Tutoring and learning are very complex processes. Traditional Tutor's activity modeling by ITS is rather heuristic and represents "bottom-up" approach that cannot guarantee reliable results. This paper presents complementary "top-down" approach to Tutor's activity modeling by ITS based on the application of very general theories introducing approved theoretical interdisciplinary solutions into ITS. The description of methodology used and modeling principles is given, including proposed System Form for modeling and its application to the modeling of main tutoring components. The Domain, Expert, Learner, and Tutor models are described. Here we describe the technological complex "Intelligent Tutor" developed on the basis of these theoretical results. It includes Shell, Authoring Tool and Application design Technology.

All the solutions described are practice-oriented on the easiest design of cost-effective ITS in any domain.

As one can judge the majority of researchers and practitioners develop CBT and ITS in layers as follows:

1. Instructional Art, Theory & Practice;
2. Applied CBT and ITS, Authoring Tools;
3. Software;
4. Hardware.

The upper layers are usually developed by instructionalists.Lower layers are developed by engineers. They are very different people of different education, experience, and mentality. It is a big problem to come to one consistent solution for them. But the fact is the development on 2-nd layer needs cooperation between instructionalists and engineers. It is an interdisciplinary layer.

When instructionalists may dominate, all cooperative team develops Applied Systems and Authoring Tool on the basis of existing instructional theories (which are different, inconsistent, and rather fuzzy) and supplements them with own interpretations, preferences, and representations (rather subjective and domain-dependent). As a rule, instructionalists do not attract general formal representations and methods at all. That is why it is extremely difficult for them to achieve nontrivial general results in CBT and ITS field which could be widely acceptable for all Domains, Learners, and Authors.

Engineers as a rule do not design applied systems. They try to develop very universal Authoring Tool for any possible instructionalists' "fantasies". The main efforts are devoted to the solution of technical problems such as: scripting, multimedia presentation, edition, cross-platform capabilities, global networking,... The main instructional problems are not solved here at all. All of them are left for authors-instructionalists (see above). Then the circle is closed.

To break this vicious circle we focus our research and development on the gap between layer #1 and #2. It is a new interdisciplinary layer that may be named as "System Modeling of Tutoring Components". In this gap we tried to realize a "top-down" approach. As meta-models we used very general, approved, and domain-independent representations of Systems Theory, Control Theory, Fuzzy Modeling, Possibilities Theory,... . It is a promising approach because the results achieved this way may pretend to be general.

This way the following has been developed:

• general system form of tutoring components modeling;
• the main structure of tutoring activity;
• mathematical models of Domain, Expert, Learner;
• mathematical methods of tutor's main tasks solving;
• the most general algorithm of tutoring (session management) with wide capability to be tuned by Author and driven by Learner without any script prepared in advance;
• the project "Intelligent Tutor" of Shell, Authoring Tool, and Technology for cost-effective applied ITS design.

With a group of programmers we have partially realized the project and built MS DOS version of "Intelligent Tutor" in C++. Now we are building Windows'95 network version of "Intelligent Tutor" in SQL Windows.

Using our Authoring Shell, Tool, and Technology subject-matter the experts have developed applied ITSs in different domains. Some of them are used now for Nuclear Power Plant personnel training in Russia and the Ukraine.

This paper presents our non-traditional approach, its background conception, and main results in theoretical and practical aspects. The special emphasis is made on methodological issues, because they are of extreme importance in such complex interdisciplinary area like ITS and predetermine all finally achieved results.

The development of each applied Intelligent Tutoring System (ITS) is an extremely complex interdisciplinary problem with a priori unknown way of solving. That is why one is forced to use intuition-heuristic approach to applied ITS design. It consists in cooperation of different specialty experts in attempting to extract and integrate all necessary knowledge from them. This rather traditional approach is very expensive and cannot guarantee good results, because experts' knowledge is very subjective, heterogeneous, fuzzy, and even contradictory. Thus, the integration of such knowledge in applied ITSs is a very serious problem too.

Computer science experts taking part in ITS design everywhere prefer to apply available Artificial Intelligence paradigms, representations, and means. As a result, each ITS represents complex, integrated application of Artificial Intelligence. Furthermore, the most applied ITSs are designed on the basis of Expert Systems preliminary elaborated in the Domain under study. These Expert Systems (in their turn based on the Domain Models) model the processes of Domain problems solving by an Expert and thus represent Expert Models. Then Learner Model is built up upon Expert System by modeling possible incorrect solving of problems by Learners. Finally some didactic functions are modeled or in other words Tutor Model is developed. Thus, the traditional ITS design may be represented by growing up modeling as shown on fig. 1.

In the process of ITS designing the main efforts are applied to the first (more familiar) steps of design process and less efforts to the last (less familiar) steps. As a result, Domain and Expert Model in ITS are the best developed, but Tutor and Learner Models which are not less important in ITS have been left the least developed. This significantly limits potentially high effectiveness of ITS (despite its huge cost).

Now it is clear that the Artificial Intelligence cannot give solutions to ITS design problems. It is only "bottom-up", partial, instrumental, and principally limited approach to ITS design. It is useless to search all ITS solutions here.

In order to solve this interdisciplinary problem one should use interdisciplinary theoretical representations. Besides, the traditional "bottom-up" approach should be supplemented by additional "top-down" approach.

Strictly speaking, the ITS Theory is necessary.

Tutoring and Learning are very complex research objects. That is why Methodology is of primary importance for ITS development. Let us consider the more general methodological ideas applied here.

3.1. Box Form for Modeling

As marked by (Burns & Capps, 1988) known theoretical results in ITS researches are based on two opposite ways of human activity modeling.

The first one is "black box" modeling. Traditionally it is used for functional modeling of external (input-output) behavior of objects with unknown internal structure. (That is rather like our case). The input-output information available from black box models may have a different internal interpretation, not necessarily corresponding to real internal structure of object. Particularly, some input-output information may have a correct mathematical internal representation, which is very convenient for computer processing. Unfortunately, mathematical modeling is suitable for relatively simple or simplified (by making some presuppositions) object and is not suitable for entire tutoring process, that is rather complicated. See (Burton & Brown, 1982) as well.

The second one is "glass box" modeling. Traditionally it is used for modeling objects with well- known internal structure. (Sure, this is not our case). Meanwhile, this way of modeling is the main in modern ITS researches. ITS researchers try to reveal and refine internal structure of tutoring process. (See for example Mizoguchi, 1996). It is right for researchers because they are professionals trying to create ITS theory. But it is not right for Authors, because they have no resources for researches and have to design cost-effective applied ITS. Otherwise, applied ITS design will be based fully on Authors' subjective presuppositions (heuristics) concerning internal essence of tutoring/learning activity. Of course, it will supply more information for Tutoring Modeling, but these heuristics will not be necessary correct. Consequently, such kind of authoring cannot guarantee any quality of tutoring systems. See (Clancey, 1981).

Meanwhile, the traditional authoring approach is a "glass box" modeling. The authors become researchers and vice versa. This is not effective for both of them.

Using these "box" terms it may be said that in our research we uphold intermediate "gray box" (or "half-transparent box") modeling principles in research and authoring aimed at the development of practice-oriented mathematical ITS theory and ITS Shell on the basis of minimum inevitable presuppositions. The central idea of our approach in this terms consists in step by step decomposition of initial "black box" of entire tutoring process into partial "black boxes" of functionally complete, natural, and widely familiar sub-process (components) which are simple enough for mathematical modeling (see fig. 2). If each of the terminal sub-processes (components) has a strict mathematical model, then the entire Tutoring represented by this "gray box" model may have mathematical representation too (see fig.3).

This is the essence of "top-down" approach. But the initial form of "black box" is too rough and non-constructive to guide researchers and authors in modeling process.

3.2. System Form for Modeling

In our understanding "top-down" approach in ITS researches must reject heuristics (as much as possible) and be based on the application of approved principles, representations, and methods, accumulated by mankind in very general theories like: Systems Analysis, General Systems Theory, Operation Researches, Cybernetics, Control and Communication Theory as well. Due to a high degree of generality these theories have wide interdisciplinary application. (Nevertheless, applicability of each theory to tutoring modeling calls for special investigations. We have conducted them, but here we cannot stop at it and present only the final solutions).

Instead of rough "black box" form for step by step modeling we propose much more detailed and constructive System Form. The System Form has been developed by assembling known approved systems representations of the most general theories capable to cover tutoring process. In this we have supposed that Tutoring is relatively Autonomous, Stable, Informational, Communicative, Discrete, Asynchronous System with Intelligent Components.

The System Form hierarchy reflects the main levels of system representation detailing. The Form is simple enough, but it is iterative and may be used for further step by step detailing of Tutoring Model and all its components on the basis of their exploration and making new inevitable suppositions.

Using this Form researchers/authors may skip or detail any of its items by their own.

0. System Representation Form:

1. External Representation Levels (Appearance, Behavior):

1. 1. Point Representation Level:

1.1.1. Name;

1.1.2. Location in Super-Systems:

1.1.2.1. Super-System (see 0 level);

1.1.2.2. Space;

1.1.2.3. Time.

1.2. Attributes Representation Level:

1.2.1.Properties:

1.2.1.1. Property:

1.2.1.1.1. Value.

1.3. Functional Representation Level:

1.3.1. Functions:

1.3.1.1. Function:

1.3.1.1.1. Inputs:

1.3.1.1.1.1. Input:

1.3.1.1.1.1.1. Message.

1.3.1.1.2. Output:

1.3.1.1.2.1. Message.

2. Internal Representation Levels (Modes, Methods, Procedures, Processes):

2.1. Point Representation Level (detailing by alternative listing):

2.1.1. States:

2.1.1.1. State.

2.1.2. Interrelations (Ex.: State Transition Diagram);

2.2. Attributes Representation Level (detailing in breadth ):

2.2.1. Parameters:

2.2.1.1. Parameter:

2.2.1.1.1. Value.

2.2.2. Interrelations (Ex.: Dependencies, Equations);

2.3. Sub-systems or Structural Representation Level (downward detailing ):

2.3.1. Sub-Systems or Components:

2.3.1.1. Sub-System or Component (see 0 level);

2.3.2. Interrelations among components (Ex.: Connections).

2.4. Super-System or Mental Representation Level (upward detailing ):

2.4.1. External Representation Levels: ...(see 1 level)

2.4.2. Internal Representation Levels:

2.4.2.1. Point Representation Level: ...(see 2.1 level)

2.4.2.2. Attributes Representation Level: ...(see 2.2 level)

2.4.2.3. Sub-System or Structural Representation Level:

2.4.2.3.1. Super-System Components:

2.4.2.3.1.1. Closest Environment Representation (see 0 level)

2.4.2.3.1.2. Self - System Representation (see 0 level )

2.4.2.3.2. Interrelations between components.

2.4.2.4. Super-System or Mental Representation Level:...(see 2.4 level)

2.4.2.5. Interrelations among Levels.

2.4.3. Interrelations between Mental External and Internal Representation Levels.

2.5. Interrelations among Internal Representation Levels.

3. Interrelations between External and Internal Representation Levels

(or Internal Interpretation of System External Appearance, Behavior).

All terminal items of this System decomposition tree marked with " see 0 level " may be considered as a System again and the decomposition may be continued.

3.3. System Form Aided Modeling

The System Form given demonstrates to researchers/authors the possible ways of Object analysis and Model synthesis. Together with researcher/author this Form represents a definite Engine of Tutoring Modeling Process. Our attempt to use it has produced the results we are presenting below. Take into account that it is not a full-scale picture of modeling process, but only several first steps . Nevertheless, it is enough to show that the presented results are constructive and domain/learner/author-independent. Therefore they may be considered as a contribution to ITS Theory and ITS Shell.

A. Supposition: Tutoring is a Complex, relatively Autonomous, Stable, Informational, Interactive, Communicative, Discrete, Asynchronous System and then may be represented in System Form given.

1.1.1. Tutoring Model.

1.1.2.1. Tutoring is located in Training, Education,...

1.1.2.2. Tutoring is a process distributed in Space.

1.1.2.3. Tutoring is a process distributed in Time.

1.2.1. The main Properties of Tutoring are Cost, Effectiveness,...

1.3.1.1. The main Tutoring function is to transform a Goal into a Result.

1.3.1.1.1.1. Input:

1.3.1.1.1.1.1. Goal Message.

1.3.1.1.2. Output:

1.3.1.1.2.1.Result Message.

2.1.1.1. One-on-one tutoring, ...

2.3.1. The biggest Components of Tutoring System:

2.3.1.1. Tutor;

2.3.1.2. Learning.

B. Supposition: Learning is Complex, relatively Autonomous, Stable, Informational, Interactive, Communicative, Discrete, Asynchronous System and therefore it may be also represented in System Form .

1.1.1. Learning Model.

1.1.2.1. Learning is located in #2.3.1.2. of Tutoring System.

1.1.2.2. Learning is distributed in Space.

1.1.2.3. Learning is distributed in Time.

1.2.1. The main Properties are Cost, Effectiveness,...

1.3.1.1. The main Learning function is to transform Goal into Result.

1.3.1.1.1.1. Input:

1.3.1.1.1.1.1. Goal Message.

1.3.1.1.2. Output:

1.3.1.1.2.1. Result Message.

2.1.1.1. Intentional Learning.

2.3.1. The biggest Components of Learning System:

2.3.1.1. Learner;

2.3.1.2. Domain.

C. Domain, in general case, is an any relatively autonomous and stable part of the World under Learner study and Tutor control. Domain in ITS is represented by computer and exists as informational interactive discrete system.

VR, HM, MM systems, simulators, games, interactive presentations are possible forms of Domain.

Domain may be presented to Learner by Tutor as a whole at once or with separate properties, functions, components (or with explanations, examples, exercises) step by step.

Domain may be pre-stored as a set of ready-made presentations to Learner (as it takes places in CBT) or generate these presentations itself under Tutor control (like in Simulator, for example).

To control Learning System Tutor manipulates by Domain parameters, functions, modes, and components under Learner's study or uses ready-made presentations, interactive in general case.

Supposition: Domain is relatively Autonomous, Stable, Informational, Interactive, Discrete System and therefore may be represented in System Form given above.

1.1.1. Domain Model.

1.1.2.1. Domain is located in # 2.3.1.2. of Learning System.

1.2.1. Domain properties are complexity, volume, ...

Further abstract filling in this Form is impossible. Given System Form that is rather all that one can abstractly say here about any possible Domain.

D. To simulate Tutor in ITS it is necessary to make clear what the Tutor in computer compatible context is.

Supposition: Tutor is a Complex, relatively Autonomous, Stable, Informational, Interactive, Communicative, Discrete, Asynchronous Systemand therefore may be represented in System Form given.

1.1.1. Tutor Model.

1.1.2.1. Tutor is located in #2.3.1.1. of Tutoring System.

E. To simulate Learner in ITS it is necessary to make clear what the Learner in computer compatible context is.

Supposition: Learner is a Complex, relatively Autonomous, Stable, Informational, Interactive, Communicative, Discrete, Asynchronous Systemtoo and then may be represented in System Form.

1.1.1. Learner Model.

1.1.2.1. Learner is located in # 2.3.1.1. of Learning System.

F. Tutor in Tutoring System is trying to achieve Tutoring Goal by making Control over Learning System.

Learner in Learning System is trying to achieve Learning Goal by exercising Control over Domain.

Supposition: Tutoring and Learning are Control Systems in general case. For Control System presentation the initial System Form may be detailed as follows.

2.3.1. Sub-Systems or Components:

2.3.1.1. Agent (Tutor in Tutoring System and Learner in Learning System):

2.3.1.1-1.3.1.1.1.1. Input: Goal Message;

2.3.1.1-1.3.1.1.1.2. Input: Reaction Message.

2.3.1.1-1.3.1.1.2. Output: Action Message.

2.3.1.2. Object (Learning in Tutoring System and Domain in Learning one):

2.3.1.2-1.3.1.1. Function 1:

2.3.1.2-1.3.1.1.1.1. Input: Action Message;

2.3.1.2-1.3.1.1.2. Output: Reaction Message.

2.3.1.2-1.3.1.2. Function 2:

2.3.1.2-1.3.1.2.1.1. Input: Action Message;

2.3.1.2-1.3.1.2.2. Output: Result Message.

2.3.2. Interrelation (interconnection)between Components:

3. Interrelation (interconnection)between External and Internal Representation:

G. The result of Tutoring is directly unobservable by Tutor. Tutor can observe only Object (Learning System = Learner + Domain) Reactions. Therefore Learning is a bad-observable Object.

Learner is an Agent in this Object (Learning System = Learner + Domain) and the learning current objectives, process, and results depend on Learner more than on Tutor. In other words, Learning is a bad -controllable Object.

Supposition: Tutoring is a Dual Control System. Then the current Model of Tutoring may be further detailed as follows:

2.3.1.1. Agent (Tutor):

2.3.1.1-2.3.1. Components:

2.3.1.1-2.3.1.1. Observation Agent:

2.3.1.1-2.3.1.1-1.3.1.1. Function of Result Assessment:

2.3.1.1-2.3.1.1-1.3.1.1.1. Inputs:

2.3.1.1-2.3.1.1-1.3.1.1.1.1.1. Possible Results Assessment;

2.3.1.1-2.3.1.1-1.3.1.1.1.1.2. Learning System Reactions.

2.3.1.1-2.3.1.1-1.3.1.1.2. Output:

2.3.1.1-2.3.1.1-1.3.1.1.2.1. Real Result Assessment.

2.3.1.1-2.3.1.1-1.3.1.2. Function of Observation Actions Generation:

2.3.1.1-2.3.1.1-1.3.1.2.1. Inputs:

2.3.1.1-2.3.1.1-1.3.1.2.1.1.1. Possible Results Assessment;

2.3.1.1-2.3.1.1-1.3.1.2.1.1.2. Learning System Reactions.

2.3.1.1-2.3.1.1-1.3.1.2.2. Output:

2.3.1.1-2.3.1.1-1.3.1.2.2.1. Observation Actions.

2.3.1.1-2.3.1.2. Control Agent:

2.3.1.1-2.3.1.2-1.3.1.1. Function of Possible Results Assessment:

2.3.1.1-2.3.1.2-1.3.1.1.1.1. Input:

2.3.1.1-2.3.1.2-1.3.1.1.1.1.1. Real Results Assessment;

2.3.1.1-2.3.1.2-1.3.1.1.2. Output:

2.3.1.1-2.3.1.2-1.3.1.1.2.1. Possible Result Assessment.

2.3.1.1-2.3.1.2-1.3.1.2. Function of Control Actions Generation:

2.3.1.1-2.3.1.2-1.3.1.2.1.1. Input:

2.3.1.1-2.3.1.2-1.3.1.2.1.1.1. Real Results Assessment;

2.3.1.1-2.3.1.2-1.3.1.2.2. Output:

2.3.1.1-2.3.1.2-1.3.1.2.2.1. Control Actions.

2.3.1.1-2.3.2. Interrelation:

H. To observe directly unobservable Learning Result Tutor presents different problems (assignments, tasks, or questions) to Learner in order to explicit observable behavior in Learning System.

Supposition: Observation Action is a Problem presentation to Learner.

I. After Control Agent's successful actions the probability of Learner's achieving Goal State is higher then it is for any other state. Then it means:

• to divide Observation into Checking of Goal State (or errors detecting) and Diagnosing of others (or search of errors causes);
• to begin Observation from Checking.

Supposition: Observation Agent includes Checking and Diagnosing Agents. Observation begins from Checking. Then the Tutoring Model may be further detailed as follows:

2.3.1.1-2.3.1.1.Observation Agent:

2.3.1.1-2.3.1.1-2.3.1. Components:

2.3.1.1-2.3.1.1-2.3.1.1. Checking Agent;

2.3.1.1-2.3.1.1-2.3.1.2. Diagnosing Agent.

2.3.1.1-2.3.1.1-2.3.2. Interrelation:

J. Now it is possible to describe a more detailed Representation of Learning System

1.1.1. Learning Model.

1.1.2.1. Learning is located in #2.3.1.2. of Tutoring System.

1.1.2.2. Learning is distributed in Space.

1.1.2.3. Learning is distributed in Time.

1.2.1. The main Properties are Cost, Effectiveness,...

1.3.1.1. The global Learning function is to transform Goal into Result.

1.3.1.1.1.1. Input:

1.3.1.1.1.1.1. Goal Message;

1.3.1.1.2. Output:

1.3.1.1.2.1. Result Message.

1.3.1.2. The local Learning function:

1.3.1.2.1.1. Input: Control Messages;

1.3.1.2.1.2. Input: Checking Problem Messages;

1.3.1.2.1.3. Input: Diagnosing Problem Messages.

1.3.1.2.2. Output: Reaction Messages;

2.1.1.1. Intentional Learning.

2.3.1. The biggest Components of Learning System:

2.3.1.1. Learner;

2.3.1.2. Domain.

2.3.2. Interrelation among Components:

3. Interrelation:

K. Tutor can realize different tutoring modes and try to arrange them in the best way. For the description of this activity of Tutor the Operation Researches Theory is suitable.

Supposition: Tutoring, Observation, Control, Checking, and Diagnostic Agents are organizational Systems. To be well organized each of this agents may includeAnalytic, Preparatory, Planning, Executive, Measuring, Assessing, Decision Making Agents as their components.

Where:

1. Analytic Agent defines Object, Goal, Strategy, and possible Actions of his/her activity;
2. Preparatory Agentprepares all necessary Means for Actions execution;
3. Planning Agent develops the best Plan (script) of Actions;
4. Executive Agent realizes the Actions in accordance with the Plan (script);
5. Measuring Agent measures Object Reactions that are directly observable;
6. Assessing Agent assesses current Results that are directly unobservable;
7. Decision Making Agentmakes all necessary decisions.

L. Tutor and Learner as human beings are able to fulfill all mentioned Agents functions. In particular, they can build internal "mental" model of external World. Due to this model they are able "play in mind" all their actions before acting, envisage their results, select and realize the best actions.

Supposition: Tutor and Learner are Intelligent Agents. The System Form for their modeling may be detailed as follows:

1. External Representation:

1.3.1.1.1.1. Input: Goal Message.

1.3.1.1.2. Output: Result Message.

2. Internal Representation:

2.4. Super-System or Mental Representation Level:

2.4.2.3. Sub-System or Structural Representation Level:

2.4.2.3.1. Super-System Components:

2.4.2.3.1.1. Object Mental Model(Object');

2.4.2.3.1.2. Agent Self-Model(Agent');

2.4.2.3.2. Interrelations between components:

2.4.3. Interrelations between Mental External and Internal Representation Levels:

3. Interrelation between External and Internal Representation:

M. Trying to control the Learning System Tutor can influence Domain and/or Learner. In the first case Tutor changes Domain and it presents to Learner its changed aspects for study. In this case it may be said that Tutor influences Learner through Domain. In the second case Tutor may present explanations directly to Learner.

Supposition: Control Action is the Delivery of Learning Materials to Learner by direct or indirect way.

N. Supposition: Now it is possible to represent Learner in the following form:

1. External Representation:

1.1.1. Learner Model.

1.1.2.1. Learner Model is located in #2.3.1.1. of Learning Model.

1.3.1.1.1.1. Input: Goal Message.

1.3.1.1.1.2. Input: Learning Material Messages;

1.3.1.1.1.3. Input: Checking Problem Messages;

1.3.1.1.1.4. Input: Diagnosing Problem Messages:

1.3.1.1.1.5. Input: Domain Reaction Messages.

1.3.1.1.2. Output: Action Messages.

2. Internal Representation:

2.4. Super-System or Mental Representation Level:

2.4.1. External Representation Levels: ...

2.4.2. Internal Representation Levels:

2.4.2.1. Point Representation Level: ...

2.4.2.2. Attribute Representation Level: ...

2.4.2.3. Sub-System or Structural Representation Level:

2.4.2.3.1. Super-System Components:

2.4.2.3.1.1. Domain Mental Model ("Domain' " in figure below);

2.4.2.3.1.2. Learner Self-Model ("Learner' " in figure below);

2.4.2.3.2. Interrelations:

2.4.3. Interrelations between Mental External and Internal Representation Levels:

3. Interrelation between External and Internal Representation:

O. Tutor mental modeling capabilities are limited. Human Tutor cannot have and effectively use very detailed mental representations of such a complex object like Learning and Learner. He/she needs to simplify them. But a simple model of complex object must be fuzzy.

Supposition: Tutor mental models are fuzzy models of real objects.

P. Supposition: Analytic activity cannot be automated in ITS so far and may be realized in ITS by Authors.

Q. Supposition: Preparatory activity (or tutoring actions generation) may be automated in ITS only particularly and may be completed by Authors.

R. Supposition: Planning, Executive, Measuring, Assessing, and Decision Making activity of each Agent may be automated in ITS.

S. Full-scale planning (or scripting) to the end has no sense in dual control systems because of:

• complex and unpredictable behavior of Object (Learner);
• Agent using simplified fuzzy models of Object;
• assessment of Object current State by Agent is approximate.

Supposition: Planning in ITS may be realized only for a few first Actions instead of full-scale planning to the end..

T. Supposition: Executive and Measuring activity may be automated in ITS as it takes place in traditional (non-intelligent) CBT systems.

U. General Structure of Tutoring activity may be represented as shown on fig. 4.

V. Let us skip some intermediate steps and show the main interrelation among all terminal Agents in Tutoring process. This relation may be named as "General Tutoring Algorithm" of ITS. See fig. 5.

W. Tutoring is realized on a different level of Learning representation: as curricular study management (strategic level), as the control over a learning session (tactic level), and as a control over a problem solving (operational level).

Supposition: The same Tutoring Agents work on different (strategic, tactic, and operational) levels.

3.4. Where to Stop Model Detailing

During Object modeling, each step of Object analysis, refinement and Model synthesis introduces more information to Model. After each modeling step the Model becomes more and more valuable (and expensive). But it is true only for relatively simple objects. For very complex object (like ours) each step of modeling is related with making suppositions about Object essence, which, generally speaking, will not be by all means correct. As a result, the potential reliability (trustworthiness) of such Model decreases after each step. >

Transfer interrupted!

During ITS Shell development by researchers, Modeling may be stopped on domain/learner/author-independent level when they can realize in Shell the terminal agents they want. It delivers to all ITS Shell users-Authors the most general and less structured initial Models with capability of further Domain detailing and Author interpreting.

During application design by Authors, it has sense to stop Model detailing on a step when current Model becomes necessary and sufficient for cost-effective control over Learning. The preferences must be given to more general and less structured models, that are more adequate to human Tutor's (and Author's) mental representation.

4.1. Application area

The above mentioned suppositions and inferred Models are theoretic, very general and have practically no limits in their tutoring application. Being unable to investigate all possible application areas of these Models we focus our efforts on simpler, wider interpretable, and more practice-oriented solutions we have been able to realize in software and applications. Sure, namely such solutions can generate cost-effective ITS and be the most popular.

Further Models presented are developed to cover application areas presented hereinafter underlined:

Training:

• for work
  • Tutoring:
    • on conceptual Domain;
      • for problem solving;
      • by problem solving;
      • on problem solving;
    • on procedural Domain;
  • Practice;
• on work;

4.2. Domain Model

Domain Model in the most general way may be represented by the given Systems Form. This form is hierarchical and Author can select any Domain representation levels for Learners by him/herself in accordance with his/her Strategy selected.

The simplest Domain Model corresponding to the given System Form is a list of Domain description Items (names, properties, functions, modes, parameters, components, ..., relations). Authors are free to select the most suitable System Form Items for their Domain modeling.

4.3. Domain Knowledge Model

Domain Knowledge Model is a Mental Model of Domain. Learner and Tutor has it. This model must correspond to Domain Model. Then it may be represented by the given Systems Form too. According to Domain Model, Domain Knowledge Model may be represented by Author on the same level of details, with Author using the same Items.

The simplest Domain Knowledge Model (of all the models corresponding to the given System Form) is a list of Domain description Items with definite degree of each Item mastery.

4.4. Expert Model

Expert Model is a Tutoring Goal. It may be represented by Author in the given Systems Form. Its simplest form may be represented as follows:

1. External Representation Levels:

1.1.1. Expert Model.

1.1.2.1. Expert Model is a part of Learner Model.

1.3. Functional Representation Level:

1.3.1.1.1.1. Input:

1.3.1.1.1.1.1. Domain Problem to solve.

1.3.1.1.2. Output:

1.3.1.1.2.1. Ideal Solving Performance of Domain Problem or correct final Result only.

2. Internal Representation Level:

2.4.2.3.1.1. Domain Knowledge Model with the highest degree of mastery of each Item.

3. Interrelation between External and Internal Representation Levels:

3.1. Fuzzy sub-set of Domain Knowledge Model Items used by Expert in Problem Solving.

(Fuzziness is explained by the fact that in a general case Author does not know the real mode of Problem Solving by Expert)

4.5. Learner Model

Learner Model is a Tutoring Goal together with any possible deviations. It may be represented by the given Systems Form. Learner differs from Expert in:

• possible deficiency of Domain Knowledge mastery;
• necessity to deliver deficient Domain Knowledge with Learning Materials;
• making errors in performance or final result of Problem Solving.

In this sense Learner Model is an extension of Expert Model.

Learner Model in the simplest form may be represented as follows:

1. External Representation Levels:

1.1.1. Learner Model

1.1.2.1. Learner Model is located in #2.3.1.1. of Learning Model.

1.3. Functional Representation Level:

1.3.1.1.1. Inputs:

1.3.1.1.1.1.1. Learning Materials (Domain Situations; Tutor's explanations, comments);

1.3.1.1.1.1.2. Domain Problems to solve.

1.3.1.1.2. Output:

1.3.1.1.2.1. Actions (Domain Problem Solving Performance or Problem Solving Results).

2. Internal Representation Level:

2.2. Attributes Representation Level:

2.2.1. Individual Psychological and Cognitive Parameters of Learner;

2.4. Super-Systems or Mental Representation Level:

2.4.2.3.1.1.Domain Knowledge Model:

2.4.2.3.1.1-2.1.1. States (Mastery Degree):

2.4.2.3.1.1-2.1.1.1. "Unknown";

2.4.2.3.1.1-2.1.1.2. "Shown";

2.4.2.3.1.1-2.1.1.3. "Known".

2.4.2.3.1.1-2.1.2. State transitions: "Unknown->Shown->Known".

2.4.2.3.1.1-2.3.1. Domain Knowledge Components:

2.4.2.3.1.1-2.3.1.1. Domain Knowledge Component (Item):

2.4.2.3.1.1-2.3.1.1- 2.1.1. States (Mastery Degree):

2.4.2.3.1.1-2.3.1.1- 2.1.1.1. "Unknown";

2.4.2.3.1.1-2.3.1.1- 2.1.1.2. "Shown";

2.4.2.3.1.1-2.3.1.1- 2.1.1.3. "Known".

2.4.2.3.1.1-2.3.1.1- 2.1.2. State transitions: "Unknown->Shown->Known".

2.4.2.3.1.1-2.3.2. Interconnections between Domain Knowledge Components:

"Knowledge Genesis" relation is a fuzzy relation among Domain Knowledge Items, which shows the necessity of all other Domain Knowledge Items for learning/teaching each separate Domain Knowledge Items (in accordance with Strategy pre-defined by Author).

2.4.2.3.1.1-2.5. Interrelations among Mental Representation Levels:

"Domain is shown if all its Components are shown";

"Domain is known if all its Components are known",...

3. Interrelation between External and Internal Representation Levels:

"Knowledge Delivery" relation is a fuzzy relation between Domain Knowledge Items and Learning Materials that tend to form these concepts. This relation shows a possibility of each Learning Material to form some Domain Knowledge Items;

"Knowledge Manifestation" relation is a fuzzy relation between Domain Knowledge Items and envisaged Performance or Results of Problems Solving. This relation shows the necessity of each Domain Knowledge Items for getting the envisaged Performance or Result by Learner. This relation includes not only correct (like Expert's), but possible incorrect and mixed Learner's Problem Solving Performance/Results. That is, this relation additionally shows that the cause (bug) of each incorrect Performance/Result (error) may be possibly non-mastering some Domain Knowledge Items by a Learner.

4.6. Mixed Initiative Paradigm

In traditional CBT, System played a passive role of Executor of fixed interactive script prepared by Author. Author is the most free, creative, and active in CBT. During scripting he/she have to envisage all possible situations in learning, plan and program all corresponding tutoring actions. It is an extremely difficult labor and as a result Authors develop very trivial scripts in practice. These fixed trivial scripts cannot provide a lot of freedom to Learners and strongly limit their learning initiatives.

Contrary to CBTs, ITSystems are capable of playing an active role in tutoring by automatically planning and executing all Tutoring Actions. They can generate the best pedagogical decisions in any learning situation. It is an excellent support for Learners'initiatives. The most Authors like ITS for their personal labor saving and tutoring improvement. But some "super-creative" Authors cannot agree with such a passive role. They wish to more actively participate in computer tutoring process.

Thus to be convenient for all Authors, ITS Authoring Tool is to have rudiment scripting capability. Moreover, it is important to support smooth Authors' transition from traditional CBT Tools to new ITS Authoring Tool.

ITSystem may be managed by Manager too. He/she is able to monitor learning process and manage it to some extent. See fig. 4.

4.7. Initiative Sharing Levels

A. Global Management of Learning is mixed initiative:

• Authors develop filling in (Courseware) for Shell.
• Manager may limit Learner' access to Courses available.
• Manager may monitor individual and collective learning process.
• Learner may select a Course from personal limited list for study.

B. Learning Management within a Course is mixed initiative:

• Author for each Course Unit pre-defines all prerequisite Units of the Course;
• Manager may limit Learner access to Units available;
• System personally presents to Learner all currently accessible Units for his/her choice;
• Learner selects a Unit to learn.

C. Learning Control within a Unit ( Session Management) is mixed initiative:

• Author for each Domain Item has defined all prerequisite Domain Items of the Unit (Strategy, Genesis);
• Author has selected all necessary System Functions, prepared, and input all necessary data for them;
• Manager may limit Learner's access to System Functions available;
• Manager may define parameters of the System tutoring style;
• System presents to Learner an entire personal current network
• of all the "available", "shown", and "known" Domain Items within the Unit selected;
• Learner can limit the content of current tutoring session by selecting on the network
• "where to start" and/or "where to stop" the session (Content of whole Unit is selected by default);
• System presents to Learner all personally accessible Functions to use;
• Learner selects any Function for using ("Tutoring" function is selected by default) ;
• System calculates all possible Tutoring Actions in current Learning situation;
• Author has optional capability for all Learning situations to advise subsequent Tutoring Actions.;
• System fulfills Tutoring Action advised by Author only provided it does not contradict possible decisions of the System.
• System itself selects and realizes the best Tutoring Action from the possible ones.

D. Learning Control within a separate Tutoring Action is mixed initiative too:

• Author has defined navigation and interactive means common for all Learners;
• System presents to Learner current navigation and interactive means personally accessible;
• Learner interacts by his/her own way inside accessible means presented.

4.8. ITS Functions Structure

Overall structure of ITS functions considered above is presented to Learners and Authors in simple and clear form as follows:

• Pre-test;
• TUTORING:
  • Delivery of Learning Materials to Learner;
  • COACHING:
    • Checking of mastery and errors detection;
    • DEBUGGING:
      • Diagnosing of errors causes;
      • Correction of errors causes by explanations.
• Post-test.

On the basis of methodology, concepts and practice-oriented solutions described above we have developed technological complex "Intelligent Tutor" for cost-effective applied ITS design. It includes:

• Shell;
• Authoring Tool;
• Technology of applied ITS design supported with Author Guide;
• Number of applied ITS for different Domains;

5.1. "Intelligent Tutor" Shell

The "Intelligent Tutor" Shell is a hollow ITS, that is not filled in with concrete Domain content. The Shell contains universal didactic knowledge. It may be said that the Shell itself knows "how to teach" Learners and needs only to know "whom to teach", "what to teach", and "which materials to use" in order to become the applied ITS. These deficiency data must be filled in Shell to convert it into applied ITS.

In accordance with described Tutoring Model this Shell contains:

• empty declarative Domain Model, Expert Model, Learner Model;
• procedural Tutor Model, including Planning, Executive, Measuring, Assessing, and Decision Making Sub-Agents of Delivery, Checking, and Diagnosing Agents;
• Parameters of tutoring stile: reliability of knowledge delivery, reliability of knowledge checking, reliability of error causes (bugs) diagnosing, frequency of knowledge checking, tolerance to Learner's errors.

Using filled in declarative Models, procedural Model, and adjusted Parameters the Shell can automatically realize the main ITS functions (see chapter 4.8) in mixed initiative (see 4.6; 4.7) interactive way with Learner in style desired by Author.

5.2. Applied "Intelligent Tutors"

Applied ITS simulates Domain and Tutor for Learners. They are based on described Shell and therefore can realize the main Tutor functions in the individualized dialogue with Learner automatically without script prepared in advance by Author. They let Learners to actively participate in their own learning by choosing the course and the unit for study, content initials ("where to start") and objectives ("where to stop") within the unit, current function of ITS to work with.

The Main Menu of Learner is expandable step by step. In its minimum form presented to novices-Learners it consists of 3 main function: Pretest, TUTORING and Posttest.

In the maximum form presented to expert-Learner it looks like in fig. 7 and includes up to 9 function ("mode" in figure 7).

After Learner makes his/her choice the system works automatically, but in any step of the Learning process Learner is allowed to change current ITS function and/or current initials and objectives of Learning. Thus, the tutoring/learning strategy used is mixed-initiative.

All Learning (in the figure: "tutoring") Materials are presented to Learner in a separate window with scrolling capability. The example of Learning Material presentation is shown on fig. 8.

As a feed-back Learner may give his or her replay (problem solving result) in the form of: multiple choice, set ordering, filling in the blank, number, simple text/digit expression, construction (scheme) of predetermined elements. The example of a Problem presentation with textual answer is shown in fig. 9.

The Learning of any course unit begins from Pretest, when System has no information about Learner's initial knowledge needed for the given unit. Further Learning is done in any Function (in the figure: "mode" ), dynamically chosen by Learner in any order. To finish a course unit studying and to get the resulting mark a Learner is to pass Posttest, if prescribed by unit Author.

5.3. Authoring Tool of "Intelligent Tutor"

Authoring Tool of "Intelligent Tutor" is used by Authors to fill in Shell with concrete learning content (courseware) in order to convert it into applied ITS.

The Main Menu of Author in Tool has hierarchical form (see Fig. 10).

The bottom level of the menu gives Authors a possibility to describe Domain Knowledge Items ("elements" in figure) of the course unit (in the figure: "theme"). This is the internal representation of the unit. The top level of the menu gives a possibility to form external presentations of the unit materials to Learners. On this level Author can use ready-made Learning Materials and Problems designed for traditional CBT systems. The middle level gives a possibility to connect bottom and top level of the unit description using above described declarative models (See corresponding "relations" in chapter 4.5).

The Authoring Tool includes:

• ordinary text, fonts, icon, and graphic editors to form external presentation of all unit materials for Learners;
• special Editor to fill in used Models and verify them;
• special Tool to input values of Parameters, defining the desired Author's style of Tutoring;
• Debugger of designed ITS for its approbation, for diagnosing and correction of its bugs, for adjusting ITS.

Described version of "Intelligent Tutor" is oriented at using IBM PC 386/387/4/EGA as a minimum. Its software is developed in the object - oriented paradigm on Borland C++ under MS DOS 5.0. ITSs have user-friendly window adjustable interface (corresponding WINDOWS standard) and uses relational DBMS "Paradox".

Shell installation takes 3 Mb HDD memory.

Applied ITS needs not less than 2 Mb extended memory.

5.4. Applications Design Technology

The full-scale technology of applied cost-effective ITS design consists of the following stages:

1. Analysis of envisaged professional activity of Learners, explication of professional tasks and knowledge. (This stage may be omitted when the content of Learning has been predetermined).
2. Structuring of Learning content, determination of courses and course units. An explication of Domain Items within each course unit. Preparing of Learning Material for explanation of each Domain Item . Data input, building up, automatic verification and debugging of Knowledge Genesis Model.
3. Collecting ready-made and designing new Learning Materials for each course unit. Data input, building up, automatic verification and debugging of Knowledge Delivery Model. (This stage may be omitted when Learning Materials prepared on the second stage are enough in Author's opinion).
4. Collecting ready-made and designing new Problems within a unit on the basis of the predetermined set of professional tasks. Data input, building up, automatic verification and debugging of Knowledge Manifestation Model.
5. Assembling, debugging and adjusting designed applied ITS.

The work of Authors in suggested technology is deeply structured, directed by guideline, and supported by Authoring Tool. It is simple and well understandable in each step for them. It does not take much intellectual efforts, does not cause the subjective errors and gives good results in practice.

5.5. Practical results

On the basis of technology described a number of applied ITSs have been designed. The themes have been taken from the following domains: mathematics, physics, chemistry, geometry, book-keeping, strength of materials, automated mechanisms.

The last most advanced commercial applied ITSs have been designed for training Nuclear Power Plant personnel.

Our experience shows that Authors easily master this technology and use it successfully. All Authors appreciated the quality of designed ITS functioning with Learner. As for Learners, they were glad to have high degree of Learning freedom and wide spectrum of intelligent didactic services simultaneously.

In nearest future we should like to focus our efforts on some of the following directions:

1. Completing of Windows'95 version of "Intelligent Tutor";
2. Development of "Intelligent Upgrade" for high-end CBT Authoring Tools available in the market;
3. Development of Shell and Authoring Tool for design simulator-based applied ITS;
4. Development of Computer Managed Instruction systems;
5. Research in ITS theory and Computer Aided ITS Engineering.

ITS is an interdisciplinary research area. To cover instructional and engineering points of view ITS Models should be very general. To be correct they must be theoretically and practically approved. To be widely applicable they must be simple and broadly interpretable. Those are the reasons for our choice and application of very general and approved systems theoretical representations to ITS modeling.

In this paper the following has been suggested:

• General System Form for modeling of tutoring/learning processes and their components;
• Methodology of Systems Modeling of tutoring/learning processes and their components;
• General theoretical Models of ITS and its main components;
• The structure of main didactic functions of ITS;
• Mixed initiative paradigm of Intelligent Tutoring/Learning processes;
• Practice-oriented declarative Models of Domain, Expert, Learner;
• Practice-oriented procedural Model of Tutor activity;

Thus we demonstrate an example of top-down approach to ITS design. This approach has been used and approved in developing technological complex "Intelligent Tutor" for applied cost-effective ITS design.

The suggested "Intelligent Tutor" enables Authors to reduce an enormously sophisticated intellectual process of applied ITS design to a more simple one, actually, to simply filling in declarative Model Forms with traditional Learning Materials on the Domain under study. This considerably reduces the labor consumption and makes designed applied ITS didactically correct and cost-effective.

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I am very thankful to:

• Russian ENIKO MIFI Corporation and American EXITECH Corporation for taking part in funding my research;
• my colleagues for their support, assistance and friendly cooperation in everyday work;
• participants of IEEE P1484 working group ("Standard for Information Technology for Education-Personal Learning System-Learner Model") for their attention to my efforts in our cooperative work;
• Peter Brusilovsky for his friendly and scientific information support.