A definition of the ARCA notation

ARCA is a programming notation intended for interactive specification and manipulation of combinatorial graphs. The main body of this report is a technical description of ARCA sufficiently detailed to allow an interpreter to be developed. Some simple illustrative programs are included. ARCA incorporates variables for denoting primitive data elements (essentially vertices, edges and scalars), and diagrams (essentially embedded graphs). A novel feature is the use of two kinds of variable: the one storing values (as in conventional procedural languages), the other functional definitions (as in nonprocedural languages). By means of such variables, algebraic expressions over the algebra of primitive data elements may represent either explicit values or formulae. The potential applications and limitations of ARCA, and more general "algebraic notations" defined using similar principles, are briefly discussed

Construals as a complement to intelligent tutoring systems in medical education

This is a preliminary version of a report prepared by Meurig and Will Beynon in conjunction with a poster paper "Mediating Intelligence through Observation, Dependency and Agency in Making Construals of Malaria" at the 11th International Conference on Intelligent Tutoring Systems (ITS 2012) and a paper "Construals to Support Exploratory and Collaborative Learning in Medicine" at the associated workshop on Intelligent Support for Exploratory Environments (ISEE 2012). A final version of the report will be published at a later stage after feedback from presentations at these events has been taken into account, and the experimental versions of the JS-EDEN interpreter used in making construals have been developed to a more mature and stable form

Evaluating definitive principles for interaction in graphics

This paper is an appraisal of current progress towards supporting interactive graphics within the framework of a general-purpose programming paradigm based upon definitions. It considers how the use of definitive principles relates to other work, why it appears promising, and what progress has been made towards the resolution of technical difficulties. It re-examines potential for applications of definitive principles in interactive graphics in the light of more recently developed ideas about dealing with control issues and dynamically changing relationships in a definitive programming framework. It also takes account of new research into notations for graphics that makes use of geometrical constructions. As a subsidiary theme, the paper contrasts the support for reference and representation of geometric relationships in various kinds of interactive graphics systems

Constructionism through construal by computer

Traditional computer programming is not well-aligned to the needs of constructionism. Orthodox programming principles are oriented towards prescribing processes that address clearly specified uses. Functional specification and optimised execution do not encourage interactive exploration and open-ended interpretation. We propose making construals by computer using Empirical Modelling principles as an alternative to conventional computer programming. The merits of this approach are discussed and illustrated using construals for Sudoku solving. Our Sudoku solving construals are made up of definitions that express dependencies between observables. Many kinds of human agency can be expressed through modifying the current set of definitions. The construal serves as a shared artefact with which developers, teachers and pupils can all interact concurrently in essentially the same way, each according to their role and experience. Our preliminary experiments with schoolchildren highlight potential for rich and radically new kinds of learning experience and unprecedented scope for recording, monitoring and intervening in support of constructionist learning. Further empirical study is a vital next step

Empirical modelling principles to support learning in a cultural context

Much research on pedagogy stresses the need for a broad perspective on learning. Such a perspective might take account (for instance) of the experience that informs knowledge and understanding [Tur91], the situation in which the learning activity takes place [Lav88], and the influence of multiple intelligences [Gar83]. Educational technology appears to hold great promise in this connection. Computer-related technologies such as new media, the internet, virtual reality and brain-mediated communication afford access to a range of learning resources that grows ever wider in its scope and supports ever more sophisticated interactions. Whether educational technology is fulfilling its potential in broadening the horizons for learning activity is more controversial. Though some see the successful development of radically new educational resources as merely a matter of time, investment and engineering, there are also many critics of the trends in computer-based learning who see little evidence of the greater degree of human engagement to which new technologies aspire [Tal95]. This paper reviews the potential application to educational technology of principles and tools for computer-based modelling that have been developed under the auspices of the Empirical Modelling (EM) project at Warwick [EMweb]. This theme was first addressed at length in a previous paper [Bey97], and is here revisited in the light of new practical developments in EM both in respect of tools and of model-building that has been targetted at education at various levels. Our central thesis is that the problems of educational technology stem from the limitations of current conceptual frameworks and tool support for the essential cognitive model building activity, and that tackling these problems requires a radical shift in philosophical perspective on the nature and role of empirical knowledge that has significant practical implications. The paper is in two main sections. The first discusses the limitations of the classical computer science perspective where educational technology to support situated learning is concerned, and relates the learning activities that are most closely associated with a cultural context to the empiricist perspective on learning introduced in [Bey97]. The second outlines the principles of EM and describes and illustrates features of its practical application that are particularly well-suited to learning in a cultural setting

The development and use of variables in mathematics and computer science

There are a wide variety of uses of variables in mathematics which we cope with in practice through conventions and tacit assumptions. Experience with computers has made us articulate, criticise and develop these assumptions much more carefully. Historically the term 'variable quantity' was introduced in the context of describing and calculating changing quantities which corresponded to phenomena in the observable world (e.g. the velocity of fluxion of a body moving under the inverse square law). The evolution of the concept has divorced it from these routes of reference and required us to establish the formal apparatus of interpretation and valuation. While the changes considered are highly structured this may be satisfactory, but computing power invites us to cope with change in vastly more complex, unstructured situations such as in simulation of 'real world' processes. We relate this challenge to the distinctive differences in the use of variables in mathematics and practical computing, and we develop a general framework in which all uses of variables can be described in a unified way

Implementing a definitive notation for interactive graphics

This paper describes the application of a definitive (definition-based) programming paradigm to graphics software. The potential merits of using definitive principles for interactive graphics were considered from a theoretical perspective in [Be87]; this paper is complementary, in that it describes the insights gained through practical experience in implementing a prototype system. The main characteristics of the prototype implementation are illustrated by simple examples. Analysis of the abstract machine model underlying this implementation suggests a general purpose programming paradigm based on definitive principles that can be applied to more ambitious applications

Alternative model-building for the study of socially interactive robots

In this discussion paper, we consider the potential merits of applying an alternative approach to model building (Empirical Modelling, also known as EM) in studying social aspects of human-robot interaction (HRI). The first section of the paper considers issues in modelling for HRI. The second introduces EM principles, outlining their potential application to modelling for HRI and its implications. The final section examines the prospects for applying EM to HRI from a practical perspective with reference to a simple case study and to existing models

Experimenting with computing

AbstractWe distinguish two kinds of experimental activity: post-theory and exploratory. Post-theory experiment enjoys computer support that is well-aligned to the classical theory of computation. Exploratory experiment, in contrast, arguably demands a broader conception of computing. Empirical Modelling (EM) is proposed as a more appropriate conceptual framework in which to provide computational support for exploratory experiment. In the process, it promises to provide integrated computational support for both exploratory and post-theory experiment. We first sketch the motivation for EM and illustrate its potential for supporting experimentation, then briefly highlight the semantic challenge it poses and the philosophical implications