Qualitative Models in Interactive Learning Environments: An Introduction

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Qualitative Models inInteractive LearningEnvironments: An IntroductionBert Bredeweg a & Radbound Winkels aa Department of Social Sciena , University ofAmsterdam , Roetersstraat 15, 1018 WB, Amsterdam,The Netherlands Fax: E-mail:Published online: 28 Jul 2006.

To cite this article: Bert Bredeweg & Radbound Winkels (1998) Qualitative Modelsin Interactive Learning Environments: An Introduction, Interactive LearningEnvironments, 5:1, 1-18, DOI: 10.1080/1049482980050101

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Qualitative Models in Interactive LearningEnvironments: An Introduction

BERT BREDEWEGRADBOUDWINKELS

It is a generally held position that the processof learning will improve when learners are givencomputer-based tutoring programs that allowfor interactive access tuned to the specific needsof each individual learner. Computer artifactsfor learning should therefore be both interactiveand articulated. Interactive learning environ-ments can be seen as engines for education thatfacilitate learning by having learners interactwith a simulation of the subject matter.

Designing, diagnosing and controlling thebehavior of "physical" systems is an importantfeature of daily human activities, both in profes-sional and non-professional situations. Interact-ing with physical systems requirescomprehension of their behavior, in particularhow manipulations of some aspect of the systemwill effect its behavior. In order to teach thesebehavioral characteristics, quantitative simula-tions are often used in computer-based learningenvironments. However, some behavioral fea-

tures are hard to communicate by a computerprogram that is based on such a quantitativesimulation. Among others, generating causalexplanations of the systems' behavior, reason-ing from structure (i.e., deriving the behaviorfrom a given structural description), and quali-tativeness in general (i.e., a vocabulary for rea-soning about behavior in qualitative terms)cannot be dealt with adequately. A large part ofthe research on qualitative reasoning originatedfrom efforts trying to cope with the limitationsthat followed from using quantitative sinulatorsfor teaching purposes.

This introduction presents an outline of howqualitative models can be used for interactivelearning environments. The first section willdiscuss in more detail the kind of learning thatthe contributions in this special issue are con-cerned with. The second section will elaborateon the typical characteristics of qualitative mod-

Interactive Learning EnvironmentsVolume 5, pages 1-18Copyright © 1998 by Swets & ZeitlingerAll rights of reproduction in any form reserved.ISSN: 1049-4820

Bert Bredeweg, Department of Social Sciena; Informat-ics (S.W.I.), University of Amsterdam, Roetersstraat 15,1018 WB Amsterdam, The Netherlands; far: +31 20525.6896, E-mail: [email protected] http://www.swi.psy.uva.nl/usr/bert/home.html.

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INTERACTIVE LEARNING ENVIRONMENTS Vol. 5

els. During the past decade a large number ofpromising results have been achieved by thequalitative reasoning community, whereas atthe same time the limitations of the currenttechniques are well understood. The third sec-tion presents a range of research topics that areinteresting to pursue with respect to usingqualitative models in interactive learning envi-ronments. This section is followed by a shortoverview of the contributions in this specialissue, which is split into two separate volumes.The introduction ends with some concludingremarks.

LEARNING ABOUT SYSTEMBEHAVIOR

Learning environments are particularly inter-esting as artificial worlds with which learnerscan interact in order to learn about the behaviorof certain systems. In this section we will de-scribe in more detail the ideas underlying thisapproach. First, the notion of "interacting withthe (physical) environment" will be explained.Second, some ideas on what it means to learnabout system behavior will be discussed, inparticular, the ability to predict and postdictbehavior. The third subsection discusses thebenefits of using individualized instruction incombination with simulation models. The lastsubsection explains why qualitative models areparticularly useful for this purpose.

Interacting with the PhysicalEnvironment

Humans have to interact with their physicalenvironment. They have to drive their cars,operate VCR's, light matches, use telephones,turn on lights, use elevators, open doors, and soon. In order to deal with these different systemshumans have to learn aboutthe behavior of eachof them. They have to learn how the breaks ofa car work, how the buttons must be used in anelevator and how their use differs from buttonson a telephone or a VCR, that matches can belit by striking them along specific parts of thebox, that doors usually have a knob that has tobe turned (counter) clockwise or pushed down,

and so forth. During their lives people spend alot of time learning about the behavior of thehuge amount of systems they have to interactwith. Sometimes this learning takes many yearsof hard work, such as learning how to fly anairplane or how to operate a power plant.

Researchers in the area of knowledge-basedsystems have been investigating the differentways in which humans can interact with physicalsystems for many years now. It turns out thatthree main categories can be identified, namely:(1) controlling and operating, (2) designing andconstructing, and (3) diagnosing and repairing(see for example Breuker & van de Velde, 1994).In the case of controlling, the goal of the humanagent is to interact with the system in such away that it performs a specific kind of, appar-ently desired, behavior. Characteristic for thissituation is also the fact that the physical struc-ture of the systems does not change, at least notsignificantly. It is only manipulated in order tohave it perform the intended behavior. In thecase of designing and constructing, the struc-ture of the system will change. In fact, that isthe key notion in this situation. When designinga system, the goal is to build a physical structuresuch that the desired behavior will be performedby it. Many of the systems that surround humansto date are indeed constructed by humans. It iscommon in this respect to make a distinctionbetween systems designed and constructed byhumans (artifacts) and systems not made byhumans (natural systems). Finally, in the case ofdiagnosing and repairing a system, the systemdoes not show the desired behavior anymore.The goal of this interaction with a system is tofind the cause for the malfunctioning and torepair it. The latter may require manipulatingthe structure of the system, such as replacing abroken part.

The difference presented here between natu-ral systems and artifacts is of course just a firststep in a classification hierarchy. Usually bothcategories can be further divided according todomain specific features. There are for examplebiological systems, chemical systems, social sys-tems, economic systems, and so forth. Often thenames given to activities concerned with inter-

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Qualitative Models in Interactive Learning Environments

acting with these systems differ across thesedomains. Also, there are many possible classifi-cations of systems. For this introduction it issufficient to know that there are many differentsystems out there in the world with whichhumans have to interact in one way or another.

Learning about Systems and theirBehavior

The large number of systems poses a bigproblem to humans, for they are born withoutknowledge of these systems, and yet, at somepoint in their lives they have to interact withthese systems. One approach would be to havehumans interact individually with these systemsand let them discover the crucial insights bythemselves. This would of course not be a veryefficient approach. First of all, it would be veryexpensive and maybe even traumatic. Think ofall the children that know nothing about carsand would get run over by them while trying todiscover "what kind of behavior this systemmight produce". Secondly, people can reasonabout the behavior of a system as it evolves intime. This is of course where education comesin: Teachers spend a lot of time teaching learn-ers about the behavior of systems in the physicalworld and, more specifically, how to interactwith them. The basic idea is that learners haveto acquire appropriate models of physical sys-tems and their behavior. These models providethe basis for successful interaction with thesesystems (cf. Clancey, 1986). From a pragmaticpoint of view, "an appropriate model" implies atleast two important notions, namely predictionand postdiction (or explanation) of the behaviorof some system (cf. Kleer, 1984; Forbus, 1984).In order to perform these reasoning capabilitiesa person has to be able to identify some physicalstructure as a stand-alone unit (a system) withits own individual behavior. A person shouldthen be able to identify the behaviors of thissystem that are important to him or her, and beable to either predict how these will change inthe near future, or explain how they came aboutfollowing some previous behavior. It is impor-tant to realize that both prediction and postdic-

tion require causal models of the system's be-havior that enable someone to relate some setof behaviors at time t1 to some set of behaviorsat time t2. Also important is the fact that thewhole notion of an "appropriate model" is arelative one. Different goals require differentmodels. For someone driving a car, it is suffi-cient to observe a red traffic light and be ableto predict that it will turn green at some pointin the near future. If, however, the red lightturns off without the green one being; lit, thedriver should be able to explain that this isprobably due to some power failure or to thelight bulb being broken. Usually there will bemore behavioral cues in the environment todisambiguate the possible interpretations. If forexample other traffic lights are still red or greenthen the chance of a power failure is less likely.The electrician who has to repair the trafficlights has different goals compared to the cardriver and therefore uses a different set of (moredetailed) models. In an educational context, thismeans that depending on the goal; to beachieved, specific models have to be learned, ortaught.

Using Computers and SimulationModels

Today computers allow learners to learnabout system behavior in a way that advancesthe traditional classroom oriented approach ina number of ways. First, there is the notion ofindividualized instruction. Learning will im-prove when learners are given comput;r-basedtutoring programs that allow for interactiveaccess tuned to the specific needs of each indi-vidual learner (cf. Wenger, 1987). Next to usingindividualized tutoring, the use of simulationsof real-world systems has a number of advan-tages in itself (cf. Jong, 1991). If, for example,the real system cannot be accessed by thelearner then computer models can provide in-teractive learning environments which are fullof genuine stimuli that closely resemble theimportant characteristics of the original system,particularly if multimedia features are included(cf. Schank & Cleary, 1995). In addition, ma-

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nipulations may be carried out with the modelof the system that are undesirable (too expen-sive or too dangerous) under normal conditions.Safety critical operations, as for example re-quired for operating power plants, can be car-ried out as many times as needed withoutmaking many additional costs. Also, in the caseof a nuclear driven power plant, a series ofmeltdowns does not provide any danger to theoutside world. Simulation models can also beused to build environments that could neverexist in reality. Often these impossible worlds,for example no gravity on earth, can be veryillustrative and therefore helpful for learners toacquire crucial insights (e.g. ARK, Smith et al.,1987). Computer simulations also allow one tomanipulate time, and by doing so speed up orslow down the behavior of some system. Thisallows learners to access more global notions ofhow the behavior of systems evolves in time (e.g.global climate changes or pollution processes)or to study complex and rapidly changing phe-nomena step by step and in close detail (e.g.chemical reactions or electrical phenomena).

What Kind of Models?

Research shows that simulations are onlyeffective when the actions of the learners aremonitored by a teacher (human or computer)and guidance is provided (cf. Elsom-Cook, 1990;Hulst, 1996). As we are concerned with com-puter simulations the question is how to relate

tutoring activities to ingredients of the simula-tion model. In order to connect the two, thesimulation model has to provide handles bywhich it can be accessed for tutoring purposes.This is an old issue already faced in early pro-grams such as Steamer (Hollan et al., 1987) andSophie (Brown et al., 1982), and very much thebasic problem that gave rise to fundamentalresearch areas such as qualitative reasoning(Bobrow, 1984). What does it take to buildarticulated models (see e.g. Forbus & Falken-hainer, 1992)? Although on the one hand it iseasy to understand the essence of building ar-ticulated models, this is often not understoodby engineers and other highly trained expertsin physics and related areas. It is only in auto-mated tutoring situations, when the computerprogram has to generate and provide feedbackto the learner by itself; that one realizes what ismissing in a quantitative simulation model forthat purpose. It turns out that there is a wholevocabulary and a corresponding reasoning strat-egy that experts use, which is not available byitself from the quantitative model (Kleer, 1990).Something has to be added in order for thecomputer to have access to that kind of knowl-edge. Before going into detail about what has tobe added and how, let us first point out theproblem by means of a simple example. In Fig-ure 1 a set of containers is shown. Each con-tainer is closed by a piston and contains anamount of gas.

State 1

State 2

State 3

Figure 1. A Container-piston Situation

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Table 1. Quantitative values for V*P =n*r*T

st 1st2st3

V

125

P

1052

n*r*T

101010

Using Boyle's law, V*P - n*r*T, we can easilycompute the values for Pressure given differentvalues for Volume and a fixed value for n*r*Tas shown in Table 1.

In fact, all kinds of calculations can be madeas long as only one of the values is unknown.Looking at Table 1, we human beings can easilysee that increasing values for V are followed bydecreasing values for P. However, in the formulaV*P - n*r*T there is nothing that captures thisnotion explicitly. Something has to be added tothis equation in order to derive that P and Vhave some kind of monotonic relationship. Atleast some procedure is required that comparesthe values of P and V and comes up with thisnotion (which is by the way a rather difficultmachine learning problem). But for tutoringpurposes we do not want to depend on quanti-tative values, per se. Not only are they unavail-able in many domains and specific situations,such an approach also ignores the fact thatthere exists this rich vocabulary that people useto communicate about the behavior of (physical)systems. In the case of the container-pistonexample, we would like to have access to a setof primitives represented in a computer pro-gram in such a way that it allows the followingkind of utterances: "if V increases then P de-creases". Moreover, we would like this languageto be general and reusable for many differentdomains, including non-physics domains such asfor example economics (Berndsen, 1992) andecology (Salles et al., 1996). This is where quali-tative reasoning comes in. Qualitative reasoningprovides a vocabulary (an ontology if one likes)by which computer programs can reason aboutthe behavior of systems in such a way that thesecomputers can communicate about the behaviorof these systems with humans. We refer to this

notion as "knowledge communication aboutsystem behavior".

CHARACTERISTICS OFQUALITATIVE MODELS

During the past decade many import ant ideashave been presented by the qualitative reason-ing community (see e.g. Weld & Kleer, 1990). Itis far beyond the scope of this section to comeup with a complete overview of all that research.Instead this section will point out some of themain characteristics that are of interest forusing qualitative models in interactive learningenvironments (for more details see also Bre-deweg, 1992).

Reasoning from Structure

An important starting point for qualitativereasoning is the notion of "reasoning fromstructure". This means that the behavior ofsome system is derived by analyzing its struc-tural appearance. An essential step ir. the con-struction of a qualitative model is therefore todetermine how entities from the physical realityare represented in the model. Two types ofabstraction have been given much attention: (1)modeling the physical world as componentsconnected by conduits (Kleer, 1984), and (2)modeling the physical world as a set of physicalobjects that interact via processes (Forbus,1984). Each of these abstractions provides spe-cific guidelines according to which systemsmust be modeled. These guidelines can in addi-tion be used for developing general purposelibraries. As soon as a model has been con-structed for a certain part of the physical world,this model can be stored in a library and usedagain in new situations.

Quantities and Changing Behavior

In a qualitative model, behavior is typicallyrepresented by quantities, which can be as-signed certain qualitative values and have aderivative that specifies a direction of change.The latter may effect the former to change andby doing so represent a changing behavior. The

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mm


• ozero plus

Figure 2. A General Quantity Space

values a quantity can have are represented as aquantity space (a set of values, usually consist-ing of alternating points and intervals). Themost general quantity space defines three val-ues for a quantity: negative [-], zero [0] andpositive: [+] (see Figure 2).

This set of values is applicable to many quan-tities in many different situations. Take for ex-ample an amount of water: Aw Qualitativelyspeaking Aw = [+] could mean that there is anamount of water, and Aw = [0] that there is nowater (Aw - [-] could then mean that there is ashortage of water). The interpretation of a quali-tative value usually depends on the kind ofquantity that has been assigned the value. Con-sider for example a pressure difference betweenthe input and output of a valve. Pin-out = [+] couldmean that the pressure at the input of the valve

is higher, Pin-out I could mean that there isno pressure difference (Pin = P0J and PilH)ut =[-] could mean that the pressure at the outputis higher.

The general quantity space {-,0,+} may notalways capture the typical characteristics of adomain in sufficient detail. In those situations adomain specific quantity space is required. Thiscan for example be true for the quantity tem-perature when it refers to the temperature ofsome substance. Typically a quantity space as

shown in Figure 3 will then be required in orderto model the different aggregation phases (quali-tative states) of the substance.

Choosing the appropriate quantity space fora quantity is often a difficult problem. Obvi-ously, if we refer to the human body temperaturewe do not want the model to represent solid,liquid and gas. A more useful quantity space forthe quantity temperature in a medical domainwould be: below normal (low), normal, abovenormal (high), as for example shown in Figure 4.

As mentioned before, derivatives are used torepresent the dynamic aspects of system behav-ior, but again only using qualitative terms. Forexample: Aw = [+] & Aw = [-], means that in thecurrent situation the amount of water is decreas-ing. Termination rules are then used to deter-mine whether the behavior in the currentsituation may change and lead to a new state ofbehavior. In this situation, the amount of watermay become [0] in the next state. This specificinference is based on the limit rule (cf. Kleer,1984) and reads as follows: IF a quantity has avalue and it is decreasing ( = [-]) THEN thisquantity will reach the next lower value from itsquantity space. More complex representations,such as using higher order derivatives, have alsobeen discussed (see for example (Kleer & Wil-liams, 1991)).

Absolutenil

point

1Solid

Freezing/melpo

titingntlt

Liquid

Boiling/conde

pofinsingint

tGas

Infinity(plus)(oo+)

Solid & Liquid Liquid & Gas

Figure 3. A Typical Quantity Space for Physics Problems

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O ^ - o -Minimum L o w

N o r m a lHigh - o

Maximum

Figure 4. A Typical Quantity Space for Medical Domains

Dependencies and Causality

An important characteristic of qualitativemodels is the notion of dependencies betweenquantities and the causality that can be modeledby these. Well understood dependencies areinfluences, proportionalities (Forbus, 1984) andregular qualitative (in)equalities (cf. Simmons,1986; Williams, 1988). A simple example asshown in Figure 5 may help to explain some ofthe basic ideas. It describes how an energy flowwill restore the equilibrium between two objectsthat differ in temperature.

Forbus refers to this specific partial model (ormodel fragment) as a heat flow process (noticethat a liquid flow process would look the sameexcept for using different quantities: Pressure,Amount, and Flow of liquid). This process isstored in a library of model fragments andapplies to any situation (structural descriptionor scenario) in which there appear two objectsthat differ in temperature (see Figure 6a). If the

description applies, the inequality between thetemperatures causes a flow of energy betweenthe objects that increases the amount of energyin the colder object and decreases the amountof energy in the warmer object. These depend-encies are modeled by influences (I- & I+). Thechanges that are caused by these influences arefurther propagated via the proportional depend-encies (P- & P+) that exist between the tem-peratures and the heats within each object.These changes in temperature will then effectthe inequality between the temperatures andlead to a new state of behavior in which thetemperatures have become equal.

A heat flow process may apply to many differ-ent physical situations as for example shown inFigure 6 (6a: two objects differing' in tempera-ture that are moved towards each other, 6b: acontainer-piston assembly containing a gas thatis being heated, and 6c: a kettle containingwater that is being heated).

Temperature 1

P+

Temperature 2

Flow (of energy)

Heatl

1+

P+

Heat2

Figure 5. A Simple Heat Flow Process

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Object I Object 2

a: two objects b: container-piston

Figure 6. Three Heat Exchanging Situations

c: kettle

Depending on that specific situation the ef-fects of the heat flow may be different. It may,for example, be the case that more than oneprocess effects some quantity. In that case theresulting change in this quantity may be am-biguous, or not, depending on the kind of influ-ences introduced by the processes and themagnitude of these influences. See for exampleForbus (1990) for more details on this matter.Another aspect is concerned with the type ofchange that may occur once quantities are in-creasing and decreasing. In the example of thetwo objects (Figure 6a), an inequality betweenthe two quantities changes to an equality. Butin some situations, as for example the kettleheating situation in Figure 6c, this may nothappen. It is very likely that the boiler staysmuch hotter than the water that is being heated

by it. Therefore, the water temperature will notbecome equal to the temperature of the heatsource, but instead it will change its value frombeing in between freezing point and boiling pointto being at the boiling point (see also Figure 3). Inthe new behavioral state the water will start toboil.

Other ways of deriving causal interpretationshave also been proposed. Causal ordering(Iwasaki & Simon, 1986) is probably the bestknown in this respect. Instead of having specificcausal interpretations attributed to certaintypes of dependencies, this method uses theorder in which (in)equalities are used by theequation solver as the basis for the causal inter-pretation. In Top & Akkermans (1991) this isreferred to as mathematical causality as op-posed to physical causality discussed above.

Structural Description(scenario)

Library ofModel Fragments

State of behavior 1

State of behavior 2

Slate of behavior 3

1 Stale of behavior ...

Changed state...

Changed itatt»

] "

Figure 7. Inferring States of Behavior

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Constructing a Running Model

Knowledge about the behavior of partialphysical structures, such as the above describedcollections of objects and their heat exchanges,can be stored in a library of model fragments.Also the rules for determining state changes canbe stored. Together with an initial structuraldescription (scenario) they can be presented asinput to a qualitative simulator (prediction en-gine) and by doing so have this simulator con-struct a "running model" of the system. This isshown in Figure 7. Provided with a structuraldescription the qualitative simulator will try tofind model fragments that apply to that situ-ation. In the figure this is referred to as specifi-cation (or classification).

Possibly this inference process may lead tomore than one state of behavior for the system.After this the qualitative engine will look forchanges in the current state(s) of behavior.Given these changes, some of the applicablemodel fragments may not apply anymore andtherefore the specification inference has to bedone again. This inference cycle may continueuntil no new changes are found by the qualita-tive simulator. A possible output of a qualitative

simulator for the kettle heating scenario isshown in Figure 8.

For a tutoring situation a "full" prediction ofall possible behaviors of a system is usually notneeded. Instead, specific trajectories of possiblebehaviors are often more useful. In the litera-ture on qualitative simulation this issue has notbeen given much attention. It is one of theproblems that has to be tackled in order to usequalitative models for tutoring purposes.

USING QR MODELS IN ILE

Qualitative techniques provide powerfulmeans to construct cognitive engines for educa-tion. This section discusses some of the mainresearch areas that have to be addressed inorder to successfully use qualitative techniquesfor that purpose.

Selecting and Sequencing SubjectMatter

One set of problems that has to be tackledconcerns the things the learning environmentwill present to the learner(s) to intend with.This may include issues such as global curricu-lum planning, model selection for each of thetopics that the learner has to acquire knowledge

What happens?

Figure 8. Behavioral States for the Kettle Heating Scenario

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10 INTERACTIVE LEARNING ENVIRONMENTS Vol. 5

about, and detailed specifications of the exer-cises or assignments that the learner has tocarry out. Relevant from a qualitative reasoningpoint of view is that all the decisions on theseissues, and the automated procedures followingfrom that, will be grounded in terms of a quali-tative ontology as much as possible. In order toclarify what is meant by this, imagine a causalmodel that may be generated by a qualitativeengine for the container-piston assembly shownin Figure 6b. Usually such a model is too big tobe comprehensible for a learner in one go. Whatis needed in such situations is a procedure thatguides the learner through the model in smallerand understandable steps. For this purpose theontology of qualitative models can be used. Itcan be regarded as a kind of meta language (cf.Harmelen, 1991) in which the steps can bedefined. Consider the following procedure:

1. Focus on the quantities of objects andassemblies

2. Follow the causal paths3. Focus on processes (and follow causal

paths)4. Consider transition to successive states

of behavior (and repeat steps)

The rational behind this procedure would readas follows: learners must first identify the ob-jects in the simulated system and their impor-tant quantities. Next, or while considering aspecific object, they have to learn about thecausal dependencies for each object and aggre-gate. Depending on the specific causal structurefor the container-piston assembly, learners willbe confronted by the environment on issuesconcerning the quantities (and objects) relevantto: (1) the gas in the container closed by a piston,(2) the air surrounding this assembly and (3) theheat source. The third major step concerns theintroduction of the processes. In the container-piston assembly there are at least four processes.One heat flow process from the heat source tothe gas in the container, one from this gas tothe surrounding air, one from the heat sourceto the surrounding air, and one "move" processeffecting the position of the piston. The typical

steps for discussing each of the processes withthe learner are:

1. Find the appropriate inequality betweenthe involved quantities

2. Discuss the flow (in the example: energy)and the initial changes (via influences)that follow from that

3. Use the causal paths to explain how theinitial changes are further propagated(via proportionalities) and possibly re-store the equilibrium

The last step in dealing with processes relatesto the fourth step of the previous procedure.The changes represented by the derivatives ofthe quantities may lead to new states of behav-ior either because inequalities between quanti-ties may change or because quantities take ondifferent values from their quantity spaces.

This procedure of selecting and sequencingsubject matter is only a first step in showing howthe qualitative ontology can be used as a basisfor driving the interactive learning environ-ment. Many additional problems have to besolved, such as determining how to automat-ically generate questions and assignments topresent to the learner. In dealing with theseissues we can also draw from other, sometimesmore traditional, approaches to instructionaldesign. The project SMISLE (Jong et al, 1994)for example, presents a set of general assign-ments that can be used for different situations.However, many of these approaches are notautomated, i.e. similar to traditional CAI, theinteraction with the learner has to be specifiedover and over again for each new situation. Aninteresting question is how we can ground theseapproaches, and thus automate them, by usinga qualitative ontology.

Some interesting publications in this direc-tion have been published. White & Frederiksen(1990) present their causal model progressionas an approach to specifying the notion ofproblem complexity in terms of a qualitativemodel. Falkenhainer & Forbus (1991) try tosolve another part of the same puzzle with theircompositional modeling approach. Here the

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Qualitative Models in Interactive Learning Environments 11

question is how to find the minimum set ofmodel fragments needed for simulating the be-havior of a system and to answer adequately aspecific question. Sime (1995) tackles the prob-lem from yet a different angle. She discusseshow a specific approach to learning can beoperationalized in terms of a qualitative ontol-ogy (see also this issue).

It is important to realize that not all didacticaspects can be grounded in a qualitative ontol-ogy. For example, when proceeding throughsuccessive states of a simulation, how oftenshould a specific causal structure that reappearsin a number of states be discussed with alearner? After a certain number of times thelearner may have understood the phenomenaand may want to move on. If the learningenvironment keeps bringing up this specificcausal structure the learner will get bored orirritated and lose interest for the environment.However, people tend to forget things and, inorder to prevent this, important issues have tobe rehearsed sufficiently. It is not likely that thequalitative ontology will provide much leveragefor determining how to deal with these issues.Research from other areas such as cognitive andlearning sciences have to be applied for thispurpose. However, from a pragmatic point ofview we can circumvent the problem by givingan amount of navigation control to the user. Forexample, after having correctly processed acausal structure once, the learner may skip it insuccessive states of behavior. In fact, finding anoptimal point in using both the learners owncontrol and the assignments set by the environ-ment provides an interesting research question.

Cognitive Diagnosis

When the learning environment is not one offree exploration, but meant to guide the learnertowards some kind of understanding and mas-tering of the domain, the system will have to beable to detect missing knowledge or misconcep-tions on the part of the learner. Relying on thelearner himself to ask for additional informationis usually not enough (they are often unawareof their knowledge gaps), but even in the case

of a request for help, the system will in mostcases have to do some reasoning in order todecide what exactly it is the learner needs toknow. In order to detect or infer learners' needsfor additional information, the system first of allneeds to know the "correct" conceptions andskills; usually this is represented in the domainmodel. Next, it has to use this "correct" or normmodel to either interpret the learner's requestfor help, or to compare the learner's answer oraction to it, to see whether that deviates fromthe norm. When the learner's behavior deviatesfrom the norm, it is an indication for missingknowledge or a misconception on the part ofthe learner (especially when accompanied by arequest for help). In that case the system couldtry to pinpoint the exact piece of knowledge thatis missing or incorrect. This process is usuallyreferred to as (cognitive) diagnosis. The out-come of this diagnostic process should be eithera lack of knowledge or a misconception of thelearner (cf. Winkels, 1992; Bredeweg & Winkels,1994). For diagnostic methods we can turn tothe field of model based diagnosis, as somepeople have suggested (cf. Self, 1992; Bredeweg& Breuker, 1993).

In model based diagnosis, one can distinguishtwo processes: generating hypotheses and test-ing them (cf. Davis & Hamscher, 1988). Mostteaching systems that do diagnosis use decisiontree-like structures, where tests are directly as-sociated with hypotheses. In the case of anexplicit and cognitively plausible domain model,for instance a qualitative model, we can use thisnorm model for generating hypotheses in amore systematic way. There are basically twoways to do that, depending on (our under-standing of) the domain: by "decomposition"and by "specialization". The first method as-sumes a hierarchical structure of parts or com-ponents at the domain level. In principle thediagnostic process is very simple: partition thesystem according to its decomposition and elimi-nate the correctly functioning parts by testing.The second approach, generating hypotheses by"specialization", requires less structure in thedomain, and works by descending taxonomies

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(e.g. as in heuristic classification; Clancey,1985).

Hypotheses can be tested against the data ofthe actual behavior of the learner, previouslyacquired data about the learner's knowledgeand competence at the task (as reflected by alearner model), or by presenting a new problemto the learner that will discriminate betweencompeting hypotheses. In principle, there aretwo solutions for picking the next problem:either selecting the best (most discriminating)problem from a stored set, or constructing acritical test on the basis of the current hypothe-sis set.

The outcome of this diagnostic process is a"faulty component". What can be wrong witheach of these elements? In analogy with trou-bleshooting of artifacts it can be said that eitherthe particular component does not work at all(the learner does not possess or cannot retrievethe particular knowledge), or it functions incor-rectly (the learner has a misconception). Thefirst case is relatively easy to check (we are notconcerned with computational tractability forthe moment). The second case is more difficult.If the correct version of the knowledge is re-placed by something else, what is it replacedwith? A pragmatic solution would be to providethe system with "fault models" that reflect (com-mon) misconceptions (as e.g. proposed by Kon-ing et al., 1996).

Take the container-piston situation in Figure6b as an example. A learner is asked to predictwhat will happen. Suppose he or she predictsthe piston will move outwards (to the left), i.e.the volume of the gas will increase. "And next?"we might ask. "It will keep on moving outwardsuntil we turn off the heat source, or it dropsfrom the container", the learner replies. This iscertainly a likely possibility, but only one of thetwo. Another possibility the qualitative reason-ing engine comes up with, is that the piston willstop moving at a certain moment, because theflow of energy from the source to the gas willbe equal to the flow of energy from the gas tothe outside world. The pressure of the gas willtherefore not increase anymore, and the pistonwill come to a hold. One possible explanation

(hypothesis) of why the learner does not see thispossibility, is that the learner misses the heatflow process between the gas and the world inhis or her model altogether. Another hypothesisis that the learner just forgot about the possibil-ity that the two flows of energy might be equal.When the learner model does not help us todistinguish between the two possibilities, wemay decide to ask the learner a question, or topresent a new problem that will resolve theambiguity, or perhaps even reveal or trigger themissing part of his or her model to the learner.We might ask the learner to tell or show us allheat flow processes in the situation. If thelearner only indicates the one between thesource and the gas, we may try to direct thelearner's attention to the increasing tempera-ture of the gas and the difference with theoutside temperature. We may also opt for thepresentation of a new "problem". It would haveto focus on the relation between the two heatflow processes, for instance one in which theheat source is very small.

Whatever the solution, the important thinghere is that the qualitative "norm" model en-ables us to detect a possible lack of knowledgeor misconception on the part of the learner, andcan be used to suggest likely candidates forthem as well. Many problems still remain in thisdiagnostic process, e.g. finding the right level ofabstraction for hypotheses, ensuring the cogni-tive tractability and plausibility of the normmodels (cf. Koning & Bredeweg, this issue),managing the search space for the diagnosticengine, generating or finding fault models, con-structing critical tests, etc.

Generating Explanations

Qualitative domain models facilitate the gen-eration of explanations in several ways. Firstand foremost, as was mentioned before, theyprovide a vocabulary and conceptual frameworkto talk and think about the domain. They dealwith "quantities", "components", "processes","influences", etc., instead of with mathematicalfunctions. Most qualitative models also providedirect access to the structure of the system it

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represents. This can be used to describe thephysical structure in terms of components andsub-components, and their function, to thelearner. As a mechanism for generating explana-tions for these static model elements, one coulduse schemata of rhetorical predicates, as de-scribed by McKeown (1985) for database ob-jects. She identified several answer schematafor specific question types of users about theseobjects. An example is the "identification"schema for providing definitions, that includesthe description of "type" and "constituency"relations, "concept attributes", and will give anexample. For instance, for the kettle example inFigure 6c, an identification schema could beused to describe the concept of a "containedliquid" when the learner asks about it, such as:"A contained liquid is a liquid that is containedby a container. An example is contained-liquidlthat is contained by container]..".

Besides the static model elements, the reason-ing on the basis of the models (pre- and postdic-tion) can be used to explain "how" the systemworks and "why" it behaves as it does (causal-ity). Provided that the qualitative model has(some) cognitive plausibility (i.e. can serve asmental model, cf. Centner & Stevens, 1983),these causal explanations can be used in teach-ing (cf. Bredeweg & Schut, 1991). For instance,the model of Figure 5 can be used to explainwhat will happen to the temperatures of the twoobjects: a flow of energy will occur which willcause an increase of energy in the colder objectand a decrease of energy in the warmer object(influences), which in turn will lead to a risingtemperature of the colder object and a droppingtemperature of the warmer object (proportion-alities), until both temperatures are equal. Forsuch a relatively simple model, the process ofexplaining a causal chain is straightforward, butfor more complex models the reasoning maycontain ambiguities, and the chains will be fartoo long to communicate to learners. Causalchains at higher levels of abstraction (a largergrain size) are then needed. This could forinstance be achieved by a chunking process,where paths that do not branch (i.e. there areno alternatives for what can happen) are col-

lapsed into fewer, or even one step. In theexample given above, one could decide to takethe influence and the proportionality in one go,and state that the flow of energy will "cause" adrop of temperature in the warmer object, anda rising temperature in the colder object. Onestep further would be to just state that the flowof energy will "cause" the temperatures to be-come equal. Later on, one can always expand(parts of) the causal chain to a more detailedlevel. What is needed for these types of explana-tions are more dynamic mechanisms that aredriven by communicative or instructional goalsand intentions (cf. Winkels, 1992; Vadillo et al.,this issue), rather than the static, content drivenapproach of McKeown (1985).

An interesting use could be made of thelibrary of model fragments for explanations,namely creating analogies (cf. Gentner, 1983).When a learner has been confronted with theheat flow process of Figure 5, we could usestructure mapping to find the analogous proc-ess of liquid flow and use it either to explain theheat flow (e.g. when the learner already under-stands the liquid flow process), or to introducethe liquid flow process once the learner under-stands the heat flow process. Suppose for in-stance that a learner holds the belief that a heatflow process, as depicted in Figure 5, terminateswhen Heatl and Heat2 are equal, instead ofwhen the temperatures are equal. This mayshow up in an example where one object is muchlarger than the other object. One could use ananalogy with the liquid flow process to show theconsequences of that belief. Will there be a flowof water in the situation of a large containerwith water connected through a tube to a muchsmaller container of water, where the fluidheights are equal in both containers (i.e. thepressures are equal)?

Of course, the story is not as simpk as theexample seems to indicate. Not all analogies arebased on structure mapping, and not all analo-gies one can find will be useful in an educationalsetting. Further research will have to unravelother mechanisms for finding analogies anddeciding on their appropriateness (cf. Hof-stadter, 1995).

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Authoring and Model ConstructionSupport

Authoring for tutoring purposes, and modelconstruction in general, is an area of researchthat is largely ignored by the qualitative reason-ing community (cf. Schut & Bredeweg, 1996).As a result there is hardly any "easy-to-use"software available to support authors during theprocess of model construction. Two areas ofresearch can be pointed out. One concerns thedevelopment of interfaces that support the taskof constructing qualitative models by an author(and the learning environment that should ac-company this). This line of research is closelyrelated to studies in human computer interac-tion (cf. Preece et al., 1994). The second areaconcerns the construction of tools that auto-mate certain subtasks of the overall authoringtask. Consider for example tools that help theauthor to diagnose and repair a buggy model.Also machine learning techniques can be usedfor this purpose (cf. Bratko et al., 1992; Mozeticet al., 1990).

Improving Qualitative Simulators

Many researchers in the qualitative reasoningcommunity are concerned with improving thereasoning capabilities of the qualitative simula-tors. This is typically what the majority of thepapers presented at the annual qualitative rea-soning workshop deal with (cf. Iwasaki & Far-quhar, 1996; Bredeweg, 1995). An interestingtopic that gets much attention is the integrationof qualitative and quantitative simulators (cf.Forbus & Whalley, this issue). Lately, within thecommunity an awareness has emerged concern-ing the importance of task-level reasoning andother more goal directed and applied researchquestions. The community is more aware of thefact that the anticipated use of the qualitativetechniques to a large extent determines thespecific improvements that are required. Someextensions specific for tutoring situations havebeen described (see for example: Bredeweg etal, 1995; Falkenhainer & Forbus, 1991; Weld,

1988). There is however still a large area ofresearch to be covered.

How to Teach?

In this introduction to using qualitative tech-niques as the basis for intelligent simulationenvironments we have not made commitmentsto a specific style of teaching. Using a qualitativemodel does in itself not require a specific choiceon this matter. On the one hand it is possible toconstruct an interactive environment which al-lows learners to freely explore the subject mat-ter. On the other hand, more restrictedapproaches, such as guided discovery, or fullytutoring are also possible. Also possible areco-operative and distributed forms of learningand alternative styles of teaching, such as hav-ing learners design certain behavioral artifactsor diagnose errors. It would in fact be veryinteresting to have more research focusing onquestions related to how the qualitative ontol-ogy can be used to support these different stylesof learning and teaching.

CONTRIBUTIONS IN THE TWOISSUES

This issue contains eight contributions, di-vided over two separate volumes. All contribu-tions deal with some of the research topicsdescribed in the previous section. We willshortly introduce them.

Issue number 1. Forbus & Whalley de-scribe CyclePad, a learning environment foranalyzing and designing thermodynamic cycles.CyclePad is focused on quantitative analysis ofthermodynamic cycles, but qualitative reason-ing is used to rule out physically impossibledesigns. It is a good example of a working andefficient system that combines quantitative andqualitative modeling for teaching by simulation.

Frederiksen & White argue that causal, typi-cally qualitative models are of particular impor-tance for obtaining transferable expertise.These models are general enough to be applica-ble across certain domains, and yet specificenough to be powerful and allow for successful

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and efficient reasoning. Frederiksen & Whitedemonstrate the use of such causal models inILEs for electronic troubleshooting, and endwith some instructional implications for thedesign of computer based learning environ-ments.

Hartley describes how learners acquireknowledge in certain domains of physics usingcomputer-based tools. In particular, how learn-ers can be guided in changing their mis- orpre-conceptions about some phenomena, by hav-ing them construct qualitative explanatory mod-els. An experimental study shows that learnersdid change their ideas when the interaction wasfocused on causal reasoning.

Koning & Bredeweg go on to examinewhether qualitative models provide the rightvocabulary and reasoning for a dialogue be-tween teachers and learners. In other words, arequalitative models good candidates for norma-tive, prescriptive models to be used for teach-ing? It turns out that their model forms a goodbasis to start from, but needs to be extended toallow for task level reasoning which is requiredfor tutoring purposes.

Issue number 2. Michau et al present aninteresting use of QR techniques, which isslightly different from the typical "reasoningfrom structure" view held usually. It deals withderiving qualitative features from graphs show-ing quantitative behavior simulation of a sys-tem. It is essential for control engineering tounderstand such graphs in terms of criticalqualitative features. These curve classificationsare than used in teaching qualitative estima-tions of process performance. Their AUTO-DI-DACT learning environment contains a module(ANAIS) that is able to do qualitative curveinterpretation and can show the result to thelearner, or guide the learner through the inter-pretation process.

Ploetzner & Spada hold the position thatboth qualitative and quantitative models arenecessary for successful problem solving, atleast in physics. They suggest the use of quali-tative problem representations to facilitate theconstruction of quantitative problem repre-

sentations in two ways. First, they can enablethe derivation of additional quantitative infor-mation, and secondly, they can provide con-straints to be met by quantitativerepresentations. Their program SEPIA demon-strates this by solving quantitative problems inthe domain of classical mechanics successfullyand more efficiently by first forming a qualita-tive representation of them. The cognitive simu-lation model SEPIA also suggests how andwhere qualitative misconceptions effect prob-lem solving.

Sime describes her work on MS-PRODS, alearner-centered learning environment to pro-mote better understanding of a process rig.Emphasis is on the use of different domainmodels, both quantitative and qualitative toachieve that understanding. She introducesseven dimensions to classify the different do-main models, and a mechanism to progressthrough the models, based on these dimensions.The system could use several strategies formodel progression. Sime's interest is mainly inthe Cognitive Flexibility Theory (CFT) (Spiro &Jehng, 1990) to guide the sequencing. Contraryto other work, e.g. QUEST (White & Frederik-sen, 1990), CFT suggests the alternating use ofdifferent models to foster better understandingof the domain, instead of moving from simple tomore complex models.

Vadillo et al. concentrate on the potential useof qualitative models for generating explana-tions to help users or learners to learn a domain.They present an extension of the INTZA system,a tutoring environment for industrial trainingsituations. In order to provide good behavioralexplanations for simulations in INTZA, theyextend domain models with a qualitative, causalviewpoint. The causal model is obtained byapplying causal ordering (Iwasaki & Simon,1986) to the set of differential equations thatdescribes the system. When the user asks forhelp, or when an error of the user in performinga task with the simulation has been detected,an explanation involving a behavioral descrip-tion of the system is often required. The causalmodel is used to generate the content of thatbehavioral description, and domain inde-

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pendent explanation strategies are used to pre-sent that information to the user in a way similarto that used in Eurohelp (Winkels, 1992).

CONCLUDING REMARKS

We have argued that it is useful for people tolearn to understand and handle systems in thephysical world through interacting with com-puter based simulations. Traditionally, thesesimulations are based on mathematical models,that are very efficient, but have several short-comings when it comes to explaining them torelative novices. This formed one of the inspira-tions for the research in qualitative reasoning.Qualitative domain models have a number offeatures that make them very interesting for usein Interactive Learning Environments (ILEs).They provide us with a conceptual frameworkto talk and reason about the physical world. Themodels are explicit and articulated repre-sentations of systems and their behavior, andcan therefore be used for causal explanations.We have addressed several research topics re-lated to interactive learning environments, andtried to show that qualitative models have greatpotential, notably in the areas of selecting andsequencing subject matter, cognitive diagnosis,and explaining domain models and their behav-ior to learners. We have outlined some ideas ofhow these tasks could be aided when the inter-active simulation is based on a qualitativemodel, and suggested research questions to beaddressed in the future. Furthermore, we havementioned other interesting areas of researchrelated to the use of qualitative models in ILE.The contributions in this special issue will ex-plore some of the issues introduced in moredepth.

Acknowledgment: We would like to thank JoostBreuker, Ken Forbus, and Barbara White for helpingus in reviewing the submissions to this special issue.We would also like to thank Kees de Koning andPaolo Salles for proofreading this introduction; asalways, all remaining mistakes are ours.

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Documents

Qualitative Models in Interactive Learning Environments: An Introduction