Unseen minerals all around us (Ockham's Razor – ABC)
I was listening to a recent episode of 'Ockhams' razor' (ABC's series of short science and technology essays) from 2020 called 'Unseen minerals all around us'. As a radio programme, the audience was likely to be diverse in terms of age, interests, and background knowledge and experiences.
The speaker was Allison Britt, Director of Mineral Resources Advice and Promotion, Geoscience Australia ("Australia's pre-eminent public sector geoscience organisation"), and she was describing the large number of elements used in constructing a modern mobile phone – apparently someone had put a phone in a laboratory blender and analysed the smoothie produced! (Please note: that is not a safe activity for a home science practical.)
Allison Britt, Director of Mineral Resources Advice & Promotion, Geoscience Australia – at a live recording of 'Okham's razor'. (Source: Twitter)
As a science teacher (well, retired – but once a science teacher, always a science teacher at heart at least) I tend to be primed to focus on the ways in which teachers and scientists 'make the unfamiliar familiar', and Britt used an analogy with multiple targets.
The source domain was something familiar from everyday life – seasoning food.
I thought this worked really well, although as a purist (and, as noted here before, something of a pedant) I would have liked the third of her comparisons to refer to a difference that was a matter of degree (e.g., 'taste better' cf. 'work more efficiently'). That said, Britt's formulation worked better as scientific poetry:
So, just like adding salt and pepper to a meal makes it taste better:
putting a little rhenium in a jet engine makes it burn faster and hotter;
putting a little scandium in an aeroplane makes it lighter and stronger;
and putting a little indium in your mobile phone makes the touchscreen work.
Britt, 2021
This was an example of a science communicator making the point of how adding a small, sometimes trace, quantity of a substance can make a substantive difference to properties. I imagine that virtually everyone listening to this would have effortlessly understood the comparison – a key criterion for an effective teaching analogy.
I am writing this open letter to the Institute of Physics and the Royal Society of Chemistry to request that as Learned Societies with some influence with government (perhaps limited, but certainly vastly more than an academic) the Societies might ask the Department for Education to correct two basic errors of science in the National Curriculum for England which is set out as the basis for teaching school age learerns and for developing public examinations specifications and papers.
The two errors relate to (a) the misuse of scientific terminology (the word substance) and (b) a failure of logic (in a reference to conservation of energy).
As you will no doubt be aware, the original published version of this iteration of the programmes of study for science in the English National Curriculum included some basic errors (incorrect physics formulae) that received wide publicity and which were quickly amended. Despite some other issues also getting early attention, these other problems have never been addressed. One more complex issue that I strongly feel deserves addressing, but which would would require considerable redrafting, is the confused and incoherent treatment of the nature of chemical reactions across the secondary phase (Key Stages 3 and 4).
I have raised these issues at various times, and have published a scholarly analysis of these problems .Whilst I obviously did not expect an article in an academic journal to directly impact policy, I thought this could be a 'springboard' to then approach government. I have contacted the relevant ministers (the Rt Hon Gavin Williamson CBE MP, Secretary of State for Education and the Rt Hon Nick Gibb MP, Minister of State for School Standards), and in response to instructions to refer this issue to the Department for Education website, I did so. My comments have been noted, but I was informed
"there are no current plans to review the curriculum".
Whilst I accept that any detailed re-working of the curriculum is not imminent, I do think the Department could still instigate minor corrections to errors which are published on the government's website, and then consequently repeated by the examination authorities, the examination boards and even individual school websites. Correcting these (surely, embarrassing) errors would require very little effort.
The first error I refer to is the incorrect use of the term 'substance'. In science, the term substance has a fairly specific meaning. Although, as with many science concepts, there may be some discussion over precise definitions and demarcations, there is general agreement at the level at which the term would be used in introductory science at school level. In the primary stages of the English National Curriculum for Science we read that Y5 learners should be
"taught to…explain that some changes result in the formation of new materials [sic], and that this kind of change is not usually reversible, including changes associated with burning and the action of acid on bicarbonate of soda".
A better term here would be 'substances', not 'materials' (although this is more a mater of the wording being imprecise than incorrect). However in relation to Y4 learners there is a reference to
"exploring the effect of temperature on substances [sic] such as chocolate, butter, cream"
none of which are substances as the word is used in science.This is a misuse of the term 'substance'. So whereas in secondary school, learners are taught to distinguish the meanings of 'material' and the more specific 'substance', it seems these terms are being used interchangeably in the National Curriculum specification itself.
The other issue relates to the statement (in the Key Stage 4 specification) that
"energy is conserved in chemical reactions so can therefore be neither created nor destroyed".
To my reading this suggests a blatant error of logic, which I can only assume does not reflect scientific ignorance by the person drafting the document – but more likely is a typographic error that has never been corrected.
Conservation of energy is a general (universal) principle, and its more specific application to chemical reactions as one class of changes is then subsumed under that principle. I have long assumed that what had been intended (but mistyped) was either "energy is conserved in chemical reactions BECAUSE it can be neither created nor destroyed" or "energy CAN be neither created nor destroyed SO THEREFORE is conserved in chemical reactions" – that is, the logic has been completely reversed in the curriculum document.
I have recently realised that there is a third possibility: that this statement is not meant as an explanation (of energy conservation in reactions under a more general principle) but as a definition, along the lines "energy is conserved in chemical reactions WHICH MEANS THAT IT CAN be neither created nor destroyed".
Whatever was meant, the current wording implies a logical non sequitur, and should, surely, be corrected.
I would hope you might agree that these kinds of errors should not be included in what teachers are asked to teach, students to learn, and examining boards to assess; and that when a suitable opportunity arrises you might make appropriate representations regarding the desirability of corrections being made.
Your sincerely,
Dr Keith S.Taber
Emeritus Professor of Science Education
(I have had constructive replies from both the RSC and IoP)
Dampening down COVID? (Image by Iván Tamás from Pixabay)
Analogy in science
Analogy is a common technique used in science and science education. In scientific work analogy may be used as a thinking tool useful for generating hypotheses to explore – "what if X is like Y, then that might mean…". That is, we think we understand system Y, so, if for a moment we imagine that system X may be similar, then by analogy that would mean (for example) that A may be the cause of B, or that if we increase C then we might expect D to decrease… Suggesting analogies has been used as a way of introducing a creative activity into school science (Taber, 2016).
Scientists also sometimes use analogies to explain their ideas and results to other scientists. However, analogies are especially useful in explaining abstract ideas to non-experts, so they are used in the public communication of science by comparing technical topics with more familiar, everyday ('lifeworld') phenomena. In the same way, teachers use analogies as one technique for 'making the unfamiliar familiar' by suggesting that the unfamiliar curriculum focus (the target concept to be taught) is in some ways just like a familiar lifeworld phenomena (the analogue or source concept).
So, I was interested to hear Prof. Andrew Hayward, Professor of Infectious Disease Epidemiology and Inclusion Health Research at UCL (University College London), being interviewed on the radio and suggesting that COVID was like a fire:
"Sometimes I like to think of, you know, COVID as a fire, if we are the fuel, social mixing is the oxygen that allows the fuel to burn, vaccines the water that stops the fuel from burning, and COVID cases are the sparks that spread the fire. So, we are doing well on vaccines, but there's lots of dried wood left."
There's quite a lot going on in that short statement. If Prof. Hayward had stopped at "sometimes I like to think of COVID as a fire" this would have been a simile where it is simply observed that one thing is conceived as being a bit like another.
Simile offers a comparison and leaves the listener or reader to work out the nature of the similarity (whereas metaphor, where one thing is described to be another, an example would be 'COVID is a fire', leaves the audience to even appreciate a comparison is being made). Analogy goes further, as it makes a comparison between two conceptual structures (two systems), such that by mapping across them we can understand how the structure of the unfamiliar is suggested to be like the more familiar structure.
That is, there is a mapping (see the figure below) that is based on pairings across the analogy. Here fire and COVID disease are each treated as systems with components that are structured in a parallel way:
COVID (illness): fire
people: fuel
social mixing: oxygen
vaccines: water
COVID cases: sparks
A graphic representation of Prof. Hayward's use of analogy
A lot of us are like kindling
Moreover, having set up this analogy, we are offered some additional information – we are doing well on vaccines (= there is plenty of water to stop fuel burning), but there is still a lot of dried wood. The listener has to understand that the dry wood refers to fuel, and this maps (in the analogy) onto lots of people who can still become infected.
I suspect most people (science teachers perhaps excepted) listening to this interview will not have even explicitly noticed the nature of the analogy, but rather automatically processed the comparison. They would have understood the message about COVID through the analogy, rather than having to actively analyse the analogy itself.
We can stop the sparks spreading the fire
Professor Hayward was asked about contact tracing and suggested that
"…the key thing is the human discussion with somebody who has COVID to identify who their contacts are and to ask them to isolate as well, and that really stops those sparks getting into the population and really helps to dampen down the fire."
That is, that potential COVID cases (that are like sparks in the fire system) can be prevented from mixing with the wider population (who are like fuel in the fire system) and this will dampen down the fire (the illness in the COVID system). {Note 'dampen down' seems to be a metaphor here rather than a true part of the analogy (in which it is the vaccines that have the effect of 'literally' {analogously} dampening down the fire). Stopping sparks mixing with fuel will limit new areas of combustion starting rather than dampening down the existing fire.}
An argument about contact tracing made using the analogy
Again, most people listening to this would likely have taken on board the intended meaning quite automatically, without having to deliberately analyse this answer – even though the response shifts between the target topics (the COVID disease system) and the analogue (the fire system) – so the sparks (fire system – equivalent to infectious cases) are stopped from getting into the population (COVID system – equivalent to the fuel supply).
This is reminiscent of chemistry teaching which slips back and forth between macroscopic and molecular levels of description – and so where references to, for example, hydrogen could mean the substance or the molecule – and the same word may have a different referent at different points in the same utterance (Taber, 2013). Whether this is problematic depends upon the past experiences of the listener – someone with extensive experience of a domain (probably most of the audience of a serious news magazine programme understand enough about combustion and infection to not have to deliberate on the analogy discussed here) can usually make these shifts automatically without getting confused.
Fire requires…AND…AND…
An analogy can only be effective when the analogue is indeed more familiar to the audience (you cannot make the unfamiliar familiar by comparing an unfamiliar target with an analogue that is also unfamiliar) so the use of the analogy by Professor Hayward assumed some basic knowledge about fire. Indeed it seemed to assume knowledge of the so-called 'fire triangle'.
Three factors are need to initiate/maintain combustion: fire may be stopped by removing one or more of these.
This is the idea that for a fire to commence or continue there need to be three things: something combustible to act as fuel; AND oxygen (or another suitable substance – as when iron filings burn in chlorine – but in usual circumstances it will be oxygen); AND a source of energy sufficient to initiate reaction (as burning is exothermic, once a fire is underway it may generate enough heat to maintain combustion – and sparks may spread the fire to nearby combustible material). To extinguish a fire, one needs to remove at least one of these factors – water can act as a heat sink to decrease the temperature, and may also reduce the contact between the fuel and oxygen. Preventing sparks from transferring hot material that can initiate further sites of combustion (providing energy to more fuel) can also be important.
Unobtrusive pedagogy
The quotes here were part of a short interview with a broadcast journalist and intended for a general public audience. Prof. Hayward introduced and developed his analogy as just sharing a way of thinking, and indeed analogy is such a common device in conversation that it was not obviously marked as a pedagogic technique. However, when we think about how such a device works, and what is expected of the audience to make sense of it, I think it is quite impressive how we can often 'decode' and understand such comparisons without any conscious effort. Providing, of course, that the analogue is indeed familiar, and the mapping across the two conceptual structures can be seen to fit.
Alternative interpretations and a study on flipped learning
Image by Please Don't sell My Artwork AS IS from Pixabay
Flipping learning
I was reading about a study of 'flipped learning'. Put very simply, the assumption behind flipped learning is that usually teaching follows a pattern of (a) class time spent with the teacher lecturing, followed by (b) students working through examples largely in their own time. This is a pattern that was (and perhaps still is) often found in Universities in subjects that largely teach though lecture courses.
The flipped learning approach switches the use the class time to 'active' learning activities, such as working through exercises, by having students undertake some study before class. That is, students learn about what would have been presented in the lecture by reading texts, watching videos, interacting with on-line learning resources, and so forth, BEFORE coming to class. The logic is that the teacher's input is more useful when students are being challenged to apply the new ideas than as a means of presenting information.
That is clearly a quick gloss, and clearly much more could be said about the rationale, the assumptions behind the approach,and its implementation.
However, in simple terms, the mode of instruction for two stages of the learning process
being informed of scientific ideas (through a lecture)
applying those ideas (in unsupported private study)
are 'flipped' to
being informed of scientific ideas (through accessing learning resources)
applying those ideas (in a context where help and feedback is provided)
Testing pedagogy
So much for the intention, but does it work? That is where research comes in. If we want to test a hypothesis, such as 'students will learn more if learning is flipped' (or 'students will enjoy their studies more if learning is flipped', or 'more students will opt to study the subject further if learning is flipped', or whatever) then it would seem an experiment is called for.
In principle, experiments allow us to see if changing some factor (say, the sequence of activities in a course module) will change some variable (say, student scores on a test). The experiment is often the go-to methodology in natural sciences: modify one variable, and measure any change in another hypothesised to be affected by it, whilst keeping everything else that could conceivably have an influence constant. Even in science, however, it is seldom that simple, and experiments can never actually 'prove' our hypothesis is correct (or false).
In education, running experiments is even more challenging (Taber, 2019). Learners, classes, teachers, courses, schools, universities are not 'natural kinds'. That is, the kind of comparability you can expect between two copper sulphate crystals of a given mass, or two specimens of copper wire of given dimensions, does not apply: it can matter a lot whether you are testing this student or that student, or if the class is taught one teacher or another.
People respond to conditions different to inanimate objects – if testing the the conductivity of a sample of a salt solution of a given concentration it should not matter if it is Monday morning of Thursday afternoon, or whether it is windy outside, or which team lost last's night's match, or even whether the researcher is respectful or rude to the sample. Clearly when testing the motivation or learning of students, such things could influence measurements. Moreover, a sample of gas neither knows or cares what you are expecting to happen when you compress it, but people can be influenced by the expectations of researchers (so called expectancy effect – also known as the Pygmalion effect).
In the study, by Ponikwer and Patel, researchers flipped part of a module on the fundamentals of analytical chemistry, which was part of a BSc honours degree in biomedical science. The module was divided into three parts:
absorbance and emission spectrosocopy
chromatography and electrophoresis
mass spectroscopy and nuclear magnetic resonance spectroscopy
Students were taught the first topics by the usual lectures, then the topics of chromatography and electrophoresis were taught 'flipped', before the final topics were taught through the usual lectures. This pattern was repeated over three successive years.
[Figure 1 in the paper offers a useful graphical representation of the study design. If I had been prepared to pay SpringerNature a fee, I would have been allowed to reproduce it here.*]
The authors of the study considered the innovation a success
This study suggests that flipped learning can be an effective model for teaching analytical chemistry in single topics and potentially entire modules. This approach provides the means for students to take active responsibility in their learning, which they can do at their own pace, and to conduct problem-solving activities within the classroom environment, which underpins the discipline of analytical chemistry. (Ponikwer & Patel, 2018: p.2268)
Confounding variables
Confounding variables are other factors which might vary between conditions and have an effect.
Ponikwer and Patel were aware that one needs to be careful in interpreting the data collected in such a study. For example, it is not especially helpful to consider how well students did on the examination questions at the end of term to see if students did as well, or better, on the flipped topics that the other topics taught. Clearly students might find some topics, or indeed some questions, more difficult than others regardless of how they studied. Ponikwer and Patel reported that on average students did significantly better on questions from the flipped elements, but included important caveats
"This improved performance could be due to the flipped learning approach enhancing student learning, but may also be due to other factors, such as students finding the topic of chromatography more interesting or easier than spectroscopy, or that the format of flipped learning made students feel more positive about the subject area compared with those subject areas that were delivered traditionally." (Ponikwer & Patel, 2018: p.2267)
Whilst acknowledging such alternative explanations for their findings might seem to undermine their results it is good science to be explicit about such caveats. Looking for (and reporting) alternative explanations is a key part of the scientific attitude.
This good scientific practice is also clear where the authors discuss how attendance patterns varied over the course. The authors report that the attendance at the start of the flipped segment was similar to what had come before, but then attendance increased slightly during the flipped learning section of the course. They point out this shift was "not significant", that is statistics suggested it could not be ruled out to be a chance effect.
However Ponikwer and Patel do report a statistically "significant reduction in the attendance at the non-flipped lectures delivered after the flipped sessions" (p.2265) – that is, once students had experienced the flipped learning, on average they tended to attend normal lectures less later in their course. The authors suggest this could be a positive reaction to how they experienced the flipped learning, but again they point out that there were confounding variables, and other interpretations could not ruled out:
"This change in attendance may be due to increased engagement in the flipped learning module; however, it could also reflect a perception that a more exciting approach of lecturing or content is to be delivered. The enhanced level of engagement may also be because students could feel left behind in the problem-solving workshop sessions. The reduction in attendance after the flipped lecture may be due to students deciding to focus on assessments, feeling that they may have met the threshold attendance requirement" (Ponikwer & Patel, 2018: p.2265).
So, with these students, taking this particular course, in this particular university, having this sequence of topics based on some traditional and some flipped learning, there is some evidence of flipped learning better engaging students and leading to improved learning – but subject to a wide range of caveats which allow various alternative explanations of the findings.
Given the difficulties of interpreting experiments in education, one may wonder if there is any point in experiments in teaching and learning. On the other hand, for the lecturing staff on the course, it would seem strange to get these results, and dismiss them (it has not been proved that flipped learning has positive effects, but the results are at least suggestive and we can only base our action on the available evidence).
Moreover, Ponikwer and Patel collected other data, such as students' perceptions of the advantages and challenges of the flipped learning approach – data that can complement their statistical tests, and also inform potential modifications of the implementation of flipped learning for future iterations of the course.
What does this tell us about the use of flipped learning elsewhere? Studies taking place in a single unique teaching and learning context do not automatically tell us what would have been the case elsewhere – with different lecturing staff, different demographic of students, when learning about marine ecology or general relativity. Such studies are best seen as context-directed, as being most relevant to here they are carried out.
However, again, even if research cannot be formally generalised, that does not mean that it cannot be informative to those working elsewhere who may apply a form of 'reader generalisation' to decide either:
a) that teaching and learning context seems very similar to ours: it might be worth trying that here;
or
b) that is a very different teaching and learning context to ours: it may not be worth the effort and disruption to try that out here based on the findings in such a different context.
This requires studies to give details of the teaching and learning context where they were carried out (so called 'thick description'). Clearly the more similar a study context is to one's own teaching context, and the wider the range of teaching and learning contexts where a particular pedagogy or teaching approach has been shown to have positive outcomes, the more reason there is to feel it is with trying something out in own's own classroom.
I have argued that:
"What are [common in the educational research literature] are individual small-scale experiments that cannot be considered to offer highly generalisable results. Despite this, where these individual studies are seen as being akin to case studies (and reported in sufficient detail) they can collectively build up a useful account of the range of application of tested innovations. That is, some inherent limitations of small-scale experimental studies can be mitigated across series of studies, but this is most effective when individual studies offer thick description of teaching contexts and when contexts for 'replication' studies are selected to best complement previous studies." (Taber, 2019: 106)
In that regard, studies like that of Ponikwer and Patel can be considered not as 'proof' of the effectiveness of flipped learning, but as part of a cumulative evidence base for the value of trying out the approach in various teaching situations.
Why I have not included the orignal figure showing the study design
* I had hoped to include in this post a copy of the figure in the paper showing the study design. The paper is not published open access and so the copyright in the 'design' (that, is the design of the figure **, not the study!) means that it cannot be legally reprodiced without permission. I sought permission to reproduce the figure here through (SpringerNature) the publisher's on line permissions request system, explaining this was to be used in an acdemics scholar's personal blog.
Springer granted permission for reuse, but subject to a fee of £53.83.
As copyright holder/managers they are perfectly entitled to do that. However, I had assumed that they would offer free use for a non-commercial purpose that offers free publicity to their publication. I have other uses for my pension, so I refer readers interested in seeing the figure to the original paper.
** Under the conventions associated with copyright law the reproduction of short extracts of an academic paper for the purposes of criticism and review is normally considered 'fair use' and exempt from copyright restrictions. However, any figure (or table) is treated as a discrete artistic design and cannot be copied from a work in copyright without permission.
On Sunday morning I heard Bernardine Evaristo reading her essay 'The Arts in Our Hearts' in BBC Radio 4's weekly 'A Point of View' slot. It was a heartfelt and compelling argument for the importance of investing in the arts in education (and well worth a listen).
Demoting creativity?
Evaristo complained about the lack of support for the arts in the current curriculum context.
"We have an educational provision that demotes and demeans creativity in the hierarchy of subjects"
Since the introduction of the Natural Curriculum in England, science, mathematics and English have had a specials status, and in recent years the arts have been squeezed – often treated as luxuries and foci for extra-curricular provision. Among the points Evaristo made were that it was inappropriate to pressure all children towards STEM (i.e., science, technology, engineering and mathematics) subjects "because [it is suggested] that's where the future lies", as education is not just about preparing for work, and (even if it were) degrees in the arts and humanities can perfectly well lead to good careers; and also arts education supports the development of creativity – "the very creativity that might one day lead them to a career in science or engineering".
I found much to agree with here.
A (personal) science bias
I was fascinated with science as a child. When I entered secondary school I was asked what I wanted to do when I left. I said I wanted to go to University to do science. (All my subsequent careers input took the form of the single annual leading question: "Do you still want to go to University to study science?") I did a chemistry degree. I trained to teach chemistry and physics. I became a science teacher, then a science lecturer, and then a science education lecturer. I was never any good at art, failed to learn to play an instrument well, cannot dance (even my swimming is a potential danger to others, and – when I am in the lane closest to the pool wall- to my own fingers)…there was no way I was going to become an artist. So, I might be considered to have a science bias.
Why educate?
But I totally agree with the gist of what Evaristo argued. Education is not about preparing people for jobs, and it should not be primarily about helping them acquire skills for the jobs market. That cannot be totally ignored, but that sounds more like training than education. Education has multiple purposes and these need to be reflected in curriculum (Taber, 2019). Certainly we want education to allow young people to have the chance to progress to achieve their goals – which may be to become a heart surgeon, a cosmologist, or a marine biologist. Or, it may be to be a journalist, novelist, choreographer, songwriter, historian, film critic…
But education is about developing the whole person, and that will not happen when the curriculum is too narrow. Education is also about inducting learners into the culture of their society (and increasingly the 'global village' moves towards being one suprasociety). Children should be supported in engaging with a wide range of different areas, even if they decide they do not wish to later follow-up some or most of these.
And this does not just mean following-up for for employment: a person who becomes a sculptor should have their life outside the studio enhanced due to what they experienced in school science, just as someone who becomes a pharmacist should have their life outside the dispensary enhanced due to what they experienced in arts classes; and someone who becomes an office cleaner or who works in a customer service call centre has the right to have their life enhanced by the range of school experiences across the curriculum.
Culture and civil-isation
I value having gone to the theatre from school, and on a trip to hear a symphony orchestra. I never went to ballet or opera, but I would want all children to be offered these experiences. Children should not leave school without some art history – not highly theoretical, but having had a chance to become familiar with different styles of painting. And so with other areas of our common inheritance – and not limited to what might be called 'high culture'. (Consider the popularity on mainstream television channels of programmes about ballroom dancing, cooking, gardening, antiques collecting, landscape and portrait painting, interior design/decoration, making/renovating/recycling, and so forth.)
This is what it means to be civilised.
Without experiencing different aspects of culture, at least having a taster of what is out there, children are not being fully inducted into that culture. Where schools do not offer this, we have a two-tier society – where some children are able to access the breadth of culture because of home background, and others (perhaps partly because socio-economic conditions do not allow, but perhaps partly simply because the parents were themselves never offered glimpses of these options in their own education) miss out. Bernstein's notion of 'restricted code' can be understood in a wider sense than just access to forms of language.
It is not acceptable that a broad education offering access to informed choices about later engagement in the wider culture is offered to those who can afford private education or extra-curricular enrichment activities, but the rest have to settle for, hopefully, being employable.
'To live without my music, would be (near) impossible to do…'
I was never going to be an artist, but works of art have given me much pleasure. Arguably music has been as important to me as science – the constant companion since my adolescence (I feel a John Miles lyric seeking to make itself felt here). I cannot sing well, play an instrument, or even whistle in tune. I cannot tell the key a piece is in. I have somewhat eclectic tastes, and indeed some might indeed suggest little taste at all – but 'I know what I like (in your wardrobe)' and what has uplifted me, puzzled me, excited me, consoled me, calmed me, comforted me – what music can do to transcend the moment and shift the mood – surely that's what really matters?
So I'm there 100% – an education that prioritises the sciences over the humanities, and, even more so, over the arts, is as distorted as the curriculum of the original grammar schools which would not have known what to with with natural philosophy (proto-science), and found the idea of adding Greek to the curriculum something of a progressive innovation. Of course, that is an ahistorical judgement (ignoring the context at the time), whereas today there is no excuse for this kind of short-sightedness.
But I do have just a couple of reservations about Evaristo's essay, or more to the point, what could be taken away from it.
We need to encourage all young people to see STEM options as open, and welcoming, to them
My first slight reservation is that although I agree that we should not pressure all children towards science and other STEM areas, we should bear in mind that some groups have historically been underrepresented in science subjects, and some children may have been given the impression that science is not for the likes of them. We need to do all we can to make science inclusive – science (as with art) is a core part of all our culture, and a universal human activity. We should not push everyone into science, but we need to make it clear that no one is excluded because of gender or ethnicity or religious faith or other kinds of (claimed or perceived) group identity. So, science teachers should encourage everyone to believe that science could be for them, but working on a level playing field with other teachers promoting their own areas.
Science IS creative
My second, slight, query is the identification of creativity with arts education. That is not to say that arts education does not offer opportunities for creativity – of course it does – but rather the potential inference that science education can not.
Evaristo recognises that creativity is important to the professional in STEM fields, so surely science education needs to develop this. Science has a rightly deserved reputation for logic, reasoning, and rational thought – but this can only work on the creative ideas that scientists develop: without the imaginative invention of novel ideas to test, there would be no experiments or data to do any logical analysis with ( Taber, 2011).
So when Bernardine Evaristo refers to "play, a.k.a the arts" she neglects the role of play in science. When this play takes place in the lab', it needs to be play subject to a careful risk assessment, certainly, but it is still a form of play. A period of familiarisation with a phenomenon is often essential background for developing an investigative strategy.
Creativity is part of an authentic science education
That is not to say I am claiming that this creativity is always obvious in science education. Over-packed curriculum specifications that make science courses seem like an endless barrage of unconnected topics, and mark schemes designed as if for automatons examining work produced by automatons having been instructed by automatons, seem designed to squeeze out any opportunities for teaching and learning that can offer an authentic feel for what science is actually like. All work, no play, makes Jacqueline a dull scientist, and so unlikely to discover anything substantially new. So yes, perhaps "We have an educational provision that demotes and demeans creativity in the hierarchy of subjects" through, first, locating STEM subjects at the pinnacle, but, then, also by misrepresenting them as not being creative.
Of course, there are enrichment activities that allow learners to be creative in science activities, and to engage with projects or topics over extended periods of time – and so give more of an authentic feel for scientific enquiry. The CREST awards scheme from 'the British Ass' (The British Science Association) is just one example (Taber & Cole, 2010). But then, like extra-curricular arts, this is not available in all schools, and, moreover, students should not need to go outside the curriculum to get authentic and creative science education.
Curriculum breadth is not a luxury
So, yes, I totally agree that:
"it's vital for the country's future that we reject, once and for all, the notion that the arts are a luxury"
But I would also argue that it is vital for humanity's future that we reject, once and for all, the notion that science is only about logic, and that only the arts offer creativity.
Everyone should be introduced in their schooling to all the key aspects of our culture. And just as art education has to involve creating, not only being taught art history or appreciation, science education has to offer a feel for science as a practice, not just a never-ending parade of theories, models, laws, and so forth, previously created by someone else (and most often a dead, 'white', male someone). Creativity in science is clearly different in its expression to creativity in the arts – and so both should be experienced in everyone's schooling.
Taber, K. S., & Cole, J. (2010). The CREST awards scheme: Challenging gifted and talented students through creative STEM project work. School Science Review, 92(339), 117-126.
Analogies can be used as pedagogic devices to make the unfamiliar familiar' – that is by suggesting that something (the unfamiliar thing being explained) is somehow like something else (that is already familiar), the unfamiliar can start to become familiar. The analogy functions like a bridge between the known and the unknown. (Note: the idea of a bridge is being used as simile there – another device that can be used to help make the unfamiliar familiar.)
For an analogy (or simile) to work, the person being taught or communicated with has to already be familiar with the 'source' that act as an analogue for the 'target' being communicated. (If someone did not know what a bridge was, what it is used for, then it would be no help to them to be told that an analogy can function like one! Indeed it would probably just confuse matters.)
An analogy is based on some mapping of structure between two different systems. For example, at one time a common teaching analogy was that the atom was like a tiny solar system. For that to be useful to a learner, they would need to be more familiar with the solar system than the atom. To be used as an effective teaching analogy, the learner would have to understand the relevant parts of the conceptual structure of the solar system idea that were being mapped across to the atom (perhaps a relatively large central mass, the idea of a number of less massive bodies orbiting in some way, a force between the central and peripheral bodies responsible for the centripetal acceleration of the orbiting bodies…).
A person might easily map across irrelevant aspects of the source to the target, perhaps as all the planets are different then all electrons must be different! This might explain why some students assume the force holding the atom together is gravitational!
In teaching science, it is common to use everyday sources as analogues for scientific ideas. But, of course, it is also possible to use scientific ideas as the source to try to explain other target ideas.
Below I reproduce an extract from a recent publication (Taber & Li, 2001). I developed an analogy between enzymatic catalysis (a scientific concept) and scaffolding of learning (an educational or psychological concept), to use is a chapter I co-wrote with Xinyue Li .
The mapping I had in mind was something like this:
Aspect
Source (Enzymatic catalysis)
Target (Scaffolding)
Process
Chemical reaction
Development of new knowledge/skills
Impediment
Large activation energy – barrier far greater than energy available to reactant species
Large learning demand – gap between current capability and mastery of new knowledge/skill exceeds manageable 'learning quantum'
Intervention
Addition of enzyme
Mediation by 'teacher'
Mechanism
Provides alternative reaction pathway with small energy barriers
Structures learning by modelling activity, and leads learner through small manageable steps
Matching
The enzyme 'fits' the reactant molecule and readily binds
A good scaffold matches the learners' current capacity to progress in learning (in the so-called 'ZPD')
Degrees of freedom
The binding of the enzyme to a substrate 'guides' the subsequent molecular reconfiguration
The scaffolding guides the steps in the learning process taken by the learner
Mapping between two analogous conceptual structures
Scaffolding Learning as Akin to Enzymatic Catalysis
"Metaphors and analogies should always be considered critically, as the aspects that do not map onto the target they are being used to illustrate can often be as salient and as relevant as the aspects that map positively. Given that, and in the spirit of offering a way to imagine scaffolding (rather than an objective description) we suggest it may be useful to think of scaffolding learning as like the enzymatic catalysis of a chemical process in the body (see Figure 3).
Figure 3. Scaffolding learning can be seen as analogous to enzymatic catalysis (b) which facilitates a reaction with a substantive energy barrier (a).
Some chemical reactions are energetically viable (in chemical terms, exothermic) and so in thermodynamic terms, occur spontaneously. However, sometimes even theoretically viable (so spontaneous) reactions occur at such a slow rate that for all practical purposes there is no reaction. For example, imagine a wooden dining table in a room at 293 K (20˚C) with an atmosphere containing about 21% oxygen – a situation found in many people's homes. The combustion of the table is a viable chemical process [1] and indeed the wood will (theoretically) spontaneously burn in the air. Yet, of course, that does not actually happen. Despite being a thermodynamically viable process, the rate is so slow that an observer would die of old age long before seeing the table burst into flames, unless some external agent actively initiated the process. If parents returned home from an evening out to be told by their teenage children that the smouldering dining table caught alight spontaneously, the parents would be advised to suspect that actually this was not strictly true. Although the process would be energetically favourable, there is a large energy barrier to its initiation (cf. Figure 3, top image). Should sufficient energy be provided to ignite the table, then it is likely to continue to burn vigorously, but without such 'initiation energy' it would be inert.
The process of catalysis allows reactions which are energetically favourable, but which would normally occur at a slow or even negligible (and in the case of our wooden table, effectively zero) rate to occur much more quickly – by offering a new reaction pathway that has a much lower energy barrier (such that this is more readily breached by the normal distribution of particles at the ambient temperature).
In living organisms, a class of catalysts known as enzymes, catalyse reactions. Enzymes tend to be specific to particular reactions and very effective catalysts, so reactions akin to the burning of organic materials (as found in our wooden table) can occur as part of metabolism at body temperature. The second image in Figure 3 represents the same chemical reaction as in the top image (note the same start and finish points) reflecting how an enzyme changes the reaction pathway, but not the overall reaction. Two particular features of this graphical metaphor are that the overall process is broken down into a number of discrete steps, and the 'initiation energy' needed to get the process underway is very much smaller.
This is similar to the mediation of learning trough scaffolding, where a task that is currently beyond the capacity of the learner is broken down into a sequence of smaller steps, more manageable 'learning quanta', and the learner is guided along a learning pathway. The parallels go beyond this. Part of the way that an enzyme functions is that the enzyme molecule's shape is extremely well matched to bind to a target reactant molecule (something reflected in the teaching analogy of the 'lock and key' mechanism of enzymatic action: the enzyme and substrate molecules are said to fit together like a lock and key). This is analogous to how effective scaffolding requires a teacher to design a scaffold that fits the learner's current level of development: that is, her current thinking and skills. Once the substrate molecule is bound to the enzyme molecule, this then triggers a specific reconfiguration: just as a good scaffolding tool suggests to the learner a particular perspective on the subject matter.
Moreover, whereas a free substrate molecule could potentially follow a good many different pathways, once it is bound to the enzyme molecule its 'degrees of freedom' are reduced, so there are then significant constraints on which potential changes are still viable. Most organic chemistry carried out in vitro (in laboratory glassware) is inefficient as there are often many 'side reactions' that lead to unintended products, just as students may readily take away very different interpretations from the same teaching, so the yield of desired product can be low. However in vivo reactions (in living cells), being enzyme-catalysed, tend to give high yields.
The process of enzymatic catalysis therefore makes the preferred pathway much 'easier', offers a guide along the intended route, and channels change to rule out alternative pathways. Digital tools that support teaching to meet curricular aims, such as apps intended to be used by learners to support study, therefore need to offer similar affordances (structuring student learning) and constraints (reducing the degrees of freedom to go 'off track'). Clearly this will rely on design features built into the tool. Here we very briefly discuss two examples."
[1] We avoid the term 'reaction' here, as strictly a chemical reaction occurs between specific substances. Wood is a material composed of a wide range of different compounds, and so the combustion of wood is a process encompassing a medley of concurrent reactions.
"If the muscles and other cells of the body burn sugar instead of oxygen…"
Do they think we cannot handle the scientific truth?
I should really have gone to bed, but I was just surfing the channels in case there was some 'must watch' programme I might miss, and I came across a screening of the film 'A few good men'. This had been a very popular movie at one time, and I seem to recall watching it with my late wife. I remembered it as an engaging film, and as an example of the 'courtroom drama' genre: but beyond that I could really only remember Tom Cruise as defence advocate questioning Jack Nicholson's as a commanding officer – and the famous line from Nicholson – "You can't handle the truth!".
This became something of a meme – I suspect now there are a lot of people who 'know' and use that line, who have never even seen the film and may not know what they are quoting from.
So, I though I might watch a bit, to remind myself what the actual case was about. In brief, a marine stationed at the U.S. Guantánamo Bay naval base and detention camp had died at the hands of two of his comrades. They had not intended to kill, but admitted mistreating him – their defence was they were simply obeying orders in subjecting a colleague who was not measuring up, and was letting the unit down, to some unpleasant, but ultimately (supposedly) harmless, punishment.
The film does not contain a lot of science, but what struck me was the failure to get some science that was invoked right. I was so surprised at what I thought I'd heard being presented as science, that I went back and replayed a section, and I then decided to see if I could find the script (by Aaron Sorkin*, screenplay adapted from his own theatre play) on the web, to see if what was said had actually been written into the script.
One of the witnesses is a doctor who is asked by the prosecuting counsel to explain lactic acidosis.
Burning sugar instead of oxygen?
The characters here are:
Capt. Jack Ross (played by Kevin Bacon) the prosecuting counsel,
Dr. Stone (Christopher Guest) and
Lt. Daniel Kaffee (Cruise's character).
On direct examination:
Ross: Dr. Stone, what's lactic acidosis?
Stone: If the muscles and other cells of the body burn sugar instead of oxygen, lactic acid is produced. That lactic acid is what caused Santiago's lungs to bleed.
Ross: How long does it take for the muscles and other cells to begin burning sugar instead of oxygen?
Stone: Twenty to thirty minutes.
Ross: And what caused Santiago's muscles and other cells to start burning sugar? [In the film, the line seems to be: And what caused this process to be speed up in Santiago's muscles?]
Stone: An ingested poison of some kind.
Later, under cross-examination
Kafee: Commander, if I had a coronary condition, and a perfectly clean rag was placed in my mouth, and the rag was accidentally pushed too far down, is it possible that my cells would continue burning sugar after the rag was taken out?
Stone: It would have to be a very serious condition.
What?
If a student suggested that lactic acid is produced when the muscles burn sugar instead of oxygen we would likely consider this an alternative conception (misconception). It is, at best, a clumsy phrasing, and is simply wrong.
Respiration
Metabolism is a set of processes under very fine controls, so whether we should refer to metabolism as burning or not, is a moot point. Combustion tends to be a vigorous process that is usually uncontrolled. But we can see it as a metaphor: carbohydrates are 'burnt' up in the sense that they undergo reactions analogous to burning.
But burning requires oxygen (well, in the lab. we might burn materials in chlorine, but, in general, and in everyday life, combustion is a reaction with oxygen), so what could burning oxygen mean?
In respiration, glucose is in effect reacted with oxygen to produce carbon dioxide and water. However, this is not a single step process, but a complex set of smaller reactions – the overall effect of which is
glucose + oxygen → carbon dioxide + water
Breaking glucose down to lactic acid also acts as an energy source, but is no where near as effective. Our muscles can undertake this ('anaerobic') process when there is insufficient oxygen supply – for example when undertaking high stamina exercise – but this is best seen as a temporary stop-gap, as lactic acid build up causes problems (cramp for example) – even if not usually death.
Does science matter?
Now clearly the science is not central to the story of 'A few good men'. The main issues are (factual)
whether the accused men were acting under orders;
(ethical)
the nature of illegal orders,
when service personal should question and ignore orders (deontology) given that they seldom have the whole picture (and in this film one of the accused men is presented as something of a simpleton who viewer may suspect should not be given much responsibility for decision making),
whether it is acceptable to use corporal or cruel punishment on an under-performing soldier (or marine) given that the lives of many may depend upon their high levels of performance (consequentialism, or perhaps pragmatics)…
There is also a medical issue, regarding whether the torture of the soldier was the primary cause of death, or whether there was an underlying health issue which the medical officer (Stone) had missed and which might also explain the poor performance. [That is a theme which featured large in a recent very high profile real murder case.]
Otherwise the film is about the characters of, and relationships among, the legal officers. Like most good films – this is film about people, and being human in the world, and how we behave towards and relate to each other.
The nature of lactic acidosis is hardly a key point.
But if it is worth including in the script as the assumed cause of death, and its nature relevant – why not get the science right?
Perhaps, because science is complicated and needs to be simplified for the cinema-goer who, after all, wants to be entertained, not lectured?
Perhaps there is no simple account of lactic acidosis which could be included in the script without getting technical, and entering into a long and complicated explanation.
In teaching science…
But surely that is not true. In teaching we often have to employ simplifications which ignore complexity and nuance for the benefit of getting the core idea across to learners. We seek the optimal level of simplification that learners can make good sense of, but which is true to the core essence of the actual science being discussed (it is 'intellectually honest') and provides a suitable basis for later more advanced treatments.
It can be hard to find that optimum level of simplification – but I really do not think that explaining lactic acidosis as burning sugar instead of oxygen could be considered a credit-worthy attempt.
Dr. Stone, can we try again?
What about, something like:
Dr. Stone, what's lactic acidosis?
It occurs when the body tissues do not have sufficient oxygen to fully break down sugar in the usual way, and damaging lactic aid is produced instead of carbon dioxide and water.
I am sure there are lots of possible tweaks here. The point is that the script did not need to go into a long medical lecture, but by including something that was simply nonsensical, and should be obviously wrong to anyone who had studied respiration at school (which should be everyone who has been to school in the past few decades in many countries), it distracts, and so detracts, from the story.
All images from 'A few good men' (1992, Columbia Pictures)
* I see that ("acclaimed screenwriter") Aaron Sorkin is planning a new live television version of 'A Few Good Men' – so perhaps the description of lactic acidosis can be updated?
BBC corrects cruel (to cats) scientific claim on its website
Keith S. Taber
I just got 80% on a science test for primary school children
I've just scored 4/5 (80%) on an on-line KS2 science test on the BBC (the British Broadcasting Corporation) educational website. 80% sounds quite good out of context, but I am a science teacher and KS2 is meant for 7-11 year olds.
The BBC awards me 4/5 for my primary level science knowledge about the states of matter
My defence is that the question I got wrong was ambiguous (but, as Christine Keeler might have said, I would say that).
I was actually getting round to checking on something from a while back.
In 2019 I came across something on the website that I thought was very misleading – and I complained to the BBC through their website form. I had an immediate, but generic response:
"Thank you for taking the time to send us your comments. We appreciate all the feedback we receive as it plays an important role in helping to shape our decisions.
This is an automated message (sorry that we can't reply individually) to let you know that we've read your comments and will report them overnight to staff across the BBC for them to read too (after removing any personal details). This includes our programme makers, commissioning editors and senior management.
Thanks again for contacting the BBC.
BBC Audience Services.
NB: Please do not reply to this email. It includes a reference number but comes from an automated account which is not monitored."
Email: 6th Sept., 2019
This kind of response is somewhat frustating. My complaint had been recieved, and would be passed on, but it looked like I would get no specific response (as presumably if my "comments" were to be reported to relevant staff "after removing any personal details", those staff would not be in a position to let me know if they were following up, dismissing, or simply ignoring, my comments.) Indeed, I never did get any follow up.
So, my intention was to check back after a decent period had elapsed (n.b., where does all the time go?) and see if anything had been changed in response to my complaint. Strictly, if there had been a change this could be because:
a) I complained
b) someone else/some other people complained (i.e., people who's complaints were taken more seriously than mine)
c) I was one of number of people who complained
d) material had been updated compleltely independently of any compaints
That is, I could not know if I personally had had any effect, BUT if the offending material (because as a chemist I was offended professionally, even if not personally) was still there then I would know my compaint had not been heeded.
So, I intended to check back; I expected to find no change (as pointing out blatant, basic, errors in the science in the English National Curriculum to government ministers did not have any effect, so the BBC…? ); and, if so, I thought of following up with an email or an old fashioned snail-mail … ("…yours, disgusted of Cambourne"*).
Well done, BBC
So, I am happy to publicly acknowledge that the BBC has changed its materials appearing under the heading 'What are the states of matter?'
The topic comprises of a short animation (with odd anthropomorphised {"guys"} geometric shapes handling examples of the states of matter: solid, liquid and gas); a series of bullet points on each state; a sorting task; and then the set of five objective (multiple choice) questions.
There are a number of issues with the examples used here, as discussed below. But the main focus of my complaint, a cartoon cat, has now been released from the indignity of being classified as a state of matter. Yes, a cat!
Limitations of the three states of matter model
The idea that matter can exist in three states is a pretty important foundation for a good deal of other science.
However there is big problem with the generality of the model. Basically it really applies to pure samples of substances: generally substances (not materials in general, and certainly not objects) exist as solids, liquids, or gases, depending on the conditions of temperature and pressure – although at high enough temperatures plasmas are formed (and theoretically when hot enough even the atomic cores, and eventually nuclei would break down – but those conditions are pretty extreme and not found in the typical home or classroom).
Examples of substances include water, salt, calcium carbonate, iron, mercury, hydrogen, graphite, carbon dioxide, sulphur… that is, elements and compounds. Of course, many of these are seldom met in pure form in everyday life outside school science labs.
Most materials that people come across are mixtures or composites. Mixtures often exist as solutions or suspensions – as gels or foams or emulsions – not as solids, liquids or gases.
This is probably why the terms 'solids', 'liquids' and 'gases' actually have two sets of meanings – the science or technical sense, and the everyday or 'life-world' sense. So milk is a liquid(everyday) as you can pour some into your tea cup and a block of wood is a solid(everyday) as it retains its shape and integrity as you nail it to another structure. But milk and wood are not substances – and so not liquid(scientific) or solid(scientific).
Does this matter? Yes, because if we are teaching children things in science lessons, it would be good to get the science right. A solid will melt at a distinct melting temperature to give a liquid which will boil at a distinct boiling temperature. Wood, for example, does not.
Wood is a complex material. It has gas pockets. It has (variable) moisture content, and the structure contains various compounds – lignin, cellulose, and many more. The response to heating reflects that complex constitution.
The BBC's examples of solids, liquids, and gases
The BBC website suggests examples of the three states of matter to introduce primary age students to the concept.
Animation:
Solids: block of ice, football
Lquids: water, honey
Gases: none are specified – animation shows the clouds (of liquid water droplets) forming around a kettle spout, and 'gas' put into in fizzy drinks is referenced.
A football is not solid, but usually air (a mixture of gases with some other components) contained in a plastic shell. (The voiceover refers simply to a 'ball', but the animation show a large ball with a traditional football pattern being used to do 'keepy uppies' by the cartoon character.)
Honey is not a liquid(scientific) but a complex mixture of sugars in solution. There is usually much more sugar than water. (So, arguably, it is more solid than liquid – but it is better to simply not consider it as either.) This is where I dropped a mark on the terminal test:
Two of the options are NOT liquids. Only one response gets credit in this test!
Web text:
The bullet points on the site list some further examples:
"Examples of solids include ice, wood and sand." (Ice and sand are solids(scientific).)
"Examples of liquids include water, honey and milk." (Only water is liquid(scientific) here.)
"Examples of gases include steam, helium and oxygen." (3/3, well done BBC!)
Sorting task:
The BBC website task invites children to sort cards showing objects into three categories. (What is that object on the front card meant to be?)
In the sorting task, children are asked to sort a number of examples shown on cards into solid, liquid, and gas:
The examples presented are air, a feather, helium, milk, a pencil, sea, steam, syrup, wood. Of these only helium and steam strictly meet the criteria for being a solid(scientific)/liquid(scientific)/gas(scientific). Yet, as suggested above, it is difficult to find genuine examples that are both scientifically correct and familiar to young children. Perhaps sea and air (at least materials) are closer approximations than a pencil or a feather ("solids retain their shape" – would a child using the website have handled a feather, and, if so, would it have retained its shape under child-handling?)
So, I still have reservations about this material, whilst acknowledging the need to balance scientific correctness with relevant (to children) examples. Strictly, some of the examples can be seen as encouraging children to get the science wrong. These things matter if only because children are learning things on this site that later in their school career will be judged as alternative conceptions and marked as wrong.
None the less, I am pleased that the BBC has at least decided to amend its sorting task, and remove the poor cat:
Which pile does the cat belong in? [This example has now been removed. Bravo.]
The website had previously been quite clear that putting the cat as anything other than solid was 'wrong'. It is classed as a solid even though a cat (like any animal) is (or would be if separated out into its constituent substances – and children should not try this at home) more water than anything else.
I had real trouble seeing how that example fitted with the criteria specified on the webpage:
"[Cats] stay in one place and can be held.
[Cats] keep their shape. They do not flow like liquids.
[Cats] always take up the same amount of space. They do not spread out like gases.
[Cats] can be cut or shaped."
Characteristics of solids, but perhaps not entirely true of cats?
* cf. the idiom 'disgusted of Tunbridge Wells' – referring to a hypothetical person who writes to media complaining about matters of concern.
Images used here are screenshots, copyright of the BBC – a publicly funded public service broadcaster.
I have recently posted on the blog about having been viewing some of the court testimony being made available to the public in the State of Minnesota v. Derek Michael Chauvin court case (27-CR-20-12646: State vs. Derek Chauvin).
Now you talked quite a bit about physics in your direct testimony, agreed?
Yes
And you would agree that physics, or the application of physical forces, is a constantly changing, er, set of circumstances.
I did not catch what you said.
Sure. You would agree with me, would you not, that when you look at the concepts of physics, these things are constantly changing, right?
Yeah, all of science is constantly changing.
Constant! I mean,
Yes.
in milliseconds and nanoseconds, right?
Yes.
And so if I put this much weight [Nelson demonstrating by shifting position] or this much weight [shifting position], all of the formulas [sic] and variations, will change from second to second, from millisecond to millisecond, nanosecond to nanosecond, agreed.
I agree.
Similarly, biology sort of works the same way. Right?
Yes.
My heart beats, my lungs breathe [sic], my brain is sending millions of signals to my body, at all times.
Correct.
Again, even, I mean, faster than the speed of light, right?
Correct.
Millions of signals every nanosecond, right?
Yes.
Day 9. 27-CR-20-12646: State vs. Derek Chauvin
Agreeing – but talking about different things?
The first thing that struck me here concerns what seems to me to be Mr Nelson and Dr Tobin talking at cross-purposes – that neither participant acknowledged (and so perhaps neither were aware of).
I think Nelson is trying to make an argument that the precise state of Mr George Floyd (who's death is at the core of the prosecution of Mr Chauvin) would have been a dynamic matter during the time he was restrained on the ground by three police officers (an argument being made in response to the expert's presentation of testimony suggesting it was possible to posit fairly precise calculations of the forces acting during the episode).
This seems fairly clear from the opening question of the exchange above:
Now you talked quite a bit about physics in your direct testimony, agreed? … And you would agree that physics, or the application of physical forces, is a constantly changing, er, set of circumstances.
However, Dr Tobin does not hear this clearly (there are plexiglass screens between them as COVID precautions, and Nelson acknowledges that he is struggling with his voice by this stage of the trial).
Nelson re-phrases, but actually says something rather different:
You would agree with me, would you not, that when you look at the concepts of physics, these things are constantly changing, right?
['These things' presumably refers to 'the application of physical forces', but if Dr Tobin did not hear Mr Nelson's previous utterance then 'these things' would be taken to be 'the concepts of physics'.]
So, now it is not the forces acting in a real world scenario which are posited to be constantly changing, but the concepts of physics. Dr Tobin's response certainly seems to make most sense if the question is understood in terms of the science itself being in flux:
Yeah, all of science is constantly changing.
Given that context, the following agreement that these changes are occurring "in milliseconds and nanoseconds" seems a little surreal, as it is not quite clear in what sense science is changing on that scale (except in the sense that science is continuing constantly – certainly not in the sense that canonical accounts of concepts shift at that pace: say, in the way Einstein's notions of physics came to replace those of Newton).
In the next exchange the original context Nelson had presented ("the application of physical forces, is … constantly changing") becomes clearer:
And so if I put this much weight [Nelson demonstrating by shifting position] or this much weight [shifting position], all of the formulas and variations, will change from second to second, from millisecond to millisecond, nanosecond to nanosecond, agreed.
I agree.
As a pedantic science teacher I would suggest that it is not the formulae of physics that change, but the values to be substituted into the system of equations derived from them to describe the particular event: but I think the intended meaning is clear. Dr Tobin is a medical expert, not a physicist nor a science teacher, and the two men appear to be agreeing that the precise configurations of forces on a person being restrained will constantly change, which seems reasonable. I guess that is what the jury would take from this.
If my interpretation of this dialogue is correct (and readers may check the footage and see how they understand the exchange) then at one point the expert witness was agreeing with the attorney, but misunderstanding what he was being asked about (how in the real world the forces acting are continuously varying, not how the concepts of science are constantly being developed). Even if I am right, this does not seem problematic here, as the conversation shifted to the intended focus quickly (an example of Bruner's 'constant transnational calibration' perhaps?).
However, this reminds me of interviews with students I have carried out (and others I have listened to undertaken by colleagues), and of classroom episodes where teacher and student are agreeing – but actually are talking at cross purposes. Sometimes it becomes obvious to those involved that this is what has happened – but I wonder how often it goes undetected by either party. (And how often there are later recriminations – "but you said…"!)
Simplifying biology?
The final part of the extract above also caught my attention, as I was not sure what to make of it.
My heart beats, my lungs breathe, my brain is sending millions of signals to my body, at all times.
Correct.
Again, even, I mean, faster than the speed of light, right?
Correct.
Millions of signals every nanosecond, right?
Yes.
How frequently do our brains send out signals?
I am a chemistry and physicist, not a biologist so I was unsure what to make of the millions of signals the brain is sending out to the rest of the body every nanosecond.
I can certainly beleive that perhaps in a working human brain there will be billions of neutrons firing every nanosecond as they 'communicate' with each other. If my brain has something like 100 000 000 000 neurons then that does not seem entirely unreasonable.
But does the brain really send signals to the rest of the body (whether through nerves or by the release of hormones) at a rate of nx106/10-9 s-1 ("millions of signals every nanosecond"), that is, multiples of 1015 signals per second, as Mr Nelson suggests and Dr Tobin agrees?
Surely not? Dr Tobin is a professor of medicine and a much published expert in his field and should know better than me. But I would need some convincing.
Biological warp-drives
I will need even more convincing that the brain sends signals to the body faster than the speed of light. Both nervous and hormonal communication are many orders of magnitude slower than light speed. The speed of light is still considered to be a practical limit on the motion of massive objects (i.e., anything with mass). Perhaps signals could be sent by quantum entanglement – but that is not how our nervous and endocrine systems function?
If Mr Nelson and Dr Tobin do have good reason to believe that communication of signals in the human body can travel faster than the speed of light then this could be a major breakthrough. Science and technology have made many advances by mimicking, or learning from, features of the structure and function of living things. Perhaps, if we can learn how the body is achieving this impossible feat, warp-drive need not remain just science fiction.
A criminal trial is a very serious matter, and I do not intend these comments to be flippant. I watched the testimony genuinely interested in what the science had to say. The real audience for this exchange was the jury and I wonder what they made of this, if anything. Perhaps it should be seen as poetic language making a general point, and not a technical account to be analysed pedantically. But I think it does raise issues about how science is communicated to non-experts in contexts such as courtrooms.
This was an expert witness for the prosecution (indeed, very much for the prosecution) who was agreeing with the defence counsel on a point strictly contrary to accepted science. If I was on a jury, and an expert made a claim that I knew was contrary to current well-established scientific thinking (whether the earth came into being 10 000 years ago, or the brain sends out signals that travel faster then the speed of light) this would rather undermine my confidence in the rest of their expert testimony.
Once upon a time there was a nometal atom that was an electron short of a full outer shell. "I wish I had an octet" she said, "if only I knew a nice metal atom that might donate their extra electron to me"… Image by S. Hermann & F. Richter from Pixabay
Today I received one of those internet notifications intended to alert you to work that you might want to read:
Tangible interaction approach for learning chemical bonding"
An invitation to read
I was intrigued. Learning (and teaching) about chemical bonding concepts has been a long-standing interest of mine, and I have written quite a lot on the topic, so I clicked-through and downloaded the paper.
The abstract began
"In this paper we present ChemicAble, a Tangible User Interface (TUI) for teaching ionic bonding to students of grade 8 to 10. ChemicAble acts as an exercise tool for students to understand better the concepts of ionic bonding by letting them explore and learn…."
Ionic bonding – an often mislearnt topic
This led to mixed feelings.
Anything that can support learners in making sense of the abstract, indeed intangible, nature of chemical bonding offered considerable potential to help learners and support teachers. Making the abstract more concrete is often a useful starting point in learning about theoretical concepts. So, this seemed a very well-motivated project that could really be useful.
It is sometimes argued that educational research is something of an irrelevance as it seldom impacts on classroom practice. In my (if, perhaps, biased) experienced, this is not so – but it is unrealistic to expect research to bring about widespread changes in educational practice quickly, and arguments that most teachers do not read research journals and so do not know who initiated particular proposals has always seemed to me to be missing the point. We are not looking for teachers to pass tests on the content of research literature, and it is quite natural that the influence of research is usually indirect through, for example, informing teacher education and development programmes, or through revisions of curriculum, recommended teaching schemes, or formal standards.
This study by Agrawal and colleagues was not a theoretical treatise but a report of the implementation of a tool to support teaching and learning – the kind of thing that could directly impact teaching. So this was all promising.
However,I also knew only too well that ionic bonding was a tricky topic. When I started research into learners' developing understanding of chemical bonding (three decades ago, now) I read several studies suggesting there were common alternative conceptions, that is misunderstandings, of ionic bonding found among students (e.g., Butts & Smith, 1987).
My own research suggested these were not just isolated notions, but often reflected a coherent alternative conceptual framework for ionic bonding that I labelled the 'molecular' framework (Taber, 1994, 1997). Research I have seen from other contexts since, leads me to believe this is an international phenomenon, and not limited to a specific curriculum context (Taber, 2013).
secondary level students very commonly develop an alternative understanding of ionic bonding inconsistent with the scientific account…
…which they find difficult to move beyond should they continue to college level chemistry…
… and which they are convinced is what they were taught
Moreover, I strongly suspect that in quite a few cases, the alternative, incorrect model, is being taught. It is certainly presented, or at least implied, in a good many textbooks, and on a wide range of websites claiming to teach chemistry. I also suspect that in at least some cases, teachers are teaching this, themselves thinking it is an acceptable approximation to the scientific account.
So, I scanned the paper to see what account of the science was used as the basis for planning this teaching tool. I found this parenthetical account:
"{As stated in the NCERT book on Science for class X, chapter 3, 4, the electrons present in the outermost shell of an atom are known as the valence electrons. The outermost shell of an atom can accommodate a maximum of 8 electrons. Atoms of elements, having a completely filled outermost shell show little chemical activity. Of these inert elements, the helium atom has two electrons in its outermost shell and all other elements have atoms with eight electrons in the outermost shell.
The combining capacity of the atoms of other elements is explained as an attempt to attain a fully-filled outermost shell (8 electrons forming an octet). The number of electrons gained, lost or shared so as to make the octet of electrons in the outermost shell, gives us directly the combining capacity of the element called the valency. An ion is a charged particle and can be negatively or positively charged. A negatively charged ion is called an 'anion' and the positively charged ion, a 'cation'. Metals generally form cations and non-metals generally form anions. Atoms have tendency to complete their octet by this give and take of electron forming compounds. Compounds that are formed by electron transfer from metals to non-metals are called ionic compounds.}"
Agrawal et al., 2013 (no page numbers)
There are quite a few ideas here, and quite a lot of his account is perfectly canonical, at least at the level of description suitable for secondary school, introductory, chemistry. However, sprinkled in are some misleading statements.
So,
Curriculum statement
Commentary
"…the electrons present in the outermost shell of an atom are known as the valence electrons."
Fine
"The outermost shell of an atom can accommodate a maximum of 8 electrons."
This is only correct for period 2.
It is false false for period 1 (2 electrons), period 3 (18 electrons), period 4 (32 electrons), etcetera.
"Atoms of elements, having a completely filled outermost shell show little chemical activity. Of these inert elements, the helium atom has two electrons in its outermost shell and all other elements have atoms with eight electrons in the outermost shell."
Fine – apart from the reference to "completely filled outermost shell"
Of the noble gases, only helium and neon have full outer shells.
'Atoms' of the heavier noble gases with full outer shells would not atoms, but ions, and these would be extremely unstable – i.e., they could not exist except hypothetically under extreme conditions of very intense electrical fields.
"The combining capacity of the atoms of other elements is explained as an attempt to attain a fully-filled outermost shell (8 electrons forming an octet). The number of electrons gained, lost or shared so as to make the octet of electrons in the outermost shell, gives us directly the combining capacity of the element called the valency."
Hm – generally the valency can be identified with the difference between an atom's electronic configuration and the 'nearest' noble gas electronic configuration – which would be an octet of valence shell electrons, except in period one.
However, the equivalence suggested here "a fully-filled outermost shell (8 electrons forming an octet)" is only true for period 2. An octet does not suffice for a full outer shell in period 3 (full at 18 electrons), or in period 4 (full at 32 electrons), etcetera.
And, in the statement, valency is described as being related to the intentions of atoms: "is explained as an attempt to attain…" (and "…electrons gained, lost or shared so as to…") which encourages student misconceptions. [Read about 'Learners' anthropomorphic thinking'.]
"An ion is a charged particle and can be negatively or positively charged. A negatively charged ion is called an 'anion' and the positively charged ion, a 'cation'. Metals generally form cations and non-metals generally form anions."
Fine.
"Atoms have tendency to complete their octet by this give and take of electron forming compounds."
This is a common notion, but actually suspect. Some elements have an electron affinity such that the atoms would tend to pick up an electron spontaneously.
However, for an element with a valency of -2, such as oxygen, once it has become a singly charged anion (O–), it will not attract a second electron, so apart from the halogens, this is misleading. The negatively charged O– ion will indeed spontaneously repel/be repelled by a (negatively charged) electron.
Metallic elements have ionisation enthalpies showing that energy has to be applied to strip electrons from them – they certainly do not have a "tendency to complete their octet by this giv[ing]" of electrons.
"Compounds that are formed by electron transfer from metals to non-metals are called ionic compounds."
This is not usually how ionic compounds are formed. Although it is possible in the lab. to use binary synthesis (e.g., burning sodium in chlorine – not for the faint-hearted), that is not how ionic compounds are prepared in industry, or how the NaCl in table salt formed naturally.
(And even when burning sodium in chlorine, neither of the reactants are atomic, so even here there is no simple transfer of electrons between atoms.)
So this account is a mixture of the generally correct; the potentially misleading; and the downright wrong.
Agrawal and colleagues describe an ingenuous apparatus they had put together so that students can physically manipulate tokens to see ionic bond formation represented. This looks like something that younger secondary children would really enjoy.
They also report a small-scale informal evaluation of a classroom test of the apparatus with an unspecified number of students, reporting very positive responses. The children generally found the apparatus easy to use, the information it represented easy to understand, and they thought it helped them learn about chemical [ionic] compound formation. So this seems very successful.
However, what did it help them learn?
The teaching model
"For example, when a token representing [a] sodium atom is placed on the table top, its valence shell (outermost shell) with 1 revolving valence electron is displayed around the token. When the student places a chlorine atom on the table, its valence shell along with 7 revolving valence electrons is displayed. The electron from the sodium atom gets transferred to the chlorine atom. +1 charge appears on the sodium atom due to loss of electron and -1 charge appears on the chlorine atom due to gain of electron. Both form a stable compound. The top bar on the user interface turns green to show success and displays the name of the stable compound so formed (sodium chloride, in this case). The valence shell of the atoms also turns green to show a stable compound."
Agrawal et al., 2013 (no page numbers)
Which sounds impressive, except NaCl is not formed by electron transfer, and with the ChemicAble the resulting structure is a single Na+-Cl– ion pair, which does not represent the structure of the NaCl compound, and indeed would not be a stable structure.
Does it matter if children are taught scientific fairy tales?
The innovation likely motivated learners. And the authors seem to be basing their 'ChemicAble' on the curriculum models set out in the model science books produced by the Indian National Council of Educational Research and Training. So, the authors have produced something that helps children learn the science curriculum in that context,and so presumably what students will subsequently be examined on. Given that, it seems churlish to point out that what is being taught is scientifically wrong.
So, I find it hard to be critical of the authors, but I do wonder why governments want children to learn scientific fairy tales that are nonsense. The electron transfer model of ionic bonding seems to be popular with teachers, and received well by learners, so if the aim of education is to find material to teach that we can then test children on (so they can be graded, rated, sequences, selected), what is the problem? After all, I am a strong advocate for the idea that what we teach in school science is usually, necessarily, a simplification of the science – and indeed is basically a set of models – and not some absolute account of the universe.
Here the children, the teacher and the researchers have all put a lot of effort into helping learners acquire a scientifically incorrect account of ionic bonding. We think children should learn about the world at the molecular, naometre scale as this is such an important part of chemistry as a science. Yet, to my mind, if we are going to ask children to put time and effort into learning abstract models of the structure of nature at submicroscopic levels, even though we know this is challenging for them, then, although we need to work with simplified models, these should at least be intellectually honest models, and not accounts that we know are completely inauthentic and do not reflect the science. This is why I have been so critical of the incoherence and errors in the chemistry in the English National Curriculum (Taber, 2020).
Otherwise, education is reduced to a game for its own sake, and we may as well ask students to learn random Latin texts, or the plots of Grimms' Fairy Tales, or even the chemical procedures obscured by disguised reagents and allegorical language in alchemical texts, and then test them on how much they retain.
Actually, no, this learning of false models is worse than that, because learning these incorrect accounts confuses students and impedes their learning of the canonical scientific models if they later go on to study the subject further. So, if it is important that children learn something about ionic bonding, let's teaching something that is scientifically authentic and stop offering fairly tales about atoms wanting to fill their shells.
Sources cited:
Agrawal, M., Jain, M., Luthra, V., Thariyan, A., & Sorathia, K. (2013). ChemicAble: Tangible interaction approach for learning chemical bonding. Paper presented at the Proceedings of the 11th Asia Pacific Conference on Computer Human Interaction.
Butts, B., & Smith, R. (1987). HSC Chemistry Students' Understanding of the Structure and Properties of Molecular and Ionic Compounds. Research in Science Education, 17(1), 192-201.
Taber, K. S. (1994). Misunderstanding the Ionic Bond. Education in Chemistry, 31(4), 100-103.
Taber, K. S. (1997). Student understanding of ionic bonding: molecular versus electrostatic thinking?School Science Review, 78(285), 85-95.
There are many postings here about things that learners said, and so presumably thought, about curriculum topics that would likely surprise, if not shock, the teachers who had taught them those topics. I am certainly not immune from being misunderstood. Today, I reflect on how someone seems to have understood some of my own teaching, and indeed seriously objected to it.
When I have called-out academic malpractice in this blog the targets have usually been conference organisers or journal administrators using misleading (or downright dishonest) techniques, or publishers mistreating authors. I feel somewhat uneasy about publicly contradicting a junior scholar. However, I also do not appreciate being publicly described as deliberately misleading a student, as has happened here, and my direct challenge to the blog author was rejected.
The accusation
A while back some Faculty colleagues referred me to a blog that included the following comments:
In the Faculty of Education students pursuing the MPhil or PhD take a research ethics lecture that presents the Tuskegee Syphilis Study as ethically sound, but only up to the year 1947 when penicillin was actively being used to treat syphilis. According to the Cambridge lecturer, that's the point when the study became unethical.
When I interrupted his lecture to object to his presentation, I was told by that lecturer that he'd never received any objections in his many, many years of teaching the same slides on the same course. That was not true. He knew and the Faculty knows and yet that false information continues to be disseminated to students, many of whom will go on to complete research in developing countries where their only reference for their ethical or unethical behavior is this lecture.
I am not named, but virtually anyone in my Faculty, or having taken graduate studies there in the last few years, would surely know who was being discussed. As is pointed out in our Educational Research course, and the Research Methods strand of other graduate courses, if you want to avoid someone being identified in your writing, it is not enough to not name them. I can be fairly confident the author of the comments above should have known that: it is a point made in the very lecture being criticised.
This blog posting seems to have received quite a lot of attention among students at the University Faculty where I worked. Yet the two claims here are simply not correct. The teaching is seriously misrepresented, and I certainly did not lie to this student.
The blog invited me to 'Leave a Reply', so I did. My comments were subject to moderation – and the next morning I found a response in my email in-box. My comments would not be posted, and the claims would not be amended: I was welcome to post my reply elsewhere, but not at the site where I was being criticised. So, here goes:
The (rejected) reply
I hope you are well.
I was directed to your blog by a group of scholars in the Faculty (Of Education at Cambridge). It is an impressive blog. However, I was rather surprised by some of what you have posted. I was the lecturer you refer to in your posting who taught the lecture on research ethics. I do indeed remember you interrupting me when I was presenting the Tuskagee syphilis study as an example of unethical research. I always encouraged students to participate in class, and would have welcomed your input at the end of my treatment of that example.
However, having read your comments here, I do need to challenge your account. I do not consider that the Tuskegee syphilis study was initially ethically sound, and I do not (and did not) teach that. I certainly did make the point that even if the study had been ethical until antibiotics were widely available, continuing it beyond that point would have been completely unjustifiable. But that was certainly not the only reason the study was unethical. Perhaps this would have been clearer if you had let me finish my own comments before interjecting – but even so I really do not understand how you could have interpreted the teaching that way.
Scheme (an annotated version of 'the ethical field', Taber, 2013a, Figure 9.1) used to summarise ethical issues in the Tuskegee syphilis study in my Educational Research lecture on ethical considerations of research.
The reference to 1947 in the posting quoted above relates to the 'continue' issue under research quality – the research (which involved medical staff periodically observing, but not treating, diseased {black, poor, mostly illiterate} men who had not been told of the true nature of their condition) was continued even when effective, safe treatment was available and any claims to the information being collected having potential to inform medical practice became completely untenable.
I may well have commented that no one had ever raised any objections to the presentation when I had given the lecture on previous occasions over a number of years – because that is true. No one had previously raised any concerns with me regarding my teaching of this example (or any aspect of the lecture as far as I can recall). I am not sure why you seem to so confidently assume otherwise: regarding this, you are simply wrong.
Usually in that lecture I would present a brief account of the Milgram 'learning' experiment, which would often lead to extended discussion about the ethical problems of that research in relation to its motivation and what was usefully learnt from it. Then, later in the session, I would talk about the Tuskegee study, which normally passed without comment. I had always assumed that was because the study is so obviously and seriously problematic that no one would see any reason to disagree with my critique. Then I would go on to discuss other issues and studies. I can assure you that no one had previously, before you, raised any concerns about my teaching of this example with me. If anyone in earlier cohorts had any concerns about this example they would have been welcome to talk to me about them – either in class, or privately afterwards. No one ever did.
I have no reason to believe that colleagues at Cambridge are deliberately disseminating false information to students, but then I do not audit other teaching officers' lectures, and I cannot speak for them. However, I can speak for myself, just as you rightly speak up for yourself. I have certainly always taken care to do my best not to teach things that are not the case. Of course, as a school and college science teacher I was often teaching models and simplifications, and not the 'whole' truth, but that is the nature of pedagogy, and is something we should make clear to learners (i.e., that they are being taught models and simplifications that can later in their studies be developed through more sophisticated treatments).
In a similar way, I used simplifications and models in my research methods lectures at Cambridge – for example, in terms of the 'shape' of a research project, or contrasting paradigms, or types of qualitative analysis, and so on, but would make explicit to the class that this is what they were: 'teaching models'. I entered the teaching profession to make a positive difference; to help learners develop, and to acquire new understandings and perspectives and skills; not to misinform people. I very much suspect that on occasions I must have got some things wrong, but, if so, such errors would always have been honest mistakes. I have never knowingly taught something that I thought was untrue.
So, whilst I admire your courage in standing up for what you believe, and I certainly wish you well, what you have written is not correct, and I trust my response will be posted so that your inaccurate remarks will not go unchallenged. I suspect that you are not being deliberately untruthful (you accuse me of telling you something I knew was not true: I try to be charitable and give people the benefit of doubt, so I would like to think that you were writing your comments in good faith), but I do not understand how you managed to come to the interpretation of my teaching that you did, and wish that you would have at least heard me out before interrupting the class, as that may have clarified my position for you. The Tuskegee syphilis study was a racist, unethical study that misled and abused some of those people with the lowest levels of economic and political power in society: people (not just the men subjected to the study, but also their families) who were betrayed by those employed by the public health service that they trusted (and should have been able to trust) to look after their interests. I do not see how anyone could consider it an ethically sound study, and I struggle to see why you would think anyone could.
Your claim that I lied about not having previously received complaints about my teaching of this topic before is simply untrue – it is a falsehood that I hope you will be prepared to correct.
What should a 'constructivist' teacher make of this?
I should be careful about criticising a student for thinking I was teaching something quite different from what I thought I was teaching. I have spent much of my career telling other teachers that learners will make sense of our teaching in terms of the interpretive resources they have available, and so they may interpret our teaching in unexpected ways. Learners will always be biased to understand in terms of their expectations and past experiences. We see it all the time in science teaching, as many of the posts here demonstrate.
I have described learning as being an incremental, interpretive, and so iterative, process and not a simple transfer of understanding (Taber, 2014). Teaching (indeed communication) is always a representation of thinking in a publicly accessible form (speech, gesture, text, diagrams {what sense does the figure above make out of the context of the lecture?}, models, etc.) – and whatever meaning may have informed the production of the representation, the representation itself does not have or contain meaning: the person accessing that presentation has to impose their own interpretation to form a meaning (Taber, 2013b). After teaching and writing about these ideas, I would be a hypocrite to claim that a learner could not misinterpret my own teaching as I can communicate perfectly to a room full of students from all around the world with different life experiences and varied disciplinary backgrounds!
Even so, I am still struggling to understand the interpretation put on my teaching in this case, despite going back to revisit the teaching materials a number of times. Most of the points I was making must have been completed disregarded to think I did not consider the study, which ran from 1932 to 1972 (Jones, 1993) unethical until 1947. So, even for someone who claims to be a constructivist teacher and knows there is always a risk of learners misconceiving teaching, this example seems an extreme case.
The confident claim that it was not true that I had not received previous complaints about my teaching of this example is even harder to understand. It is at least a good reminder for me not to assume I know what students are thinking or that they know what I am thinking, or can readily access the intended meaning in my teaching. I've made those points to others enough times, so I will try to see this incident as a useful reminder to follow my own advice.
Sources cited:
Jones, J. H. (1993). Bad Blood: The Tuskegee Syphilis Experiment (New and expanded ed.). New York: The Free Press.
When is "a case study" not a case study? Perhaps when it is (nearly) an experiment?
Keith S. Taber
I read this interesting study exploring learners shifting conceptions of the particulate nature of gases.
Mamombe, C., Mathabathe, K. C., & Gaigher, E. (2020). The influence of an inquiry-based approach on grade four learners' understanding of the particulate nature of matter in the gaseous phase: a case study. EURASIA Journal of Mathematics, Science and Technology Education, 16(1), 1-11. doi:10.29333/ejmste/110391
Key features:
Science curriculum context: the particulate nature of matter in the gaseous phase
Educational context: Grade 4 students in South Africa
Pedagogic context: Teacher-initiated inquiry approach (compared to a 'lecture' condition/treatment)
Methodology: "qualitative pre-test/post-test case study design" – or possibly a quasi-experiment?
Population/sample: the sample comprised 116 students from four grade four classes, two from each of two schools
This study offers some interesting data, providing evidence of how students represent their conceptions of the particulate nature of gases. What most intrigued me about the study was its research design, which seemed to reflect an unusual hybrid of quite distinct methodologies.
In this post I look at whether the study is indeed a case study as the authors suggest, or perhaps a kind of experiment. I also make some comments about the teaching model of the states of matter presented to the learners, and raise the question of whether the comparison condition (lecturing 8-9 year old children about an abstract scientific model) is appropriate, and indeed ethical.
Learners' conceptions of the particulate nature of matter
This paper is well worth reading for anyone who is not familiar with existing research (such as that cited in the paper) describing how children make sense of the particulate nature of matter, something that many find counter-intuitive. As a taster for this, I reproduce here two figures from the paper (which is published open access under a creative common license* that allows sharing and adaption of copyright material with due acknowledgement).
Conceptions are internal, and only directly available to the epistemic subject, the person holding the conception. (Indeed, some conceptions may be considered implicit, and so not even available to direct introspection.) In research, participants are asked to represent their understandings in the external 'public space' – often in talk, here by drawing (Taber, 2013). The drawings have to be interpreted by the researchers (during data analysis). In this study the researchers also collected data from group work during learning (in the enquiry condition) and by interviewing students.
What kind of research design is this?
Mamombe and colleagues describe their study as "a qualitative pre-test/post-test case study design with qualitative content analysis to provide more insight into learners' ideas of matter in the gaseous phase" (p. 3), yet it has many features of an experimental study.
The study was
"conducted to explore the influence of inquiry-based education in eliciting learners' understanding of the particulate nature of matter in the gaseous phase"
p.1
The experiment compared two pedagogical treatments :
"inquiry-based teaching…teacher-guided inquiry method" (p.3) guided by "inquiry-based instruction as conceptualized in the 5Es instructional model" (p.5)
"direct instruction…the lecture method" (p.3)
These pedagogic approaches were described:
"In the inquiry lessons learners were given a lot of materials and equipment to work with in various activities to determine answers to the questions about matter in the gaseous phase. The learners in the inquiry lessons made use of their observations and made their own representations of air in different contexts."
"the teacher gave probing questions to learners who worked in groups and constructed different models of their conceptions of matter in the gaseous phase. The learners engaged in discussion and asked the teacher many questions during their group activities. Each group of learners reported their understanding of matter in the gaseous phase to the class"
p.5, p.1
"In the lecture lessons learners did not do any activities. They were taught in a lecturing style and given all the notes and all the necessary drawings.
In the lecture classes the learners were exposed to lecture method which constituted mainly of the teacher telling the learners all they needed to know about the topic PNM [particulate nature of matter]. …During the lecture classes the learners wrote a lot of notes and copied a lot of drawings. Learners were instructed to paste some of the drawings in their books."
pp.5-6
The authors report that,
"The learners were given clear and neat drawings which represent particles in the gaseous, liquid and solid states…The following drawing was copied by learners from the chalkboard."
This figure shows increasing separation between particles moving from solid to liquid to gas. It is not a canonical figure, in that the spacing in a liquid is not substantially greater than in a solid (indeed, in ice floating on water the spacing is greater in the solid), whereas the difference in spacing in the two fluid states is under-represented.
Such figures do not show the very important dynamic aspect: that in a solid particles can usually only oscillate around a fixed position (a very low rate of diffusion not withstanding), where in a liquid particles can move around, but movement is restricted by the close arrangement of (and intermolecular forces between) the particles, where in a gas there is a significant mean free path between collisions where particles move with virtually constant velocity. A static figure like this, then, does not show the critical differences in particle interactions which are core to the basic scientific model
Perhaps even more significant, figure 2 suggests there is the same level of order in the three states, whereas the difference in ordering between a solid and liquid is much more significant than any change in particle spacing.
In teaching, choices have to be made about how to represent science (through teaching models) to learners who are usually not ready to take on board the full details and complexity of scientific knowledge. Here, Figure 2 represents a teaching model where it has been decided to emphasise one aspect of the scientific model (particle spacing) by distorting the canonical model, and to neglect other key features of the basic scientific account (particle movement and arrangement).
External teachers taught the classes
The teaching was undertaken by two university lecturers
"Two experienced teachers who are university lecturers and well experienced in teacher education taught the two classes during the intervention. Each experienced teacher taught using the lecture method in one school and using the teacher-guided inquiry method in the other school."
p.3
So, in each school there was one class taught by each approach (enquiry/lecture) by a different visiting teacher, and the teachers 'swapped' the teaching approaches between schools (a sensible measure to balance possible differences between the skills/styles of the two teachers).
The research design included a class in each treatment in each of two schools
An experiment; or a case study?
Although the study compared progression in learning across two teaching treatments using an analysis of learner diagrams, the study also included interviews, as well as learners' "notes during class activities" (which one would expect would be fairly uniform within each class in the 'lecture' treatment).
The outcome
The authors do not consider their study to be an experiment, despite setting up two conditions for teaching, and comparing outcomes between the two conditions, and drawing conclusions accordingly:
"The results of the inquiry classes of the current study revealed a considerable improvement in the learners' drawings…The results of the lecture group were however, contrary to those of the inquiry group. Most learners in the lecture group showed continuous model in their post-intervention results just as they did before the intervention…only a slight improvement was observed in the drawings of the lecture group as compared to their pre-intervention results"
pp.8-9
These statements can be read in two ways – either
a description of events (it just happened that with these particular classes the researchers found better outcomes in the enquiry condition), or
as the basis for a generalised inference.
An experiment would be designed to test a hypothesis (this study does not seem to have an explicit hypothesis, nor explicit research questions). Participants would be assigned randomly to conditions (Taber, 2019), or, at least, classes would be randomly assigned (although then strictly each class should be considered as a single unit of analysis offering much less basis for statistical comparisons). No information is given in the paper on how it was decided which classes would be taught by which treatment.
Representativeness
A study could be carried out with the participation of a complete population of interest (e.g., all of the science teachers in one secondary school), but more commonly a sample is selected from a population of interest. In a true experiment, the sample has to be selected randomly from the population (Taber, 2019) which is seldom possible in educational studies.
The study investigated a sample of 'grade four learners'
In Mamombe and colleagues' study the sample is described. However, there is no explicit reference to the population from which the sample is drawn. Yet the use of the term 'sample' (rather than just, say, 'participants') implies that they did have a population in mind.
The aim of the study is given as to "to explore the influence of inquiry-based education in eliciting learners' understanding of the particulate nature of matter in the gaseous phase" (p.1) which could be considered to imply that the population is 'learners'. The title of the paper could be taken to suggest the population of interests is more specific: "grade four learners". However, the authors make no attempt to argue that their sample is representative of any particular population, and therefore have no basis for statistical generalisation beyond the sample (whether to learners, or to grade four learners, or to grade four learners in RSA, or to grade four learners in farm schools in RSA, or…).
Indeed only descriptive statistics are presented: there is no attempt to use tests of statistical significance to infer whether the difference in outcomes between conditions found in the sample would probably have also been found in the wider population.
(That is inferential stats. are commonly used to suggest 'we found a statistically significant better outcome in one condition in our sample, so in the hypothetical situation that we had been able to include the entire population in out study we would probably have found better mean outcomes in that same condition'.)
This may be one reason why Mamombe and colleagues do not consider their study to be an experiment. The authors acknowledge limitations in their study (as there always are in any study) including that "the sample was limited to two schools and two science education specialists as instructors; the results should therefore not be generalized" (p.9).
Yet, of course, if the results cannot be generalised beyond these four classes in two schools, this undermines the usefulness of the study (and the grounds for the recommendations the authors make for teaching based on their findings in the specific research contexts).
If considered as an experiment, the study suffers from other inherent limitations (Taber, 2019). There were likely novelty effects, and even though there was no explicit hypothesis, it is clear that the authors expected enquiry to be a productive approach, so expectancy effects may have been operating.
Analytical framework
In an experiment is it important to have an objective means to measure outcomes, and this should be determined before data are collected. (Read about 'Analysis' in research studies.). In this study methods used in previous published work were adopted, and the authors tell us that "A coding scheme was developed based on the findings of previous research…and used during the coding process in the current research" (p.6).
But they then go on to report,
"Learners' drawings during the pre-test and post-test, their notes during class activities and their responses during interviews were all analysed using the coding scheme developed. This study used a combination of deductive and inductive content analysis where new conceptions were allowed to emerge from the data in addition to the ones previously identified in the literature"
p.6
An emerging analytical frame is perfectly appropriate in 'discovery' research where a pre-determined conceptualisation of how data is to be understood is not employed. However in 'confirmatory' research, testing a specific idea, the analysis is operationalised prior to collecting data. The use of qualitative data does not exclude a hypothesis-testing, confirmatory study, as qualitative data can be analysed quantitatively (as is done in this study), but using codes that link back to a hypothesis being tested, rather than emergent codes. (Read about 'Approaches to qualitative data analysis'.)
Much of Mamombe and colleagues' description of their work aligns with an exploratory discovery approach to enquiry, yet the gist of the study is to compare student representations in relation to a model of correct/acceptable or alternative conceptions to test the relative effectiveness of two pedagogic treatments (i.e., an experiment). That is a 'nomothetic' approach that assumed standard categories of response.
Overall, the author's account of how they collected and analysed data seem to suggest a hybrid approach, with elements of both a confirmatory approach (suitable for an experiment) and elements of a discovery approach (more suitable for case study). It might seem this is a kind of mixed methods study with both confirmatory/nomothetic and discovery/idiographic aspects – responding to two different types of research question the same study.
Yet there do not actually seem (**) to be two complementary strands to the research (one exploring the richness of student's ideas, the other comparing variables – i.e., type of teaching versus degree of learning), but rather an attempt to hybridise distinct approaches based on incongruent fundamental (paradigmatic) assumptions about research. (** Having explicit research questions stated in the paper could have clarified this issue for a reader.)
So, do we have a case study?
Mamombe and colleagues may have chosen to frame their study as a kind of case study because of the issues raised above in regard to considering it an experiment. However, it is hard to see how it qualifies as case study (even if the editor and peer reviewers of the EURASIA Journal of Mathematics, Science and Technology Education presumably felt this description was appropriate).
Mamombe and colleagues do use multiple data sources, which is a common feature of case study. However, in other ways the study does not meet the usual criteria for case study. (Read more about 'Case study'.)
For one thing, case study is naturalistic. The method is used to study a complex phenomena (e.g., a teacher teaching a class) that is embedded in a wider context (e.g., a particular school, timetable, cultural context, etc.) such that it cannot be excised for clinical examination (e.g., moving the lesson to a university campus for easy observation) without changing it. Here, there was an intervention, imposed from the outside, with external agents acting as the class teachers.
Even more fundamentally – what is the 'case'?
A case has to have a recognisable ('natural') boundary, albeit one that has some permeability in relation to its context. A classroom, class, year group, teacher, school, school district, etcetera, can be the subject of a case study. Two different classes in one school, combined with two other classes from another school, does not seem to make a bounded case.
In case study, the case has to be defined (not so in this study); and it should be clear it is a naturally occurring unit (not so here); and the case report should provide 'thick description' (not provided here) of the case in its context. Mamombe and colleagues' study is simply not a case study as usually understood: not a "qualitative pre-test/post-test case study design" or any other kind of case study.
That kind of mislabelling does not in itself does not invalidate research – but may indicate some confusion in the basic paradigmatic underpinnings of a study. That seems to be the case [sic] here, as suggested above.
Suitability of the comparison condition: lecturing
A final issue of note about the methodology in this study is the nature of one of the two conditions used as a pedagogic treatment. In a true experiment, this condition (against which the enquiry condition was contrasted) would be referred to as the control condition. In a quasi-experiment (where randomisation of participants to conditions is not carried out) this would usually be referred to as the comparison condition.
At one point Mamombe and colleagues refer to this pedagogic treatment as 'direct instruction' (p.3), although this term has become ambiguous as it has been shown to mean quite different things to different authors. This is also referred to in the paper as the lecture condition.
Is the comparison condition ethical?
Parental consent was given for students contributing data for analysis in the study, but parents would likely trust the professional judgement of the researchers to ensure their children were taught appropriately. Readers are informed that "the learners whose parents had not given consent also participated in all the activities together with the rest of the class" (p.3) so it seems some children in the lecture treatment were subject to the inferior teaching approach despite this lack of consent, as they were studying "a prescribed topic in the syllabus of the learners" (p.3).
I have been very critical of a certain kind of 'rhetorical' research (Taber, 2019) report which
begins by extolling the virtues of some kind of active / learner-centred / progressive / constructivist pedagogy; explaining why it would be expected to provide effective teaching; and citing numerous studies that show its proven superiority across diverse teaching contexts;
then compares this with passive modes of learning, based on the teacher talking and giving students notes to copy, which is often characterised as 'traditional' but is said to be ineffective in supporting student learning;
then describes how authors set up an experiment to test the (superior) pedagogy in some specific context, using as a comparison condition the very passive learning approach they have already criticised as being ineffective as supporting learning.
My argument is that such research is unethical
It is not genuine science as the researchers are not testing a genuine hypothesis, but rather looking to demonstrate something they are already convinced of (which does not mean they could not be wrong, but in research we are trying to develop new knowledge).
It is not a proper test of the effectiveness of the progressive pedagogy as it is being compared against a teaching approach the authors have already established is sub-standard.
Most critically, young people are subjected to teaching that the researchers already believe they know will disadvantage them, just for the sake of their 'research', to generate data for reporting in a research journal. Sadly, such rhetorical studies are still often accepted for publication despite their methodological weaknesses and ethical flaws.
I am not suggesting that Mamombe, Mathabathe and Gaigher have carried out such a rhetorical study (i.e., one that poses a pseudo-question where from the outset only one outcome is considered feasible). They do not make strong criticisms of the lecturing approach, and even note that it produces some learning in their study:
"Similar to the inquiry group, the drawings of the learners were also clearer and easier to classify after teaching"
"although the inquiry method was more effective than the lecture method in eliciting improved particulate conception and reducing continuous conception, there was also improvement in the lecture group"
p.9, p.10
I have no experience of the South African education context, so I do not know what is typical pedagogy in primary schools there, nor the range of teaching approaches that grade 4 students there might normally experience (in the absence of external interventions such as reported in this study).
It is for the "two experienced teachers who are university lecturers and well experienced in teacher education" (p.3) to have judged whether a lecture approach based on teacher telling, children making notes and copying drawings, but with no student activities, can be considered an effective way of teaching 8-9 year old children a highly counter-intuitive, abstract, science topic. If they consider this good teaching practice (i.e., if it is the kind of approach they would recommend in their teacher education roles) then it is quite reasonable for them to have employed this comparison condition.
However, if these experienced teachers and teacher educators, and the researchers designing the study, considered that this was poor pedagogy, then there is a real question for them to address as to why they thought it was appropriate to implement it, rather than compare the enquiry condition with an alternative teaching approach that they would have expected to be effective.
Sources cited:
Mamombe, C., Mathabathe, K. C., & Gaigher, E. (2020). The influence of an inquiry-based approach on grade four learners' understanding of the particulate nature of matter in the gaseous phase: a case study. EURASIA Journal of Mathematics, Science and Technology Education, 16(1), 1-11. doi:10.29333/ejmste/110391
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