Resourced-based view of education

We all adore Caloric

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We all adore a Kia-Ora

Advertising slogan for ‘Kia-Ora’ orange drink (c. 1985)

Energy is harder to define than you would think. Nobel laureate Richard Feynman defined ‘energy’ as

a numerical quantity which does not change when something happens. It is not a description of a mechanism, or anything concrete; it is just a strange fact that we can calculate some number and when we finish watching nature go through her tricks and calculate the number again, it is the same. […] It is important to realize that in physics today, we have no knowledge of what energy is. […] It is an abstract thing in that it does not tell us the mechanism or the reasons for the various formulas.

Feynman Lectures on Physics, Vol 1, Lecture 4 Conservation of Energy (1963)

Current secondary school science teaching approaches to energy often picture energy as a ‘quasi-material substance’.

By ‘quasi-material substance’ we mean that ‘energy is like a material substance in how it behaves’ (Fairhurst 2021) and that some of its behaviours can be modelled as, say, an orange liquid (see IoP 2016).

The eight energy stores as suggested by the IoP

And yet, sometimes these well-meaning (and, in my opinion, effective) approaches can draw some dismissive comments from some physicists.

The Simpsons Comic Book Guy character saying "Picturing energy as a quasi-material substance? That teaching approach smacks of the oh-so-discredited 'Caloric' theory of energy to me . . ."
The Simpsons’ Comic Book Guy weighs in the ‘Teaching Energy’ debate

What was the ‘Caloric Theory of Energy’?

To begin with, there was never a ‘Caloric Theory of Energy’ since the concept of energy had not been developed yet; but the Caloric Theory of Heat was an important step along the way.

Caloric was an invisible, weightless and self-repelling fluid that moved from hot objects to cold objects. Antoine Lavoisier (1743-1794) supposed that the total amount of caloric in the universe was constant: in other words, caloric was thought to be a conserved quantity.

Caloric was thought to be a form of ‘subtle matter’ that obeyed physical laws and yet was so attenuated that it was difficult to detect. This seems bizarre to our modern sensibilities and yet Caloric Theory did score some notable successes.

  • Caloric explained how the volume of air changed with temperature. Cold air would absorb caloric and thus expand.
  • The Carnot cycle which describes the maximum efficiency of a heat engine (i.e. a mechanical engine powered by heat) was developed by Sadi Carnot (1796-1832) on the basis of the Caloric Theory

Why Caloric Theory was replaced

It began with Count Rumford in 1798. He published some observations on the manufacturing process of cannons. Cannon barrels had to be drilled or bored out of solid cylinders of metal and this process generated huge quantities of heat. Rumford noted that cannons that had been previously bored produced as much heat as cannons that were being freshly bored for the first time. Caloric Theory suggested that this should not be the case as the older cannons would have lost a great deal of caloric from being previously drilled.

The fact that friction could seemingly generate limitless quantities of caloric strongly suggested that it was not a conserved quantity.

We now understand from the work James Prescott Joule (1818-1889) and Rudolf Clausius (1822-1888) that Caloric Theory had only a part of the big picture: it is energy that is the conserved quantity, not caloric or heat.

As Feynman puts it:

At the time when Carnot lived, the first law of thermodynamics, the conservation of energy, was not known. Carnot’s arguments [using the Caloric Theory] were so carefully drawn, however, that they are valid even though the first law was not known in his time!

Feynman Lectures on Physics, Vol 1, Lecture 44 The Laws of Thermodynamics

In other words, the Caloric Theory is not automatically wrong in all respects — provided, that is, it is combined with the principle of conservation of energy, so that energy in general is conserved, and not just the energy associated with heat.

We now know, of course, that heat is not a form of attenuated ‘subtle matter’ but rather the detectable, cumulative result of the motion of quadrillions of microscopic particles. However, this is a complex picture for novice learners to absorb.

Caloric Theory as a bridging analogy

David Hammer (2000) argues persuasively that certain common student cognitive resources can serve as anchoring conceptions because they align well with physicists’ understanding of a particular topic. An anchoring conception helps to activate useful cognitive resources and a bridging analogy serves as a conduit to help students apply these resources in what is, initially, an unfamiliar situation.

The anchoring conception in this case is students’ understanding of the behaviour of liquids. The useful cognitive resources that are activated when this is brought into play include:

  • the idea of spontaneous flow e.g. water flows downhill;
  • the idea of measurement e.g. we can measure the volume of liquid in a container; and
  • the idea of conservation of volume e.g. if we pour water from a jug into an empty cup then the total volume remains constant.

The bridging analogy which serves as a channel for students to apply these cognitive resources in the context of understanding energy transfers is the idea of ‘energy as a quasi-material substance’ (which can be considered as an iteration of the ‘adapted’ Caloric Theory which includes the conservation of energy).

The bridging analogy helps students understand that:

  • energy can flow spontaneously e.g. from hot to cold;
  • energy can be measured and quantified e.g. we can measure how much energy has been transferred into a thermal energy store; and
  • energy does not appear or disappear: the total amount of energy in a closed system is constant.

Of course, a bridging analogy is not the last word but only the first step along the journey to a more complete understanding of the physics involved in energy transfers. However, I believe the ‘energy as a quasi-material substance’ analogy is very helpful in giving students a ‘sense of mechanism’ in their first encounters with this topic.

Teachers are, of course, free not to use this or other bridging analogies, but I hope that this post has persuaded even my more reluctant colleagues that they need a more substantive argument than a knee jerk ‘energy-as-substance = Caloric Theory = BAD’.

References

Fairhurst P. (2021), Best Evidence in Science Teaching: Teaching Energy. https://www.stem.org.uk/sites/default/files/pages/downloads/BEST_Article_Teaching%20energy.pdfhttps://www.stem.org.uk/sites/default/files/pages/downloads/BEST_Article_Teaching%20energy.pdf [Accessed April 2022]

Hammer, D. (2000). Student resources for learning introductory physics. American Journal of Physics, 68(S1), S52-S59.

Institute of Physics (2016), Physics Narrative: Shifting Energy Between Stores. Available from https://spark.iop.org/collections/shifting-energy-between-stores-physics-narrative [Accessed April 2022]

Understanded of the pupils

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It is a thing plainly repugnant . . . to Minister the Sacraments in a Tongue not understanded of the People.

Gilbert, Bishop of Sarum. An exposition of the Thirty-nine articles of the Church of England (1700)

How can we help our students understand physics better? Or, in more poetic language, how can we make physics a thing that is more ‘understanded of the pupils’?

Redish and Kuo (2015: 573) suggest that the Resources Framework being developed by a number of physics education researchers can be immensely helpful.

In summary, the Resources Framework models a student’s reasoning as based on the activation of a subset of cognitive resources. These ‘thinking resources’ can be classified broadly as:

  • Embodied cognition: these are simple, irreducible cognitive resources sometimes referred to as ‘phenomenological primitives’ or p-prims such as ‘if-resistance-increases-then-the-output-decreases‘ and ‘two-opposing-effects-can-result-in-a-state-of-dynamic-balance‘. They are typically straightforward and ‘obvious’ generalisations of our lived, everyday experience as we move through the physical world. Embodied cognition is perhaps summarised as our ‘sense of mechanism’.
  • Encyclopedic (ancillary) knowledge: this is a complex cognitive resource made of a large number of highly interconnected elements: for example, the concept of ‘banana’ is linked dynamically with the concept of ‘fruit’, ‘yellow’, ‘curved’ and ‘banana-flavoured’ (Redish and Gupta 2009: 7). Encyclopedic knowledge can be thought of as the product of both informal and formal learning.
  • Contextualisation: meaning is constructed dynamically from contextual and other clues. For example, the phrase ‘the child is safe‘ cues the meaning of ‘safe‘ = ‘free from the risk of harm‘ whereas ‘the park is safe‘ cues an alternative meaning of ‘safe‘ = ‘unlikely to cause harm‘. However, a contextual clue such as the knowledge that a developer had wanted to but failed to purchase the park would make the statement ‘the park is safe‘ activate the ‘free from harm‘ meaning for ‘safe‘. Contextualisation is the process by which cognitive resources are selected and activated to engage with the issue.

Using the Resources Framework for teaching

I have previously used aspects of the Resources Framework in my teaching and have found it thought provoking and helpful to my practice. However, the ideas are novel and complex — at least to me — so I have been trying to think of a way of conveniently organising them.

What follows in my ‘first draft’ . . . comments and suggestions are welcome!

The RGB Model of the Resources Framework

The RGB Model of the Resources Framework

The red circle (the longest wavelength of visible light) represents Embodied Cognition: the foundation of all understanding. As Kuo and Redish (2015: 569) put it:

The idea is that (a) our close sensorimotor interactions with the external world strongly influence the structure and development of higher cognitive facilities, and (b) the cognitive routines involved in performing basic physical actions are involved in even in higher-order abstract reasoning.

The green circle (shorter wavelength than red, of course) represents the finer-grained and highly-interconnected Encyclopedic Knowledge cognitive structures.

At any given moment, only part of the [Encyclopedic Knowledge] network is active, depending on the present context and the history of that particular network

Redish and Kuo (2015: 571)

The blue circle (shortest wavelength) represents the subset of cognitive resources that are (or should be) activated for productive understanding of the context under consideration.

A human mind contains a vast amount of knowledge about many things but has limited ability to access that knowledge at any given time. As cognitive semanticists point out, context matters significantly in how stimuli are interpreted and this is as true in a physics class as in everyday life.

Redish and Kuo (2015: 577)

Suboptimal Understanding Zone 1

A common preconception held by students is that the summer months are warmer because the Earth is closer to the Sun during this time of year.

The combination of cognitive resources that lead students to this conclusion could be summarised as follows:

  • Encyclopedic knowledge: the Earth’s orbit is elliptical
  • Embodied cognition: The closer to a heat source you are the warmer it is.

Both of these cognitive resources, considered individually, are true. It is their inappropriate selection and combination that leads to the incorrect or ‘Suboptimal Understanding Zone 1’.

To address this, the RF(RGB) suggests a two pronged approach to refine the contextualisation process.

Firstly, we should address the incorrect selection of encyclopedic knowledge. The Earth’s orbit is elliptical but the changing Earth-Sun distance cannot explain the seasons because (1) the point of closest approach is around Jan 4th (perihelion) which is winter in the northern hemisphere; (2) seasons in the northern and southern hemispheres do not match; and (3) the Earth orbit is very nearly circular with an eccentricity e of 0.0167 where a perfect circle has e = 0.

Secondly, the closer-is-warmer p-prim is not the best embodied cognition resource to activate. Rather, we should seek to activate the spread-out-is-less-intense ‘sense of mechanism’ as far as we are able to (for example by using this suggestion from the IoP).

Suboptimal Understanding Zone 2

Another common preconception held by students is all waves have similar properties to the ‘breaking’ waves on a beach and this means that the water moves with the wave.

The structure of this preconception could be broken down into:

  • Embodied cognition: if I stand close to the water on a beach, then the waves move forward to wash over my feet.
  • Encyclopaedic knowledge: the waves observed on a beach are water waves

Considered in isolation, both of these cognitive resources are unproblematic: they accurately describes our everyday, lived experience. It is the contextualisation process that leads us to apply the resources inappropriately and places us squarely in Suboptimal Understanding Zone 2.

The RF(RGB) Model suggests that we can address this issue in two ways.

Firstly, we could seek to activate a more useful embodied cognition resource by re-contextualising. For example, we could ask students to imagine themselves floating in deep water far from the shore: do the waves carry them in any particular direction or simply move them up or down as they pass by?

Secondly, we could seek to augment their encyclopaedic knowledge: yes, the waves on a beach are water waves but they are not typical water waves. The slope of the beach slows down the bottom part of the wave so the top part moves faster and ‘topples over’ — in other words, the water waves ‘break’ leading to what appears to be a rhythmic back-and-forth flow of the waves rather than a wave train of crests and troughs arriving a constant wave speed. (This analysis is over a short period of time where the effect of any tidal effects is negligible.)

Both processes try to ‘tug’ student understanding into the central, optimal zone.

Suboptimal Understanding Zone 3

Redish and Kuo (2015: 585) recount trying to help a student understand the varying brightness of bulbs in the circuit shown.

4 bulbs in a circuit: Bulbs A, B and D are in series with the cell but bulb C is in parallel across bulb B.
All bulbs are identical. Bulbs A and D are bright; bulbs B and C are dim.

The student said that they had spent nearly an hour trying to set up and solve the Kirchoff’s Law loop equations to address this problem but had been unsuccessful in accounting for the varying brightnesses.

Redish suggested to the student that they try an analysis ‘without the equations’ and just look at the problems in simpler physical terms using just the concept of electric current. Since current is conserved it must split up to pass through bulbs B and C. Since the brightness is dependent on the current, the smaller currents in B and C compared with A and D accounts for their reduced brightness.

When he was introduced to [this] approach to using the basic principles, he lit up and was able to solve the problem quickly and easily, saying, ‘‘Why weren’t we shown this way to do it?’’ He would still need to bring his conceptual understanding into line with the mathematical reasoning needed to set up more complex problems, but the conceptual base made sense to him as a starting point in a way that the algorithmic math did not.

Analysing this issue using the RF(RGB) it is plausible to suppose that the student was trapped in Suboptimal Understanding Zone 3. They had correctly selected the Kirchoff’s Law resources from their encyclopedic knowledge base, but lacked a ‘sense of mechanism’ to correctly apply them.

What Redish did was suggest using an embodied cognition resource (the idea of a ‘material flow’) to analyse the problem more productively. As Redish notes, this wouldn’t necessarily be helpful for more advanced and complex problems, but is probably pedagogically indispensable for developing a secure understanding of Kirchoff’s Laws in the first place.

Conclusion

The RGB Model is not a necessary part of the Resources Framework and is simply my own contrivance for applying the RF in the context of physics education at the high school level. However, I do think the RF(RGB) has the potential to be useful for both physics and science teachers.

Hopefully, it will help us to make all of our subject content more ‘understanded of the pupils’.

References

Redish, E. F., & Gupta, A. (2009). Making meaning with math in physics: A semantic analysis. GIREP-EPEC & PHEC 2009, 244.

Redish, E. F., & Kuo, E. (2015). Language of physics, language of math: Disciplinary culture and dynamic epistemology. Science & Education, 24(5), 561-590.

Starting From Here

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It’s a variation on a classic Celtic joke which I’m sure that you’ve heard before, but here it is anyway.

Motorist: Can you tell me the way to Llanpumsaint please?

Welshman: Why yes, but I wouldn’t start from here if I were you…

I wouldn’t start from here. The joke, of course, is that we rarely have a choice of where we start from. We start from here because here is where we are.

David Hammer (2000) in “Student Resources For Learning Introductory Physics” offers a fascinating perspective on the varied points that students start from as they begin to learn physics. He likens a student’s preexisting conceptual structures to the computational resources used by programmers. These conceptual resources inside our students’ heads can be (loosely) compared to “chunks of computer code”, if you will. He goes on to point out that:

Programmers virtually never write their programs from scratch. Rather, they draw on a rich store of routines and subroutines, procedures of various sizes and functions . . . Those who specialize in graphics have procedures for translating and rotating images, for example, which they use and reuse in a variety of circumstances. And, often, a programmer will try to use a procedure in a way that turns out to be ineffective.

Image from: https://www.tripadvisor.co.uk/LocationPhotos-g1545129-w2-Llanpumsaint_Carmarthenshire_Wales.html#184967057. Yes, they really do have an elephant there.

Hammer argues that although many teachers have an instinctive but unspoken understanding of the conceptual resources that students possess, all-too-often it is assumed that any preconception is automatically a misconception that must be rooted out and replaced. Hammer suggests that a more productive approach is to understand and use the often detailed knowledge that students already possess.

Refining “Raw Intuitions”

For example, Hammer summarises the work of Andrew Elby who suggests a strategy for refining the raw intuitions that students have.

A truck rams into a parked car, which has half the mass of the truck. Intuitively, which is larger during the collision: the force exerted by the truck on the car, or the force exerted by the car on the truck? That most students responded that the truck exerts a larger force on the car than the car exerts on the truck is not surprising; this is a commonly recognized “misconception.”

In other words, students fail to apply Newton’s Third Law correctly to the situation, which would predict that the forces acting on two such objects are equal and opposite.

However, all is not lost as Elby believes that his students do have a fundamentally correct intuition about the situation. They rightly intuit that the car will respond twice as much as the truck. The problem is to refine this intuition so that it is consistent with the laws of Newtonian physics. Elby posed a follow up question:

Suppose the truck has mass 1000 kg and the car has mass 500 kg. During the collision, suppose the truck loses 5 m/s of speed. Keeping in mind that the car is half as heavy as the truck, how much speed does the car gain during the collision? Visualize the situation, and trust your instincts.

The students, thus guided, came to the conclusion that because the truck lost 5 m/s of speed, the car gained 10 m/s of speed. Since the mass of the car is half the mass of the truck, the car gains exactly the amount of momentum lost by the truck. Since the exchange occurred over the exact same time period, the rate of change of momentum, and hence the force acting on each object, is equal.

In other words, Elby used the students’ intuition that “the car reacts twice as much as the truck” as the raw material to build a correct and coherent physical understanding of the situation.

Hammer then makes what I think is a very telling point: like computer subroutines, intuitions are neither correct or incorrect. They become correct or incorrect depending on how they are used.

In this way, a resources-based account of student knowledge and reasoning does not disregard difficulties or phenomena associated with misconceptions. Rather, on this view, a difficulty represents a tendency to misapply resources, and misconceptions represent robust patterns of misapplication.

As teachers, we do not have the luxury of selecting our starting points. Often, I think that talk of student misconceptions resembles the “I wouldn’t start from here” joke. The misconception has to be eliminated before the proper teaching can start.

As teachers, we don’t have the luxury of selecting our starting points. We start from where our students start. We’re teachers: we start from here.

References
Elby, A. (2001). Helping physics students learn how to learn. American Journal of Physics, 69(S1), S54-S64. http://134.68.135.20/JiTT_NMSU_workshop/pdfs/HelpingStudentsLearn_Elby.pdf
Hammer, D. (2000). Student resources for learning introductory physics. American Journal of Physics, 68(S1), S52-S59. http://mapmf.pmfst.unist.hr/~luketin/Physics_education/resources_Hammer.htm

The p-prim path to enlightenment…?

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The Duke of Wellington was once asked how he defeated Napoleon. He replied: “Napoleon’s plans were made of wire. Mine were made of little bits of string.”

In other words, Napoleon crafted his plans so thay they had a steely, sinewy strength that carried them to completion. Wellington conceded that his plans were more ramshackle, hand-to-mouth affairs. The difference was that if one of of Napoleon’s schemes broke or miscarried, it proved impossible to repair. When Wellington’s plans went awry, he would merely knot two loose bits of string together and carry on regardless.

I believe Andrea diSessa (1988) would argue that much of our knowledge, certainly emergent knowledge, is in the form of “little bits of string” rather than being organised efficiently into grand, coherent schemas.

For example, every human being has a set of conceptions about how the material world works that can be called intuitive physics. If a ball is thrown up in the air, most people can make an accurate prediction about what happens next. But what is the best description of the way in which intuitive physics is organised?

diSessa identifies two possibilities:

The first is an example of what I call “theory theories” and holds that it is productive to think of spontaneously acquired knowledge about the physical world as a theory of roughly the same quality, though differing in content from Newtonian or other theories of the mechanical world [ . . .]

My own view is that . . . intuitive physics is a fragmented collection of ideas, loosely connected and reinforcing, having none of the commitment or systematicity that one attributes to theories.

[p.50]

diSessa calls these fragmented ideas phenomenological primitives, or p-prims for short.

David Hammer (1996) expands on diSessa’s ideas by considering how students explain the Earth’s seasons.

Many students wrongly assume that the Earth is closer to the Sun during summer. Hammer argues that they are relying, not on a misconception about how the elliptical nature of the Earth’s orbit affects the seasons, but rather on a p-prim that closer = stronger.

The p-prims perspective does not attribute a knowledge structure concerning closeness of the earth and sun; it attributes a knowledge structure concerning proximity and intensity, Moreover, the p-prim closer means stronger is not incorrect.

[p.103]

diSessa and Hammer both argue that a misconceptions perspective assumes the existence of a stable cognitive structure where, in fact, there is none. Students may not have thought about the issue previously, and are in the process of framing thoughts and concepts in response to a question or problem. In short, p-prims may well be a better description of evanescent, emergent knowledge.

Hammer points out that the difference between the two perspectives has practical relevance to instruction. Closer means stronger is a p-prim that is correct in a wide range of contexts and is not one we should wish to eliminate.

The art of teaching therefore becomes one of refining rather than replacing students’ ideas. We need to work with students’ existing ideas and knowledge — piecemeal, inarticulate and applied-in-the-wrong-context as they may be.

Let’s get busy with those little bits of conceptual string. After all, what else have we got to work with?

REFERENCES

diSessa, A. (1988). “Knowledge in Pieces”. In Forman, G. and Pufall, P., eds, Constructivism in the Computer Age, New Jersey: Lawrence Erlbaum Publishers

Hammer, D. (1996). “Misconceptions or p-prims” J. Learn Sci 5 97