On choosing a selection of stores

Here comes the physics

Energy is energy and a calculated quantity which is conserved, but which can be dissipated


But on the way, decisions

On the way to being able to do such calculations, and appreciate the implications of conservation and dissipation, it is possible to develop qualitative descriptions to assist the transition from the physical descriptions to the energy calculations. These descriptions help focus on noticing changes in certain facets of the physical world and using them as clues to suspect that there might be calculable changes which might yield insightful energy descriptions.

Developing a description in terms of stores is a suggestion for a milestone on an imagined learning journey[1] culminating in such calculations. That some might not complete the journey, and that many of these will be functioning voting citizens adds implications about the consequences of wise choices.

So the slogan find energy in stores is only a start, albeit a useful one because it lays a foundational principle for the didactical transposition of the idea of energy. It would help if you then considered the uses to which your representations of energy will be put and design them accordingly. In this, discussion about depleting energy resources to power our warm houses, cook our food and satiate our predilection for rushing about is a non-trivial consideration. That provides a framework for making choices. Ally this to a concern to develop a parsimonious and elegant description, that segue smoothly into later formal as an additional consideration to this essential citizenship role. In addition to this pair, other significant constraints include:

You'll have to make choices, so base decisions on explicit reasons.

SPT settled on eight stores and four pathways. Here I'll discuss some reasoning behind the selection and naming of the eight stores. Neither the names or the graphical representations are to-be-learnt. Instead, they are equal partners in enabling the constructing insightful energy descriptions: both words and diagrams stand for the idea that there is a recognisable physical change which could result in a calculation of a change in energy.

While writing SPT the terms sound energy, light energy and electrical energy were in everyday use, and often led to descriptions which were not a didactical transposition of how the idea of energy is used in the sciences. Similarly, chains of energy forms were commonplace, again not representing practice in the sciences at all well. And there were a lot of word games in play, not least in mark schemes for public exams.

So this suggestion focusses on eight stores, each of which is mapped onto one or more calculations.

The physical changes you look for support calculations you can do are here.

The elastic store functions as a prototype, because it is physically manipulable, and its evident stability as a store. Simply put, stretch a rubber band, hook it up at that stretched length, and leave it there (as you cannot do with the unhelpful trio of light/sound and electric, met above). Later relax the band a bit, and you can get a job done. Not any job, but one constrained by how much relaxing you have allowed in the band. The energy shifted from a store is, therefore, a constraint on what can happen: some things are impossible if depleting the energy in the store does not shift enough energy. Plus energy = 12 × k × x 2 is a calculation that lies not too far in the future, in a learning journey. I avoided elastic potential energy because any qualifying adjective for energy diminishes the force of the unity of energy and on the grounds of eliminating unnecessary words (bye-bye potential).

You could choose to stretch the spring of the earth otherwise known as gravity and make similar points about being able to hook it up (maybe by storing water in a reservoir and leave it there). You might choose to call this a gravistatic store. Still, simplicity won out over pedantry here (allocating SPAG marks never was a fav. activity, and was never much about the ideas). Being able to identify a change in the separation of two massive objects, and associate this change with a difference in the energy in the store, linking to the separations of the ends of the spring in the comparable elastic store, is a crucial teaching move.

Since the energy stored in the band is now the energy stored in the field, your thoughts might move on towards electrostatic stores and magnetostatic stores. Or even further, to field potential stores, covering all three. Or it might not. The idea of a field potential store was considered briefly, then rejected mostly on the grounds of too much abstraction, too soon.

So why not electrostatic and magnetostatic—after all in principle you could think of separate calculations corresponding to filling or emptying each store? Well, for starters, the word electrostatic is just too likely to be simplified, it's just temptingly close to electric, which had an unfortunate history of practice in the topic(as alluded to above). And, if you use electrostatic, then you really ought to go for gravistatic to match, which is just ugly. Then there is also the issue of potential collateral damage. You might lead others astray in representing electric circuits, mainly because of how a gravistatic analogy is often used to introduce a potential difference. But this analogy is not with an electrostatic situation, so again the electrostatic is deprecated because of the possible conflation of ideas. Finally, one cannot feel electrostatic forces as a result of separated charges directly, as you can with separated masses and gravity, leading to the need for multi-step explanations to link changes in the energy in that store to the physical changes.

Magnetostatic has the benefit of being able to associate physical experiences of forces when separating magnets with changes in the energy store, but this does not map onto calculations that will be done any time soon. So this could be a contender but is hobbled by its necessary association with electrostatic, where the multiple reasons why this might not be sound suggestion are not enough to offset the advantages of the physical experiences associated with magnetostatic.

But that we can enable children to feel magnetic springs in action, and that there is a close connection between the electric and the magnetic, and to be made in short order in conventional curricula, suggests that there is value in describing a compound store, the electromagnetic. This decision is further bolstered by the unification of the electric and the magnetic fields, not something we have yet managed to do with the gravitational, which is a further point against the field potential store.

Again, using the elastic store as a metaphor, one can think of chemical springs, where atoms are re-arranged to store more of less energy, and nuclear springs, where it is the nucleons that are similarly re-arranged.

Which leaves the vibrational store, standing in for calculations of 12kA 2. The interplay of energy changes associated with changes in movement and with changes in position are essential to the energy calculation and the nature of a vibrating object: taking a snapshot and calculating wreaks a fatal distortion of what it is to be a vibrating object. It is not something that occasionally happens to be in such a physical situation that you can calculate the energy that's been shifted to a gravity or elastic or electricmagnetic store. At other times fortuitously you can calculate a change in an energy store. That's also true, after all, of a large number of processes which are not vibrators. Apart from the utility in the discussion of the depletion of resources, such a store provides a useful starting point for a discussion of waves, and how they might fill or empty stores.

These stores represent the calculations to come, so laying the groundwork for thinking about constraints – about what cannot happen. But there is also some semi-quantitative reasoning that is of immense value in thinking about depleting resources and in planning for sustainability which typically appears too early on in curricula for calculations to be possible. Whatever the choice of stores, this should encourage and enable such discussion, linking the real decisions to be made to the energy descriptions.

[1] I like this description of 'imagined learning sequences', although others would call this a didactical pathway. In any case, it is an invitation to try a 'teaching experiment', to persevere with implementing the line of thinking in your classroom, because it is well-enough supported by plausible reasons that you can see a local adaption. There are also explicit principles, giving you and your children a better chance of making sense of a connected set of ideas in the sciences.