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Computational Mathetics:
Towards a Science of Learning Systems
Design
John Self
(johnself@gn.apc.org)
November 1995
CONTENTS
1. Introduction............................................................................................... 1
1.1 The AI-ED context.................................................................. 1
1.2 What is education?................................................................ 3
1.3 What is AI?............................................................................. 3
1.4 What is AI in Education?...................................................... 4
1.5 Outline...................................................................................... 4
2. A brief review of AI-ED............................................................................ 5
2.1 The nature of knowledge....................................................... 5
2.1.1 Objectivism.................................................................... 5
2.1.2 Constructivism.............................................................. 6
2.1.3 Situationism.................................................................. 7
2.1.4 Connectionism.............................................................. 8
2.2 The nature of learning............................................................ 8
2.2.1 Failure-driven learning.............................................. 8
2.2.2 Case-based learning.................................................... 9
2.2.3 Learning through experimentation.......................... 9
2.2.4 Learning through dialogue........................................ 10
2.2.5 Learning as a social activity...................................... 10
2.3 Styles of interaction............................................................... 11
2.4 New technologies in education............................................ 11
2.5 Measures of effectiveness.................................................... 12
2.5.1 External evaluation..................................................... 12
2.5.2 Internal evaluation...................................................... 12
2.6 On-going debates................................................................... 13
3. Introducing computational mathetics................................................... 15
3.1 The need for computational mathetics................................ 15
3.2 An analogy with aeronautics................................................ 18
3.3 An analogy with computational linguistics........................ 19
3.4 The definition of computational mathetics......................... 20
3.5 The approach of computational mathetics......................... 20
3.6 The language of computational mathetics.......................... 22
3.7 The aims of computational mathetics.................................. 24
4. Representing knowledge........................................................................ 27
4.1 Behaviour, belief and knowledge......................................... 27
4.2 Propositions and logic........................................................... 29
4.3 Modal representations........................................................... 31
4.4 Situation calculus................................................................... 32
4.5 Structured representations.................................................... 34
4.6 Multiple representations....................................................... 35
4.7 Social knowledge.................................................................... 36
4.8 Procedural representations................................................... 37
5. Reasoning.................................................................................................... 39
5.1 Reasoning schemata.............................................................. 39
5.1.1 Reasoning in standard logics.................................... 39
5.1.2 Reasoning in nonstandard logics............................. 41
5.1.3 Reasoning in modal logics......................................... 42
5.2 Limited reasoning................................................................... 43
5.2.1 Implicit and explicit beliefs........................................ 43
5.2.2 Local reasoning............................................................ 45
5.3 Nonmonotonic reasoning...................................................... 46
5.3.1 Circumscription............................................................ 46
5.3.2 Default logics................................................................ 47
5.3.3 Autoepistemic logics.................................................... 48
5.3.4 Multi-agent nonmonotonic reasoning..................... 48
5.4 Reasoning with inconsistent knowledge............................ 49
5.5 Probabilistic reasoning.......................................................... 49
5.5.1 Bayesian networks....................................................... 50
5.6 Qualitative reasoning............................................................. 51
5.7 Reasoning about time and action......................................... 53
5.8 Diagrammatic reasoning........................................................ 53
5.9 Distributed reasoning............................................................ 55
6. Metacognition............................................................................................. 57
6.1 Meta-level architectures...................................................... 59
6.2 Metaknowledge..................................................................... 59
6.3 Metacognitive schemata...................................................... 60
6.3.1 Problem-solving........................................................... 62
6.3.2 Metareasoning.............................................................. 64
6.4 Planning................................................................................... 66
6.5 Monitoring............................................................................... 68
6.6 Reflecting 69
6.6.1 Reflective learning....................................................... 69
6.6.2 Self-explanation........................................................... 70
6.7 Transfer.................................................................................... 71
6.8 Distributed metacognition..................................................... 72
6.9 Attributes, aptitudes and attitudes...................................... 73
6.9.1 Stereotypes.................................................................... 75
6.9.2 Aptitudes........................................................................ 75
6.9.3 Affects.............................................................................. 76
7. Learning.................................................................................................... 78
7.1 Perceptual learning................................................................. 79
7.2 Analytical learning................................................................. 79
7.2.1 Failure-driven learning.............................................. 79
7.2.2 Explanation-based learning...................................... 80
7.2.3 Analogy.......................................................................... 81
7.2.4 Conceptual change and belief revision................... 82
7.3 Inductive learning................................................................... 83
7.3.1 Version spaces.............................................................. 84
7.3.2 Numerically-based methods....................................... 85
7.3.3 Constructive induction............................................... 86
7.4 Active situated learning........................................................ 87
7.5 Social learning......................................................................... 88
7.6 Simulated students................................................................. 89
8. Diagnosis................................................................................................... 91
8.1 Analytical diagnosis.............................................................. 92
8.1.1 Model-based diagnosis............................................... 92
8.1.2 Differential modelling................................................. 95
8.1.3 Fault-based diagnosis................................................. 96
8.1.4 Explanation-based diagnosis.................................... 96
8.1.5 Diagnosis by metareasoning...................................... 97
8.2 Inductive diagnosis................................................................ 98
8.2.1 Numerically-based methods....................................... 99
8.2.2 Diagnosis using inductive learning methods......... 100
8.2.3 Diagnosis by automatic programming..................... 101
8.3 Model maintenance techniques........................................... 101
8.4 Goal-driven diagnosis............................................................ 103
8.5 Plan diagnosis......................................................................... 104
8.6 Interactive diagnosis.............................................................. 108
9. Dialogue..................................................................................................... 110
9.1 Discourse structure................................................................ 111
9.2 Speech acts.............................................................................. 112
9.3 Dialogue game theory............................................................ 113
9.4 Rational dialogue.................................................................... 113
9.5 Explanation.............................................................................. 114
9.6 Argumentation........................................................................ 116
9.7 Negotiation.............................................................................. 117
9.8 Multimedia dialogues............................................................. 119
10. Instruction................................................................................................. 121
10.1 Theories of instruction.......................................................... 121
10.2 Instructional systems design................................................ 124
10.3 Instructional planning............................................................ 125
10.3.1 Lessons........................................................................... 127
10.3.2 Curricula....................................................................... 127
10.4 Modes of interaction.............................................................. 127
10.4.1 Individualised instruction.......................................... 127
10.4.2 Tutoring......................................................................... 128
10.4.3 Group instruction......................................................... 130
10.5 Evaluation 130
References.......................................................................................................... 132
The aim of this report is simply to help put the design of computer-based systems to support learning on a more scientific footing. The aim is simply stated, but its achievement is more difficult. For one thing, it is not at all obvious what "more scientific" means in this context.
The rather clumsy expression "computer-based systems to support learning" will henceforth be abbreviated to "AI-ED systems", that is, "Artificial Intelligence in Education systems" on the grounds that the design principles will be primarily derived from and expressed in the language of Artificial Intelligence. It will become clear that we intend a broad interpretation of the term 'AI-ED system'. We mean any computer-based learning system which has some degree of autonomous decision-making with respect to some aspect of its interaction with its users. This decision-making is necessarily performed on-line, during its interaction with users. Consequently, the system needs access to various kinds of knowledge and reasoning processes to enable such decisions to be made.
Of course, computers may be used as presentational devices, through which carefully pre-designed instruction involving the new technological media is delivered to students. There are, no doubt, considerable potential benefits in this, as computers enable special effects, such as altered time-scales and alluring graphics, to focus students' attention. However, pre-designed instruction assumes that the designer can fully anticipate the reactions of all its users and can build in responses to those reactions, or that users themselves are sufficiently self-aware that they can reliably decide how to use systems (assuming that the required options are, in fact, available). It takes no account of the computer's ability to reason, for itself, about the course of the interaction, as we assume that a good human teacher needs to do.
As we will discuss, the field of Artificial Intelligence in Education (AI-ED) has had a short but chequered history. The initial explorations in the 1970s were marked by the kind of enthusiastic optimism characteristic of AI in general. This early work made significant contributions to both AI and Education. By the 1980s, the successful applied AI work on expert systems and several national programmes seeking to capitalise on AI research led to an imperative to develop AI-ED systems which were practically useful, rather than theoretically interesting. It is notable that few of the AI-ED pioneers ever expressed much confidence that the time was right for practical development. Inevitably, the eventual, perceived failure of the applied projects only confirmed that learning and teaching are intrinsically difficult processes.
Meanwhile, the new technologies, especially multimedia and networking, promised other solutions to what were considered to be serious educational problems. Consequently, it became unwise to continue suggesting AI-ED system development. Now, however, the pendulum is swinging back, again inevitably, as it is realised that the new technologies need to be supported by the kinds of analysis of learning and teaching which AI-ED research carries out.
Below the ebb and flow of research fashion, there has been continuing, if slow, progress in understanding the nature of AI-ED system design. Eventually, this understanding will find a proper place in the design of computer-based systems to help people learn. AI-ED systems are neither a panacea nor an irrelevance - they have a contribution to make. One of our aims is to help develop techniques to clarify its potential contribution.
In order to help place AI-ED systems in a realistic context, let us briefly consider four learning vignettes:
Aboriginal culture
Until recently, Australian aboriginal children would sit under the coolabah tree and listen to stories such as following:
"Brolga was the favourite of everyone in the tribe, for she was not only the merriest among them, but also the best dancer. The other women were content to beat the ground while the men danced, but Brolga must dance; the dances of her own creation as well as those she had seen. Her fame spread and many came to see her. Some also desired her in marriage but she always rejected them. An evil magician, Nonega, was most persistent in his attention, until the old men of the tribe told him that, because of his tribal relationship and his unpleasant personality, they would never allow Brolga to become his wife. "If I can't have her," snarled Nonega, "she'll never belong to anyone else." One day, when Brolga was dancing by herself on an open plain near her camp, Nonega, chanting incantations from the centre of a whirlwind in which he was travelling, enveloped the girl in a dense cloud of dust. There was no sign of Brolga after the whirlwind had passed, but standing in her place was a tall, graceful bird, moving its wings in the same manner as the young dancer had moved her arms."
The brolga is a beautiful grey bird which dances on the flood plains of northern Australia. Many aboriginal myths explain features of the environment (animals, rocks, stars, and so on) as being derived in some way from human beings. These stories, which were entirely verbal, there being no written form of communication, were accepted as truth and dictated all aspects of aboriginal behaviour. According to Roberts and Mountford (1969), young children did not "receive any formal education as we know it. They appear to do just as they please". At a certain age, a youth was taken from the main camp to live with the old men of the tribe, the sole repositories of tribal law and wisdom, who during many years of training, taught him the laws of his community, the relationship he bore to every member of it, and the secret myths and rituals of adult life.
All cultures have their myths and rituals which are communicated in a similar way. Only the most fervent technologist would imagine that computer systems could or should change these processes in any significant way. Whatever one's views of Australian aboriginal culture, its transmission by some multimedia AI-ED system is a bleak vision.
Funfair
physics
The traditional funfair provides many opportunities for children to learn or reinforce concepts of physics. The helter-skelter (a high spiral slide) gives lessons on centrifugal force, gravity and friction: most children can predict the effect of a higher slide or a heavier child, and know the direction they will shoot out at the bottom. The bumper car or dodgem is an exercise in the conservation of momentum: children soon learn where to bump to cause the maximum effect. The big dipper tells them about potential energy and kinetic energy: children know where to sit in the train to experience the greatest acceleration. The coconut shy is about force and impulse. And the ghost train warns children not to believe what they see and feel.
Funfairs are increasingly out of fashion but there are many other activities which enable children to develop intuitive notions of physics. Nowadays, children are more likely to find amusement in computer games, which may show activities violating the laws of physics and much else besides. We can, of course, imagine designing computer games which set out to be faithful to real-world physics and which may therefore lead to sound intuitive concepts. Maybe such games would help in the transition from intuition to a more scientific view of physics. In such a case, the computer game might benefit from some understanding of the nature of 'informal' and 'formal' physics. As we will see, AI-ED systems will be concerned with the nature of intuitive understandings and how they might be changed, and with the degree to which understanding has to be grounded in authentic situations.
The Play of
Daniel
University music students might be asked to write an essay on Beauvais' Play of Daniel, a medieval cathedral play. The successful completion of such a task requires the use of a range of skills and knowledge. Students need to know how to write essays in general, which presumes, of course, knowledge of a natural language. They need to be able to adapt the essay to meet the requirements, bearing in mind who will read it and for what purpose. They will need to have a broad knowledge of music in order to be able to make sense of the unusual Play of Daniel. They will also need to know about the social context at the time the Play was composed in order to understand the point of the Play. From all this, they will need to know just what points to emphasise to make a successful essay. Not all this knowledge will be to hand at the time the task is set, so students need also to know how to acquire the knowledge they need. This might involve knowing how to use various computer-based aids for accessing resources.
There are various ways in which computer-based systems might support this activity. Essay-writing is a rather complex skill with which computer-based systems will not (in the near future) be able to give detailed guidance, although various kinds of clerical assistance are possible. Computer-based systems might be able to give advice on how to set about gathering the information probably needed, for example, to determine the date of the music and how it was typically performed. They might also be able to monitor the student's use of the resources and to give advice if the student exhibits problems or deficiencies in her search strategies. Overall, the sheer volume and complexity of the knowledge involved suggests that computer systems will not be able to provide reliable step-by-step guidance for the whole process. However, given the nature of the students involved, this is not what is required, anyway.
Satellite
surveillance
Satellite activity analysts are employed by government defence departments to maintain dossiers on the behaviour of earth-orbiting satellites. In particular, they have to provide possible explanations for unusual behaviour, for example, that the satellite is mal-functioning or has been diverted to survey Colombian drug plantations. The satellite's behaviour is displayed on a complex computer graphics screen, which must, of course, be interpreted by the analysts. Naturally, their employers would like the analysts to develop excellent explanatory skills, because the cost of reacting to a faulty explanation can be considerable.
The analyst's task is not a simple one of mapping patterns of observations onto explanations. The data is generally voluminous but also incomplete and possibly unreliable. It would not be adequate to train analysts to recognise specific situations: they need to be helped to develop general explanation-forming skills, in which they propose hypotheses, gather evidence for those hypotheses, assess the reliability of evidence, and present a convincing argument for their conclusions. It is hard to imagine this training being successful in a context separate from that in which the task is normally performed. The trainee analysts would need full access to the computer display of satellites' behaviour and a way of exploring that system to create and test out hypotheses. In this case, then, the training would necessarily be computer-based, being embedded in the system used for task performance or in an extension of it. The computer-based system would probably need to know about general hypothesis-forming skills if it is to guide the trainee towards improving them. (I am grateful to the Mitre Corporation for showing me a prototype computer-based tutor for this task.)
If a field is to call itself 'AI in Education', then it seems necessary for it to say what it considers 'education' to be. However, despite its name, AI-ED has never been concerned with education in its broad sense but only with the specific issue of learning. We may believe that the whole purpose of education is to promote learning but in reality the process of education includes many activities only indirectly related to learning, as any textbook or conference on 'education' will confirm.
The term 'education' is generally taken to mean 'formal education', that is, 'paid-for education', rather than the 'informal education' that we receive for free from our culture. There is a nostalgic preference for the latter, with the former being considered to stunt individual learning capabilities. These polemic views will not be our concern. We will be concerned only with the nature and effectiveness of the learning processes.
We will avoid simplistic assertions that learning happens in a particular way. Advocates of one method of learning will naturally belittle other methods. However, learning is a complex, many-faceted kind of activity, as our vignettes above indicate. The nature of computer-based support for learning will depend on the context and there is no particular approach which can be categorically labelled as wrong-headed.
Consider, for example, the teaching and learning of a skill such as playing the violin. This has evolved largely outside the formal education system and it shows an amalgam of many different kinds of activity. There is a lot of rather repetitive practice of scales. There is a fair amount of 'academic learning' to develop fluency with musical notation. There are occasional intense one-to-one tutorial sessions. There are some sessions in a group, as music playing is a social activity. There are specialised 'learning environments', such as small-scale violins and the Suzuki method. No one of these learning methods is intrinsically better than the others: they must all be integrated in a successful learning experience.
The key difference between AI and other forms of computer programming is that AI programs respond intelligently to situations not specifically anticipated by the programmer. In conventional programming, the programmer arranges for anticipated problems to be solved by specifying all the steps towards a solution. In AI programming, the programmer provides the means for the computer to solve problems as they arise. For example, a program to translate between languages could not be written by anticipating all possible sentences and providing translations of them, nor even by listing all the words and their translations and combining them in a simple way. A comprehensive translation program would need to reason about the meaning of the sentences, which implies that it has knowledge about both languages, about the content of the sentences, and about the world, so that ambiguities may be resolved.
AI is both an applied and a theoretical subject. AI applications are very diverse:
• to recognise bridges and buildings from photographs (so that they may be bombed perhaps).
• to work as autonomous robots in dangerous situations, for example, underwater mining.
• to help plan traffic flow.
• to diagnose diseases.
and so on. All these applications require skills we would normally describe as intelligent: some demand specialist knowledge (for example, of obscure diseases); others use everyday knowledge, which we all use without being aware of how complex it is (for example, recognising what is depicted in a photograph).
Important though AI applications might be, we will be more concerned with the theoretical side of AI. AI is not a science that studies objects in the natural world: it studies objects that AI programmers create. In order for these creations to be understood and analysed, their design has to be based on clearly-articulated principles capable of some kind of rigorous analysis. A program for, say, medical diagnosis should be based upon a computational theory of diagnosis. By a 'computational theory' we mean one that is amenable to conventional mathematical analysis and that is oriented towards implementation as a computer program. It should be possible to prove practical results, for example, that under specified conditions, a diagnosis will be possible in a certain time. It should also be possible to carry out empirical experiments with the program, for example, to measure how it performs under different conditions. The theory develops by coordinating mathematical and empirical studies. In this way, AI leads to the development of new theories, because if an adequate theory already existed it would presumably be programmed in a conventional way.
However, AI would not be a coherent field of study if every application required the development of its own computational theory. It turns out that a theory of diagnosis contains many components which are the same or similar to those required for a computational theory of, for example, planning traffic flow. Both, for example, require forming hypotheses from observations (a rash of purple spots suggests meningitis; a traffic jam suggests a traffic light failure), both require a form of hypothetical reasoning of the "What would happen if .." kind, both perhaps require reasoning from a library of previous cases so that the system does not have to solve every problem from scratch, and so on. Theoretical AI is concerned with the development of methods for analysing such processes independent of any particular application.
The field of AI in Education is concerned with the application of AI techniques to educational problems. Therefore, AI in Education is part of applied AI, and indeed most practitioners are happy to regard it as so, seeking to develop important, practically useful systems based on AI. Most reports of AI-ED projects give details of the technical design of systems and provide some evidence that the systems are effective. In the next chapter, we will review the status and achievements of AI-ED research.
Our emphasis will be more on relating AI-ED to theoretical AI. As an application area, AI-ED is immensely complicated, not just because of technical difficulties but more especially because education and learning are controversial topics about which there are endless arguments. Any particular AI-ED project has to commit itself to a point of view if it is make any progress in implementing a useful system, which will then, no doubt, be criticised by those with a different view.
AI-ED is interesting because of this constant interplay of ideas and it is important because of the potential contribution to the socially central aim of improving the quality of learning. Contributions to AI-ED come from many directions: primarily from computer science, psychology and educational research, but also from sociology, anthropology, philosophy and the many fields which are the topic of AI-ED systems. Theoretical debate in AI-ED is generally expressed in lowest common denominator terms so that it is accessible to all participants, that is, in informal language. Our aim is to suggest that it is time AI-ED begins to move in the direction that all scientific endeavours take in due course, by developing a formal, technical language which can be used to make arguments more precise and AI-ED system design more analytic. The language of theoretical AI is the most promising starting point, because it already has partial formalisations of processes such as reasoning, learning, diagnosis and dialogue which are central to AI-ED.
The next chapter attempts to provide a brief, non-technical review of the AI-ED field. This is somewhat hard to do without lapsing into providing a catalogue of AI-ED systems, the various techniques used to implement them, and the educational philosophies which they demonstrate. It is also difficult because the boundaries of AI-ED are rather vague. The chapter tries to give an impression of the kinds of issues which concern AI-ED researchers at the moment and to indicate the level of practical achievement. The intention is that this chapter provide sufficient background to justify the need for the more theoretical descriptions of following chapters.
Chapter 3 introduces what we have chosen to call 'computational mathetics', for reasons that will be explained there. The general need for computational mathetics and its aims and methodologies are described. In brief, computational mathetics is intended to provide the more formal analyses needed to complement present informal argumentation and design. However, the level of formality is still low compared to other areas of theoretical AI, reflecting the difficulty of AI-ED and the little work so far done in this direction. At least this enables the discussion to be followed by those of a non-formal orientation.
The following chapters each consider a topic within the scope of computational mathetics: representing knowledge, reasoning, metacognition, learning, diagnosis, dialogue and instruction, respectively. These chapters review work in theoretical AI and in AI-ED itself from a computational mathetics perspective. There are two main objectives in these chapters. First, to show that there is a large volume of potentially relevant work which can be adopted and adapted to form a basis for the theoretical analysis of AI-ED research. If it is, we believe that it will lead, in due course, to improvements in AI-ED system design. The second objective is to show that there is much that needs to be done before the aims of computational mathetics may be achieved and hence to provide some targets and challenges for future AI-ED research.
The preface to Wenger's comprehensive panorama of AI-ED before 1987 (Wenger, 1987) remarked that a similar review of a field then considered to be at an "important threshold of development" would not be possible five years later because there would be too much material to review. There has, in fact, been no general book published on AI-ED since Wenger (1987). All the many books related to the topic which have been published since 1987 have been monographs describing a particular project or edited collections of papers presented at workshops or conferences (Bierman, Breuker and Sandberg, 1989; Birnbaum, 1991a; Brna, Ohlsson and Pain, 1993; Clancey, 1987; Costa, 1992; de Corte, Linn, Mandl and Verschaffel, 1991; Elsom-Cook, 1990; Farr and Psotka, 1992; Frasson and Gauthier, 1990; Goodyear, 1991; Greer and McCalla, 1994; Lajoie and Derry, 1993; Larkin, Chabay and Sheftic, 1992; Mandl and Lesgold, 1988; Moyse and Elsom-Cook, 1992; Polson and Richardson, 1992; Regian and Shute, 1992; Schank and Cleary, 1995; Self, 1988). In addition to this spasm of new books, three new journals have started up (Journal of Artificial Intelligence in Education, Journal of the Learning Sciences, and Interactive Learning Environments) alongside longer-established journals with broader remits (such as the International Journal of Human-Computer Studies and Instructional Science). It is not easy therefore to gain a broad, balanced picture of the contemporary AI-ED field.
This brief chapter can hardly aspire to give such a picture. It aims merely to give a background to the issues which have been discussed in recent years sufficient for appreciating the more technical perspectives of later chapters. It is not organised, as Wenger's book was, as a historical catalogue of systems and projects. Today it is not possible to identify a similar set of classic on-going projects. The AI-ED field may have been on the 'threshold of development' in 1987 but it has, if anything, stepped back from this threshold rather than crossed it. There has been continued development of perhaps smaller-scale systems along 'traditional' lines, as we will see, but there has been much more debate about the direction of the AI-ED field, with many of the pioneers mentioned in the Wenger book leading the attempt to change it.
Any review of AI-ED should logically begin with a discussion of the educational problems which are being addressed before embarking on a survey of how AI might contribute to solutions. The main relevant issues appear to be the following:
• What is the nature of knowledge?
• How may knowledge be learned?
• Should systems instruct, tutor, guide or train students?
• How should new technologies be used in education?
• What are the measures of effectiveness?
Educationalists will debate such issues at great length but it is not the aim of this chapter to contribute to that debate except to the extent that it discusses the AI-ED field's views (implicit and explicit) on them. The review focusses on providing a basis for considering the technical contribution that AI is making and might make to education.
The following sections consider each of the
above issues in turn. Each section
illustrates a general discussion about AI-ED's views with exemplar AI-ED
systems. The sections do not
attempt to give a comprehensive account of implemented systems (there are now
too many for a short review) and those systems referred to are described only to
the extent necessary for the point under discussion. Technical concepts are usually only
mentioned, with a fuller discussion to come in later chapters (although we have
not interrupted with a multitude of forward references). The chapter ends with a discussion of
the main controversies within the AI-ED field today.
Most AI-ED systems are intended to help their student-users become more knowledgeable in some respect. AI-ED system designers are well aware that education has broader aims - to develop ethical and moral values, to improve attitudes, to nurture better citizens, and so on - but this awareness has only indirectly influenced their system designs. It has been rather assumed (or hoped) that the context in which AI-ED systems will be used will convey these broader goals.
Given the focus on the knowledge-to-be-learned, it seems natural that AI-ED system designers often begin by trying to specify this knowledge as precisely as possible. To achieve this, the full panoply of AI knowledge representation techniques (production systems, frames, semantic networks, predicate logic, and so on) has been applied in AI-ED systems. In so doing, AI-ED designers might be considered to be adopting a philosophy of knowledge called objectivism