Category: alternative conception

Scientific errors in the English National Curriculum

Keith S. Taber

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)

We can't handle the scientific truth

"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?

Thank you, BBC: I'll give you 4/5

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.

(Read 'Are plants solid?')

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.

Do nerve signals travel faster than the speed of light?

Keith S. Taber

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).

[Read 'Court TV: science in the media']

Prof. Martin J. Tobin, M.D., Loyola University Chicago Medical Center

I was watching the cross examination of expert witness Dr Martin J. Tobin, Professor of Pulmonary and Critical Care Medicine by defence attorney Eric Nelson, and was intrigued by the following exchange:

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.

 

 

 

Temperature is measuring the heat of something …

Keith S. Taber

Image by Peter Janssen from Pixabay 

Bill was a participant in the Understanding Science Project. Bill, then in Y7, was telling me about work he had done in his science class on the states of matter, and what happened to the particles that made up objects during a change of state. He suggested that "when a solid goes to a liquid, the heat gives the particles energy to spread about, and then when its a liquid, it's got even more energy to spread out into a gas". Later in the interview I followed up to find out what Bill understood by heat:

Now you mentioned earlier, something about heat. When you were talking about the experiment you did.

Yeah.

Yeah. So tell me about the heat again, what's, how does the heat get involved in this solids, liquids and gases?

When I heat, when heat comes to a solid, it will have, erm, a point where it will go down to a liquid,

Okay,

A melting points of the, the object.

Do you know what heat is? If you had a younger brother or sister, and they said to you, 'you are good at science, what's heat?'

I'm not sure how I can explain it, 'cause it's, it can be measured at different temperature, it can be measured at temperature, erm, by degrees Celsius, degrees Fahrenheit, and – I'm not really sure how I could explain what it is, but, I know it can be measured and changed.

So is it the same thing as temperature, do you think, or is it something different?

Erm, I think temperature is measuring the heat of something.

So they're related, they're to do with each other?

Yeah.

But they are not exactly the same?

No.

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

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

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

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

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

.

A tangible user interface for teaching fairy tales about chemical bonding

Keith S. Taber

Image by S. Hermann & F. Richter from Pixabay
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:

"You wrote the paper A common core to chemical conceptions: learners' conceptions of chemical…. A related paper is available on Academia.

Tangible interaction approach for learning chemical bonding"

an invitation to read
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).

(Read about 'the Understanding Chemical Bonding project')

Ionic bonding – an often mistaught topic?

Indeed, I feel confident in suggesting:

  • 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.

(Read about 'The molecular framework for ionic bonding')

A curriculum model of ionic bonding

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:
 
 

 

Chlorine atoms share electrons to fill in their shells

Umar was a participant in the Understanding Chemical Bonding project. When I spoke to him in the first term of his course he was unsure whether tetrachloromethane (CCl4) would have ionic or covalent bonding.

When I spoke to him near the start of his second term, I asked him again about this. Umar then thought this compound would have polar bonding, however he seemed to have difficulty explaining what this meant ⚗︎ . Given his apparently confused notion about the C-Cl bond I decided to turn the conversation to a covalent bond which I knew, well certainly believed, was more familiar to him.

Is it possible for chlorine to form a bond with another chlorine?

[Pause, c.2s]

Yeah.

What substance would you get if two chlorine atoms formed a bond?

[Pause, c.2s]

You get, it still, you get, if you had like two chlorines it depends what groups are attached to it, to see how electronegative or electropositive they are.

What about if you just had two chlorine atoms joined together and nothing else, is that possible?

[Pause, c.3s]

No.

No?

On their own.

Not on their own?

No.

Umar's response here rather surprised me, as I was pretty confident that Umar had met chlorine as an element, and would know it was comprised of diatomic molecules: Cl2.

So you couldn’t have sort of Cl2, a molecule of Cl2?

[Pause, c.1s]

Yeah, you could do.

Could you?

[Pause, c.2s]

They might be just, they might be like, be covalently bonded.

Perhaps the earlier context of talking about polar bonds and the trichloroethane molecule somehow acted as a kind of impediment to Umar remembering about the chlorine molecule. It seemed that my explicit reference to the formula, Cl2, (eventually) activated his knowledge of the molecule bringing to mind something he had forgotten. Although he suggested the bond was (actually "might be") covalent, this seemed less something that he confidently recalled, than something he was inferring from what he could remember – or perhaps even guessing at what seemed reasonable: "they might be just, they might be like, be covalently bonded".

As often happens in talking to learners in depth about their ideas it becomes clear that thinking of students 'knowing' or 'not knowing' particular things is a fairly inadequate way of conceptualising their cognition, which is often nuanced and context-dependent. This suggests that what students respond in written tests should be considered only as what they were triggered to write on that day in response to those particular questions, and may not fully reflect their knowledge and understanding of science topics. Other slightly different questions may well have cued the elicitation of different knowledge. Now Umar had recalled that chlorine comprises of covalent molecules, I asked him about the nature of the bond:

So what would that be, covalently bonded?

They share the electrons.

So how many electrons would they have then?

They’ll have

[Pause, c.7s – n.b., quite a long pause]

like the one on it, the one of the chlorines shares electrons with the other chlorine to fill in its shell on the other one, and the same does it with the other.

In thinking about covalent bonding, Umar (in common with many students) drew upon the full shells explanatory principle that considered bonding to be driven by the needs of atoms to 'fill' their outer electron shells. (The outer shell of chlorine would only actually be 'full' with 18 electrons, but that complication is seldom recognised, as octets and full shells are usually considered synonymous by students).

So how many electrons does each chlorine have to start with?

In the outer shell, seven.

And how many have they got after this?

They’ve got seven, but they share one.

[Pause, c.1s]

Maybe.

So that’s a covalent bond, is it?

Yeah.

So how many electrons are involved in a covalent bond?

[Pause, c.3s]

Erm,

[Pause, c.3s]

Two.

Two electrons.

So where do those two electrons come from?

They like, one that fills up the gap, fills up the – last electron needed in one of the chlorine shells, and the other chlorine shell fills it up in the other one.

So where do they come from?

Each chlorine. Outer shell.

One from each chlorine?

Yeah.

Okay, and that’d be a covalent bond?

Yeah.

Here, again, Umar is using the full shells explanatory principle as the basis for explaining the bond in terms of electrons 'filling up the gaps' in the electron shells, rather than considering how electrical interactions can hold the structure together. Umar's suggestion that the sharing of electrons "fills up the – last electron needed in one of the chlorine shells" demonstrates the anthropomorphic language (e.g., what an atom wants or needs) commonly used when learners have acquired aspects of the common octet rule framework that is developed from the full shells explanatory principle and used by many learners to explain bonding reactions, chemical reactions, patterns in ionisation energy, and chemical stability.

Responding to a misconception about my own teaching

Keith S. Taber

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:

The cell nucleus is probably bigger than an atomic nucleus

A cell is about ten times larger than an atom

Keith S. Taber

Dividing cell image by  ar130405 from Pixabay

Bert was a participant in the Understanding Science Project. Bert was interviewed in Y10 and asked about the topics he had been studying, which included circulation in biology, static electricity in physics, and oxidation in chemistry.

He talked about protons, electrons and atoms in both chemistry and physics, and was asked if this could also link with biology. Bert suggested that the nucleus comes up in chemistry (in the context of atomic structure) and physics (in the context of static electricity), and in biology in the context of cells (see 'The nucleus is the brain of the cell'). From the perspective of the science teacher, there is little basis for confusing the nucleus of an atom with that of a cell: obviously a cell is a complex entity with many components, each of which has itself a complex supra-molecular structure – so clearly the atomic nucleus is on a scale many orders of magnitude smaller than a cell nucleus.

However, the expert perspective is based on relating a lot of knowledge that the novice may not yet have, or at least, may not yet be coordinating. In Bert's case, he was only just starting to coordinate these ideas, as became clear when Bert was asked about the relative sizes of atomic and cell nuclei:

Which do you think is bigger, an atom or a cell, or are they both about the same size?

I'd say a cell.

A correct, but hardly confident and definitive, response. I followed up:

Which do you think is bigger, an atom or a cell, or are they both about the same size?

I'd say a cell.

So which do you think is bigger, the nucleus of a cell or the nucleus of an atom, or do you think they're both about the same size?

I think they're both about, well I should, oh. (Laughs) I'd say the one in the cell is probably bigger.

Why do you think that?

Well it's a cell, I'd have thought it was bigger than the atom. And you know, if the nucleus is kind of the main part of it, then it would probably be about, it would be the • same sort of – If the atom was brought to the size of the cell then the nucleus would be the same size I would have thought. So if the atom is smaller then the nucleus is a lot smaller.

I see, so you are sort of like scaling it, accordingly?

Yeah.

I see. So any idea roughly, just very roughly, how much bigger a cell is than an atom?

Erm oh, it's, they're both really microscopic so, I couldn't really say how much bigger they are than each other.

So it seems that Bert would "have thought [the cell] was bigger than the atom", but he did not seem entirely certain of this, whereas from the scientific perspective the difference in scale is considered vast and highly significant. Although cells are generally microscopic entries, they are more like familiar macroscopic objects that we can handle in everyday life than quanticles such as atoms which do not behave like familiar objects. (So, there is sense in which it is meaningless to talk about the size of atoms as they have no edges or surfaces but rather fade away to infinity.)

Erm oh, it's, they're both really microscopic so, I couldn't really say how much bigger they are than each other.

Mm. No, okay. So if I said a cell was ten times bigger than an atom, a hundred times bigger than an atom, a thousand times bigger than an atom?

I wouldn't say that, I'd say, I'd probably go with the first one you said, ten times bigger.

So roughly ten times bigger than an atom. So a nucleus of a cell you'd expect to be roughly ten times bigger than the nucleus of an atom?

Yeah.

But you're not really sure?

Well no, there are a lot more parts in a cell than there is in an atom. So I'd say the nucleus is… if they're both brought to the same size again, I'd say the nucleus of the atom would be bigger than the cell. But I could be totally wrong.

Oh I see, so you've got two arguments there. That because they, because they both have a nucleus in the middle, that in terms of scale, if the cell is quite a bit bigger than the atom, you'd expect the nucleus of the cell would be quite a bit bigger than the atom. But an atom is quite a simple structure, whereas a cell has a lot more things in it, it's a lot more complex.

Yeah.

So maybe there's not so much room for the nucleus of the cell as there is for an atom because you've got to fit so much more in.

Yeah.

Is that what you're thinking?

Yeah.

Bert's thinking here is quite reasonable, within the limits of his knowledge. He suggests that a cell nucleus will be larger than an atomic nucleus, because a cell is larger than an atom. However, he only think the cell nucleus will be about ten times the size of the atomic nucleus as he suspects the cell is only about ten times the size of an atom – after all they are both "really microscopic".

However, he also points out that a cell seems to have a more a lot more components to be fitted in, which would suggest that perhaps there is less space to fit the nucleus, so perhaps it would not be as much as ten times bigger than the atomic nucleus.

So Bert is able to consider a situation where there may be several factors at work (the size of the cell versus the size of the atom; the multitude of cellular components versus the sparsity of atoms) and appreciate how they would operate in an opposite sense within his argument so one could compensate for the other. (This type of thinking is needed a lot in studying science. One example is comparisons of ionisation enthalpies between different atoms and ions. I also recall physics objective examination questions that asked students to compare, say, the conductance of two wires with different resistivity, length and area.)

It is not reasonable to expect Bert to know just how much larger a typical cell nucleus is to an atomic nucleus, however, it is likely the science teacher would expect Bert to be aware that the nucleus is one small part of the atom, which is a constituent of the molecules and ions that are the chemical basis for the organelles such as nuclei found in cells. Bert had told me "there are lots of atoms in you", but he did not seem to have understood the role those atoms played in the structure of all tissues. This would seem to be an example of a fragmentation learning impediment, where a learner has not made the connections between topics and ideas that a science teacher would have intended and expected.

Some stars are closer than the planets

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

Keith S. Taber

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

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

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

Do you know what a planet is?

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

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

Er

(pause, c.5s)

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

Good, and what would that be?

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

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

Why do they [the stars] look so little?

Because they are a long way away.

Oh, I see. So they are big really?

Yeah.

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

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

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

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

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

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

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

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

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

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

The sun is the closest of the eleven planets

Keith S. Taber

Sophia was a participant in the Understanding Science Project. When I interviewed her in her first year of secondary school (Y7 in the English school system). I asked her about what she remembered about the science she had studied in primary school. She told me about she had studied the topic of space.

So what did you learn about space?

All the planets, and – 

(pause, c.2 s)

So how many planets are there?

Nine.

Nine, okay. Do you know them all?

No (laughs)

Do you know some of them?

Erm. Pluto, Jupiter, Venus, Uranus, Earth, the Sun, the Moon – (pause, c.2s) hm.

[This was a few years back, and I think was before Pluto was demoted from full planet status in the scientific community.] So, Sophia seemed to have an alternative conception of what would be considered a planet, and she was counting both the moon and the sun among the planets. After a little further conversation about other candidates we came up with a list of more than nine planets.

So how many does that make?

(Sophia laughs)

(Pause, c.6s)

Is there eleven?

Well you said there was nine, didn't you?

Yeah. (laughing)

How could that be, how could we get these extra two?

(Pause, c.4s)

… So, Mercury, is that a planet?

Hm.

Okay, Venus?

Yep.

Earth?

Uh hm.

Mars?

Yeah.

The Moon?

Hm, yeah.

Yeah, Jupiter?

(Pause, 2.s)

Saturn?

(Pause, 2.s)

The Sun?

I'm not sure about the Sun.

Not sure about the Sun.

I think so.

Neptune?

Uranus?

Yep.

Pluto?

Uh hm.

So Sophia was not entirely sure the sun should be considered as planet, although she seemed more confident about the moon. The earth and moon are not technically considered as a double planet system, even though the moon is unusually large satellite compared the the planet it orbits, as the system's centre of mass is within the earth. (Strictly, the earth, as well as the moon, orbits their joint centre of mass.)

As Sophia thought the sun might be a planet, I asked her what a planet was, and the difference between planets and stars. She suggested that some stars are closer to us than the planets.

[Read 'Some stars are closer than the planets']

Not considering luminosity to be a factor, Sophia did not consider the sun to be a star:

What's the closest planet to you?

Erm – the Sun?

Yeah?

If it is a planet.

I think that might there might have been a trick question there. Which is the closest planet to you?

To me?

Yeah.

Earth.

Is mass conserved when water gets soaked up?

Setting up a thought experiment on plant growth and mass

Keith S. Taber

Image by truthseeker08 from Pixabay 

Sophia was a participant in the Understanding Science Project.

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

"The extra [mass of a growing tree] comes from the things it eats and drinks from the ground. It's just like us eating and getting larger."

Response of 15 year old student in the National science survey carried out the Assessment of Performance Unit of the Department of Education and Science, as reported in Bell and Brook, 1984: 12.

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

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

The scenario outlined to Sophia

There seemed two likely outcomes of this thought experiment:

  • A learner considers that the mass of pot, seed and water is collectively 450g, and assumes that as the mass of plant grows, the mass of soil decreases accordingly to conserve total mass at 450g.
  • A learner is aware that in photosynthesis carbon is 'captured' from carbon dioxide in the air, so the mass of the plant in the soil will exceed 450g once the plant grows.

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

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

Any idea how much it would weigh now?

[Four] hundred and fifty, no, cause, no cause it will soak it up, wouldn't it, so just over four hundred (400).

So we had four hundred (400) grammes of soil plus pot, didn't we?

Uh hm.

…And we had one (1) gramme of erm, of plant seed. Just one little seed, one (1) gramme. And forty nine (49) grammes of water. But the water gets soaked up into the soil, does it? So when it's soaked up, you reckon it would be, what?

Erm, four hundred and twenty (420).

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

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

If you poured the water in, quite quickly, not so quickly that it splashes everywhere, but quite quickly. Before it had a chance to soak up, if you could read what it said on the balance before it had a chance to soak up, do you think it would say four hundred and twenty (420) grammes straight away?

No, it would probably be just under, erm, four hundred and fifty (450).

And it would gradually drop down to about four twenty (420) say, would it?

Yeah.

Might be four hundred and fifteen? (415) Could be four hundred and twenty five (425)?

Yeah.

Not entirely sure,

No

but something like that?

Yeah.

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

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

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

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

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

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