thought I knew the answer to that, and I don't'.
Yeah, it's never occurred to me.
And so it helps you advance your own understanding. I really appreciate that.
I found a very kind invitation from an organisation calling itself "Peak Performance International" in my email Inbox this morning * ('Parents Workshop on 12th September 2015')), inviting me to a 'free' 2 hour workshop (in Nairobi) – free as long as I booked before a certain date.
The organisation claims to be run by two parents who had been concerned at their daughter's lack of progress at school and so (as one does) had travelled to various countries including "the US, Singapore, Indonesia, Malaysia" to learn about programmes of "Accelerated Learning and Brain Development". They claim that what they found was "mind blowing":
We saw children who would flip through a 200 page book of completely new material, at high speed for just a few minutes and then give an accurate account of what the book was about. Others would mentally calculate long mathematical equations and give the correct answers instantly while Professors took so long and still [did] not get the correct answer.
During our tour we attended several trainings. I learnt more about the brain than I had ever done in my whole life. I understood how easy it was to assist children tap into their genius realm and experience quantum leaps in IQ and EQ (Emotional Intelligence) by synchronizing the two brain hemispheres.
It seems Peak Performance International are now keen to share their findings with other parents, thus the invitation to their workshop. How I would have liked to think this is a genuine (even if misguided) and kind gesture. There may be the odd savant who can complete complex calculations faster than professors – but I doubt there is much that can be learnt from those to advise others. As for such extreme speed reading and retention of information: this can be understood two ways. It is either just a complete fabrication (the human brain works slowly with 'completely new material' which has to be understood in terms of familiar material, and engaged with through modest learning quanta) – or is trivial. Any good reader could actually 'flip through a 200 page book of completely new material, at high speed for just a few minutes and then give an accurate account of what the book was about' – by focusing on the blurb or an introduction. However, there would be very little knowledge of the book's detailed contents.
I am not sure whether I should be upset or pleased about this invitation. It is always annoying that some people want to cheat, mislead and swindle others. Often the widows of dictators, dying philanthropists, senior bankers or lawyers, or american military personnel seem to have a problem moving vast amounts of money out of some national jurisdiction and offer to make me rich if I help them. They clearly feel I am especially deserving or suitably skilled to undertake such projects. It is hard to have too much sympathy for anyone who is so stupid and greedy that they respond to such approaches.
Here, however, the scammers are playing upon parents who do not want to get rich quick, but just want to help their children learn more effectively and do better in school. I wonder how much money they will be asked to part with to share in the Peak Performance Programme with its surely fraudulent claims? Shame on the scammers. The only positive aspect of this sorry tale is that people consider education and learning important enough for scammers to think they can make a 'fast buck' out of the selling the pedagogic equivalent of snake oil. Perhaps this is not so different form the companies in countries like the UK where so much of professional development in the education sector has become commercialised, with 'providers' selling programmes in 'learning styles' which often have very little evidential support. (There is good research into some models of learning styles – but where popular ideas like VAK work this is likely either placebo, or the focus on multi-model teaching, rather than the underlying model which is more a distortion of multiple intelligence theory than based on the research on student learning styles.)
When I first saw the email I seriously wondered if this was a genuine but misguided or exaggerated attempt to apply genuinely effective learning/study techniques. I was persuaded otherwise by a link in the email that directed me to "one of our students". Actually this was a 'youtube' video of a young boy on a television programme who allegedly could read whilst blindfolded. He struggled to read an autocue whilst blindfolded – although to be fair he struggled equally to read the same autocue before the blindfold was put on. Looking at the video, and in particular how the boy angled his head, I very much suspect he was looking through the fabric of the black eyeshades (in the section of the programme I watched it did not seem to have occurred to the presenter to provide his own blindfold). Even if this was a genuine sensory skill and not the trick it seemed to be, it appeared to have nothing to do with "Accelerated Learning and Brain Development" or Peak Performance International.
Does our whole system of physics forbid us from believing someone has been on the moon?
Keith S. Taber
Image by WikiImages from Pixabay (with Emoji superimposed)
I never had the chance to interview Ludwig for my research, but was intrigued when I found out about his outright dismissal of the possibility of manned missions to the moon.
There are of course people who are strongly committed to ideas at odds with current scientific consensus – suggesting the earth is flat; that evolution does not occur; that COVID-19 was deliberately produced in a laboratory; that governments have physical evidence of alien visitors, but deny it and keep all relevant documentation classified; and so forth.
Moon landing deniers
Even in the United States of America, the home of the Apollo missions, surveys regularly show that a substantial minority of people doubt that people ever actually went to the moon, and think the Apollo moon landings were faked. Why would NASA have gone to such trouble with the collusion of the US Government machinery and the support of Hollywood studios?
As President Kennedy had put such weight on (American) people getting to the moon before the end of the 1960s, then – the argument goes – once it became clear this was technically impossible, it became important to convince the population that JFK's challenge had been met by a massive initiative to forge and disseminate evidence. There has been something of an industry in explaining how the photographs released by NASA can be seen to have been clearly faked if one looks carefully enough and knows a little science.
Unreasonable doubt?
I try to be someone who is always somewhat sceptical (as any scientist should be) of any claims, no matter how widely believed, as in time some canonical ideas are found to be flawed – even in science. But I tend to give little credence to such conspiracy theories.
Sometimes there are good reasons why science is doubted by sections of the public when it seems to conflict with well established world-view beliefs deriving from religious traditions or traditional ecological knowledge which has sustained a culture for a great many generations. So, even when the science is well supported, we can sometimes understand why some people find it difficult to accept. But the Apollo missions being faked in a film studio: surely that is just the kind of nonsense that only ignorant cranks like to believe – isn't it?
Ludwig on the sure belief that no one has been to the moon
Thus my interest in Ludwig, who was certainly not an ignorant person. Indeed he was highly intelligent, and something of an intellectual – a deep thinker who was very interested in the nature of knowledge and considered issues of how we could ground our beliefs, given that the evidence was never sufficient to be absolutely sure.
He thought that individual ideas were convincing when they were embedded in a 'nest' of related ideas – what we might call a conceptual framework. One example he discussed was his accepting that people always had parents: he thought this "sure belief" was based "not only on the fact that I have known the parents of certain people but on everything that I have learnt about the sexual life of human beings and their anatomy and physiology: also on what I have heard and seen of animals". Ludwig thought that although this could not be considered definite proof, it was robust grounds for someone to accept the belief.
Another example of such a sure belief was that a person could be confident that they had never been on the moon,
A principal ground for [a person] to assume that he was never on the moon is that no one ever was on the moon or could come [i.e., get] there; and this we believe on grounds of what we learn.
¶171
Physics forbids moon landings
Ludwig seemed to consider the impossibility of people getting to be on the moon was something he could be pretty sure of,
"But is there no objective truth? Isn't it true, or false, that someone has been on the moon?" If we are thinking within our system, then it is certain that no one has ever been on the moon. Not merely is nothing of the sort ever seriously reported to us by reasonable people, but our whole system of physics forbids us to believe it. For this demands answers to the questions "How did he overcome the force of gravity?" "How could he live without an atmosphere?" and a thousand others which could not be answered…
The intellectual status of unreasonable people
So someone making such a claim would not be a 'reasonable' person in Ludwig's evaluation. So how would Ludwig feel about such an unreasonable person?
We should feel ourselves intellectually very distant from someone who said this.
¶108
But of course there are people who claim this has indeed happened, that we have been to the moon,and walked there and whilst there collected rocks and indeed played golf. (Had this been more recent, we would perhaps instead have danced the tango and baked cakes.) NASA astronauts have since often acted as ambassadors for space science, and told their stories across the world, including to the young – enthusing many of them about space and science.
How might Ludwig respond to a child who had met one of those Apollo astronauts who claimed to have walked on the moon?
Suppose some adult had told a child that he had been on the moon. The child tells me the story, and I say it was only a joke, the man hadn't been on the moon, no one has ever been on the moon, the moon is a long way off and it is impossible to climb up there or fly there.
Ludwig adds, rhetorically,
If now the child insists, saying perhaps there is a way of getting there which I don't know, etc. what reply could I make to him?
¶106
Believers in moon landings are ignorant and wrong
So how could Ludwig explain that there are many people, indeed a majority today, who do believe that people have visited the moon, and returned to earth to tell others about the experience?
What we believe depends on what we learn. We all believe that it isn't possible to get to the moon; but there might be people who believe that that is possible and that it sometimes happens. We say: these people do not know a lot that we know. And, let them be never so sure of their belief-they are wrong and we know it.
If we compare our system of knowledge with theirs then theirs is evidently the poorer one by far.
¶286
So, just as I might suspect the moonshot deniers are somewhat ignorant, for Ludwig it is the reverse: it is those who think people can get to the moon who have poor knowledge systems and are simply wrong.
Now I suggested above that Ludwig was an intelligent and reflective person – indeed he worked as a school teacher, both in primary and secondary education – so his views may seem incongruent. As some readers may have suspected, I am being a little unfair to Ludwig. I pointed out at the outset that I never had the chance to interview Ludwig – indeed I never met him, although he did spend part of his life in Cambridge where I now work.
We can all be wrong
Ludwig did not live to see the moon landings, as he died in 1951 almost a decade before I was born (of parents – he was right about that), shortly after he wrote the material that I have quoted above. That is a few years before Sputnik was launched by the Soviet Union and the 'space race' began. So, Ludwig was not a denier of the moon landings as such, refusing to accept the media accounts, but rather a denier of the possibility of there ever being moon landings at a time when no one was yet actively planning the feat.
Ludwig was wrong. But had he lived another 20 years I am pretty sure he would have changed his mind. That's because one of the things he was best known for was changing his mind.
Having written a highly influential book of philosophy that convinced many intellectuals he was one of the greatest thinkers of his time, if not all time (the Tractatus Logico-Philosophicus) he took a long sabbatical from Academia, only to later write an equally influential and profound book (that he did not live to see published – the Philosophical Investigations) that contradicted his earlier ideas. Had Ludwig seen the technological developments of the 'space race' in the 1960s, it seems certain – well, a sure belief – that he would have accepted the possibility of people going to the moon.
However, when I first read the comments I quote above I was struck by how such a highly intelligent and deep thinker could be so sure that getting people to the moon was not possible that he actually chose to use the idea of people on the moon as an exemplar of something that was impossible ("it is certain that no one has ever been on the moon"), and indeed contrary to the laws of physics.
Presumably at the time he was writing he could assume most intelligent people would fully accept his position (as "we all believe that it isn't possible to get to the moon") and see the suggestion of people going to the moon as absurd enough to stand as an example of an idea that could not be accepted by us reasonable people, only by someone "intellectually very distant" from us.
However, barely a decade later JFK was convinced enough of the possibility of getting people safely to the moon and back to commit his nation to achieving it – and a decade after that men being on the moon was already ceasing to be seen as anything out of the ordinary (until the near disaster of the Apollo 13 mission got the flights back into the popular imagination).
I do not present this example to ridicule Ludwig Wittgenstein. Far from it. But it does make me reflect on those things that we think we can treat as 'sure beliefs'. Even the most intelligent and reflective of us can be very wrong about things we may treat as certain knowledge. That's always worth keeping in mind.
Nothing is absolutely certain, except, perhaps, uncertainty itself!
All citations are from ¶ in Wittgenstein, L. (1975). On Certainty (D. Paul & G. E. M. Anscombe, Trans. G. E. M. Anscombe & G. H. v. Wright Eds. Corrected 1st ed.). Malden, Massachusetts: Blackwell Publishing.
The higher resistance is when there is less current flowing around the circuit when you have the same voltage – but how does that relate to the formula?
There were two apparent alternative conceptions there. One was that 'Resistance is current over voltage', but as Adrian believed that he was not good at remembering formulae, this would be a conception to which he did not have a high level of commitment. Indeed, on another occasion perhaps he would have offered a different relationship between R, I, and V. I felt that if Adrian had a decent feel for the concepts of electrical resistance, current and voltage then he should be able to appreciate that 'resistance is current over voltage' did not reflect the correct relationship. Adrian was not confident about formulae, but with some suitable leading questioning he might be able to think this through. I describe my attempts to offer this 'scaffolding' below.
The other alternative conception was to conflate two things that were conceptually different: the defining equation for resistance (that R=V/I, by definition so must be true) and Ohm's law that suggests for certain materials under certain conditions, V/I will be found to be constant (that is an empirical relationship that is only true in certain cases). (This is discussed in another post: When is V=IR the formula for Ohm’s law?)
So, I then proceeded to ask Adrian how he would explain resistance to a younger person, and he suggested that resistance is how much something is being slowed down or is stopped going round. After we had talked about that for a while, I brought the discussion back to the formula and the relationship between R, V and I.
Linking qualitative understanding of relating concepts and the mathematical formula
As Adrian considered resistance as slowing down or stopping current I thought he might be able to rationalise how a higher resistance would lead to less current for a particular potential difference ('voltage').
Okay. Let’s say we had, erm, two circuits, and they both have resistance and you wanted to get one amp of current to flow through the circuits, and you had a variable power supply.
Okay.
And the first circuit in order to get one (amp) of current to flow through the circuit.
Yes.
You have to adjust the power supply, until you had 10 volts.
Okay.
So it took 10 volts to get one amp to flow through the circuit. And the second (unclear) the circuit, when you got up to 10 volts, (there is) still a lot less than one amp flowing. You can turn it up to 25 volts, and only when it got to 25 volts did you get one amp to flow through the circuit.
Yes, okay.
In mathematical terms, the resistance of the first circuit is (R = V/I = 10/1 =) 10Ω, and the second is (25/1 =) 25Ω, so the second – the one that requires greater potential difference to drive the same current, has more resistance.
Do you think those two circuits would have resistance?
Erm, (pause, three seconds) Probably yeah.
This was not very convincing, as it should have been clear that as an infinite current was not produced there must be some resistance. However, I continued:
Same resistance?
No because they are not the same circuit, but – it would depend what components you had in your circuit, if you had different resistors in your circuit.
Yeah, I've got different resistors in these two circuits.
Then yes each would have a different resistance.
Can you tell me which one had the bigger resistance? Or can’t you tell me?
No, I can’t do that.
You can’t do it?
No I don’t think so. No.
Adrian's first response, that the circuits would 'probably' have resistance, seemed a little lacking in conviction. His subsequent responses suggested that although he knew there was a formula he did not seem to recognise that if different p.d.s were required to give the same current, this must suggest there was different resistance. Rather he argued from a common sense position that different circuits would be likely to have different components which would lead to them having different resistances. This was a weaker argument, as in principle two different circuits could have the same resistance.
We might say Adrian was applying a reasonable heuristic principle: a rule of thumb to use when definite information was not available: if two circuits have different components, then they likely they have different resistance. But this was not a definitive argument. Here, then, Adrian seemed to be applying general practical knowledge of circuits, but he was not displaying a qualitative feel for what resistance in a circuit was about in term of p.d. and current.
I shifted my approach from discussing different voltages needed to produce the same current, to asking about circuits where the same potential difference would lead to different current flowing:
Okay, let me, let me think of doing it a different way. For the same two circuits, erm, but you got one let's say for example it’s got 10 volts across it to get an amp to flow.
Yeah. So yes okay so the power supply is 10 volts.
Yeah. And the other one also set on 10 volts,
Okay.
but we don’t get an amp flow, we only get about point 4 [0.4] of an amp, something like that, to flow.
Yeah, yeah.
Any idea which has got the high resistance now?
The second would have the higher resistance.
Why do you say that?
Because less erm – There’s less current amps flowing around the circuit erm when you have the same voltage being put into each circuit.
Okay?
Yes.
This time Adrian adopted the kind of logic one would hope a physics student would apply. It was possible that this outcome was less about the different format of the two questions, and simply that Adrian had had time to adjust to thinking about how resistance might be linked to current and voltage. [It is also possible too much information was packed close together in the first attempt, challenging Adrian's working memory capacity, whereas the second attempt fed the information in a way Adrian could better manage.]
You seem pretty sure about that, does that make sense to you?
Yes, it makes sense when you put it like that.
Right, but when I had it the other way, the same current through both, and one required 10 volts and one required 25 volts to get the same current.
Yes.
You did not seem to be too convinced about that way of looking at it.
No. I suppose I have just thought about it more.
Having made progress with the fixed p.d. example, I set Adrian another with constant current:
Yes. So if I get you a different example like that then…let’s say we have two different circuits and they both had a tenth of an amp flowing,
Okay. Yes.
and one of them had 1.5 volt power supply
Okay yes.
and the other one had a two volt power supply
Yeah.
but they have both got point one [0.1] of an amp flowing. Which one has got the high resistance?
Currents the same, I would say they have got different voltages, yeah, so erm (pause, c.6s) probably the (pause, c.2s) the second one. Yeah.
Because?
Because there is more voltage being put in, if you like, to the circuit, and you are getting less current flowing in and therefore resistance must be more to stop the rest of that.
Yes?
I think so, yes.
Does that make sense to you?
Yeah.
So this time, having successfully thought through a constant p.d. example, Adrian successfully worked out that a circuit that needed more p.d. to drive a certain level of current had greater resistance (here 2.0/0.1 = 20Ω) than one that needed a smaller p.d. (i.e. 1.5/0.1 = 15Ω). However, his language revealed a lack of fluency in using the concepts of electricity. He referred to voltage being "put in" to the circuits rather than across them. Perhaps more significantly he referred to their being "less current flowing in" where there was the same current in both hypothetical circuits. It would have been more appropriate to think of there being proportionally less current. He also referred to the greater resistance stopping "the rest" of the current, which seemed to reflect his earlier suggestion that resistance is how much something is being slowed down or is stopped going round.
My purpose in offering Adrian hypothetical examples, each a little 'thought experiment', was to see if they allowed him to reconstruct the formula he could not confidently recall. As he had now established that
greater p.d. is needed when resistance is higher (for a fixed current)
and that
less current flows when resistance is higher (for a fixed p.d.)
he might (perhaps should) have been able to recognise that his suggestion that "resistance is current over, voltage" was inconsistent with these relationships.
Okay and how does that relate to the formula you were just telling me before?
Erm, No idea.
No idea?
Erm (pause, c.2s) once you know the resistance of a circuit you can work out, or once you know any of the, two of the components you can work out, the other one, so.
Yeah, providing you know the equation, when you know which way round the equation is.
Yes providing you can remember the equation.
So can you relate the equation to the explanations you have just given me about which would have the higher resistance?
So if something has got a higher resistance, so (pause, c.2s) so the current flowing round it would be – the resistance times the voltage (pause, c.2s) Is that right? No?
Erm, so the current is resistance time voltage? Are you sure?
No.
So Adrian suggested the formula was "the current flowing round it would be the resistance times the voltage", i.e., I = R × V (rather than I = V /R ), which did not reflect the qualitative relationships he had been telling me about. I had one more attempt at leading him through the logic that might have allowed him to deduce the general form of the formula.
Go back to thinking in terms of resistance.
Okay.
So you reckoned you can work out the resistance in terms of the current and the voltage?
Yes, I think.
Okay, now if we keep, if we keep the voltage the same and we get different currents,
Yes.
Which has, Which has got the higher resistance, the one with more current or the one with less current?
Erm (Pause, c.6s) So, so, if they keep the same voltage.
That’s the way we liked it the first time so.
Okay.
Let’s say we have got the same voltage across two circuits.
Yes.
Different amounts of current.
Yes.
Which one’s got the higher resistance? The one with more current or the one with less current?
The one with less current.
So less current means it must be more resistance?
Yes.
Ok, so if we had to have an equation R=.
Yes.
What’s it going to be, do you think?
Erm
(pause, c.7s)
R=
(pause, c.3s)
I don’t know. It's too hard.
Whether it really was too hard for Adrian, or simply something he lacked confidence to do, or something he found too difficult being put 'on the spot' in an interview, is difficult to say. However it seems fair to suggest that the kind of shift between qualitative relationships and algebraic representation – that is ubiquitous in studying physics at this level – did not come readily to this advanced level physics student.
I had expected my use of leading (Socratic) questioning would provide a 'scaffold' to help Adrian appreciate he had misremembered "resistance is current over, voltage, I think", and was somewhat disappointed that I had failed.
"Resistance is how much something is being slowed down or is stopped going round"
Adrian was a participant in the Understanding Science Project. When I interviewed him in Y12 when he was studying Advanced level physics he told me that "We have looked at resistance and conductance and the formulas that go with them". However, when asked about the formula, he suggested, without conviction, that "resistance is current over voltage". So, I asked him how he might go about explaining resistance to a younger student:
We will come back to the formula in a minute then, so let us say you had a younger brother or sister who hasn’t done much physics.
Yes.
And doesn’t do, doesn’t like maths, doesn’t like formulas.
Okay.
So what does it mean though? Why is it important? What’s resistance about?
Erm – I would say it was how much something is being slowed down, or erm how much it is being stopped going round. If it is in electric¬… electricity then it is in a circuit. If it’s in like the wide open range of things it's like erm how resistant is something if you push it? How much force does it give back?
So Adrian was aware of electrical resistance, and also aware of resistance in the context of mechanics.
Oh I see, so, erm if I asked you to push that table over there
Yes.
There might be resistance to that?
Yes.
And that’s different to if we were talking about meters and wires and things?
Yes.
Are they similar in some way?
They have got the same name. {laughs}
Got the same name, okay.
They probably are similar. I've never really thought about it.
So although Adrian associated electrical resistance with 'resistance' in mechanical situations, the similarity between the two types of resistance seemed primarily due to the use of the same linguistic label. This was despite him describing the two forms of resistance in similar terms – "how much something is being slowed down… how much it is being stopped going round" cf. "how resistant is something if you push it".
To a physicist, a property such as resistance should be defined precisely, and therefore preferably mathematically – and so operationally in the sense that there is no ambiguity in how it would be measured. However when students are learning, definitions and formulae may be abstract and have little meaning or connection to experience, so qualitative understanding is important. Students' initial suggestions of what technical terms mean when they first learn about them may be vague and flawed, but if this is linked to a feeling for the concept this may ultimately be a better starting point than a formula which cannot be interpreted meaningfully – as seemed to be the case with Adrian.
Arguably, understanding a relationship in qualitative terms can support later formalising the relationship in mathematical terms, whereas trying to learn a formulae by rote may lead to misremembering and algorithmic application (and so, for example, not noticing when non-feasible results are calculated).
Adrian's suggestion that resistance might be"how resistant is something if you push it? How much force does it give back?" presumably linked to his own experiences of pushing and pulling objects around. However, it seemed to confuse notions of inertia and reaction force (as well as possibly frictional forces). If Adrian were to push with a force of 100N on the wall of a building, a puck on an ice rink, or on a sledge on gravel the reaction force would be 100N in each case (cf. Newton's third law) – although the subjective experience of resistance would be very different in the different situations – as would the outcome on the object pushed.
In these situations it may be difficult for a teacher to know if a vague or confused description reflects conceptual confusion (and/)or limited expression. Yet, students need time and opportunities to be able to explore concepts in their own terms to link the abstract scientific ideas with the 'spontaneous conceptions' they have developed based on their own experiences of acting in the world.
The teacher should offer feedback, and model clear language, but needs to recognise that understanding abstract scientific ideas takes time. After all, Aristotle would be considered to have alternative conceptions of mechanics by comparison with today's science, but Aristotle was clearly highly intelligent and gave the matter a lot of thought!
After this there was extended discussion on the way resistance related to current and voltage, following Arian's comment that resistance is current over voltage. As part of this he was asked about ⚗︎ an example where different voltages were needed in different circuits to allow the same current to flow. ⚗︎ He suggested that the circuit with the higher resistance would be the one where "there is more voltage being put in, if you like, to the circuit, and you are getting less current flowing in, and therefore resistance must be more to stop the rest of that".
Adrian's way of talking about the current in the circuits did not seem to reflect a view of current as driven by a given p.d. across a circuit and limited by a certain resistance, but almost as a fixed potential flow, some of which would be permitted to pass, but some of which would be stopped by the resistance ("how much it is being stopped going round", "resistance … to stop the rest of that"). Yet, as suggested above, it can take time, and opportunities for exploration and discussion, for students' concepts and ways of talking about them to mature towards canonical science.
That Adrian could talk of "more voltage…less current…therefore resistance must be more" seemed promising, although ⚗︎ Adrian could not relate his qualitative description to the mathematical representation of the formula. ⚗︎
