The discussions of EM for concurrent engineering and software development reflected a shift in perspective from computer science towards engineering. Our first thoughts in trying to give a satisfactory account of EM focused on 'modelling external 'real-world' referents' as a foundation. This might be seen as echoing Cantwell Smith's claim that 'formality, in the end, reduces to first factor notions of physical realisability' (see footnote 3 in Two Lessons of Logic). It also reflects the central role for the artefact in EM: in something like the sense that the existence of a model is evidence for the consistency of a set of axioms in logic, embodiment and existence can be taken as evidence of 'freedom from contradiction'. The controversial nature of linking what is consistent with what can be experienced is underlined by Bradley's objections to Radical Empiricism: "... mere experience ... furnishes no consistent view. [The direct products of experience] I find that my intellect rejects because they contradict themselves.". It is of interest to note James's response to this criticism: "The difficulty of understanding what happens here is ... not a logical difficulty: there is no contradiction involved. It is an ontological difficulty rather.". It is this ontological difficulty that is involved in giving an adequate account of EM.

Useful as it may prove to be to think of physically-based modelling when applying EM in practical engineering contexts, a deeper consideration of what is involved in EM in general points to the need for a broader foundation. In particular, terms such as 'objective', 'real', 'exists', 'physical', 'embody' are all terms that (in the spirit of William James's Essays in Radical Empiricism) can be regarded as relating to the classification of our experience and are not to be viewed as primitive in the context of EM (cf. James's remark that "subjectivity and objectivity are affairs not of what an experience is aboriginally made of, but of its classification"). In thinking about EM in relation to educational technology and 'human computing' it is essential to link observation of the natural world with cognitive and social issues. This is in line with the breadth of the concerns that EM ventures to address in concurrent engineering, which include the personal subjective elements of design and the managerial socially-constructed conventions and commitments that emerge through negotiation within design frames. (Cf. also the work of Naur and Gooding, both of whom are centrally concerned with meaning in relation to abstract theoretical speculation and concrete practical interaction, and recognise the limitations of classical formal methods of knowledge representation.)

Subject to accepting the sort of philosophical position that is represented in Radical Empiricism, the appropriate frame of reference for studying educational issues is supplied by the Experiential Framework for Learning (EFL). This perspective is to be understood as a framework within which to interpret knowledge of different kinds, and in particular to trace knowledge to its empirical roots. In broad terms, it is concerned with how to account for all kinds of knowledge in terms of private personal subjective knowledge such as is embodied in an EM artefact. This can be seen as mapping out the territory within which educational activity is situated, rather than prescribing how it is typically conducted. For instance, much learning is mediated by language and symbolism that we are not in the habit of interpreting or validating through practical interaction in the world, even though (at least from an EM perspective) it is fundamentally attributable to such interaction. By way of illustration, to assert that 6+4=10 we don't consider it necessary to count on our fingers; we may accept that (on consulting a calculator) the value of pi is approximately 3.14159265358979 without performing very precise measurements on the circumference and radius of a circle; we may count the number of people attending a theatre by counting those in the front stalls, rear stalls, gallery and upper gallery as they enter and adding the results without feeling the need to count the entire audience again when all are seated. In the same spirit, we believe what we are told by witnesses that we deem to be reliable, though we are unable to verify their evidence from direct experience.

The general principles by which EM can be used to represent activities within the EFL is set out in the transition from private personal modelling to social interaction aimed at shared understanding that is traced out in studying what can be termed "Empirical Modelling for the single agent". (The role of social interaction in the educational process is of particular interest to Crook.) The traffic lights case study is used to illustrate aspects of this transition in outline, and leads onto a description of how such modelling can be adapted to serve a variety of different (what can broadly be interpreted as) educational purposes. The 'onion' metaphor is useful in conveying the relationship between theoretical and empirical knowledge: how the theories about which we are most certain correspond to the domains of which we have most experience; how an instructionist approach to teaching develops the most advanced theory from the most commonplace theoretical principles; how the constructionist approach to education relates the acquisition of advanced theoretical knowledge to the narrowing of the open experimental context to situations that are ever more specific and contrived. The significance of EM in this connection is that, by modelling our construals, it allows shades of plausibility that aptly reflect the nature of our practical insight into a domain (cf. the fact that what is not consistent with the axioms of a theory is incapable of carrying any meaning). There are those things of which we have such certain expectations that our whole world-view would be completely disrupted were they to be confounded; there are expectations we have of neighbouring possible states whose plausibility can be assessed by our perception of possible agency; there are the speculative tentative models of dependency and agency that we introduce where we have no certain knowledge and limited, unreliable or barely comprehensible experience.

There is a danger of talking too simplistically about 'the layers of the onion' as if they were objective levels in the learning of a specialised domain. (This lack of objectivity is reflected in EM models, which typically offer many different plausible organisations associated with such layering.) That there is some kind of progressive enrichment of experience that is associated with mastering a domain is nonetheless clear in some contexts - as in learning the skills of a game, for instance. The progression from throwing a ball and trying to hit it with a piece of wood to understanding the nuances of bouncers, googlies, square legs, off drives, square cuts, run outs, reverse swing, leg byes etc illustrate that sophisticated specific uses of language evolve in conjunction with essential complementary development of practical experience - it doesn't make sense to use such rich categories to qualify our first attempts to play cricket. This idea of 'nearness in the space of sense' is acknowledged in education in such concepts as Vygotsky's 'Zone of Proximal Development' (ZPD), and the related notion of 'scaffolding' the transition from one level of understanding and appreciation to the next.

From a practical educational technology perspective, EM still has a great deal to prove. With our current tools, and in the current educational context for education in schools, it is hard to envisage teachers being able to use EM to construct or modify models. There is a general thesis underlying the potential use of EM in an educational setting that may one day be vindicated: that the modelling of construals is an activity that is in its essence centred on the learning domain (i.e. it involves the identification of agency, dependency and observables whose significance is independent of the programming task and does not demand the conceptual models of programs accessible only to a specialist programmer), and that in principle this activity is a route to developing educational software that is more satisfying to the learner (because models can embody and integrate a wide variety of construals and configurations) and more accessible to the teacher (because models are relatively easily adapted to neighbouring construals and configurations). For the present, given the current status of development of EM tools and of education about EM principles, this claim can only be put to the test by enabling an informed teacher to work alongside an expert modeller.

There are many models that have been designed with an educational agenda in mind, especially in association with the COMICAL (Cognitive Observation-oriented Modelling for Interactive Computer Assisted Learning) project. Models such as Roe's coordinate geometry environment (COG), the Virtual Electrical Laboratory (VEL) developed by D'Ornellas and Sheth, the complex numbers tutorial created by Gardner [complexGardner1999] and the mathematical visualisation of FDL4 constructed by Buckle and Beynon [fdl4Beynon2002] demonstrate the potential for using EM to build educational software in a variety of traditional styles. A common characteristic of this software is that it is less polished than commercial software (it is intrinsically less optimised to specific function and specification) but offers wide scope for modification and extension at relatively small cost. Other models such as Gardner's racing cars model, the OXO models and the bubblesort/heapsort models, demonstrate the way in which the elaboration of a model can trace a possible path through the 'cognitive layers' from primitive to more sophisticated knowledge of a domain. The most important recent development has been Roe's observation that navigation within the space of sense represented in the onion metaphor can be usefully linked both to activities associated with the EFL and to scaffolding and the ZPD. The discussion of variations of the heapsort model whereby colour conventions at nodes serve to transform the task of learning heapsort from what it might be possible to teach a pigeon to do to a task that requires intelligent interpretation of the comparison of numbers (see CS-RR-346) illustrates the potential to adapt artefacts in ways that may scaffold learning in its pre-articulate phases. (Further extensions of the same model by Rungrattanaubol [heapsortextendRun-bol2001] show how interaction with such an artefact can be linked to a formal specification for heapsort, and so to a language-centred account.) Other models, such as Roe's clown-in-maze model [krustyRoe2002], and the SQLEDDI environment (as represented in sqleddiBeynon2001) show how similar scaffolding principles can operate in the realm of language. In EM, the key to this development has been the introduction of Brown's agent-oriented / observation-oriented parser [agentparserBrown2001], and its refinement by Harfield [agentparserHarfield2003], which has made it possible to adapt the parser for a notation in an interactive fashion within the tkeden interpreter. This means that - in principle - it is easy to give different nuances to notations to suit different learning objectives, and to implement the progressive refinement of language within a single domain that was remarked in connection with the allusions to cricket above. The notes on the development of the SQLEDDI environment (which should ideally be read in conjunction with practical use of the release of tkeden and other associated resources introduced in the CS233 module in 2001) illustrate how this concept can be applied in practice. For instance, they highlight the role of the Uneddifying Interface as an artefact, and of SQL0 as a notation, in scaffolding the understanding of how standard SQL departs from relational theory, and how this contributes to problems in developing a satisfactory operational semantics and implementation. They also serve to give more insight into how the incremental development of an EM model can evolve in the absence of a specification in ways that reflect emerging understanding on the part of the teacher/modeller, and how this differs from the traditional progressive disclosure of features that are familiar to the teacher from the outset, and have been programmed to become accessible following a preconceived pattern.

References

William James, Essays in Radical Empiricism, New York: Longman Green and Co (1912), reprinted Bison Books 1996

Brian Cantwell-Smith Two Lessons of Logic  Comput. Intell. Vo 3, 1987, 214-218

F. H. Bradley  Appearance and Reality: A Metaphysical Essay (1893), reprinted OUP 1963

Peter Naur Knowing and the Mystique of Logic and Rules : Including True Statements in Knowing and Action Springer 1995

David Gooding Experiment and the Making of Meaning:  Human Agency in Scientific Observation and Experiment, Kluwer Academic, 1990

Charles Crook  Computers and the Collaborative Experience of Learning Routledge 1994