Modeling for communicating physics

Three roles for modeling in teaching and learning physics

Models and analogies

There are two widely used and contested terms that almost need stipulative definitions to be useful: model and analogy.

Whenever I use the term model I will be expecting some add kind of similitude between the model and what is modelled that relies on a functional mimicry. I may not always find it, as not all models are successful, but this is the criterion for what it is to be a model. That is the behaviour of the model must catch some essence of the behaviour of what is modelled. It is not enough just to look like what is modelled, so for example a plastic ear would not count an example of a model, in the sense that I will use the word.

An analogy I'll take to be something different. It too relies on a certain similitude between the source and the target of the analogy, but does not require a functional mimicry. Analogies are often use in an illustrative way and are commonly used to render phenomena believable or more acceptable, so enabling a psychological connection with the phenomena. Lacking functional mimicry as an essential component, analogies cannot be used to make reliable predictions.

Both models and analogies in these senses have a role in physics education, but those functions are not interchangeable: I think the distinction is worth preserving so that we can be clear about what the learning outcomes are.

Artefacts to reason with

Models are best thought of as artefacts to reason with, and only secondarily as objects to reason about. This secondary use is the metaphorical use of models, which maybe the most frequent use in learning physics, but to make it effective you'd expect to draw on experience with real models. If there is no such real experience, it's like expecting children to learn about magnets without ever having to handle a magnet, and few would expect to achieve that.

To the extent that they are objects the reason with, computational models are the mirrors of the original mental models of Johnson-Laird. These are public depictions of systems which can be run forward in 'time' to see how such systems behave. This is exactly what a mental model as envisaged by Johnson-Laird is: a system you can run forward in your imagination in order to see how things evolve. In a real sense computational models function as prosthetics for this kind of mental model, allowing you to offload some of the processing and some of the memorising so as to enable you to achieve more than you would unaided.

The model is much more than just a picture, or a three-dimensional simalcrum (or even 4-dimensional). You expect to be interact with the model, and to be in control.

Even with the idea of model as functional mimic established, there are subdivisions: there are both teaching models and physics models. Pedagogical practitioners use the former: research practitioners use the latter. A carefully reasoned didactical articulation between the two kinds of models ensures that the cultural artefact of physics is a reality shared by the users of both kinds of models.

Interacting with models necessarily enables some kind of computing, allowing the space of possibilities inherent in the model to be explored, so making predictions. In computational modeling, we offloaded the processing to the computer: in mental modeling, unless you have an imperial computer such as Kepler to hand, it happens in our own wetware. In both cases there is no necessity that the computation is fully quantified: making semi-quantitative predictions is something of the mark of expert, and so we should respect the use of models that facilitate this kind of output. After all, topic-based educational research shows that it's the qualitative and semi-quantitative understandings that are hardest to develop accurately, and are also at most lasting value in solving problems in new and unfamiliar situations.

A spectrum, with possible practices baked into structure

An animation, to visualise

You might use these for situations where teachers just knows what happens, but rendering this via a tractable mathematical model is just too hard. Maybe you could also usefully deploy animations to encourage thinking about counterfactual situations, or emphasised seeing, as a kind of visual attention director, often from an unlikely angle.

A simulation, to depict

You could use simulations for developing a functional understanding, connecting input and output. As a consequence they're not so good at going deeper, since the attention is focussed on the surface appearances.

A computational model, to understand

Such model are fully fledged tools to think with.

All three kinds of artefacts have an imagined author and reader, that is they are only fully intelligible once you investigate the practices of those who use them. How each community of such practices uses them will shift the artefact along the spectrum a little, but arguably only in the direction of somewhat less explicit representations. So a modeling tool could be used as a simulation, but a simulation does not allow access to changing the rules in such a way that you could use it as a modeling tool. And a simulation could be used as an animation, but an animation could not be used as a simulation.

A note on the interactives used in SPT

Interactives, as used in SPT, are either simulations or animations: some are calculated and therefore simulate some facet of the physicist world, some are simply drawings, whether moving or not.

The interactives:

Therefore you can use the interactives to explore how ideas in the imagined world hang together.

Engagement in computational modeling

To engage children in computational modeling is to give them an enhanced chance to theorise—by giving them carefully shaped building blocks to assemble in a place where this assemblage is open to inspection and commentary by their peers and teachers. Giving children these opportunities in physics lessons is in many ways only equivalent to allowing children to draw in art lessons—they engage in some practice of physics in order to better appreciate the nature of physics (both what and how it represents—rather than just engaging in the equivalent of art appreciation classes).

The purpose of these assemblages is usually not too difficult to communicate in outline in the classroom, although the finer detail and the comparison of differing constructions might well be. Children assemble the blocks to produce a dynamic artefact that mimics some aspects of nature's behaviour. They invent a world that has some important similarities to the lived-in world around them. Their invented world will also have some differences—for a start it will necessarily be somewhat stripped down, paying attention to only a few of the aspects of the real world. Using computer based tools can make these models more explicit, inspect-able and so more public than in some other cases where "models" are used in science lessons.

Here I've just been clearing away the undergrowth on the way to exemplifying some cases where introducing computational modeling can be made to have significant paybacks.

Computational physics, or physics through computation

Computational thinking brings you closer to the physics, so long as you concentrate on encoding the fundamental relationships and combing those in an algorithm, rather than just encoding the solutions.

So the trick is to use the computer to express a physically meaningful algorithm, not to use it as a glorified calculator. Its a synthetic and creative activity.

'The computer programmer is a creator of universes for which he alone is responsible. Universes of virtually unlimited complexity can be created in the form of computer programs.' (Joseph Weizenbaum in Computer Power and Human Reason).

Having your thoughts reflected back is a real aid to seeing what you 'really' meant. As a rather famous aphorism has it: "How will I know what I think until I see what I write?". Imagining worlds, seeing how they behave, and comparing that behaviour with the lived-in world, is the process of computational modeling as described here.

Programming art and skillful modeling

The art of programming is the skill of controlling complexity, as is building tractable models

A part of the power of programming languages is that they take care of little details for us: the design of the language takes care of what counts as a detail, allowing a focus on the fruitful difficulty.

Introduction to a programming systems often stress different facets of the process. Here is an adapted ontology, that could be useful in physics classrooms where code is being used to express physics.

This has a lot in common with broad-brush constructivist theories of learning . And nearly everyone in physics teaching seems to be somewhere on the constructivist spectrum. Some may even be constructionists: even more amenable to acticvities where things get built and thought about.