System Intelligence in Constructivist...

International Journal of Artificial Intelligence in Education (2000), 11, 344-376

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System Intelligence in Constructivist Learning

Fabio N. Akhras∗ and John A. Self Computer Based Learning Unit, University of Leeds,Leeds, LS2 9JT, EnglandE-mail: [email protected], [email protected]

Abstract. The aim of this paper is to present a perspective on intelligent systems to supportlearning that is in line with constructivist views of learning. In order to develop such aperspective we have defined formal mechanisms to support knowledge representation,reasoning, and decision making in intelligent systems, that are attuned to the values ofconstructivist views of learning. These point to the importance of the context of learning, stressthat learning involves active interaction, and emphasise the process rather than the product oflearning. The theoretical models that constitute our approach enable intelligent learningenvironments to evaluate learning according to four properties of constructivist learningprocesses: cumulativeness, constructiveness, self-regulatedness, and reflectiveness, and to makedecisions about the learning opportunities to be provided to the learners, taking intoconsideration the affordances of learning situations regarding these properties. The approach hasbeen implemented in INCENSE, which is an intelligent learning environment in the domain ofsoftware engineering.

INTRODUCTION

Constructivist theories of learning emphasise an active and autonomous role for the learners toconstruct their own understanding through interacting in an environment in which theknowledge of the domain is not explicitly separated from the context in which it applies. Thefocus is on the process through which the learners experience the environment and interprettheir experiences rather than on the acquisition of a previously defined target domainknowledge.

These emphases of constructivism point to a general shift in focus from teaching tolearning and bring to the fore a set of issues that differ in fundamental ways from the issues thathave been addressed in the design of intelligent systems to support learning.

Intelligent systems to support learning have emphasised the use of artificial intelligence ineducation with three main purposes: representation of the knowledge to be learned, inference ofthe learner’s state of knowledge, and planning of instructional steps to be followed by thelearner. The focus of these systems on the explicit definition of a model of the domainknowledge to be acquired by the learner, and on modelling the learner’s knowledge state interms of the learner’s correct knowledge or misconceptions, which are used as a basis toevaluate learning and guide instructional interventions, seemed difficult to reconcile withconstructivist views of learning, and have led researchers engaged in the development ofcomputational support for constructivist learning to move away from the idea of usingintelligent systems to provide this support (Derry and Lajoie, 1993; De Corte, 1995). Thegeneral view, as stressed by Kommers, Lenting and van der Veer (1996), is that constructivismindicates "a trend towards more autonomy for the learner, instead of an ever increasingcybernetic sophistication of so-called ’system intelligence’ in tutoring programs" (p. 408).

However, it may be that it is not the idea of a "system intelligence" that is antithetical toconstructivist forms of learning but the particular kind of system intelligence that has so far beendesigned in intelligent systems to support learning.

∗ Currently at the Department of Computer Engineering, Polytechnic School, University of SãoPaulo, CP 61548, 05425-970, São Paulo, SP, Brazil (e-mail: [email protected]).


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For instance, it is clear that the focus of intelligent systems to support learning in terms ofknowledge representation, reasoning, and decision making, as discussed above, reflects thevalues of the particular view of learning that is emphasised in these systems in regard to thenature of knowledge, the way learners learn, and the way learning can be promoted. Therefore,alternative views of learning, such as constructivism, may similarly benefit from a systemintelligence in which the mechanisms of knowledge representation, reasoning, and decisionmaking, originate from a formal interpretation of the values of that view of learning. As aconsequence, the resulting intelligent behaviour of the system will (by definition) not be incontradiction with the values emphasised by that view of learning, as it appears to be todaywhere there is a tension between the underlying values emphasised by intelligent systems tosupport learning and the values emphasised by constructivist views of learning.

Therefore, what is needed is the development of a different kind of system intelligence thatis based on methods of knowledge representation, reasoning, and decision making, betterattuned to the values of constructivist views of learning. For example, given the shift in focusoffered by constructivist views, from the product to the process of learning, the issue ofevaluating learning which is central to the individual adaptation of the learning experiences tothe learner’s perceived needs, shifts away from a model of "what" is learned into a model of"how" knowledge is constructed.

In this paper we discuss some of the main issues that concern constructivist theories oflearning, and provide a theoretical, computational basis for addressing these issues in the designof a system intelligence to support constructivist forms of learning. The paper is organised asfollows. After the discussion of constructivist issues in the next section, the following sectionoutlines the implications of these issues to the design of a system intelligence. The followingfour sections present our main theoretical developments related to the issues of context,interaction, process and affordances. Then, the next section describes INCENSE, an intelligentsystem to support learning of software engineering concepts. This system, implemented inProlog, reasons about context, interaction, process and affordances using the formalismspresented in the theoretical sections. For example, as it interacts with the student it builds up apicture of the affordances of potential situations to the student connected with that particularinteraction. The final section presents the conclusions.

A CONSTRUCTIVIST VIEW OF LEARNING

A view that is emerging from constructivist theories of learning emphasises four aspects asholistically coexisting in any learning process:

1. Context - an essential part of what is learned is the situation in which learning takesplace, which refers to the physical as well as to the social environment in which thelearner is engaged in activity, and might include physical entities, tools, and otherpeople.

2. Activity - all knowledge is constructed by the learners through actively interacting insituations in which they experience a domain and interpret their own experiences.

3. Cognitive structures - previously constructed knowledge influences the way learnersinterpret new experience and affects their thinking and acting.

4. Time-extension - the construction of knowledge occurs over time from the learners’attempts to connect their previously developed experiences to the new ones.

To take these four aspects into consideration in a holistic way means to assume aninseparability between context, physical and psychological phenomena, and the flow ofexperience, in order to understand learning. It implies a focus on the relationships that developbetween these four aspects in a process of learning, rather than on their independentcharacteristics.

Support for this view is found in recent research on education that has pointed to the needfor developing theoretical frameworks in which psychological and environmental aspects are

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integrated. For example, Vosniadou (1996) suggests that research is needed to improve ourunderstanding of how cognitive processes and structures interact with environmental variables.According to her:

"cognitive psychology provided rich descriptions of what is learned but failed toprovide fruitful hypotheses about how learning happens and more specifically aboutthe environmental variables that influence the knowledge acquisition process" (p. 104).

This tendency towards the study of psychological and environmental aspects of phenomenain an integrated way is also in line with what has been proposed as a transactional perspectivefor research and theory in psychology (Altman and Rogoff, 1987). According to thisperspective, however, the focus is not only on the relations between individuals and theirenvironments, but also on the temporal qualities of these relations considered as inherent aspectsof phenomena, and embodying the flow and dynamics of the individual’s relations to social andphysical settings.

The Focus on Interaction

The focus on the relations between individuals and their environments aims to stress that,according to constructivism, learning is essentially interactive. Knowledge (or knowing) doesnot arise solely from the entities of the environment nor from the learner but from theinteractions between them. A fundamental consequence of this is that individual cognitions canonly be explained in terms of their contributions to interaction (Greeno, 1997).

In addition, the entities of the situation in which the learner is interacting, i.e., the meaningsof these entities for the learner, can also only be explained in terms of their contributions tointeraction. In fact, when learners are interacting with these entities they are not interacting withentities "as they really are", but rather dealing with their previously constructed perceptual andconceptual structures (von Glasersfeld, 1996). This means that the context of a learner’sexperience is a flexible notion whose meaning is subject to the learner’s interpretation.

Therefore, to understand the way in which interaction influences learning we need tounderstand the ways in which environmental properties (or their interpretations) and propertiesof the individual cognitive structures contribute to interaction.

To characterise these contributions Gibson (1977) proposed the notion of affordances,which refer to things in the environment that can contribute to interaction taken with referenceto an individual. One of Gibson’s examples is the postbox that affords letter-mailing to a letter-writing human in a community with a postal system. In addition, Greeno, Moore and Smith(1993) propose that an ability for a particular kind of interactive activity is what enables anindividual to engage in interactions of particular kinds in a situation. According to this view,affordances and abilities to interact are relative to each other, i.e., a situation can afford aninteractive activity for an individual who has appropriate abilities, and an individual can have anability for an interactive activity in a situation that has appropriate affordances. Neither anaffordance nor an ability is specifiable without considering the other (Greeno, 1994).

This illustration, given by the notions of affordance and ability, of the way in whichinteraction can be holistically shaped by aspects such as: the context in which interaction takesplace, the activity developed by the learner, and the cognitive structures of the learnerinteracting in the context; indicates the need to better understand the roles that these threeaspects of interaction play in learning. It also indicates that the way these three aspects areintertwined might give rise to very complex issues. For example, Saada-Robert and Brun (1996)have pointed to studies that show that even acquired knowledge is not simply applied to asituation but reconstructed according to the structure of the situation. Or, according to Brown,Collins and Duguid (1989), a constructed concept "will continually evolve with each newoccasion of use, because new situations, negotiations, and activities inevitably recast it in new,more densely textured form" (p. 33).


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The Role of Context

Concerned with the role of the context in learning interactions, researchers have investigated thedifferences between the kinds of learning activity that take place in school and the ones that takeplace in everyday real life and work situations (Resnick, 1987; Brown, Collins and Duguid1989), and have suggested that in order that students become able to think with and about theentities of a domain, rather than just learning what these entities are, students need more thanabstractions and self-contained examples. They need to learn how these entities are generatedand how they work in authentic activities (Greeno, 1989; Brown et al. 1989).

According to Bednar, Cunningham and Perry (1992), one of the practical consequences ofthese ideas to the design of learning situations is to focus on portraying tasks that take intoconsideration what real people typically do in real life contexts where knowledge domains arenot readily separated and information from many sources as well as varied perspectives arenecessary.

The Role of Activity

Concerning the role of activity, a basic premise of constructivism is that all knowledge issubordinated to action. According to Piaget and Garcia (1991), there are two aspects thatcharacterise the meanings of objects. First, it is the action of utilising objects, or "what can bedone" with the objects either physically, such as moving or breaking them into pieces, ormentally, such as classifying or relating them. Second, it is the action of constructing objects, or"what the objects are made of". As for the meanings of actions themselves, they arecharacterised by "what the actions lead to" in the transformations they produce on objects orsituations.

It follows that the meanings of objects are then characterised by the particular activities inwhich these objects are utilised or constructed, and by the particular situations in which theseactivities take place.

The Role of Cognitive Structures

Concerning the role of cognitive structures in learning interactions, a fundamental implication ofa view of learning that emphasises the active participation of the learners in constructing theirown knowledge from the activities that they develop in situations is that, in this process,everything is subject to the learners’ interpretation. Situations and activities do not have anobjective reality but rather reflect what the learners are "able to fit" into the cognitive structuresthat they already have, which correspond to their prior knowledge.

A key issue in this process is what is meant by "able to fit", which in its positive sense isrelated to the issue of transfer - when knowledge learned in one situation is used later in anothersituation; while in its negative sense has to do with the problem of inert knowledge - failure touse in one situation relevant knowledge learned before. In general, according to Greeno, Mooreand Smith (1993) the issue involves an understanding of "how learning to participate in anactivity in one situation can influence (positively or negatively) one’s ability to participate inanother activity in a different situation" (p. 100).

The Focus on Process

The focus on interaction has implied that we should take into consideration in the analysis oflearning phenomena the properties of the interactions that develop from the learners’ activities inthe physical and social contexts of their environments, rather than isolated aspects of learners’cognitive structures, learners’ activities, or contexts in which the interactions take place. Itsuggests that learning can be better understood from the circumstances provided by therelationships between the learner’s activity, the context in which the activity develops, and thecognitive structures that the learner brings to the activity.

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In addition, the focus on the temporal qualities of aspects of interaction implies that weshould take into consideration the properties of the relations that develop over time betweenaspects of single interactions in a process of learning. It suggests that an interaction, andconsequently, the learning that derives from it, can be better understood from the circumstancesprovided by the flow of experience that connects that interaction to other interactions located indifferent times.

Therefore, a fundamental issue for research is to understand the meaningful ways in whichaspects of an interactive learning experience in one situation can connect to aspects of aninteractive learning experience in another situation, in a course of interaction between learnerand environment, which will characterise ways of developing process-related properties ofconstructivist learning, such as the properties of being cumulative, constructive, self-regulated,and reflective, that have been described by Shuell (1992) and Simons (1993), among others.These properties will be considered in detail later.

Pedagogical Situations

According to the constructivist view of learning presented in the previous sections, learning mayresult from time-extended processes of interacting in situations. However, not all kinds ofinteraction in situations lead to the same sort of learning and some interactions may not lead toany learning at all. Indeed, the discussion about the roles of context, activity and cognitivestructures, indicates that different situations for different learners, or for the same learner atdifferent times, may lead to different kinds of learning. Similarly, the process that emerges fromthe way successive interactions in situations are chained over time, may result in different flowsof learning experience for different learners.

Based on the notion of affordance, conceived by Gibson (1977), we can say that the utilityof a situation for a learner at a certain time is determined by the affordances of that situationwith respect to features of single interactions (involving relations between context, activity andcognitive structures) and with respect to features of time-extended processes of interaction(involving relations between single interactions). As Resnick (1996) points out, "learning anddevelopment occur when individuals prepared for certain concepts encounter environments withthe kinds of affordances they need to elaborate these prepared structures" (p. 39).

Therefore, a pedagogical situation, i.e., a situation that can provide learning opportunitiesfor a particular learner at a particular time, shall afford interaction in contexts that embedopportunities for activities, for learners capable of recognising and acting in the situation inways that can develop further their cognitive structures. As for time-extended processes, apedagogical situation shall afford certain interactive experiences - involving particular aspectsof context, activity, and learner’s cognitive structures - that allow the development of relationsover time with aspects of interactive experiences developed by the learner in past situations. Inthis way, the situation will afford the development of courses of interaction exhibiting certainproperties that might denote, for example, learning processes that have been cumulative,constructive, self-regulated or reflective, for a learner.

IMPLICATIONS FOR A SYSTEM INTELLIGENCE

As we have argued, to be consistent with constructivist views of learning a system intelligenceshould be based on knowledge representation, reasoning, and decision making mechanisms thataddress the issues that are relevant to constructivist learning, such as the issues discussed in theprevious section.

These issues indicate that in order to understand learning it is necessary to consider thecontexts in which learning takes place, the interactions that happen in these contexts, and theway these interactions are chained over time. Furthermore, in order to facilitate learning it isnecessary to consider the affordances of learning situations regarding all these aspects.Concerning the system intelligence, this requires the development of explicit theories that makeit possible to formalise the relevant aspects of contexts, interactions, time-extended processes


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of interaction, and affordances of learning situations, in order to allow reasoning and decisionmaking about these aspects.

A context theory will offer means of formalising the content and dynamics of learningsituations and the basic aspects of the interactions that develop in these situations, such as theoccurrence of learning events or the changes in the content of learning situations caused bylearning events.

While a context theory allows a system to perceive basic aspects of interaction insituations, it is an interaction theory that helps in interpreting these interactions. Given a formalaccount of learning situations and of how they change during learning interactions, the role ofan interaction theory is to formalise the various ways in which the three aspects of interaction –the situation in which the interaction occurs, the cognitive structures of the learner involved inthe interaction, and the nature of the activity that is developed by the learner in the situation –combine to give meaning to learning interactions.

The interpretation of single interactions involving context, activity, and cognitive states is abasic step in order to understand time-extended processes of interaction. As a time-extendedprocess, learning depends on the relations that develop over time between aspects of singleinteractions in situations. Therefore, the role of a theory of time-extended processes ofinteraction is to formalise the various ways in which interactions relate to one another over timein a course of interaction, to give an account of how process-related qualities of learningprocesses, such as cumulativeness, constructiveness, self-regulatedness, and reflectiveness,develop in a sequence of interactions with situations.

In designing a system intelligence that is attuned to constructivist values, the role oftheories of context, interaction, and time-extended process of interaction is to support reasoningabout the process of learning in the broad sense that includes the context of learning interactionsand the temporal qualities of these interactions, in order to evaluate learning. On the other hand,given an evaluation of learning in these terms, in order to change the environment to facilitatelearning, in ways that conform with constructivist views, we need a theory of affordances,which will allow a system to make decisions about the learning opportunities to be provided to alearner whose time-extended process of interaction with the situations of the environment is in acertain state.

Therefore, while the state of a learning process is given in precise terms by the theories ofcontext, interaction, and time-extended process of interaction, the utility of a situation for alearner whose learning process is in a certain state, at a certain time, is given by a theory ofaffordances.

In the next sections we describe our approach to the development of these theoriesillustrating with examples from a simple application in the domain of salad design. Later on, weshow how these theories are used to support a system intelligence in a more extendedimplementation of an intelligent learning environment for the domain of software engineering.

FORMALISING THE CONTEXT OF LEARNING

The issue of formalising context is becoming central to research in artificial intelligence andrelated areas (Akman and Surav, 1996). Among the approaches that have been developed,situation theory (Barwise and Perry, 1983; Devlin, 1991) was particularly influential in thedevelopment of our approach to formalising the context of learning interactions, althoughsituation calculus (McCarthy and Hayes, 1969), histories (Hayes, 1985) and other related work(Davis, 1990; Reiter, 1991), have also been considered. Below we briefly point to some of themain issues that were relevant to the development of our approach.

The basic idea of situation theory is that all sorts of information about the world areorganised in terms of situations. According to the theory, agents usually find themselves in, orrefer to, situations as structured parts of the world that constitute the context for their behaviouror communication. The main elements of situation theory's ontology are: situations, whichrepresent structured parts of the world; and infons, which represent items of information aboutthe world. Situations are defined intentionally and are related to the infons that hold in the

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situation by means of the support relation (situation supports infon). Infons are represented byordered sets denoted by <<R, a1, ..., an, i>>, where R is a n-place relation; a1, ..., an are thearguments of R; and i is the polarity, which can assume the values 1 or 0, to indicate whetherthe relation does or does not hold. Some of the entities that can be placed as arguments of therelation are: individuals, relations, spatial locations, temporal locations, and situations.

A relevant issue that has not been particularly explored in the formulation of situationtheory is the development of explicit mechanisms to represent actions and the changes insituations that may be caused by the occurrence of actions. There is, however, a proposal of anapproach in which actions are represented by pairs of sets of infons, in which the first set ofinfons corresponds to the action precondition, while the second corresponds to the actionpostcondition (Ohsawa and Nakashima, 1991).

A problem associated with reasoning about changes in situations caused by actions is theframe problem (McCarthy and Hayes, 1969), which derives from the fact that although one canapply a temporal representation like the situation calculus to determine what changes followfrom the events that happen in the world, one cannot determine the changes that do not follow.As a way of addressing the frame problem in a first-order logic, Davis (1990) has introducedsome extensions to situation calculus involving the definition of a set of axioms to assert waysin which particular types of events do not change particular types of states. Generalising thiskind of approach, Reiter (1991) has defined a logical theory to specify the effects of actions onstates of the world, which includes two kinds of axioms: axioms to specify the conditions for theoccurrence of an action (action precondition axioms), and axioms to specify the ways in whichactions affect the states of the world (successor state axioms). These axioms, along with a set ofgeneral axioms, allow inference of the facts that hold in a new situation after the occurrence ofan action.

Taking into consideration the issues involved in formalising context, such as the onesdiscussed above, we have developed an approach for modelling contexts of learninginteractions. The formalism is a many-sorted first-order predicate theory for modellingstructural information about learning situations as well as temporal information associated withthe way situations develop. The entities included in the formalism address the following aspectsof contexts of learning interaction: situations, content of situations, dynamics of situations, andsituation development.

In the next sections we describe this formalism, illustrating with examples taken from aninitial application of our approach, which was an intelligent learning environment for thedomain of salad design, called SAMPLE (SAlad Making Process-Sensitive LearningEnvironment), whose goal is to help students learn concepts of salad making. Before we embarkon the discussion of the formalism, however, we briefly introduce the characteristics of thecontexts for learning interactions provided by SAMPLE.

In SAMPLE, the world is populated with tools and salad ingredients. There are sevengroups of ingredients, such as, leafy vegetables (e.g. lettuce), or herbs (e.g. parsley). Each ofthese groups is characterised by a particular set of states through which the ingredient may passin its preparation before it is added to the salad or dressing. For example, some of the states andtransitions of state that characterise ingredients of the leafless vegetables group are:

unwashed → washedwhole → chopped

In each learning situation provided by SAMPLE there is a set of ingredients available. Thetools available for the learner allow basic actions, such as, wash-ingredient, chop-ingredient,add-ingredient-to-salad, or taste-salad. Through these actions the learner can change the statesof ingredients, add ingredients to the salad or dressing, dress the salad, or taste the wholepreparation. The tasting mechanism gives to the learner feedback from her or his preparation,determining its taste on the basis of the tastes of each individual ingredient that is part of thesalad or dressing.


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Situation Types

The notion of context appears in our theory in two ways. First, as contexts for the developmentof learning interactions, denoted by situation types. Second, as contexts of developed learninginteractions, denoted by situations (see later). For example, the description of a set of things thata child can do to play with a doll in the circumstances of a living room in which there is a doll,characterises a situation type, as it is more concerned with possibilities for the development ofinteraction, and is not located in any particular time. On the other hand, the description of thecircumstances of a living room at midnight when Melissa was kissing her doll characterises aparticular situation of the above type.

Therefore, situation types are intended to denote open worlds for learning interaction,comprising many kinds of entities and holding various possibilities for action. The internalstructure of a situation type is defined in terms of two kinds of entities: entities that denote theway things stand in a learning situation - the content of the situation type; and entities thatdenote the way learners can interact with the other entities of a learning situation - the dynamicsof the situation type.

To specify that a certain entity x (of content or dynamics) is part of the definition of asituation type s, we use the notation define(x, s).

Content of Situation Types

To represent the content of situation types we define objects, relations between objects,properties of objects, states of objects and transitions of states, and relations of generalisationand aggregation.

Objects are the units of content in situation types and represent the physical or conceptualentities that are part of a learning situation. Objects are represented by n-place predicates, suchas in the two examples below taken from SAMPLE.

saladingredient(tomato)

To represent physical and conceptual aspects of complex phenomena in learning situationsthe units provided by objects have to be combined in many different ways, according to theroles that objects perform in relation to each other. This is represented in terms of relationsbetween objects, properties of objects, and states of objects. For example:

relation(describe(salad, recipe))property(ingredient(lettuce), taste(light))state(ingredient(greens), washed)

Besides representing actual states, we might need to represent the states in which objectsmight be in, and the transitions of states that objects might go through, i.e., their state graphs,which we represent by means of types of states and types of state transitions. For example:

state-type(ingredient(tomato), whole)tran-type(ingredient(tomato), whole, sliced)

In modelling the content of learning situations, two hierarchical relations that are usefulare: generalisations, that characterise is-a relations between sub-class entities and super-classentities, and aggregations, that characterise part-of relations between component entities andaggregate entities. For example:

kind(leafy-vegetable, ingredient(watercress))part(salad, ingredient(cucumber))

Dynamics of Situation Types

To represent the dynamics of situation types we define events, preconditions and effects ofevents, and contexts of events.

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Apart from physical and conceptual entities, learning situations have at least one livingentity, the learner, and may have several others. These living entities interact with the physicaland conceptual entities, and with each other, by means of events. Each of these living entitiesmay have roles attributed to it in the learning situation, and there are a set of events thatcharacterise the actions involved in performing these roles. To define the potential events in asituation type we use the notation event(a, e), where a is an agent and e is an event type. Forexample:

event(learner, wash-ingredient)event(learner, add-ingredient-to-salad)

The set of event types that are used to describe the role of an agent in a situation typerepresents the formal alphabet of that agent. In the above example, the role defined for thelearner in the situation type includes doing things like washing ingredients, and adding them to asalad.

The conditions of activation of an event and the changes in a learning situation caused bythe occurrence of an event are stated in the preconditions and effects defined for the event type,which are denoted by pre(e, x, pa), and effect(e, x, pa), where e is an event type, x is anycontent entity and pa is the participation of x in the precondition or effect, which can assume thevalues 1 or 0 to indicate whether x must hold or not to satisfy the precondition, or whether x willhold or not in the effect. For instance:

pre(e, x, 1) means that the precondition for e is xpre(e, x, 0) means that the precondition for e is not(x)

Preconditions and effects are particularly important to capture the circumstances involvedin a learning event which are essential for the definition of our formal account of interaction.

Events are sometimes associated in particular ways to other content of a situation type,which may refer to the background for the event, the sociocultural aspects related to the event,the authentic setting of the event, and so on. To capture this sort of relation we introduce thenotion of context of an event, which we denote by context(e, x), where e is an event type and xis a content entity that characterises a context for events of type e. As an example, suppose thatamong the entities that are part of the content of learning situations in SAMPLE, there is thisbook: book("Well balanced salads"), which may characterise a context for events of type add-ingredient-to-salad. This is represented as:

context(add-ingredient-to-salad, book("Well balanced salads"))

Situation Development

Interactions develop in a situation type by the occurrence of events and give rise to situations.Although situation types are independent of time, a situation is temporally located and denotesthe state of a situation type at a certain time. Situations are, thus, defined by the pair:

(situation type, time)

Events occur in situation types at certain times, which is the same as saying that eventsoccur in situations. To denote the occurrence of events in situations we introduce the notationoccurs(e, a, s, t), where e is an event type, a is an agent, and (s, t) is the situation in which theevent occurs. For example:

occurs(wash-ingredient, learner, salad-lab-a, 6)

To denote the content entities that hold in situations we introduce the notation in(x, s, t),where x is any content entity, and (s, t) is the situation in which the content entity is present. Forexample, the following content entities may hold in the situations before and after theoccurrence of the event above, if the ingredient washed is a lettuce:

in(state(ingredient(lettuce), unwashed), salad-lab-a, 6)in(state(ingredient(lettuce), washed), salad-lab-a, 7)


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In order to address the problem of tracking the changes that occur in situations throughinteractions, which is an instance of the frame problem, we have defined three kinds of axioms.A set of axioms of situation development, called effect axioms, specify the content entities thatmust hold at the end of an event that occurs if the content entities that are preconditions for theevent hold at the beginning of that event. Table 1 presents the first two of these axioms. Othertwo axioms (SD3 and SD4) are variations of SD-1 and SD-2 in which the value of theparticipation of content entities in the definitions of effects is 0.

Table 1. Axioms of situation development_____________________________________________________________________Effect axioms

SD-1: occurs(e, a, s, t) ∧ define(pre(e, x, 1), s) ∧ define(effect(e, y, 1), s) ∧ in(x, s, t) ⇒ in(y, s, t+1)

SD-2: occurs(e, a, s, t) ∧ define(pre(e, x, 0), s) ∧ define(effect(e, y, 1), s) ∧ ¬ in(x, s, t) ⇒ in(y, s, t+1)

_____________________________________________________________________

The effect axioms allow us to infer the changes in content entities caused by the occurrenceof events in situations. However, they do not solve the general problem of determining thecontent entities that hold in a certain situation. This is determined in our theory by taking intoconsideration the histories of participation of content entities in the preconditions or effects ofevents that have occurred, as described below.

As well as content entities that can hold in situations, actual preconditions and effects ofevents can also hold in situations. This is represented using the notation in(y, s, t), as before,with y taking the form of pre(e, x, pa) or effect(e, x, pa) to denote the actual preconditions andeffects that hold at the beginning and at the end of an event e, with x being an instantiatedcontent entity and pa assuming 0 or 1. For example, some of the actual preconditions and effectsthat hold when the event wash-ingredient occurs, are:

in(pre(wash-ingredient, state(ingredient(lettuce), unwashed), 1), salad-lab-a, 6)in(effect(wash-ingredient, state(ingredient(lettuce), washed), 1), salad-lab-a, 7)

These actual preconditions and effects of events characterise points in the histories ofparticipation of content entities in the preconditions and effects of events that occur. Thesehistories are used in determining the content entities that hold in situations. In addition, we havedescribed earlier that the initial state of a situation type is given by the content of the situationtype defined using the formula define(x, s). Now, when the interaction in a situation type sbegins, events that occur give rise to histories of participation of content entities inpreconditions and effects of events, which characterise changes in the initial state of s.Therefore, to determine whether certain content entities do or do not hold in a situation we musttake into consideration this initial definition of the situation type as well as the changes ofcontent caused in situations by the occurrence of events, characterised by these histories.

To allow this kind of inference we have formulated three further axioms of situationdevelopment: SD-5 and SD-6, which refer to points of histories of content entities that hold insituations, and SD-7, which allows to infer the content entities that hold in situations. Theseaxioms are shown in Table 2.

As interactions progress over time and situations of a single or various types are developed,sequences of situations are formed, giving rise to the development of courses of interaction. Acourse of interaction is defined in our theory by a sequence of situations and is denoted bycourse(s1, t1, ..., sn, tn), where (s1, t1) and (sn, tn) are any two situations, which can possiblybe of the same type, and for which n>=2 and tn>t1. A particular case of a course of interactionis the course of two situations course(s1, t1, s2, t2), which we will be using in the rest of thispaper.

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Table 2. Further axioms of situation development_____________________________________________________________________History axioms

SD-5: define(pre(e, x, pa), s) ∧ occurs(e, a, s, t) ⇒ in(pre(e, x, pa), s, t)SD-6: define(effect(e, x, pa), s) ∧ occurs(e, a, s, t) ⇒ in(effect(e, x, pa), s, t+1)

State axiom

SD-7: [in(pre(e, x, 1), s, t) ∨ in(effect(e, x, 1), s, t)] ∨ [(∃ t1)[t1<t ∧ in(x, s, t1)] ∧ (∀ t2)[t1<t2<t ∧ ¬ in(effect(e, x, 0), s, t2)] ∨[define(x, s) ∧ (∀ t1)[t1<t ∧ ¬ in(effect(e, x, 0), s, t1)] ⇒ in(x, s, t)

_____________________________________________________________________

Note that according to this definition, courses of interaction are not necessarily contiguous,as there may be other situations located between (s1, t1) and (s2, t2). Therefore, courses ofinteraction can overlap in many ways, and a situation can appear in more than one course ofinteraction. As situations are a way of preserving the context of events that occur, courses ofinteraction are a way of preserving the history of the interaction, which is essential to theanalysis of properties of time-extended processes of interaction.

UNITS OF ANALYSIS OF LEARNING INTERACTIONS

Research on interaction in artificial intelligence is recent and has aimed at the development ofcomputational theories of agents’ involvements in their environments, with two main purposes:to guide the analysis of living agents and the design of artificial ones. The central point of thework on computational theories of interaction and agency, as reported by Agre (1995), is to takean interactional perspective on understanding the behaviour of agents in their environments.Instead of units of analysis based on the agent’s cognitive process, the focus is on units ofanalysis that refer to interactions, whose definition requires research focused on the discovery ofstructures in the world and of properties of interactions. To illustrate, Agre (1995) considers acontroller (the agent) of an oil refinery (the environment), with the general task of the agentbeing the adjustment of certain devices in its environment so that a desired flow of oil issustained within the refinery. Given a proposed design for this controller, how can we knowwhether it will work? The answer, it is argued, cannot rely only on an analysis of the controlleritself, and obviously, nor on an analysis of the plant in isolation. Instead, it is crucial to analysehow the controller will interact with the plant.

Therefore, in order to understand an agent’s interaction with its environment this approachfocuses on reasoning to recognise structures in the relationships among the properties of agents,environments, and forms of interaction between them (which may not have an internal state inthe agent’s mind), rather than on the more classical AI approach of reasoning to recognise plansthat can be attributed to an agent.

Concerning human learners interacting in their learning environments, the interactionalperspective that is necessary to interpret learning phenomena, as we have discussed, requiresthat we take the three aspects that characterise a learning interaction - context, activity, andcognitive structures, and look for regularities in the ways these three aspects relate to each otherin interactions that are developed in learning processes.

In our model of learning situations, we have defined contexts of learning interactions astypes of situations and introduced a set of formal entities to denote the content of these contexts,and the activities that can be developed on them, which characterise the dynamics of thesecontexts. In addition, we have defined a set of formal entities to denote aspects of theinteractions that are developed in these contexts when the potential activities defined in thedynamics of a situation type actually occur. These three sets of formal entities: entities ofcontent, entities of dynamics, and entities of situation development, are the basic elements from


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which a set of types of regularities of interaction in learning situations, which we call patternsof interaction, can be formally defined.

Therefore, the formalism introduced earlier for modelling structural information aboutlearning situations as well as temporal information associated with the way situations develop,is now extended to include patterns of interaction, which are formal entities that model higher-order regularities of interaction in learning situations.

Exploring the connections that are formed as learners interact in situations, among aspectsof interaction such as the context of activity, the nature of activity, and the cognitive states thatlearners bring to activity, we have defined three types of patterns of interaction: patterns thatrelate learner’s actions to the situations in which they happen, patterns that relate learner’scognitive states to the situations in which they hold, and patterns that capture relations betweensituations. In the next sections we discuss these patterns and present some of their formaldefinitions, illustrating with examples taken from SAMPLE.

Patterns of Learner’s Actions in Situations

Situations develop by the occurrence of events which may affect or be affected in various waysby the content of the situation. Therefore, the nature of a learner’s action in a situation is givenby the way it affects or is affected by the content of the situation. The different ways in whichthis happens characterise different patterns of learner’s actions in situations. Following thediscussion about the role of activity in learning, our definitions of these patterns intend tocapture the various ways in which meaning is constructed from acting in situations. Some ofthese definitions, which correspond to learner’s actions of utilising, generating, and accessingentities in situations, are:

Definition (Utilising entities in situations) A learner a utilises an entity x through an event e ina situation (s, t), iff the event e, defined in situation type s as part of the alphabet of the learnera, occurs in (s, t), and x is a precondition of e that holds in (s, t), i. e. the participation of x inthe precondition is 1.

define(event(a, e), s) ∧ occurs(e, a, s, t) ∧ in(pre(e, x, 1), s, t) ⇔ utilises(a, x, e, s, t)

For example, suppose that we have the situation type salad-lab-a in which the followingentities are defined:

define(event(learner, wash-ingredient), salad-lab-a) (1)define(pre(wash-ingredient, ingredient(X), 1), salad-lab-a)define(pre(wash-ingredient, state(ingredient(X), unwashed), 1), salad-lab-a)define(effect(wash-ingredient, state(ingredient(X), washed), 1), salad-lab-a)

And suppose that in situation (salad-lab-a, 8), the learner washes a lettuce, and thefollowing entities hold:

in(ingredient(lettuce), salad-lab-a, 8)in(state(ingredient(lettuce), unwashed), salad-lab-a, 8)occurs(wash-ingredient, learner, salad-lab-a, 8) (2)in(pre(wash-ingredient, ingredient(lettuce), 1), salad-lab-a, 8) (3)in(pre(wash-ingredient, state(ingredient(lettuce), unwashed), 1), salad-lab-a, 8) (4)

Therefore, according to the definition of the pattern utilises and according to theexpressions (1), (2) and (3) above, we say that the learner utilises the ingredient lettuce bywashing it in the situation (salad-lab-a, 8), which is the same as saying that the following patternholds:

utilises(learner, ingredient(lettuce), wash-ingredient, salad-lab-a, 8)

Additionally, note that according to the expression (4) above, the learner also utilises in thesame event the notion of an ingredient lettuce being in a state of unwashed. In SAMPLE, someof the main things that a learner can utilise are: all sorts of ingredients, salad and dressing, the

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notions of ingredients being in some sorts of states, and the notions of some sorts of transitionsof ingredients’ states.

Definition (Generating entities in situations) A learner a generates an entity x through anevent e in a situation (s, t), iff the event e, defined in situation type s as part of the alphabet ofthe learner a, occurs in (s, t), and x is an effect of e that holds in (s, t+1).

define(event(a, e), s) ∧ occurs(e, a, s, t) ∧ in(effect(e, x, 1), s, t+1) ⇔ generates(a, x, e, s, t)

In the situation (salad-lab-a, 8) of the previous example, after the learner has washed theingredient lettuce, the following entities hold in situation (salad-lab-a, 9):

in(effect(wash-ingredient, state(ingredient(lettuce), washed), 1), salad-lab-a, 9) (5)in(state(ingredient(lettuce), washed), salad-lab-a, 9)

Therefore, according to the definition of the pattern generates and according to theexpression (5) above, we say that the learner generates the notion of an ingredient lettuce beingin a state of washed, by washing it in the situation (salad-lab-a, 8), or, more formally:

generates(learner, state(ingredient(lettuce), washed), wash-ingredient, salad-lab-a, 8)

In general, in interaction with SAMPLE a learner can generate: the notions of ingredientsbeing in some sorts of states, the notions of an ingredient being part of a salad or dressing, andthe taste of a salad.

Here we can see how some limitations may be identified in learning environments such asSAMPLE. Ingredients, which are the main building blocks in the salad preparation world for thelearner, can be utilised but cannot be generated. This is because in many learning environments(computational or not) some things happen to be ready for the learner, requiring no construction.This has strong implications for learning environments that intend to achieve a higher level ofconstructiveness, as we will discuss later.

Definition (Accessing entities in situations) A learner a accesses an entity x through an event ein a situation (s, t), iff the learner a utilises the entity x in situation (s, t), and x is a preconditionof e that holds in (s, t), and the learner does not generate any entity in the same event.

utilises(a, x, e, s, t) ∧ in(pre(e, x, 1), s, t) ∧ (∀ y)¬ generates(a, y, e, s, t)⇔ accesses(a, x, e, s, t)

In situations of SAMPLE, the learner can access: information in books or archives, thecontents of the salad or dressing being prepared, and characteristics of ingredients such as theirtastes or their current states.

Patterns of Learner’s Cognitive States in Situations

According to constructivist views of learning, cognitive structures develop from acting insituations. Therefore, some relevant cognitive structures may be developed from actions ofutilising, generating, or accessing entities in situations. These cognitive structures influence inmany ways the learner’s view of the content and dynamics of subsequent situations. Followingthe discussion about the role of cognitive structures in learning, our definitions of these patternsare intended to capture the various ways in which entities of a situation are related to thelearner’s previously formed cognitive structures. Some of these definitions, which correspond tothe learner’s cognitive states in which entities of situations are new or old, are:

Definition (New content entities in situations) A content entity x is new for a learner a in asituation (s, t), iff the entity x holds in situation (s, t), and x has neither been utilised norgenerated by the learner a in any situation previous to (s, t).

in(x, s, t) ∧ (∀ ei, si, ti)[ti<t ∧¬ utilises(a, x, ei, si, ti)] ∧(∀ ej, sj, tj)[tj<t-1 ∧ ¬ generates(a, x, ej, sj, tj)]

⇔ new(a, x, s, t)


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For an example, consider the situation (salad-lab-a, 8) of the previous example, in whichthe following entity holds:

in(state(ingredient(lettuce), unwashed), salad-lab-a, 8)

Assuming that the entity state(ingredient(lettuce), unwashed) has neither been utilised norgenerated by the learner before, then according to the definition of the pattern new for contententities, we say that the notion of an ingredient lettuce being in a state of unwashed is new forthe learner in the situation (salad-lab-a, 8), which means that the following pattern holds:

new(learner, state(ingredient(lettuce), unwashed), salad-lab-a, 8)

Definition (Old content entities in situations) A content entity x is old for a learner a in asituation (s, t), iff the entity x holds in situation (s, t), and x has been utilised or generated by thelearner a in some situation previous to (s, t).

in(x, s, t) ∧ [ (∃ ei, si, ti)[ti<t ∧ utilises(a, x, ei, si, ti)] ∨(∃ ej, sj, tj)[tj<t-1 ∧ generates(a, x, ej, sj, tj)] ]

⇔ old(a, x, s, t)

Note that old is different from not new because in both cases the entity that is new or oldmust be present in the situation, as denoted by the primitive in(x, s, t). This derives from the factthat these patterns refer to cognitive states in relation to situations. Therefore, if an entity is notnew and is not present in a situation it does not characterise the kind of old that we are capturingin these particular patterns, although in the common sense of the word it would be old.

Patterns of Relations Between Situations

A characteristic of the constructivist view of learning that we have discussed is that learningoccurs in situations that correspond to real life contexts and, therefore, requires multiple types ofsituations where varied perspectives are portrayed and learners can explore various aspects of adomain. As learners go from situation to situation, interacting in this kind of environment, theyare likely to connect through experience knowledge of different kinds, and these experiencesand the connections that derive from them will be influenced by the relations that exist betweenentities of situations. The different ways in which entities of one situation may be related toentities of another situation characterise different patterns of relations between situations.

Therefore, our definitions of these patterns are intended to capture the various ways inwhich entities of one situation are related to entities of another situation. The patterns that wehave defined are of two kinds: patterns of relations in which situations share some characteristic,and patterns of relations in which a situation has an additional, but related, characteristic withrespect to another situation. The specific patterns of each of these kinds correspond to thedifferent ways in which situations can share characteristics or have additional characteristicswith respect to other situations. The definition of one of these patterns is shown below (othersimilar definitions are given in Akhras(1997)).

Definition (Sharing content entities) Two situations (s1, t1) and (s2, t2) share a content entityx, iff x holds in situation (s1, t1) and in situation (s2, t2).

in(x, s1, t1) ∧ in(x, s2, t2)⇔ share(s1, t1, s2, t2, x)

UNITS OF ANALYSIS OF TIME-EXTENDED LEARNING PROCESSES

Courses of interaction are formed from sequences of situations that develop by the occurrenceof events when learners are engaged in interaction with the situation types of their learningenvironments. As we have discussed earlier, the focus on the situations that develop whenevents occur, rather than on the events alone, to account for the progression of the interactionbetween learner and environment, is a way of preserving the context in which the events take

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place. The preservation of the context in understanding learning phenomena was a major pointin the development of our formal account of interaction in the previous section, where a set ofpatterns of interaction were formally defined in terms of more basic entities.

Now, a second major point of our theory is the preservation of the history of theinteraction, which encompasses the process and structure by which aspects of interactionsdeveloped in different situations are connected to one another during a course of interaction.The focus on sequences of situations to account for courses of interaction is a way of preservingthe history of the interaction.

Histories of interaction when preserved will embed information about particular ways inwhich courses of interaction develop, according to the particular patterns of interaction that holdin the situations of the course of interaction. These particular ways in which courses ofinteraction develop will characterise regularities of a higher order than the patterns of interactionas they will relate patterns of interaction that hold in different situations.

To model these regularities, our theory (that already encompasses formal entities to denotethe content and dynamics of situation types, aspects of situation development and patterns ofinteraction) is now extended to include properties of courses of interaction, which are formalentities that denote regularities of time-extended learning processes.

In order to model some of the process-related notions that are addressed by constructivistlearning approaches, we have defined four types of properties of courses of interaction:cumulativeness, constructiveness, self-regulatedness, and reflectiveness. These properties aredefined in terms of patterns of interaction and of entities of situation type and of situationdevelopment.

In the next sections we discuss these properties and present their formal definitions(variations of these definitions are given in Akhras (1997)), illustrating with examples takenfrom SAMPLE. Although the approach can be applied to any kind of course of interaction, theproperties that we have defined are based on courses of interaction involving only twosituations.

Property of Cumulativeness

Cognitive conceptions of learning stress that learning is cumulative in nature (Shuell, 1986).Nothing has meaning or is learned in isolation. Instead, prior knowledge, and consequently,previous learning experiences, influence and relate to new learning in many ways. Repetition ofsimilar experiences in different contexts and involving different ways of looking at theexperiences may enable access to prior knowledge and the exploitation of similarities anddifferences between the current and the previous experiences. Ultimately, this leads to acumulative process in which new meanings are added to elements of previous experiences andcurrent experiences are interpreted in the light of previous ones. Although cumulativeness alonemay not be an indicator of learning, it is part of a learning process.

In our theory, cumulativeness refers to the property that a course of interaction exhibitswhen entities experienced by the learner in one situation are in some way revisited in a latersituation of the course of interaction. A particular way in which a course of interaction can becumulative is through a shared entity, which happens when the same entity is experienced in thetwo situations of a course of interaction. Other ways may involve experiencing entities in thetwo situations that are not the same but are in some ways related. Below we present thedefinition of cumulativeness from a shared entity.

Definition (Cumulative with respect to a shared content entity) A course of interactioncourse(s1, t1, s2, t2) is cumulative with respect to a content entity x for a learner a, if situations(s1, t1) and (s2, t2) share the entity x, and the learner a utilises x in (s1, t1) or generates it in(s1, t1-1), and further utilises x in (s2, t2) or generates it in (s2, t2-1).

share(s1, t1, s2, t2, x) ∧[utilises(a, x, e1, s1, t1) ∨ generates(a, x, e1, s1, t1-1)] ∧ [utilises(a, x, e2, s2, t2) ∨ generates(a, x, e2, s2, t2-1)] ∧ t2>t1

⇒ cumulative(course(s1, t1, s2, t2), a, x)


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For example, suppose that the following patterns of interaction hold in the situations below.

share(salad-lab-a, 8, salad-lab-a, 11, ingredient(lettuce))utilises(learner, ingredient(lettuce), wash-ingredient, salad-lab-a, 8)utilises(learner, ingredient(lettuce), add-ingredient-to-salad, salad-lab-a, 11)

Then, according to the definition above, we say that the course of interaction course(salad-lab-a, 8, salad-lab-a, 11) is cumulative for the learner with respect to the ingredient lettuce,which means that the following property holds:

cumulative(course(salad-lab-a, 8, salad-lab-a, 11), learner, ingredient(lettuce))

Property of Constructiveness

In essence, to construct new knowledge involves relating one’s existent knowledge to newexperiences in meaningful ways. In this process, not only is the knowledge associated with thenew experience constructed but also the learner’s existent knowledge is sometimes re-interpreted in the light of the new experience. According to Shuell (1992), learning isconstructive in the sense that the new information that is perceived and interpreted by thelearner in a unique way must be elaborated and related to other information in order that it canbe learned.

Therefore, an essential feature of learning processes is the integration of aspects of newlearning experiences with the learner’s existent knowledge. As the learner interacts in situations,information from several sources, including previous experiences, must be elaborated andcombined in meaningful ways, so that the new information that is generated and interpreted bythe learner can be related to the learner’s existent knowledge, which may also be re-interpretedin the light of the new experience. Ultimately, this leads to a constructive process in which newknowledge is generated and related to elements of previous experiences.

In our theory, constructiveness refers to the property that a course of interaction exhibitswhen entities experienced by the learner in one situation are in some way related to new entitiesthat the learner generates in a later situation of the course of interaction. A particular way inwhich a course of interaction can be constructive is from an event, which involves experiencingan entity that is old for the learner, in one situation of a course of interaction, and furthergenerating a new entity, through an event that utilises the old entity, in another situation of thecourse of interaction, which will then be constructive with respect to the new entity. Thisdefinition is presented below. Other ways may involve generating a new entity that is connectedto the old entity in several other ways.

Definition (Constructive with respect to a content entity from an event) A course of interactioncourse(s1, t1, s2, t2) is constructive with respect to a content entity x for a learner a, if thelearner a utilises an entity xo in (s1, t1) or generates it in (s1, t1-1), and further utilises xo in(s2, t2-1) which is old for the learner in this situation, to generate in the same event an entity xwhich is new for the learner in situation (s2, t2).

[utilises(a, xo, e1, s1, t1) ∨ generates(a, xo, e1, s1, t1-1)] ∧ utilises(a, xo, e, s2, t2-1) ∧ old(a, xo, s2, t2-1) ∧generates(a, x, e, s2, t2-1) ∧ new(a, x, s2, t2) ∧ t2>t1

⇒ constructive(course(s1, t1, s2, t2), a, x)

For example, suppose that the following patterns of interaction hold in the situations below.

utilises(learner, ingredient(lettuce), chop-ingredient, salad-lab-a, 22)utilises(learner, ingredient(lettuce), add-ingredient-to-salad, salad-lab-a, 28)old(learner, ingredient(lettuce), salad-lab-a, 28)generates(learner, part(salad, ingredient(lettuce)), add-ingredient-to-salad, salad-lab-a, 28)new(learner, part(salad, ingredient(lettuce)), salad-lab-a, 29)

Then, according to the definition above, we say that the course of interaction course(salad-lab-a, 22, salad-lab-a, 29) is constructive for the learner with respect to the notion of an

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ingredient lettuce being part of a salad, which is the same as saying that the following propertyholds:

constructive(course(salad-lab-a, 22, salad-lab-a, 29), learner,part(salad, ingredient(lettuce)))

Note that, although learning comes from acting, our definitions of cumulativeness andconstructiveness take not just the patterns utilises or generates (i.e. not just acting), but alsoother patterns of interaction, relating acting to aspects of contexts and cognitive states involvedin action.

Property of Self-Regulatedness

As learners interact in situations they have to make decisions about what actions to take in orderto attain their goals or even to help in defining their goals. This requires an awareness of howthey are progressing in their learning experiences and an ability to regulate their involvement inthese experiences. In a constructivist view of learning, the activities that bring this awarenessand help in regulating the learner’s actions are performed by the learner, and involve learnersregulating their actions based on several kinds of information that they obtain from theirinteractions in situations. Ultimately, this leads to a self-regulated process in which aspects ofthe learning experience are analysed and used to drive the learner’s actions.

In our theory, self-regulatedness refers to the property that a course of interaction exhibitswhen a learner’s action performed in one situation is in some way evaluated by the learner inanother situation of the course of interaction, and this evaluation is taken into consideration toguide the next learner’s actions or change the effects of previous actions. The learner’s actionscorrespond to events that are part of the learner’s alphabet and occur in situations. These eventshave an associated context which represents the information that is relevant to evaluating thecorresponding actions. This information can be defined as part of the situation type and accessedwhen needed or be generated by the learner in a dynamic evaluation. The different ways inwhich this information is produced and used characterise different ways in which a course ofinteraction can be self-regulated for a learner.

Among the many different ways in which a course of interaction can be self-regulated, wehave identified two main classes of self-regulatedness: self-regulatedness from access and self-regulatedness from generation, which involve acting in one situation of a course of interaction,and accessing (or generating) information that helps in evaluating that action, in anothersituation of the course of interaction. The information accessed (or generated) is an evaluationcontext for that action, and the course of interaction will then be self-regulated with respect tothe result of the action from the point of view of the evaluation context accessed (or generated).Below we present a definition of self-regulatedness from access.

Definition (Self-regulated with respect to a content entity, accessing the context before theevent) A course of interaction course(s1, t1, s2, t2) is self-regulated with respect to generating acontent entity x through an event e and accessing a context c before the event, for a learner a, ifthe learner a accesses the entity c that is an evaluation context for the event e, in (s1, t1), andfurther generates the entity x in (s2, t2) through the event e, with t2-t1 being the time gapbetween accessing the evaluation context and performing the related action.

accesses(a, c, e1, s1, t1) ∧ in(context(e, c), s1, t1) ∧generates(a, x, e, s2, t2) ∧ t2>t1 ∧ t2-t1=time gap

⇒ self-regulated(course(s1, t1, s2, t2), a, x, e, c)

For an example, suppose that the following context is defined in situation type salad-lab-afor the event type add-ingredient-to-salad:

context(add-ingredient-to-salad, book("Well balanced salads"))

In addition, suppose that the following entity of situation development and patterns ofinteraction hold in the situations below.


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in(context(add-ingredient-to-salad, book("Well balanced salads")), salad-lab-a, 26)accesses(learner, book("Well balanced salads"), view-book, salad-lab-a, 26)generates(learner, part(salad, ingredient(lettuce)), add-ingredient-to-salad, salad-lab-a, 28)

Then, according to the definition above, we say that the course of interaction course(salad-lab-a, 26, salad-lab-a, 28) is self-regulated for the learner with respect to adding an ingredientlettuce to a salad, in the context provided by the book "Well balanced salads", which means thatthe following property holds:

self-regulated(course(salad-lab-a, 26, salad-lab-a, 28), learner, part(salad, ingredient(lettuce)), add-ingredient-to-salad, book("Well balanced salads"))

Property of Reflectiveness

When learners interact in situations and develop their own activities, for instance, to solve aproblem or to construct an artefact, reflection involves them being aware of the process bywhich they are developing these activities, and to take this process as the object of theirthinking. According to Dewey (1933), quoted in (Ertmer and Newby, 1996), reflection involves"reconstruction or reorganization of experience which adds to the meaning of experience andwhich increases ability to direct the course of subsequent experience" (p.76). This reflectiveactivity allows the learners to focus on the process of interacting and learning in situations,rather than on the product.

The first main activity required for reflection about a particular experience is therepresentation of that particular experience, or, as von Glasersfeld (1995) would prefer: the re-presentation of the experience, as it involves the learner presenting again, or replaying, toherself a past experience. In this process, the learner has to recollect what has taken place in theexperience and replay the events that have happened noticing everything that might be relevant(Boud, Keogh and Walker, 1985). The second main activity, which comes after this recollectionof information about an experience, is the evaluation. Based on this information the learnerevaluates the experience, focusing primarily on the process by which the course of interactionhas developed. This allows the learner to determine how effective her overall process was inachieving her goals and to determine the extent of her achievements (Ertmer and Newby, 1996;Simons, 1993). Ultimately, this leads to a reflective process in which the learners assess theirlearning experiences focusing primarily on the overall process by which their interactions insituations have developed.

In our theory, reflectiveness refers to the property that a course of interaction exhibits whenaspects of the learner’s process of interaction in some situations are the objects of reflectiveactivities carried out by the learner in later situations of the course of interaction. Basic aspectsof the process of interaction are represented by the entities that denote the occurrence of eventsand the presence of entities in situations. These entities are basic process entities and willconstitute the basic elements of other types of process entities defined in types of situations. Forexample, a trace, which is a kind of process entity, can be generated as a sequence of eventoccurrences, and its generation can be defined as part of the dynamics of situation types.Similarly to the case of self-regulation, we have identified two main classes of reflectiveness:reflectiveness from access and reflectiveness from generation, which involve acting in a set ofsituations of a course of interaction, and further accessing (or generating) an entity that containsinformation about the process of interaction in those situations, in another situation of the courseof interaction, which will then be reflective with respect to the entity accessed (or generated).Below we present a definition of reflectiveness from access.

In this definition we use the term process entity to denote particular kinds of contententities that contain information about aspects of the process of interaction. Formally, a processentity is a content entity that is related in some ways to an entity of situation development, suchas occurs( ) or in( ). Therefore, the two main types of process entities are: process entitiesderived from collecting occurrences of events in situations, and process entities derived fromcollecting states of situations or presences of entities in situations.

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Definition (Reflective from access with respect to occurrences) A course of interactioncourse(s1, t1, s2, t2) is reflective with respect to a process entity x that collect occurrences ofevents in situations, for a learner a, if the process entity x is generated or updated in (s1, t1)and further accessed by the learner in (s2, t2).

generates(a, part(x, occurs(e1, a, s1, t1)), e1, s1, t1) ∧ accesses(a, x, e2, s2, t2) ∧ t2>t1

⇒ reflective(course(s1, t1, s2, t2), a, x)

For an example, suppose that the following process entity can be accessed in situation typesalad-lab-a to show the sequence of events which occurred in the process of interaction with thatsituation type, where t1 is the time of the first occurrence and tn is the time of the lastoccurrence.

trace-salad(salad-lab-a, t1, tn)

Accessing this entity after developing the events that are collected in the trace willcharacterise a reflective course of interaction.

The properties that we have discussed and defined above characterise regularities that mayhappen in courses of interaction which denote particular ways in which learning processes canbe cumulative, constructive, self-regulated or reflective. Following the same approach we may,of course, define variations and refinements of these definitions and may seek to define furtherproperties. Our definitions could also be extended to adopt more complex models of theseproperties, such as Winne and Hadwin’s (1998) model of self-regulation, or the model of self-regulation and reflection described by Ertmer and Newby (1996).

AFFORDANCES OF LEARNING SITUATIONS

According to the theory that we have described in the previous sections, courses of interactiondevelop properties such as cumulativeness, constructiveness, self-regulatedness andreflectiveness, when learning events that occur in the situations involved in these courses ofinteraction lead to certain patterns of interaction that are relevant for the development of theparticular properties. Therefore, after a sequence of learning events, several patterns ofinteraction hold in the situations where the learner had been interacting, and a set of propertiesof courses of interaction hold as a consequence of these patterns. These patterns of interactionand properties of courses of interaction that hold throughout the situations of the learningprocess up to a certain time characterise the state of the learning process at that time.

Now, suppose that a learner has interacted for some time with an environment, in severalsituation types, and is about to engage in interaction with a further situation type. Each eventavailable for the learner in this new situation type characterises a possibility for interaction.However, not all events characterise the same possibilities for learning, i.e., not all events leadto the development of courses of interaction that exhibit the same properties. Whether or notpossibilities for interactions entail possibilities for properties of courses of interaction willdepend on the state of the learning process.

Therefore, according to the characteristics of the events defined as part of the dynamics ofa given situation type, and according to the previous history of the learner’s interaction withother situation types, interaction in this new situation type may lead to the development ofparticular patterns of interaction, and consequently, allow certain properties of courses ofinteraction to hold. If a system can know in advance the possibilities offered by a situation typefor the development of these properties for a learning process that is in a certain state, then thesystem can use this information to support its decision making concerning the kinds of situationtypes that will be made available for the learner in the environment’s space of interaction at aparticular time.

In order to allow an intelligent system to consider these possibilities in advance, we havedeveloped a formal account of possibilities for interactions and for time-extended processes ofinteraction that exhibits particular characteristics, based on the notion of affordance introduced


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by Gibson (1977). Formalising affordances will make possible for an intelligent learningenvironment to reason about the features of situation types that afford the desired patterns ofinteraction and properties of courses of interaction to be developed in the following events of alearning process that is in a certain state.

Concerning interactions, a situation type may afford to a learner the development ofparticular patterns of interaction. For example, a situation type s in which the followingdefinitions hold:

define(event(a, e), s)define(effect(e, x, pa), s)

affords to the learner a generating the entity x through the event e (according to the definition ofthe pattern generates). For another example: if an entity of a situation type is new to a learnerand there are ways in the situation type in which the learner can utilise this entity, which thenwould become old for the learner (according to the definition of the pattern old), then we cansay that an affordance of this situation type to that learner is the possibility of developing thepattern of interaction in which the referred entity is old for the learner. Of course, after thisevent happens, i.e. the utilisation of the entity and it becoming old, the affordance will no longerbe there, although the learner may still be interacting with the same situation type.

In addition to what a situation type can afford to a learner in an interaction, namely thedevelopment of patterns of interaction such as the ones that we have defined earlier, a situationtype can also afford to a learner the development of courses of interaction that exhibit particularproperties. For example, suppose that the following pattern of interaction holds in a situation(s1, t1) in which the learner has interacted:

utilises(a, x, e1, s1, t1)

and suppose that the same definitions of the previous example hold for the situation type s.Then, the occurrence of the event e at time t, would indicate the development of the followingpatterns of interaction:

share(s1, t1, s, t, x)generates(a, x, e, s, t)

and, if we take into consideration the course of interaction from situation (s1, t1) to the nowdeveloped situation (s, t), the holding of these patterns, according to the definition ofcumulativeness, would indicate the development of a course of interaction course(s1, t1, s, t+1)that is cumulative with respect to the entity x for the learner a. Therefore, we can say that thesituation type s affords to the learner a, at a certain time greater than t1, the development of acourse of interaction that is cumulative with respect to the entity x.

Therefore, concerning time-extended processes, a situation type may afford to a learner thedevelopment of courses of interaction that possess particular properties such as the ones that wehave defined in the previous section. Note that the way in which the affordance is relative to thelearner refers to relativeness to the whole process that the learner has gone through, and not onlyto individual characteristics of the learner. In the example above, if the learner has not utilisedthe entity x in any previous situation, the situation type s would not be able to affordcumulativeness with respect to that entity at this time.

In our theory, we have identified two types of affordances of situation types: affordancesfor patterns of interaction, which represent possibilities in situation types for the developmentof patterns of learner’s actions in situations, learner’s cognitive states in situations, or relationsbetween situations, and affordances for properties of courses of interaction, which representpossibilities in situation types for the development of courses of interaction that are cumulative,constructive, self-regulated, or reflective. Below we present some of these definitions (a moreextended set of definitions of these two kinds of affordances is given in Akhras(1997)).

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Affordance for Patterns of Learner’s Actions in Situations

In order that a situation type can afford to a learner the development of patterns of learner’sactions in situations, the situation type must contain types of events with the kinds ofpreconditions and effects that allow the learner to utilise, generate, or access entities of thecontent of the situation type, according to the definitions of these patterns presented before.Below is the definition of one of these affordances.

Definition (Affords generating entities in situations) A situation type s affords to a learner agenerating an entity x through an event e, iff the event e is defined in situation type s as part ofthe alphabet of the learner a, and x is an effect of e defined in s.

define(event(a, e), s) ∧ define(effect(e, x, pa), s) ⇔ affords(s, generates, a, x, e)

For an example, consider the effect of the event type slice-ingredient as defined in situationtype salad-lab-a:

define(event(learner, slice-ingredient), salad-lab-a)define(effect(slice-ingredient, state(ingredient(X), sliced), 1), salad-lab-a)

Then, according to the definition above, we say that the situation type salad-lab-a affords tothe learner generating the notion of an ingredient being in a state of sliced through slicing it,which means that the following affordance holds:

affords(salad-lab-a, generates, learner, state(ingredient(X), sliced), slice-ingredient)

Affordance for Patterns of Learner’s Cognitive States in Situations

To afford to a learner the development of patterns of learner’s cognitive states in situations, asituation type must contain the kind of content and dynamics that allow a learner who is in acertain cognitive state to develop the patterns in which entities of the situation type become newor old to the learner, according to the definitions of these patterns presented before. Below wepresent the definition of the affordance for the pattern new, in which these conditions areformally stated.

Definition (Affords new content entities in situations) A situation type s affords to a learner aan entity x being new at the current time tc or after, iff the entity x is defined or can begenerated in the situation type s, and x has not been utilised nor generated by the learner a inany situation previous to (s, tc).

[define(x, s) ∨ affords(s, generates, al, x, el)] ∧(∀ ei, si, ti)[ti<tc ∧ ¬ utilises(a, x, ei, si, ti)] ∧(∀ ej, sj, tj)[tj<tc-1 ∧ ¬ generates(a, x, ej, sj, tj)]

⇔ affords(s, new, a, x, tc)

For example, if the state of an ingredient cabbage is defined in a situation type asunwashed, and no pattern of utilising or generating this ingredient state holds in previoussituations, then, according to the definition above, we say the situation type affords to thelearner, at the current time or after, the notion of an ingredient cabbage in a state of unwashedbeing new, which is the same as saying that the following affordance holds:

affords(salad-lab-a, new, learner, state(ingredient(cabbage), unwashed), tc)

Affordance for Cumulativeness

In order that a situation type can afford to a learner the development of courses of interactionthat are cumulative, the situation type must afford to the learner the development of the kinds ofpatterns of interaction that will lead to particular kinds of cumulativeness being developed,according to the definitions of cumulativeness presented before. Below we present the definitionof one of these affordances.


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Definition (Affords cumulativeness with respect to a content entity) A situation type s affordsto a learner a the development of a course of interaction from situation (si, ti) that is cumulativefor the learner with respect to a content entity x, if the learner utilises x in (si, ti) or generates itin (si, ti-1) and the situation type s affords to the learner a situation that shares the entity x withsituation (si, ti) and also affords to the learner utilising or generating x.

[utilises(a, x, ei, si, ti) ∨ generates(a, x, ei, si, ti-1)] ∧affords(s, share, si, ti, x) ∧ [affords(s, utilises, a, x, e) ∨ affords(s, generates, a, x, e)]

⇒ affords(s, si, ti, cumulative, a, x)

For an example, suppose that the following pattern of interaction holds in situation (salad-lab-a, 8):

utilises(learner, ingredient(lettuce), wash-ingredient, salad-lab-a, 8)

In addition, suppose that the following affordances for patterns of interaction hold insituation type salad-lab-b:

affords(salad-lab-b, share, salad-lab-a, 8, ingredient(lettuce))affords(salad-lab-b, utilises, learner, ingredient(lettuce), add-ingredient-to-salad)

Therefore, according to the definition above, we say that the situation type salad-lab-baffords to the learner the development of a course of interaction from situation (salad-lab-a, 8)that is cumulative for the learner with respect to the ingredient lettuce, which means that thefollowing affordance holds:

affords(salad-lab-b, salad-lab-a, 8, cumulative, learner, ingredient(lettuce))

Affordance for Self-Regulatedness

Self-regulatedness of courses of interaction develops from particular ways in which a learner’saction performed in one situation is in some way evaluated by the learner in another situation ofthe course of interaction, and this evaluation is taken into consideration to guide the nextlearner’s actions or change the effects of previous actions. To afford to a learner thedevelopment of courses of interaction that are self-regulated, a situation type must containparticular content entities and afford to the learner the development of particular patterns ofinteraction that will lead to particular kinds of self-regulatedness being developed. Below is onedefinition.

Definition (Affords self-regulatedness with respect to a content entity from access to contextafter the event) A situation type s affords to a learner a the development of a course ofinteraction from situation (si, ti) that is self-regulated for the learner with respect to a contententity x, which is generated through an event e, from access to an evaluation context c, if thelearner generates the entity x through the event e in (si, ti), and the entity c is defined insituation type s as an evaluation context for e, and the situation type s affords to the learneraccessing the context c through event ec.

generates(a, x, e, si, ti) ∧define(context(e, c), s) ∧ affords(s, accesses, a, c, ec)

⇒ affords(s, si, ti, self-regulated, a, x, e, c)

For an example, suppose that the following pattern of interaction holds in situation (salad-lab-a, 4).

generates(learner, part(salad, ingredient(lettuce)), add-ingredient-to-salad, salad-lab-a, 4)

Furthermore, suppose that the following context is defined in situation type salad-lab-b forthe event type add-ingredient-to-salad, and the following affordance holds:

define(context(add-ingredient-to-salad, book("Well balanced salads")), salad-lab-b)affords(salad-lab-b, accesses, learner, book("Well balanced salads"), view-book)

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Then, according to the definition above, we say that the situation type salad-lab-b affords tothe learner the development of a course of interaction from situation (salad-lab-a, 4) that is self-regulated for the learner with respect to adding an ingredient lettuce to a salad, in the contextprovided by the book "Well balanced salads", which is the same as saying that the followingaffordance holds:

affords(salad-lab-b, salad-lab-a, 4, self-regulated, learner,part(salad, ingredient(lettuce)), add-ingredient-to-salad, book("Well balanced salads"))

INCENSE

Based on the theoretical models described in the previous sections, we have implementedINCENSE – an INtelligent Constructivist ENvironment for Software Engineering learning.INCENSE is capable of analysing a time-extended process of interaction between a learner anda set of software engineering situations provided by the environment, in terms of itscumulativeness, constructiveness, self-regulatedness, and reflectiveness. It can then adapt thespace of interaction provided by the environment in order to make available to the learner thetypes of situations that afford the development of further courses of interaction that lead to thedesired properties holding.

The Domain of INCENSE

The domain of INCENSE includes three main phases of software engineering activities:software project planning, software requirements specification, and software design. Thegeneral setting is a software engineering laboratory in which two main needs shall arise:

• Modelling a software engineering processWhich involves the learner constructing a model of a particular process of softwareengineering, such as the process of software project planning, so that the model can beapplied when there is a need for it in a project of software development.

• Applying a model of a software engineering process in a project of softwaredevelopmentWhich involves the learner using a model of a particular process of softwareengineering, such as a model of the project planning process, as a basis for developingthe activities related to this particular process in a project of software development.

The situations of INCENSE correspond to particular cases in which modelling a softwareengineering process, or applying a software engineering process model, or both, are needed. Insituations that involve modelling a software engineering process, the model created by thelearner is defined in terms of the following concepts:

• Processes that are part of the model (e.g. specify requirements)

• Materials used in the processes (e.g. description of the project scope)

• Results of the processes (e.g. data flow diagram)

• Contents of materials or results (e.g. data)

• Sequences of processes (e.g. specify requirements > check consistency)

Figure 1 shows the setting of a learning situation of INCENSE for modelling the process ofsoftware project planning.


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Figure 1. The setting of a learning situation of INCENSE

In situations that involve applying a model of a software engineering process, such as inplanning a software development project, the application is defined in terms of the model beingapplied. Therefore, the learner’s actions, instead of focusing on creating a model, would beactions to:

• define the scope of the particular project

• define the work breakdown structure for the particular project

• define the activity graph for the particular project

• perform the critical path analysis for the particular project

• etc.

Therefore, an essential feature of INCENSE that overcomes a limitation of SAMPLE interms of constructive activity is the possibility of constructing a notion in a modelling situation(e.g. the fact that project planning involves defining an activity graph), and then using thisnotion constructed, which was not given, to construct another notion (e.g. the particular activitygraph that is part of planning a particular project). This would correspond, in the salad designsituations of SAMPLE, to constructing the notion that a salad is made of ingredients, which isgiven in SAMPLE, and then constructing the notion that a particular ingredient is part of aparticular salad.

Learning Situations of INCENSE

Software engineering situations of INCENSE have content and dynamics. The content includessources of information that can be consulted by the learner while modelling software

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engineering processes or applying models of software engineering processes. These sources ofinformation also include the details of the model being created in the situation or the applicationbeing developed. Physically, these sources of information are archives that are presented in thesituations in graphical form and can be opened using the mouse.

As illustrated in Figure 1, each situation has two sets of archives: the situation archives,which contain information about the situation types and, in this case, about software projectplanning; and the learner archives, which contain the information created by the learner duringher or his interaction with the situation.

The dynamics of INCENSE situations include a set of interaction events that can beactivated by the learner using the mouse and which activate procedures that correspond to theseveral kinds of actions necessary to create models of software engineering processes, as shownin Figure 1 (e.g. create-process, create-material, etc.), or to apply models of softwareengineering processes. For example, to include the process "specify requirements" with result"data flow diagram" in her model, the learner activates the procedure create-process, whichallows to add a process to the model, which is selected from a list of process-concepts, and thenactivates the procedure create-result, which allows to define a result for a process (in this case,the process created earlier), selecting from a list of information-concepts.

These characteristics of the content and dynamics of INCENSE situations correspond to theexternal view of INCENSE situations, as these characteristics are physically part of therepresentation of the situation setting that appears in the screen and with which the learnerphysically interacts. The formal, internal representation of these and other characteristics of thecontent and dynamics of INCENSE situations is presented below, for the situation type model-rs2, which is a situation type for modelling the process of software requirements specification.

The content of this situation type includes three kinds of objects: the set of archives that arethe sources of information for modelling the particular software engineering process, and twosets of software engineering concepts: process concepts and information concepts. Processconcepts are used to create processes in the model. Information concepts are used to creatematerials, results or contents in the model. Some of the objects of these kinds defined in model-rs2 are:

archive(’Requirements analysis’)archive(’Interaction trace’)process-concept(’specify requirements’)process-concept(’check specification completeness’)information-concept(’project scope’)information-concept(’data flow diagram’)

The dynamics of the situation type includes the definition of the events that supportmodelling, with their preconditions, effects and associated contexts. To create processes in themodel being constructed the following event is defined:

event(learner, create-process)

Its precondition is the existence of a concept that the learner selects from the set of process-concepts defined above, during the execution of the event:

pre(create-process, concept(X), 1)

Its effects are: the process created, the information that the process is created being introducedin the lists of process-material and process-results that are shown in the corresponding archives,and the update of the trace of modelling that is shown in the interaction trace archive.

effect(create-process, process(X), 1)effect(create-process, part(list-process-material(S, T1), in(process(X), S, T1)), 1)effect(create-process, part(list-process-result(S, T1), in(process(X), S, T1)), 1)effect(create-process, part(trace-modelling(S, T1), occurs(create-process, S, T)), 1)


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Finally, some of the contexts defined for this event type are:

context(create-process, archive(’Requirements modelling situation’))context(create-process, archive(’Requirements development’))

Other situation types that are represented in INCENSE include: model-pp1, which is asituation type for modelling the process of software project definition; model-rs1, which is asituation type for modelling the process of software requirements definition; and model-d1,which is a situation type for modelling the process of data design.

According to our approach, the engaging of learners in situation types in which they wishto interact is made from the space of interaction, which contains a selection of situation typesthat are likely to be beneficial to the learner. As we will see later, the analyses of interaction,process, and affordances, all contribute to the creation of the space of interaction.

Interacting in INCENSE’s Situations

Interaction in situations develops by the occurrence of events. After entering a situation type,the occurrence of the events defined in this situation type give rise to situations that characterisea succession of contexts in which the interaction develops. In the example that we have run,after entering the situation type model-rs2 a sequence of learning events was developedinvolving the content and dynamics of this situation type.

Formally, the events that occurred and the changes in the content of the situationsdeveloped by the occurrence of these events are described in terms of the entities of situationdevelopment defined earlier. For example, the occurrence of an event in situation (model-rs2, 1)in which a learner creates a process "specify requirements" is encoded as below.

occurs(create-process, learner, model-rs2, 1)in(pre(create-process, process-concept(specify requirements), 1), model-rs2,1)

As a consequence, the effect of the event holds in situation (model-rs2, 2) as well as the processcreated. This is encoded as below.

in(effect(create-process, process(specify requirements), 1), model-rs2, 2)in(process(specify requirements), model-rs2, 2)

Table 3. Representation of occurrences of learning events_____________________________________________________________________

time 1occurs create_process

time 2in process(specify requirements)in part(trace_modelling(model_rs2, 2), occurs(create_process, model_rs2, 1))occurs access_archive

time 3occurs create_material

time 4in relation(material(concept(project scope), process(specify requirements)))in information(project scope)in part(trace_modelling(model_rs2, 4), occurs(create_material, model_rs2, 3))occurs access_interaction_trace

time 5occurs create_result

time 6in relation(result(concept(data flow diagram), process(specify requirements)))in information(data flow diagram)in part(trace_modelling(model_rs2, 6), occurs(create_result, model_rs2, 5))

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In Table 3 we present, in a simplified form, the main entities of situation development generatedin the whole interaction (six steps). The fragment of the software engineering process modelconstructed in these few events is shown in Figure 2.

In practical terms, what happened in these six steps of interaction is that the learner startedto create her or his model of the process of software requirements specification, whose partialproduct is illustrated in Figure 2. This model fragment represents that the activity of specifyingthe software requirements uses the description of the project scope as material and produces adata flow diagram as result. In the course of this interaction, the learner has also accessed thearchive that contains information about how software requirements are analysed. Although thisarchive contains information that helps the learner to build her or his own model, the meaning ofentities such as "project scope", "specify requirements", and "data flow diagram" has to beconstructed by the learner as she or he applies her or his model in other situations.

speci fy requirement s

project scope

data flow diagram

Figure 2. Fragment of a software engineering process model being constructed

Analysing Interactions

In INCENSE, after the learner leaves the situation type in which she or he has been interacting,the system analyses the interactions to determine the patterns of interaction that have beendeveloped, which correspond to the system’s interpretation of the learner’s interactions in thesituations. The procedures for doing this in INCENSE, implemented in prolog, follow quitestraightforward from the formal definitions of the patterns of interaction. An extract is presentedbelow.

After the learner A has interacted in situation S from Tm to TnFor each T from Tm to Tn

For all X, E such that in(pre(E, X, P),S, T)And for the learner A such that occurs(E, A, S, T)The system asserts that utilises(A, X, E, S, T) holds

In addition, if in(X, S, T)and for all Ti<T and Tj<T-1 such that

neither utilises(A, X, E, S, Ti)nor generates(A, X, E, S, Tj)

The system asserts that new(A, X, S, T) holdsOtherwise, it asserts that old(A, X, S, T) holds

Similar procedures are used to obtain the other patterns.

Figure 3 shows the system’s interpretation of the interactions developed in our exampleconcerning the patterns of learner’s actions in situations (utilises, generates, and accesses) andthe patterns of cognitive states in situations (new and old). In the Figure, software engineeringconcepts are represented by wiggly bubbles, processes by round bubbles, materials or results byrectangles, and the arrows indicate input and output of learner’s events.


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t ime 1

s pecify r equi rements s pecify

requir e-ments

Requir ements analys is

acces ses

t ime 2

t ime 3

project s cope

acces ses

t ime 4

> - - - > - - - > - - -

T race

project s cope

s pecify r equi re-ments

t ime 5

data flow diagr am

time 6

data flow diagr am

s peci fy r equire-ments

ut il ises

ut il ises

ut ili ses

generates

generates

generates

new

new

new

newold

newnewold

ut ilis es

ut ilis es

Figure 3. Patterns of interaction in the situation for modelling the process of requirementsspecification

Analysing the Time-Extended Process of Interaction

Following the analysis of interaction, INCENSE proceeds with the analysis of courses ofinteraction to determine the properties of cumulativeness, constructiveness, reflectiveness, andself-regulatedness, which correspond to the system’s interpretation of the time-extended processof interaction developed. In reasoning about courses of interaction, INCENSE uses itsknowledge about properties of courses of interaction that we have formally described earlier toobtain the properties that hold in a process of interaction. Table 4 shows some of the propertiesdeveloped from the interactions of our example.

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Table 4. Properties of courses of interaction in the situation for modelling the process ofrequirements specification

_____________________________________________________________________time 1 → time 2self-regulated with respect to process(specify requirements)

and context archive(Requirements analysis)

time 2 → time 3cumulative with respect to process(specify requirements)

time 3 → time 4constructive with respect to relation(material(concept(project scope),

process(specify requirements)))constructive with respect to information(project scope)reflective with respect to trace_modelling

time 3 → time 6constructive with respect to relation(result(concept(data flow diagram),

process(specify requirements)))constructive with respect to information(data flow diagram)

_____________________________________________________________________

Determining the Affordances of Situation Types

After determining the patterns of interaction and the process-related properties of a sequence oflearning events developed in the situation that the learner has just left, INCENSE analyses thesituation types that are part of the environment so that the affordances of these situations to thelearner can be determined. As we have discussed earlier, this is done taking into considerationthe interactions developed in the situations up to the current time and the possibilities of the newsituation types for the development of further interactions that lead to properties ofcumulativeness, constructiveness, self-regulatedness, and reflectiveness holding in the followinglearning interactions. In Table 5 we show some of these affordances for situation type model-rs2. (Note that if an entity contains a variable, such as in the case of process(X), this variable isbound to the name "Var" which then means that the affordance refers to an unbounded entity.)

Table 5. Affordances for properties of courses of interaction in situation type model-rs2_____________________________________________________________________

time 1 → time ncumulative with respect to concept(specify requirements)

time 2 → time ncumulative with respect to process(specify requirements)constructive with respect to relation(material(concept(Var), process(Var)))

time 3 → time ncumulative with respect to concept(project scope)constructive with respect to relation(material(concept(Var), process(Var)))constructive with respect to relation(before(process(Var), process(Var))) . . .time 5 → time nconstructive with respect to information(Var) . . .time 6 → time nself-regulated with respect to process(Var)

and context archive(Requirements development)reflective with respect to trace_modelling


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In practical terms, what the analysis of affordances presented above tells the system is thatif, for example, model-rs2 is the next situation to be selected by the learner in the space ofinteraction (in case it is there to be selected), then there are possibilities for cumulativeness withrespect to the notions of "project scope", "specify requirements", etc., and for constructiveness,self-regulatedness, and reflectiveness with respect to several other entities.

Creating a Space of Interaction

As a result of the affordances determined above, a set of situation types qualifies as candidatesfor the next space of interaction. In our example, we can see that all the four situation typesafford some of the desired properties of courses of interaction to be developed in the followingprocess. To sort this set of situation types in terms of their potential benefit for the learner wehave defined the following policies:

• Cumulativeness policy: consider situation types that afford more first-time cumulations.

• Constructiveness policy: consider situation types that afford more constructions.

• Self-regulatedness policy: consider situation types that afford more first-time self-regulations.

• Reflectiveness policy: consider situation types that afford reflections about entities thathave had less time spent on them by reflection in previous situations.

The results of the analysis of affordances in relation to the policies, for our example, aresummarised in Table 6. As the affordances for reflectiveness and self-regulatedness did notchange from one situation type to another due to the situation types of the example being all formodelling and having similar mechanisms for self-regulation (access to similar archives), theselection of situation types for the space of interaction in our example was based only on theresults of the analysis of affordances in relation to the policies concerning cumulativeness andconstructiveness, whose summary is shown in Table 6, in terms of the number of entities thatthe situation types afford a first time cumulation and the number of entities that the situationtypes afford construction.

Table 6. Summary of affordances

situation type cumulativeness constructiveness

model-pp2 2 11model-rs1 3 11model-rs2 7 32model-d1 1 5

Therefore, following from the selection of the situation type model-rs2 in the first space ofinteraction, which contained the situation types model-pp2 and model-rs2, and according to thesequence of learning events developed in the situations derived from the situation type model-rs2, the next two situation types that are more likely to enable, for the learner, the developmentof courses of interaction that exhibit the desired properties, are the situation types model-rs2 andmodel-rs1. In practical terms this means that the objects and the possibilities for action that thelearner will encounter in the contexts provided by these two types of situations allow thedevelopment of learning interactions that make connections with aspects of interactionsdeveloped in previous situations and, therefore, help to ensure a continuing learning experiencethat is meaningful for the learner, as a process.

INCENSE Used by Real Students

In order to observe some students using INCENSE we have carried out a brief study in whichtwo students used INCENSE, each one interacting individually for about thirty minutes with the

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system, producing courses of interaction that extended over fifty events, in which they had tomodel a process of software engineering project planning. The main goal of this study was toobserve the development of properties of cumulativeness, constructiveness, self-regulatednessand reflectiveness in more extended sequences of learning events developed by real students.The results are summarised in the table below.

student A student Bnumber of different entities cumulated 25 8number of different entities constructed 32 22number of different entities self-regulated 1 9number of different entities reflected upon 0 0

Neither student developed reflective courses of interaction, which in INCENSE means thatthe interaction traces were not accessed. Concerning the properties developed, the numbersshow that student A cumulated and constructed more than student B but spent less time self-regulating, which in INCENSE corresponds to accessing archives that contain information aboutsoftware engineering concepts. Following an analysis of affordances, the system might tend tooffer to student A situations that allow fewer new constructions and more self-regulation of theconstructions made before, while to student B the system might offer situations that allow morenew constructions.

CONCLUSION

In this paper we have argued that the change in perspective provided by constructivist views oflearning, in regard to the nature of knowledge, the way learners learn, and the way learning canbe promoted, rather than pointing to a move away from the idea of system intelligence in thecomputational support to constructivist learning, points to a new kind of system intelligence thatis better attuned to constructivist views, which stress the importance of the context of learning,the fact that learning involves active interaction, and the process rather than the product oflearning.

Focusing on these issues, we have developed a set of formal mechanisms that support thekinds of knowledge representation, reasoning, and decision making that are necessary in orderthat a constructivist learning environment can develop an evaluation of learning with a focus onthe process rather than on the product of learning and can then use this evaluation in order toadapt the environment to the learner needs, aiming for the development of further processes oflearning that possess certain desired properties rather than the acquisition of a target knowledge.

The whole approach was implemented in INCENSE, which is an intelligent learningenvironment for software engineering learning that follows a constructivist perspective.INCENSE is able to evaluate learning processes in terms of the four main properties that havebeen put forward by constructivist theorists as conducive to learning: cumulativeness,constructiveness, self-regulatedness, and reflectiveness. It is also able to adapt the learningenvironment in a way that facilitates the occurrence of these properties in following courses ofinteraction.

Acknowledgements

Thanks are due to the National Council of Scientific and Technological Development (CNPq),Brazil, for sponsoring the research reported in this paper.

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