Dialogic Development of Children’s Ideas Using Computation in the Classroom: Keeping it Simple

Abstract

Computers can be usefully thought of as representation tools. Many demonstrated difficulties in learning physics depend on re-representing the world to yourself: imagining it as other than it appears and then reasoning with that new representation, to develop new expectations about the lived-in world. To keep physics live in classrooms during this process requires the most responsive and adaptable tool we can lay our hands on, to encourage teachers to do physics with children. Rather careful thinking about matching the desirable affordances and resistances present in the practices enabled by any tool to the existing physics curriculum suggests casting the net more widely than numerical integration of differential equations. This paper draws on a number of years of working with computational modelling tools with teachers and with pupils (8–18), as well as significant work in constructing teaching sequences and supporting representations in the Supporting Physics Teaching initiative and Advancing Physics (both supported by the Institute of Physics). The foci are on exploiting flexible diagrammatic representations without being able to draw and on evolving responsive representations to support developing ideas during teaching sequences whilst seeking also to exploit the new enthusiasm for coding in a culturally valuable way and on keeping the implementation straightforward enough that teachers might be persuaded to use it.

1 A Place for Diagrams in Learning Physics

Discussions between teachers and students have been studied and extensively theorised over the past few decades in ways that have had impact on practice and on reflections about practice. Some work has also been done on developing drawn representations and some work on what it would take to make computational modelling possible with younger children. I think it would be fair to say that these have not challenged the hegemony of speech, either in research output or as what is seem on classroom walls, at least in the UK, as ‘topic words’. In spite of those who have theorised about communication in science classrooms, writing about the nature of explanation in the classroom, research, examining and classroom practice has tended to emphasise words as the primary medium for expressing ideas in physics.

The use of all three media—words, diagrams and computational models—in teaching and learning physics is concerned with developing and using representations to reason about situations or processes, whether exploring existing representations or shaping your own. Reasoning is possible with either exploratory or expressive use of representations.

Delineating this division between exploratory and expressive use of a (modelling) medium was a significant outcome of the London Mental Models group that did so much to establish the possibilities of computational modelling with younger children.

In classrooms, the different communicative modes described in studies of dialogic conversations point to a similar difference between exchanges used to elucidate expressions from students and other exchanges used to explore the ideas of teachers.

Diagrams are a third kind of medium for reasoning but appear as less plastic than words, being more difficult to construct and more difficult to adapt. The skill of a hand-constructed diagram is not something that seems to be as well practised as the skill of a well-constructed sentence. And many diagrams in physics are highly compressed representations, adopting any inventions that encapsulate many kinds of knowledge, both tacit and declarative.

Perhaps because we expect language to be more flexibly interpreted, we are better at filling in the gaps with language than with diagrams, especially highly encoded or compressive diagrams, that use many conventions. The lack of plasticity affects the interpretation, as the communicative act is more constrained than in the case of language: usually in the direction of requiring more commitment on the part of the person creating the attempted communicative act. An example may help. There is more precision associated with this diagram than with the statement ‘there is a force exerted on the mass’. In part this is because of the conventions associated with the diagrams, but it is also the case that constructing the diagram requires more decisions to be made by the constructor.

But there is a pedagogic danger in the propensity and ability to interpret what is ‘missing’ in linguistic acts: the filling-in carried out by teacher and children often leaves them at cross-purposes, both ‘hearing’ what they want to. Both parties adapt the inputs to fit their own ideas of the purposes of the transaction and of the ideas communicated by the transaction. This is an amalgam of constructivism and the asymmetric relationships of classroom behaviours. The plasticity of words impedes the clear communication of the ideas in physics.

More exploratory and expressive use of diagrams in classrooms, thus, seems likely to reduce this mismatch, given the greater rigidity of the diagram as a communicative tool. There are trade-offs, implicit in the encoding and decoding of diagrams, that any pedagogy that advocates their use will have to work on, but it seems that the gains from such an approach make it worth exploring.

The use of computational models in classrooms can make the rendering of the ideas being expressed or explored even more rigid, forcing a more explicit commitment of what the author intends. However this use is currently a minority interest, in spite of decades of encouragement and exploratory studies. Again the potential for gain seems substantial, but so far access to this potential has not been widely or evenly distributed, as the practice seems to happen in only a few classrooms.

2 Perspectives on Research and Practice

2.1 Words: A Common Probe

Formative assessment is a part of successful classrooms, and often this relies on expository writing as a probe. Children write, and teachers try to work out from their writing what they are thinking and how that can be worked on so that they can think in about physics more helpfully. All too often this writing is to satisfy external goals: it is not about the child representing and reasoning in order to figure out what is going on. So there is often an element of trying to guess what the teacher wants in the exercise. This, together with the plasticity of interpretation and the often extensive inferences about the stability of ideas revealed by these words, suggests that at the least this kind of probing might usefully be supplemented. If the idea is put to work, then we might find out more about how robust it is and how widely applied. But still there are limits to the medium, partly driven by the plasticity of the mode of expression, and partly by the nature of physics, which has adopted the quantitative route to rigour. Words are rarely sufficient—hence the unsuitability of ‘What do you mean by?’ as a probe.

Ideas, not words, are the real target, and we do not really know what an idea means until I see what I can do with it: ideas do not function in splendid isolation: you need to connect them up, and in particular connect them up to the lived-in world, to see what they really mean. This is a form of triangulation, of assembling different multiple perspectives on an idea by using different illuminating probes. Many research papers focus on streams of words, and this focus on language has perhaps supported teacher dialogue which so often, perhaps particularly with the harder ideas such as ‘energy’, seeks to settle on the correct form of words as the arbiter for what is correct and to be effectively transmitted. Words are useful, but they are not everything. For physics, which has essential connections to the lived-in world and is therefore intrinsically multimodal, the quote misattributed to E.M. Forster (‘How do I know what I think until I see what I write?’) is necessary, but not sufficient.

However the most common formative assessment pattern is a series of questions and answers—usually teacher’s questions and children’s answers. If anything this is even more subject to flexible reinterpretation than written words. Whereas the underdetermination of meaning by syllables uttered is an advantage in supporting everyday speech, this plasticity is often unhelpful in exploring understanding and misunderstanding, because there is simply too much flexibility in interpretation available to both participants in the communicative act. This warping of meaning can still be seen in action even if there are serious attempts probing the meanings—itself a hard job in busy classrooms. And the difficulties in communication persist across both expressive transactions, teacher and children working together finding out what children think, and exploratory transactions, teacher and children working together finding out what the a canonical view is.

There is also the difficulty of knowing whether the thinking is final or provisional or more likely some superposition of the two. To engage in dialogue is partly to work out what you think. There is more than a kernel of truth in the aphorism: ‘How can I tell what I think till I see what I say?’

In the light of this, I think there is a case to be made for more exploratory and expressive use of diagrams, whether dynamic or static, to increase the range and variety of evidence on which we base our understanding of the ideas the children are deploying and developing. Whereas there is some work on developing representations towards the canonical (Tytler et al. 2013), there seems to be a dearth of tools that allow children and teachers to codevelop diagrams. The tools should provide some assistance and some prosthetic building blocks so that we do not need to start from just a pencil and a blank canvas. Just as words are deployed to package up collections of conventions and understandings, however particularly, so elements of diagrams carry centuries of refinement in thinking about depicting situations of processes. Consider the simple (obvious?) act of representing the force of gravity acting on an object. A diagram is rather unambiguous, and perhaps straightforward to read, after some practice (Fig. 2.1).

Fig. 2.1

A gravity arrow

However saying the precisely the same thing in words takes a lot of them and requires significant explicit commitment to precision that is implicit in the diagram, being encapsulated in elements of the diagram. This kind of assisted disambiguation has, I think, considerable potential to encourage commitment and clarity in communicative acts.

3 Developing Sketching and Drawing

Words are commonly used and reused as an understanding develops in classrooms, adapted in both meaning and context as they are used by teachers and children. They’re relatively easy to mix and match into new sentences, in which meaning and understanding evolve, whether spoken or written. There are not only many different tools for creating and rearranging written words, from pencil, paper and eraser to the many varieties of text editor on a smartphone, but it is also the case that cultural expectations and norms firmly encourage people to acquire a competence with such tools. The inability to write grammatically is widely considered an impairment. By contrast, the inability to express yourself well using diagrams is less valued (Fig. 2.2).

Fig. 2.2

A circuit with series connections, simply drawn

Diagrammatic representations are not so often developed in classrooms: contrasting this with the affordances available for such developments in words reveals several possible reasons. Firstly elements of diagrams are less easily used and reused in such ways, when compared with the simplicity in mixing and matching words. There is, for a start, no equivalent to the enforced linear structure of the sentence (or the parallel linear interpretative framework as a result of an utterance in time, if the communication is oral). This structural freedom in diagrams adds an extra burden in both authoring and interpreting diagrams. But it may also be partly because the tools to rearrange elements of existing diagrams are somewhat more complex than text processors and partly because communicating with well-formed diagrams is less widely valued than communicating with well-formed sentences. There seems to be less of a cultural or educational imperative to develop this competence.

Yet reasoning with diagrams is a rich resource in physics: one only needs to look at the space-time diagram in relativity, the Feynman diagram in quantum mechanics and the free-body diagram in Newtonian mechanics. All three encapsulate knowledge about the domain, and manipulating the representations guides methods of reasoning about that domain.

In the educational sphere, several approaches have been made. One interesting example is to explore a set of particular geometrical interpretations in the relationships between electrical measures in resistive circuits: the AVOW diagrams. However successful, this has not been exploitable in other domains, and so there is a real question about the feedback on investment. There is a reasonable case that learning to work with these diagrams enables children to reason successfully about a restricted class of resistive circuits. There is a question about the generalisability of the approach, as it relies on simple geometrical interpretation of relationships: it is difficult to see how this would work even in the case of the simplest non-linear relationships. This may explain why the work has not spread to other domains.

Another recent approach has explored children reworking their own representations, getting a better understanding of the value of the canonical representations. However this starts at a very low level, with the equivalent of a pencil and paper, but no words. Everything has to be built from the simplest possible operations, and there seem to be no building blocks, which to adapt and remix to construct their own diagrams.

Here I am after a meso-level, incorporating some culturally valued attributes into the elements of the diagram but allowing these to be assembled in ways that enable a degree of shaping of the communication by the teachers and children in a classroom (Figs. 2.3, 2.4, and 2.5).

Fig. 2.3

A simple circuit

Fig. 2.4

A simple circuit, labelled

Fig. 2.5

A circuit with parallel connections, from a simple change in the code

Sharing an adaptable diagram is as easy as sharing the few lines of code, and changing the diagram is simple, after making the investment of time to find out how. There are inevitably questions about investment of time and trade-off between what is gained and lost: probably only pervasive use of such diagrams will tip the balance in favour of use. And diagrams are no more ‘self-documenting’ or self-evident than words.

3.1 On Making Adaptable Diagrams a Part of Classroom Discourse

The idea is that a kind of structured drawing can enter the classroom conversations, as a partner. Here is a connected series of diagrams, complete with the code that generates the diagram. It should not be imagined that these are all to be deployed in a single lesson, or even in adjacent lessons, but rather that they illustrate the way in which such a technology can encourage the expressive and exploratory use of diagrams (Figs. 2.6, 2.7, and 2.8).

Fig. 2.6

A circuit with series connections, with the code prepared, but commented out, ready for a dialogic sequence

Fig. 2.7

The same circuit but now with a part of the circuit marked off as being ‘internal’ to be battery

Fig. 2.8

The circuit labelled, preparatory to the next step of measuring or modelling. All of the commenting out of the code is now removed

A particular concern is to exploit the idea in the processing language of a ‘sketch’: the code remains adaptable, and one should expect to iterate the diagram, exploring your expressions and using both canonical and personal representations to hope meaning. The diagrams should be purposeful, rather than independent artefacts, open to interpretation and open to reinterpretation. Users are able to inhabit the purposes of the diagram, in the same way that readers can be drawn into inhabiting a novel, seeing how the narrative plays out as the characters evolve: because diagrams, and elements of diagrams have connotations, just as words and paragraphs have associations through which they tell a story (Figs. 2.9 and 2.10).

Fig. 2.9

This is just a bulb, but it is perhaps not obvious to the learner how this very conventional representation relates to the objects that they handle in the laboratory

Fig. 2.10

Two versions of a diagram for a bulb drawn by Lisa, brought into the system as code and encapsulated so that they can be incorporated into more complex diagrams

Here the different representations will have different implicit and explicit connotations: as the conversation evolves, we can draw on these, hiding what we do not want. again the computer is functioning as a representation machine, encapsulating operations and encapsulating meanings. Elements of diagrams have a compressive function, just as technical words do (Sutton 1992), and these need constructing, and sometimes unpacking, to remind both teachers and children of the judgements that enable, and perhaps even constitute, that depiction.

Such diagrams can explore situations, exploring possibilities: one can construct and modify interactive diagrams (whether constructed and deployed as animations, simulations or models) to be used flexibly by teachers as a part of a conversation (Figs. 2.11 and 2.12).

Fig. 2.11

This is a mathematical representation of the circuit in Fig. 2.8. Here you only vary the ‘external’ load resistance

Fig. 2.12

Here the model is adapted so that both the internal and external resistances can be varied, so allowing the conditions under which the maximum power is dissipated to be explored

This is, of course, simply the maximum power theorem, where we can intervene to explore the possibilities. The representations define a kind of possibility space, where the relationships we have encoded into the imagined world constrain what is possible.

It might be worth pausing to consider how this standard piece of physics is represented in other modelling systems (say Stella, Modellus, Coach) to see how these constraint relationships and the idea of a possibility space are presented. There is no time evolution here, and the chosen representation system should not nudge user into depicting the situation in ways that imply that there is.

Above all else this system should remain an open system, built to be adapted as uses evolve. There will need to be adaption at many scales, from a simple taking of one diagram and making simple alterations to rather more significant adaptions of deciding the degree of encapsulation appropriate for the conversation at hand.

4 Dialogic Physics

4.1 Dialogic Approaches: Words

The dialogic approach to teaching has been advocated, and varieties of conversation have been identified to deploy in different phases of teaching. Through this, and other means, teachers have been able to become more sensitised to words and their deployment and indeed to ways in which the structure of conversations can enable the learning and structure what kinds of learning are available (Mortimor and Scott 2003).

4.2 Once Again, with Drawing

Reorganising words to make them your own may not be easy but at least has many accessible technologies to support the process. Words appear rather easy to process and both in writing and editing. Drawings are rather harder to mix and adapt.

Currently diagrams tend to be presented, rather than created or adapted, and that rather begs the question of who decides what is on offer. Treating teachers as professionals entails that some significant pedagogic decisions are made in the classroom, and this requires end-user flexibility, just as with dialogue. There may be common elements, or words, but the dialogue is not fixed. In the same way diagrams that are a part of such a dialogue accept that if developing, teachers will always adapt what you intend, so one should not make it too hard.

4.3 Do Physics: Develop Explanations

A particular concern has been to promote the doing of physics with evolving diagrams playing their part. All too often diagrams form only a part of the declarative phase of physics—representing known outcomes or certain relationships. The aim is to promote selflessness to encourage sharing the pleasure of doing physics.

Here is some physics, already done. Whilst that is a possible use of this expressive medium, it is hardly unique and not of central interest here. However it is a readable model and therefore adaptable (Fig. 2.13).

Fig. 2.13

A completed simulation: still adaptable but unlikely to be adapted by any but the most confident of teachers live in the classroom

Rather I am interested in children being active participants in the representing and reasoning, in expression and exploration and in using these processes as a rich source of live metaphors for reflecting on what it is to learn physics. The work is firmly in the mental model tradition, inspired more than a little, albeit at a distance, by the work of the London Mental Models Group. The representation tools should allow range of communicative possibilities, just like language.

4.4 Resonances: Coding and Modelling

I was invited to present this paper on behalf of MPTL, and it should come as no surprise that a theme is that one of the strengths of a computer as a representation machine is that it can compute: this is an ability we should exploit in thinking of them as pedagogic tools. And computational thinking itself has parallels with doing physics. Here are two aphorisms:

• The art of programming is the skill of controlling complexity.

• Doing physics is representing things as simply as possible, and no simpler.

Both are handy paraphrases, but there is a commonality of style that getting computational modelling going in classrooms seeks to exploit. In both cases the author has an end purpose: in the case of physics, it is to generate an imagined world that functionally mimics the lived-in world—a physics model. In the case of the programmer, the purpose is more varied, but the program will support some meaningful functionality. In this the role of the computer as a ‘representation machine’ is crucial. Below the surface appearances of similarities in mimicry, the core programming processes of encapsulation and abstraction provide a good basis to believe that computational models can be pedagogically useful, in describing both processes and situations in physics.

Describing and modelling situations or processes involve both abstraction and encapsulation: just considering the Earth as a point mass requires both transpositions. This commonality of style suggests that computational modelling of situations or processes—expressing your thoughts about physics in a computational medium—could benefit learners:

• As they explore models built by others

• As they create their own models

• As they use their experiences of such explorations and expressions to reason about situations and processes

So there is something to be gained at quite a deep level by linking developments in teaching physics to the current interest in teaching children to code.

4.5 Representing a Chain of Reasoning

Dialogue often navigates a chain of reasoning, and it would be useful if the time-based evolution could be transmuted into a spatial arrangement that allows an overview of the chain. This is possible, and there may be value in having a standard graphical language for the transitions between the steps and the kinds of steps, as well as for the contents of the steps in the chain of reasoning (Fig. 2.14).

Fig. 2.14

Both panes, containing steps in an argument, and transitions, moving between such steps, can be incorporated into the diagrams

But even within a step, the readability of the code can be optimised to enable the line of argument to be followed.

It is possible that well-written code (perhaps even moving towards literate programming) may be more intelligible than any other process for connecting a chain of reasoning that relies on computation. It is often very hard to disentangle a computational model built using a spreadsheet and see the flow of the algorithm at work: indeed exactly this issue has motivated whole libraries in python to try and move data journalism on from using spreadsheets, exactly so that interested readers can check how the raw data is connected to the assertions. For the purpose at hand, the code needs to be both readable and writeable, without having to rework one’s understanding of the physics or have it refracted through distorting metaphors. The chain of reasoning should be clear from the code, as far as possible.

4.6 Reworking Explanations with Code

Another advantage of using code is that sequences can be traversed by reworking the code. An example is probably more powerful than general arguments (Figs. 2.15, 2.16, 2.17, and 2.18).

Fig. 2.15

A manipulable diagram, with the explicit code on the left. Naturally, only the diagram can be presented, whilst maintaining the interactivity

Fig. 2.16

Some simple changes in the code result in a description of a new situation, with the same flow from what is varied to the power dissipated remaining explicit

Fig. 2.17

A model to smooth the transitions between Figs. 2.15 and 2.16, where a simple click adds an extra loop

Fig. 2.18

An alternative presentation of the same move, from one loop to two, that might make the move easier to follow for some learners

Doing such reworking live enables supported exemplification of physics being done, revealing it as effortful thinking (Kahneman 2011), reworking the mental modelling clay (Ogborn and Jennison 1994) until the imagined world becomes a functional mimic of the lived-in world, at least in salient and valued respects.

5 Constraints in Designing a Diagram Playground

The focus here has been on reasoning with diagrams in physics and on making an amalgam of practices and tools available to teachers and children: a diagram playground. Such a playground will embody rules, perhaps as transitional objects, that facilitate access to thinking in culturally valuable ways. The possibilities for perceiving geometrical relations were fundamentally altered by the intellectual ecosystem of the turtle in Logo: a new playground was created for thinking about certain kinds of mathematical relationships and for encapsulating created patterns, which were then rather easily varied. Here I hope to make a step towards creating such a system for thinking about physics in secondary schools, as far as possible tilting the playground space so as to create a gradient that nudges teachers and pupils towards a cultured representation of physics, highlighting the fundamental epistemically moves and intellectual style.

5.1 Respecting Relationships in Physics

Physics describes both situations, where there is no time evolution of the physical quantities, and processes, where there is time evolution of the physical quantities. Both are important, but to date both have not been equally available in representational tools that are computer mediated. For example, both Stella and Modellus, which have perhaps been most widely used in computational modelling in upper secondary schools, very naturally represent time-evolving relationships such as that between velocity and acceleration but do struggle to capture the full richness of assertions of identity, such as the relationships between the quotient of force and mass and acceleration or any other constraint relationship. Given the importance of such formal relationships in elementary physics and their importance in reasoning, for example, in Piagetian explorations of compensation, such inelegance will impede the tool in supporting thinking about situations: so states. This is not simply an observation about the conflation of the assignment and equality operators. Such a slide between reasoning about time-independent states and time-evolving processes has real consequences. Viennot’s work on the prevalence and perils of linear causal reasoning (Viennot 2001) stands as a continuing warning beacon as one considers the kinds of tools that one might want to make available to children and teachers: these tools should not contain a mixture of affordances and resistances that switch their thinking off down the wrong tracks.

In general, the time evolution implicit in procedural computational languages reinforces the tendency towards linear causal reasoning: creating an affordance gradient. That is, computational modelling systems exist in an Aristotelian space with a tendency to clump at their natural place: in mathematical space the corresponding location is occupied by Newtonian fluents and fluxions: formally studied as differential equations. Yet these mathematical forms and the corresponding region of space in developed physics descriptions are only really pencilled in for population later, in future studies in secondary physics schooling. Much of the action in representing and reasoning is about states or situations and not about processes or time-evolving relationships.

In designing for pedagogical utility, this affordance gradient will need to be explicitly designed out: creating structures that step outside what is naturally available in procedural computer languages. There are functional or pattern-matching languages, but the thinking underpinning these seems less well spread amongst the target audiences, and I do not find much evidence of widespread understanding and use of the style of thinking that would make them more accessible amongst teachers and children in the sciences. Indeed the extensive evidence that we have something of a tendency to explain both situations and processes to ourselves in terms of causal, time-dependent stories suggests that this absence is not at all surprising.

An expressive medium for reasoning about physics should greet both situations and processes in an even-handed way. Since the discovered rules that structure the world of physics are expressed as relationships, then such a system should be able to express constraint and time-evolving relationships equally elegantly, allowing users to express what they intend without requiring particular specialised intellectual contortions.

Both constraining and accumulating relationships should be equally prominent if the medium is to guide thinking in fruitful ways. If an approach is made through code, then some of the primitives will have to incorporate some hidden code in order to adapt any procedural language to something better suited to express constraints: accumulations can be more directly and easily expressed in procedural languages, but we may still be better building a presentational skin over the language, as is the case, for example, in Easy Java Simulations.

5.2 Implementing Both Kinds of Relationships

Here are two simple models that show how accumulations and constraints are achieved in the current implementation (Figs. 2.19, 2.20, and 2.21).

Fig. 2.19

A pair of prebuilt constraint confections. Easy to author, perhaps not so easy to read the code, which allows you to drag either the current or pd representations (the resistance is constant here) and see how varying one alters the other. You can also explore the constraints between force and acceleration in a similar manner, given that the mass is constant here

Fig. 2.20

Here the constraining is much more explicit, which may be more fruitful for the pedagogic intentions of the particular teacher

Fig. 2.21

This is an explicit accumulation relationship, where acceleration accumulates velocity. As the acceleration representation is draggable, the user is able to set both positive and negative accumulations as the model is running

In elementary physics teaching, there are lots of situations where the descriptions require constraining relationships, but only a few where there are processes where there is a natural need for accumulating relationships. (These few are nevertheless important and are often core relationships, foundational for whole topic areas in physics, such as kinematics.) In existing computational modelling tools, it has been the other way around: the affordances in the tools make accumulations easy but constraints difficult—technology can derail pedagogy.

5.3 Two Paths to Developing Descriptions

Faced with a new phenomenon, an approach is to notice certain features, operationalise some identified features into a series of measurements and then hunt for patterns amongst these measures. This is a perfectly reputable analytic and empirical approach. Data capture and analysis tools (often used in MBL), prioritising creating scatter graphs as a discovery tool, lend themselves well to this function-fitting approach to the development of a descriptions containing relationships between physical quantities. Yet it is far from the only way that physicists proceed in representing and reasoning about phenomena. The theoreticians approach to representing and reasoning places a powerful focus on imagining things as they might be and seeing how that imagined world plays out. This approach is a natural fit for a computationally enabled playground for ideas as the ‘playing out’ of the rules is a strength of the computer: the pre-requisite is that the imagined world is simple enough to construct it and easy enough to explore. Exploration will be needed if the ability to reasoning about situations is required: it would be an unhelpful move to build in a natural assumption that the imagined world will explore some planned sequence of possibilities, however tempting that might be. Such an exploration would be much too close to an evolution and so could be mistaken for the description of a process rather than a situation. This idea of imagined worlds and the promotion of theoretical thinking are not new, reaching back to and beyond the London Mental Models group. It may actually be the purest form of a public representation of a mental model in the sense that Johnson-Laird intended, in that it is possible to see for ourselves how our world actually plays out: the computer screen may function as a non-distorting mirror for our thinking. (The computer is notorious for allowing little room for wish fulfilment in the matter of executing instructions.)

This idea of an invented world that is compared back to the lived-in world serves well as a metaphor for thinking about the whole edifice of physics as a set of provisional human constructions, there to make sense of the world. In fact a story we tell back to ourselves is but a story constrained by the need for functional mimicry. As Gaiman wrote ‘We who make stories know that we tell lies for a living. But they are good lies that say true things…’. In seeking to see courteous representations of physics take hold, I see no need to play second fiddle to the writers of fiction. The case for the narrative structure of explanations has been extensively made elsewhere.

5.4 Multistep Reasoning

Some narratives, often construed as arguments leading to a particular way of seeing pieces of the world as being connected in a particular way, have a story arc that proceeds a series of connected acts. These acts, or steps, are often related in particular ways: that is, there are certain intellectual moves that we make habitually.

Being able to reveal the structure of the argument and making the moves explicit support an understanding of the thinking that is being shared and so can help supporting the development of thinking like a physicist in the children: the ability to zoom in and out. Finally, often facilitated by simple familiarity, there is the identified issue of the ‘hidden moves’: steps which are so natural to the teacher that they seem to need neither representing nor mentioning, but which may well blindside the children, or indeed less experienced teachers.

So a representational medium, besides expressive or metaphorical use, might also have an exploratory use: that is, children and their teachers could explore a representation or a series of linked representations, so as to unpick the thinking behind them (Fig. 2.22).

Fig. 2.22

A complex document, with an overlay showing the location of the current step in the whole three-step argument. Each step consists of an interactive diagram

This idea of switching perspective moving from one point of view to another, supported by a limited number of graphical markers, owes much to a careful reading of McCloud (1994).

5.5 Encapsulation

To think assisted by a computer, it is no longer necessary to set switches one by one—a compiler takes care of that task, allowing the user to think in more human-friendly terms. Now there are a large number of expressive computational environments, more or less abstracted from the underpinning actions of the CPU. You are able to choose a level of abstraction, selecting the representations you want to work with, so freeing up your mind to operate with the intellectual tools you choose. Of course, you can only choose from amongst available tools, and this development aims to provide one such tool from which to choose, one tuned to thinking in physics. In selecting such a tool, you are selecting a surface of thinking, able to choose to reason with entities of cultural value to physics and see how they interact in the world in which you place them. The representation to hand and the ways in which they can be induced to interact together present some affordances and resistances which could combine with practices to generate an environment where theoretical thinking in physics is encouraged.

In generating narratives there may be a need to inject representations that are not canonical and have them interact with other parts of the system. This is possible, as one can take drawn objects and render them in code, encapsulating them, as with Lisa’s bulbs, met earlier.

The process is not as simple as it could be, but it’s possible without huge technical overheads and could be developed further if practice supports such investment.

This move to render graphics as code might seem to introduce an unnecessary step: why not draw everything, so keeping the system entirely graphical? I think there are several good answers to that, based on current graphical programming practice and in pedagogical research.

5.6 More Natural Just to Draw?

Starting with the pedagogical, there is at least one long-term research project in getting children to create computable models based on their drawings (van Joolingen 2015). As things stand the visual representations can be drawn, with the computer understanding the drawings, using image processing. However expressing the rules that govern how these drawn entities interact is not done with drawing. I think that is because rules, expressions and intentions are not easy to derive from gestures without imposing serious constraints on the expressive range(in a way this is much like speech processing—the more constrained the environment, the better the intentions can be reliably recognised). One way of injecting these constraints is to make the drawing interface more like a vector drawing package, but use of such packages soon leads to the recognition that the presentational complexity of vector drawing software is necessary and not accidental. And such software is expensive to develop. There has been some very interesting exploratory work on dynamic drawing of the kind that might support reasoning about entities in physics, but at the moment, these are early explorations and for a more restrained range of expressive tasks that might be useful for a widely applicable tool in reasoning about physics (see, e.g. Victor 2013).

Similarly there have been construction sets based on graphical elements, sometimes to minimise syntactical errors in coding (such as Scratch) and sometimes to enable complex instrumentation to be built (such as LabVIEW). All of these graphical systems embody design decisions about what can easily be expressed in the playground, which may be more or less well adapted to the task at hand. For example, StarLogo is well suited to certain kinds of situations, but not others, and the overlap with elementary physics is not so good (e.g. in Resnick 1997).

Here we’re after an open system, built to be adapted as uses evolve. For now, alphanumeric code presents the designers and users’ options for graphical communication, melding structured drawings with computation, at moderate cost and with moderate commitment to possible future development paths.

5.7 A Didactical Perspective

If only all children were fluent in algebra (in expression, in manipulation and in interpretation) and as good at geometrical reasoning as Newton, then a tool such as this might be entirely superfluous. But they are not: so this diagram playground might be something of a prosthetic, to assist the learning journey. Along this journey, which is a cultured induction into physics, children should be encouraged to both represent and intervene in their collection of representations and in a manner that makes it plain to them and to others what those actions entail: that is, both the representing and the intervening should be with public representations. I am co-opting the computer as representation machine, to create a mirror for thinking in physics. That is the process of doing the physics should be as well-illuminated as possible, with exemplification of thinking in physics in the foreground.

6 A Step Towards a Playground: The CMR Ecosystem

For all the theorising and attempts at careful designing, the CMR ecosystem is simple and adaptable. It consists of:

• The processing.js language.

• A series of dedicated functions, written in processing.js, that allow physics representations, either interactive or static, to be shown rather simply.

• A dedicated two-pane on-line editor: in one pane a text editor to create or adapt sketches, customised to perform code completion and code highlighting with these same dedicated functions; a second pane, where the generated output appears.

• A sketch, which is a short piece of code, always contains two chunks, setup and draw, constructed using the text editor.

• A dedicated on-line player that presents the output of completed sketches, from locally saved sketch files or sketch files with a URL.

• Extensive and comprehensive documentation.

This is currently (2016) implemented and available at http://supporting physicsteaching.net/cmr.

7 Moderate Progress

7.1 A Useful Tool

The aim here has been to produce a publicly accessible tool, useable by teachers in classrooms, as well as enabling preparatory work that elevates the status of diagrams in developing an understanding of physics to that of words.

In such a tool, there are a considerable number of possibilities, just as there are in a piece of apparatus, except that we’re using a computer, which in its very nature is a representation machine and therefore in its essence even more flexible than a multimeter, a clock or a metre rule. But as with any piece of apparatus, it is the stories of use and practices that make it pedagogically useful and shape the future development. For now, the technology is widely used in Supporting Physics Teaching at supportingphysicsteaching.net, where it presents canonical resources that are teacher-adaptable, designed both to encourage engagement with the tool and so that teachers can adapt teaching approaches that make significant use of diagrams.

Teachers may or may not use this or similar tools: what we do know for sure is that computational modelling tools, however good, are not enough. The focus on diagrams for physics, on making those adaptable, and allowing, but not insisting on a computed model, are intended to explore a new possible approach. As is the exposure of rather simple code. Whether the implementation proves sticky and widely adopted remains to be seen: it could be made to work. However the design principles and considerations are, I think, applicable to any future tool that seeks to exploit the affordances of computed diagrams in the service of productive conversations in physics classrooms.