Pop goes the comparison
Keith S. Taber
The order of corn popping is no more random than the roll of a dice.
I was pleased to read about a 'new' teaching analogy in the latest 'Education in Chemistry' (the Royal Society of Chemistry's education magazine) – well, at least it was new to me. It was an analogy that could be demonstrated easily in the school science lab, and, according to Richard Gill (@RGILL_Teach on Twitter), went down really well with his class.
Teaching analogies
Analogies are used in teaching and in science communication to help 'make the unfamiliar familiar', to show someone that something they do not (yet) know about is actually, in some sense at least, a bit like something they are already familiar with. In an analogy, there is a mapping between some aspect(s) of the structure of the target ideas and the structure of the familiar phenomenon or idea being offered as an analogue. Such teaching analogies can be useful to the extent that someone is indeed highly familiar with the 'analogue' (and more so than with the target knowledge being communicated); that there is a helpful mapping across between the analogue and the target; and that comparison is clearly explained (making clear which features of the analogue are relevant, and how).
Read about analogies in science
Richard Gill suggests that 'Nuclear decay is a tough concept' to teach and learn, but after making some popcorn he realised that popping corn offered an analogy for radioactive decay that he could demonstrate in the classroom.
Richard Gill describes how
"I tell the students I'm going to heat up the oil; I'm going to give the kernels some energy, making them unstable and they're going to want to pop. I show them under the visualiser, then I ask, 'which kernel will pop first?' We have a little competition. Why do I do this? It links to nuclear decay being random. We know an unstable atom will decay, but we don't know which atom will decay or when it will decay, just like we don't know which kernel will pop when."
Gill, 2022
In the analogy, the corn (maize) kernels represents atoms or nuclei of an unstable isotope, and the popped corn the decay product, daughter atoms or nuclei. 1
(Image by Paulo Marcos pmarcos6821 from Pixabay)
(Image by Leonardo Alvarado from Pixabay)
Richard Gill homes in on a key feature of radioactive decay which may seem counter-intuitive to learners, but which is actually a pattern found in many different phenomena – exponential decay. The rate of radioactive decay falls (decays, confusingly) over time. Theoretically the [radioactive] decay rate follows a very smooth [exponential] decay curve. Theoretically, because of another key feature of radioactive decay that Gill highlights – its random nature!
It may seem that something which occurs by random will not lead to a regular pattern, but although in radioactivity the behaviour of an individual nucleus (in terms of when it might decay) cannot be predicted, when one deals with vast numbers of them in a macroscopic sample, a clear pattern emerges. Each different type of unstable atom has an associated half-life which tells us when half of a sample will have decayed. These half-lives can vary from fractions of a second to vast numbers of years, but are fixed for a particular nuclide.
Richard Gill notes that he can use the popping corn demonstration as background for teaching about half-life,
I usually follow this lesson with the idea of half-lives. The concept of half-lives now makes sense. Why are there fewer unpopped kernels over time? Because they're popping. Why do radioactive materials become less radioactive over time? Because they're decaying.
Gill, 2022
Perhaps he could even develop his demonstration to model the half-life of decay?
Modelling the popcorn decay curve
The Australian Earth Science Education blog suggests
"Popcorn can be used to model radioactive decay. It is a lot safer than using radioactive isotopes, as well as much tastier"
and offers instructions for a practical activity with a bag of corn and a microwave to collect data to plot a decay curve (see https://ausearthed.blogspot.com/2020/04/radioactive-popcorn.html). Although this seems a good idea, I suspect this specific activity (which involves popping the popping corn in and out of the oven) might be too convoluted for learners just being introduced to the topic, but could be suitable for more advanced learners.
However, The Association of American State Geologists suggests an alternative approach that could be used in a class context where different groups of students put bags of popcorn into the microwave for different lengths of time to allow the plotting of a decay curve by collating class results (https://www.earthsciweek.org/classroom-activities/dating-popcorn).
Another variants is offered by The University of South Florida's' Spreadsheets Across the Curriculum' (SSAC) project. SSAC developed an activity ("Radioactive Decay and Popping Popcorn – Understanding the Rate Law") to simulate the popping of corn using (yes, you guessed) a spreadsheet to model the decay of corn popping, as a way of teaching about radioactive decay!
This is more likely to give a good decay curve, but one cannot help feeling it loses some of the attraction of Richard Gill's approach with the smell, sound and 'jumping' of actual corn being heated! One might also wonder if there is any inherent pedagogic advantage to simulating popping corn as a model for simulating radioactive decay – rather than just using the spreadsheet to directly model radioactive decay?
Feedback cycles
The reason the popping corn seems to show the same kind of decay as radioactivity, is because it can be represented with the same kind of feedback cycle.
This pattern is characteristic of simple systems where
- a change is brought about by a driver
- that change diminishes the driver
In radioactive decay, the level of activity is directly proportional to the number of unstable nuclei present (i.e., the number of nuclei that can potentially decay), but the very process of decay reduces this number (and so reduces the rate of decay).
So,
- when there are many unstable nuclei
- there will be much decay
- quickly reducing the number of unstable nuclei
- so reducing the rate of decay
- so reducing the rate at which unstable nuclei decay
- so reducing the rate at which decay is reducing
- …
and so forth.
(source: ASCEND project)
Recognising this general pattern was the focus of an 'enrichment' activity designed for upper secondary learners in the Gatsby SEP supported ASCEND project which presented learners with information about the feedback cycle in radioactive decay; and then had them set up and observe some quite different phenomena (Taber, 2011):
- capacitor discharge
- levelling of connected uneven water columns
- hot water cooling
In each case the change driven by some 'driver' reduced the driver itself (so a temperature difference leads to heat transfer which reduces the temperature difference…).
Read about the classroom activity
In Richard Gill's activity the driver is the availability of intact corn kernels being heated such that water vapour is building up inside the kernel – something which is reduced by the consequent popping of those kernels.
Mapping the analogy
A key feature of an analogy is that it can be understood as a kind of mapping between two conceptual structures. The making popcorn demonstration seems a very simple analogue, but mapping out the analogy might be useful (at least for the teacher) to clarify it. Below I present a representation of a mapping between popping corn and radioactive decay, suggesting which aspects of the analogue (the popping corn) map onto the target scientific concept.
In this mapping I have used colour to highlight differences between the two (conceptual) structures. Perhaps the most significant difference is represented by the blue (target concept) versus red (analogue) features.
Most analogies only map to a limited extent
There will be aspects of an analogue that do not map onto anything on the target, and sometimes there will be an important feature of the target which has no analogous feature in the analogue. There is always the possibility that irrelevant features of an analogue will be mapped across by learners.
As one example, the comparison of the atom with a tiny solar system was once an image often used as a teaching analogy, yet it seems learners often have limited understandings of both analogue and target, and may be transferring across inappropriately – such as assuming the electrons are bound to the atom by gravity (Taber, 2013a). Where students have an alternative conception of the analogue (the earth attracts the sun, but not vice versa) they will often assume the same pattern in the target (the nucleus is not attracted to the electrons).
Does this matter? Well, yes and no. A teaching analogy is used to introduce a technical scientific concept by making it seem familiar. This is a starting point to be built upon (so, Richard Gill tells us that he will build upon the diminishing activity of cooking corn in his his popcorn demonstration to introduce the idea of half-life), so it does not matter if students do not fully understand everything immediately. (Indeed, it is naive to assume most learners could acquire a new complex set of ideas all at once: learning is incremental – see Key ideas for constructivist teaching).
Analogies can act as 'scaffolds' to help learners venture out from their existing continents of knowledge towards new territory. Once this 'anchor' in learners' experience is established one can, so to speak, disembark from the scaffolding raft the onto the more solid ground of the shore.
Read about scaffolding learning
However, it is important to be careful to make sure
- (a) learners appreciate the limitations of models (such an analogies) – that they are thinking and learning tools, and not absolute accounts of the natural word; and that
- (b) the teacher helps dismantle the 'scaffolding' once it is not needed, so that it is not retained as part of the learners 'scientific' account.
Weak anthropomorphism
An example of that might be Gill's use of anthropomorphism.
…unstable atoms/nuclei need to become stable…
…I'm going to give the kernels some energy, making them unstable and they're going to want to pop…
Anthropomorphism
This type of language is often used to offer narratives that are more readily appreciated by learners (making the unfamiliar familiar, again) but students can come to use such language habitually, and it may come to stand in place of a more scientific account (Taber & Watts, 1996). So, 'weak' anthropomorphism used to help introduce something abstract and counter-intuitive is useful, but 'strong' anthropomorphism that comes to be adopted as a scientific explanation (e.g., nuclei decay because they want to be stable) is best avoided by seeking to move beyond the figurative language as soon as students are ready.
The 'negative' analogy
The mapping diagram above may highlight several potential teaching points that may be considered (perhaps not to be introduced immediately, but when the new concepts are later reinforced and developed).
Where does the energy come from?
One key difference between the two systems is that radioactive decay is (we think) completely spontaneous, whereas the corn only pops because we cook it (Gill used a Bunsen burner) and left to its own devices remains as unpopped kernels.
Related to this, the source of energy for popping corn is the applied heat, whereas unstable nuclei are already in a state of high energy and so have an 'internal' source for their activity. This a key difference that will likely be obvious to some, but certainly not all learners in most classes.
When is random, random?
A more subtle point relates to the 'random' nature of the two events. I suggest subtle, because there are many published reports written by researchers in science education which suggests even supposed experts can have a pretty shaky ideas of what counts as random (Taber, 2013b).
Read 'Nothing random about a proper scientific evaluation?'
Read about the randomisation criterion
As far as scientists understand, the decay of one unstable nucleus in a sample of radioactive material (rather than another) is a random process. It is not just that we are not yet able to predict when a particular nucleus will decay – according to current scientific accounts it is not possible to predict in principle. This is an idea that even Einstein found difficult to accept.
That is not true with the corn. Presumably there are subtle differences between kernels – some have slightly more water content, or slightly weaker casings. Perhaps more significantly, some are heated more than others due to their position in the pan and the position of the heat source, or due differential exposure to the cooking oil… In principle it would be possible to measure relevant variables and model the set up to make good predictions. (In principle, even if in practice a very complex task.) The order of corn popping is no more random than…say…the roll of a dice. That is, physics tells us it follows natural laws, even if we are not in a position to fully model the phenomenon.
(We might suggest that a student who considered the corn popping as a random event because she saw apparently identical kernels all being heated in the same pan at the same time is simply missing certain 'hidden variables'. Einstein wondered if there were also 'hidden variables' that science had not yet uncovered which could explain random events such as why one nucleus rather than another decays at a particular moment.)
On the recoil
Perhaps a more significant difference is what is observed. The corn are observed 'jumping' (more anthropomorphic language?) Physics tells us that momentum must always be conserved, and the kernels act like tiny jet propelled rockets. That is, as steam is released when the kernel bursts, the rest of the kernel 'jumps' in the opposite direction. (That is, by Newton's third law, there is a reaction force to the force pushing the steam out of the kernel. Momentum is a vector, so it is possible for a stationary object to break up into several moving parts with conservation of momentum.)
Something similar happens in radioactive decay. The emitted radiation carries away momentum, and the remaining 'daughter' nucleus recoils – although if the material is in the solid state this effect is dissipated by being spread across the lattice. So, the radioactivity which is detected is not analogous to the jumping corn, but to the steam it has released.
Is this important? That likely depends upon the level being taught. If the topics is being introduced to 14-16 years-olds, perhaps not. If the analogy is being explored with post-compulsory students doing an elective course, then maybe. (If not in chemistry; then certainly in physics, where learners are expected to to apply the principle of conservation of momentum across various scenarios.)
Will this be on the exam?
When I drafted this, I suspected most readers might find my caveats above about the limitations of the analogy, a bit pernickety (the kind of things an academic who's been out of the school classroom too long and forgotten the realities of working with pupils might dream up), but then I found what claims to be an Edexcel GCE Physics paper from 2012 (paper reference 6PH05/01) on line. In this paper, one question begins:
"In a demonstration to her class, a teacher pours popcorn kernels onto a hot surface and waits for them to pop…".
Much to my delight, I found the first part of this question asked learners:
"How realistic is this demonstration as an analogy to radioactive decay?
Consider aspects of the demonstration that are similar to radioactive decay and aspects that are different"
Examination paper asking physics students to identify positive and negative aspects of the analogy.
Classes of radioactivity
One further difference did occur to me that may be important. At some level this analogy works for radioactivity regardless of what is being emitted from an excited nucleus. However, the analogy seems clearer for the emission of an alpha particle, or a beta particle, or a neutron, than in the case of gamma radiation.
Although in gamma decay an excited nucleus relaxes to a lower energy state emitting a photon, it may not be as obvious to learners that the nucleus has changed (arguably, it has not 'substantially' changed as there is no change of substance) – as it has the same mass number and charge as before. This may be a point to be raised if moving on later to discuss different classes of radioactivity.
Or, perhaps, with gamma decay one can use a different version of the analogy?
Another corny analogy
Although I do not think I had never come across this analogy before reading the Education in Chemistry piece (perhaps because I do not make myself popcorn), Richard Gill does not seem to be the only person to have noticed this comparison. (They say 'great minds think alike' – and not just physicist Henri Poincaré thinking like Kryten from'Red Dwarf'). When I looked around the world-wide web I found there were two different approaches to using corn kernels to model radioactivity.
Some people use a similar demonstration to Mr Gill.2 However, there was also a different approach to using the corn. There were variations on this 3, but the gist was that
- one starts with a large number of kernels
- they are agitated (e.g., shaken in a box with different cells, poured onto the bench…)
- then inspected to see which are pointing in some arbitrary direction designated as representing decay
- the 'decayed' kernels are removed and counted
- the rest of the sample is agitated again
- etc.
(Original image by Susie from Pixabay)
This lacks the excitement of popping corn, but could be a better model for gamma decay where the daughter nucleus is at a different energy after decay, but is otherwise unchanged.
Perhaps this version of the analogy could be improved by using a tray with an array of small dips (like tiny spot tiles) just the right size to stand corn kernels in the depressions with their points upwards. Then, after a very gentle tap on the bench next to the tile, those which have 'relaxed' from the higher energy state (i.e., fallen onto their sides) would be considered decayed. This would more directly model the change in potential energy and also avoid the need to keep removing kernels from the context (just as daughter atoms usually remain in a sample of radioactive material), as further gentle tapes are unlikely to excite them back to the higher energy state. 4
Or, dear reader, perhaps I've just been thinking about this analogy for just a little too long now.
Sources:
- Gill, R. (2022). Popping corn – or nuclear decay? Education in Chemistry, 59(4), 30. [Also at https://edu.rsc.org/ideas/popping-corn-or-nuclear-decay/4015780.article ]
- Taber, K. S. (2011). Patterns in nature: challenging secondary students to learn about physical laws. Physics Education, 46(1), 80-89. https://doi.org/10.1088/0031-9120/46/1/010
- Taber, K. S. (2013a). Upper Secondary Students' Understanding of the Basic Physical Interactions in Analogous Atomic and Solar Systems. Research in Science Education, 43(4), 1377-1406. doi:10.1007/s11165-012-9312-3
- Taber, K. S. (2013b). Non-random thoughts about research. Chemistry Education Research and Practice, 14(4), 359-362. doi:10.1039/c3rp90009f
- Taber, K. S. and Watts, M. (1996) The secret life of the chemical bond: students' anthropomorphic and animistic references to bonding, International Journal of Science Education, 18 (5), pp.557-568.
Notes
1 Referring to the nuclei before and after radioactive decay as 'parents' and 'daughters' seems metaphorical, but this use has become so well established (in effect, these are now technical terms) that these descriptors are now what are known (metaphorically!) as 'dead metaphors'.
Read about metaphors in science
2 Here are some examples I found:
Jennifer Wenner, University of Wisconsin-Oshkosh uses the demonstration in undergraduate geosciences:
"I usually perform it after I have introduced radioactive decay and talked about how it works. It only takes a few minutes and I usually talk while I am waiting for the "decay" to happen 'Using Popcorn to Simulate Radioactive Decay'"
https://serc.carleton.edu/quantskills/activities/popcorn.html
The Institute of Physics (IoP) include this activity as part of their 'Modelling decay in the laboratory Classroom Activity for 14-16' but suggest the pan lid is kept on as a safety measure. (Any teacher planing on carrying out any activity in the lab., should undertake a risk assessment first.)
I note the IoP also suggests care in using the term 'random':
Teacher: While we were listening to that there didn't seem to be any fixed pattern to the popping. Is there a word that we could use to describe that?
Lydia: Random?
Teacher: Excellent. But the word random has a very special meaning in physics. It isn't like how we think of things in everyday life. When do you use the word random in everyday life?
Lydia: Like if it's unpredictable? Or has no pattern?
https://spark.iop.org/modelling-decay-laboratory
Kieran Maher and 'Kikibooks contributors' suggests readers of their 'Basic Physics of Nuclear Medicine' could "think about putting some in in a pot, adding the corn, heating the pot…" and indeed their readers "might also like to try this out while considering the situation", but warn readers not to "push this popcorn analogy too far" (pp.20-21).
3 Here are some examples I found:
Florida High School teacher Marc Mayntz offers teachers' notes and student instructions for his 'Nuclear Popcorn' activity, where students are told to "Carefully 'spill' the kernels onto the table".
Chelsea Davis (a student?) reports her results in 'Half Life Popcorn Lab' from an approach where kernels are shaken in a Petri dish.
Redwood High School's worksheet for 'Radioactive Decay and Half Life Simulation' has students work with 100 kernels in a box with its sides labelled 1-4 (kernels that have the small end pointed toward side 1 after "a sharp, single shake (up and down, not side to side)" are considered decayed). Students are told at the start to to "Count the popcorn kernels to be certain there are exactly 100 kernels in your box".
This activity is repeated but with (i) kernels pointing to either side 1 or 2; and in a further run (ii) any of sides 1, 2, or 3; being considered decayed. This allows a graph to be drawn comparing all three sets of results.
The same approach is used in the Utah Education network's 'Radioactive Decay' activity, which specifies the use of a shoe box.
A site called 'Chegg' specified "a square box is filled with 100 popcorn kernels". and asked "What alteration in the experimental design would dramatically change the results? Why?" But, sadly, I needed to subscribe to see the answer.
The 'Lesson Planet' site offers 'Nuclear Popcorn' where "Using popcorn kernels spread over a tabletop, participants pick up all of those that point toward the back of the room, that is, those that represent decayed atoms".
'Anonymous' was set a version of this activity, but could not "seem to figure it out". 'Jiskha Homework Help' (tag line: "Ask questions and get helpful responses") helpfully responded,
"You ought to have a better number than 'two units of shake time…'
Read off the graph, not the data table."
(For some reason this brought to mind my sixth form mathematics teacher imploring us in desperation to "look at the ruddy diagram!")
4 Consider the challenge of developing this model to simulate nuclear magnetic resonance or laser excitation!
