International Journal of Artificial Intelligence in Education (2000), 11, 344-376
System Intelligence in Constructivist Learning
Fabio N. Akhras and John A. Self Computer Based Learning Unit, University of Leeds,
Leeds, LS2 9JT, England
E-mail: akhras@pcs.usp.br, J.A.Self@cbl.leeds.ac.uk
Abstract. The aim of this paper is to present a perspective on intelligent systems to support
learning that is in line with constructivist views of learning. In order to develop such a
perspective we have defined formal mechanisms to support knowledge representation,
reasoning, and decision making in intelligent systems, that are attuned to the values of
constructivist views of learning. These point to the importance of the context of learning, stress
that learning involves active interaction, and emphasise the process rather than the product of
learning. The theoretical models that constitute our approach enable intelligent learning
environments to evaluate learning according to four properties of constructivist learning
processes: cumulativeness, constructiveness, self-regulatedness, and reflectiveness, and to make
decisions about the learning opportunities to be provided to the learners, taking into
consideration the affordances of learning situations regarding these properties. The approach has
been implemented in INCENSE, which is an intelligent learning environment in the domain of
software engineering.
INTRODUCTION
Constructivist theories of learning emphasise an active and autonomous role for the learners to
construct their own understanding through interacting in an environment in which the
knowledge of the domain is not explicitly separated from the context in which it applies. The
focus is on the process through which the learners experience the environment and interpret
their experiences rather than on the acquisition of a previously defined target domain
knowledge.
These emphases of constructivism point to a general shift in focus from teaching to
learning and bring to the fore a set of issues that differ in fundamental ways from the issues that
have been addressed in the design of intelligent systems to support learning.
Intelligent systems to support learning have emphasised the use of artificial intelligence in
education with three main purposes: representation of the knowledge to be learned, inference of
the learner's state of knowledge, and planning of instructional steps to be followed by the
learner. The focus of these systems on the explicit definition of a model of the domain
knowledge to be acquired by the learner, and on modelling the learner's knowledge state in
terms of the learner's correct knowledge or misconceptions, which are used as a basis to
evaluate learning and guide instructional interventions, seemed difficult to reconcile with
constructivist views of learning, and have led researchers engaged in the development of
computational support for constructivist learning to move away from the idea of using
intelligent systems to provide this support (Derry and Lajoie, 1993; De Corte, 1995). The
general view, as stressed by Kommers, Lenting and van der Veer (1996), is that constructivism
indicates "a trend towards more autonomy for the learner, instead of an ever increasing
cybernetic 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 to
constructivist forms of learning but the particular kind of system intelligence that has so far been
designed in intelligent systems to support learning.

Currently at the Department of Computer Engineering, Polytechnic School, University of São
Paulo, CP 61548, 05425-970, São Paulo, SP, Brazil (e-mail: akhras@pcs.usp.br).
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For instance, it is clear that the focus of intelligent systems to support learning in terms of
knowledge representation, reasoning, and decision making, as discussed above, reflects the
values of the particular view of learning that is emphasised in these systems in regard to the
nature 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 system
intelligence in which the mechanisms of knowledge representation, reasoning, and decision
making, originate from a formal interpretation of the values of that view of learning. As a
consequence, the resulting intelligent behaviour of the system will (by definition) not be in
contradiction with the values emphasised by that view of learning, as it appears to be today
where there is a tension between the underlying values emphasised by intelligent systems to
support learning and the values emphasised by constructivist views of learning.
Therefore, what is needed is the development of a different kind of system intelligence that
is based on methods of knowledge representation, reasoning, and decision making, better
attuned to the values of constructivist views of learning. For example, given the shift in focus
offered by constructivist views, from the product to the process of learning, the issue of
evaluating learning which is central to the individual adaptation of the learning experiences to
the 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 of
learning, and provide a theoretical, computational basis for addressing these issues in the design
of a system intelligence to support constructivist forms of learning. The paper is organised as
follows. After the discussion of constructivist issues in the next section, the following section
outlines the implications of these issues to the design of a system intelligence. The following
four sections present our main theoretical developments related to the issues of context,
interaction, process and affordances. Then, the next section describes INCENSE, an intelligent
system to support learning of software engineering concepts. This system, implemented in
Prolog, reasons about context, interaction, process and affordances using the formalisms
presented in the theoretical sections. For example, as it interacts with the student it builds up a
picture of the affordances of potential situations to the student connected with that particular
interaction. The final section presents the conclusions.
A CONSTRUCTIVIST VIEW OF LEARNING
A view that is emerging from constructivist theories of learning emphasises four aspects as
holistically coexisting in any learning process:
1. Context - an essential part of what is learned is the situation in which learning takes
place, which refers to the physical as well as to the social environment in which the
learner is engaged in activity, and might include physical entities, tools, and other
people.
2. Activity - all knowledge is constructed by the learners through actively interacting in
situations in which they experience a domain and interpret their own experiences.
3. Cognitive structures - previously constructed knowledge influences the way learners
interpret 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 an
inseparability between context, physical and psychological phenomena, and the flow of
experience, in order to understand learning. It implies a focus on the relationships that develop
between these four aspects in a process of learning, rather than on their independent
characteristics.
Support for this view is found in recent research on education that has pointed to the need
for 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 our
understanding of how cognitive processes and structures interact with environmental variables.
According to her:
"cognitive psychology provided rich descriptions of what is learned but failed to
provide fruitful hypotheses about how learning happens and more specifically about
the environmental variables that influence the knowledge acquisition process" (p. 104).
This tendency towards the study of psychological and environmental aspects of phenomena
in an integrated way is also in line with what has been proposed as a transactional perspective
for research and theory in psychology (Altman and Rogoff, 1987). According to this
perspective, however, the focus is not only on the relations between individuals and their
environments, but also on the temporal qualities of these relations considered as inherent aspects
of phenomena, and embodying the flow and dynamics of the individual's relations to social and
physical 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) does
not arise solely from the entities of the environment nor from the learner but from the
interactions between them. A fundamental consequence of this is that individual cognitions can
only 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 meanings
of these entities for the learner, can also only be explained in terms of their contributions to
interaction. In fact, when learners are interacting with these entities they are not interacting with
entities "as they really are", but rather dealing with their previously constructed perceptual and
conceptual structures (von Glasersfeld, 1996). This means that the context of a learner's
experience 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 to
understand the ways in which environmental properties (or their interpretations) and properties
of 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 reference
to an individual. One of Gibson's examples is the postbox that affords letter-mailing to a letterwriting 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 an
individual 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 an
interactive activity for an individual who has appropriate abilities, and an individual can have an
ability for an interactive activity in a situation that has appropriate affordances. Neither an
affordance 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 which
interaction can be holistically shaped by aspects such as: the context in which interaction takes
place, the activity developed by the learner, and the cognitive structures of the learner
interacting in the context; indicates the need to better understand the roles that these three
aspects of interaction play in learning. It also indicates that the way these three aspects are
intertwined 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 a
situation 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 new
occasion 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 the
differences between the kinds of learning activity that take place in school and the ones that take
place in everyday real life and work situations (Resnick, 1987; Brown, Collins and Duguid
1989), and have suggested that in order that students become able to think with and about the
entities of a domain, rather than just learning what these entities are, students need more than
abstractions and self-contained examples. They need to learn how these entities are generated
and how they work in authentic activities (Greeno, 1989; Brown et al. 1989).
According to Bednar, Cunningham and Perry (1992), one of the practical consequences of
these ideas to the design of learning situations is to focus on portraying tasks that take into
consideration what real people typically do in real life contexts where knowledge domains are
not readily separated and information from many sources as well as varied perspectives are
necessary.
The Role of Activity
Concerning the role of activity, a basic premise of constructivism is that all knowledge is
subordinated to action. According to Piaget and Garcia (1991), there are two aspects that
characterise the meanings of objects. First, it is the action of utilising objects, or "what can be
done" with the objects either physically, such as moving or breaking them into pieces, or
mentally, 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 are
characterised by "what the actions lead to" in the transformations they produce on objects or
situations.
It follows that the meanings of objects are then characterised by the particular activities in
which these objects are utilised or constructed, and by the particular situations in which these
activities take place.
The Role of Cognitive Structures
Concerning the role of cognitive structures in learning interactions, a fundamental implication of
a view of learning that emphasises the active participation of the learners in constructing their
own 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 an
objective reality but rather reflect what the learners are "able to fit" into the cognitive structures
that 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 is
related to the issue of transfer - when knowledge learned in one situation is used later in another
situation; while in its negative sense has to do with the problem of inert knowledge - failure to
use in one situation relevant knowledge learned before. In general, according to Greeno, Moore
and Smith (1993) the issue involves an understanding of "how learning to participate in an
activity in one situation can influence (positively or negatively) one's ability to participate in
another 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 of
learning phenomena the properties of the interactions that develop from the learners' activities in
the 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. It
suggests that learning can be better understood from the circumstances provided by the
relationships between the learner's activity, the context in which the activity develops, and the
cognitive 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 we
should take into consideration the properties of the relations that develop over time between
aspects of single interactions in a process of learning. It suggests that an interaction, and
consequently, the learning that derives from it, can be better understood from the circumstances
provided by the flow of experience that connects that interaction to other interactions located in
different times.
Therefore, a fundamental issue for research is to understand the meaningful ways in which
aspects of an interactive learning experience in one situation can connect to aspects of an
interactive learning experience in another situation, in a course of interaction between learner
and environment, which will characterise ways of developing process-related properties of
constructivist 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 may
result from time-extended processes of interacting in situations. However, not all kinds of
interaction in situations lead to the same sort of learning and some interactions may not lead to
any learning at all. Indeed, the discussion about the roles of context, activity and cognitive
structures, indicates that different situations for different learners, or for the same learner at
different times, may lead to different kinds of learning. Similarly, the process that emerges from
the way successive interactions in situations are chained over time, may result in different flows
of learning experience for different learners.
Based on the notion of affordance, conceived by Gibson (1977), we can say that the utility
of a situation for a learner at a certain time is determined by the affordances of that situation
with respect to features of single interactions (involving relations between context, activity and
cognitive structures) and with respect to features of time-extended processes of interaction
(involving relations between single interactions). As Resnick (1996) points out, "learning and
development occur when individuals prepared for certain concepts encounter environments with
the kinds of affordances they need to elaborate these prepared structures" (p. 39).
Therefore, a pedagogical situation, i.e., a situation that can provide learning opportunities
for a particular learner at a particular time, shall afford interaction in contexts that embed
opportunities for activities, for learners capable of recognising and acting in the situation in
ways that can develop further their cognitive structures. As for time-extended processes, a
pedagogical situation shall afford certain interactive experiences - involving particular aspects
of context, activity, and learner's cognitive structures - that allow the development of relations
over time with aspects of interactive experiences developed by the learner in past situations. In
this way, the situation will afford the development of courses of interaction exhibiting certain
properties 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 intelligence
should be based on knowledge representation, reasoning, and decision making mechanisms that
address the issues that are relevant to constructivist learning, such as the issues discussed in the
previous section.
These issues indicate that in order to understand learning it is necessary to consider the
contexts in which learning takes place, the interactions that happen in these contexts, and the
way these interactions are chained over time. Furthermore, in order to facilitate learning it is
necessary to consider the affordances of learning situations regarding all these aspects.
Concerning the system intelligence, this requires the development of explicit theories that make
it 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 decision
making about these aspects.
A context theory will offer means of formalising the content and dynamics of learning
situations and the basic aspects of the interactions that develop in these situations, such as the
occurrence of learning events or the changes in the content of learning situations caused by
learning events.
While a context theory allows a system to perceive basic aspects of interaction in
situations, it is an interaction theory that helps in interpreting these interactions. Given a formal
account of learning situations and of how they change during learning interactions, the role of
an 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 in
the 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 a
basic step in order to understand time-extended processes of interaction. As a time-extended
process, learning depends on the relations that develop over time between aspects of single
interactions in situations. Therefore, the role of a theory of time-extended processes of
interaction is to formalise the various ways in which interactions relate to one another over time
in a course of interaction, to give an account of how process-related qualities of learning
processes, 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 of
theories of context, interaction, and time-extended process of interaction is to support reasoning
about the process of learning in the broad sense that includes the context of learning interactions
and 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 facilitate
learning, 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 a
learner whose time-extended process of interaction with the situations of the environment is in a
certain state.
Therefore, while the state of a learning process is given in precise terms by the theories of
context, interaction, and time-extended process of interaction, the utility of a situation for a
learner whose learning process is in a certain state, at a certain time, is given by a theory of
affordances.
In the next sections we describe our approach to the development of these theories
illustrating with examples from a simple application in the domain of salad design. Later on, we
show how these theories are used to support a system intelligence in a more extended
implementation 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 and
related areas (Akman and Surav, 1996). Among the approaches that have been developed,
situation theory (Barwise and Perry, 1983; Devlin, 1991) was particularly influential in the
development of our approach to formalising the context of learning interactions, although
situation 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 the
main 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 are
organised in terms of situations. According to the theory, agents usually find themselves in, or
refer to, situations as structured parts of the world that constitute the context for their behaviour
or communication. The main elements of situation theory's ontology are: situations, which
represent structured parts of the world; and infons, which represent items of information about
the 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 by
ordered sets denoted by <<R, a1, ..., an, i>>, where R is a n-place relation; a1, ..., an are the
arguments of R; and i is the polarity, which can assume the values 1 or 0, to indicate whether
the relation does or does not hold. Some of the entities that can be placed as arguments of the
relation are: individuals, relations, spatial locations, temporal locations, and situations.
A relevant issue that has not been particularly explored in the formulation of situation
theory is the development of explicit mechanisms to represent actions and the changes in
situations that may be caused by the occurrence of actions. There is, however, a proposal of an
approach in which actions are represented by pairs of sets of infons, in which the first set of
infons corresponds to the action precondition, while the second corresponds to the action
postcondition (Ohsawa and Nakashima, 1991).
A problem associated with reasoning about changes in situations caused by actions is the
frame problem (McCarthy and Hayes, 1969), which derives from the fact that although one can
apply a temporal representation like the situation calculus to determine what changes follow
from 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 introduced
some extensions to situation calculus involving the definition of a set of axioms to assert ways
in which particular types of events do not change particular types of states. Generalising this
kind of approach, Reiter (1991) has defined a logical theory to specify the effects of actions on
states of the world, which includes two kinds of axioms: axioms to specify the conditions for the
occurrence of an action (action precondition axioms), and axioms to specify the ways in which
actions affect the states of the world (successor state axioms). These axioms, along with a set of
general axioms, allow inference of the facts that hold in a new situation after the occurrence of
an action.
Taking into consideration the issues involved in formalising context, such as the ones
discussed above, we have developed an approach for modelling contexts of learning
interactions. The formalism is a many-sorted first-order predicate theory for modelling
structural information about learning situations as well as temporal information associated with
the way situations develop. The entities included in the formalism address the following aspects
of contexts of learning interaction: situations, content of situations, dynamics of situations, and
situation development.
In the next sections we describe this formalism, illustrating with examples taken from an
initial application of our approach, which was an intelligent learning environment for the
domain of salad design, called SAMPLE (SAlad Making Process-Sensitive Learning
Environment), whose goal is to help students learn concepts of salad making. Before we embark
on the discussion of the formalism, however, we briefly introduce the characteristics of the
contexts for learning interactions provided by SAMPLE.
In SAMPLE, the world is populated with tools and salad ingredients. There are seven
groups of ingredients, such as, leafy vegetables (e.g. lettuce), or herbs (e.g. parsley). Each of
these groups is characterised by a particular set of states through which the ingredient may pass
in its preparation before it is added to the salad or dressing. For example, some of the states and
transitions of state that characterise ingredients of the leafless vegetables group are:
unwashed  washed
whole  chopped
In each learning situation provided by SAMPLE there is a set of ingredients available. The
tools 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 states
of ingredients, add ingredients to the salad or dressing, dress the salad, or taste the whole
preparation. 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 the
salad or dressing.
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Situation Types
The notion of context appears in our theory in two ways. First, as contexts for the development
of learning interactions, denoted by situation types. Second, as contexts of developed learning
interactions, denoted by situations (see later). For example, the description of a set of things that
a 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 of
interaction, and is not located in any particular time. On the other hand, the description of the
circumstances of a living room at midnight when Melissa was kissing her doll characterises a
particular 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 internal
structure of a situation type is defined in terms of two kinds of entities: entities that denote the
way things stand in a learning situation - the content of the situation type; and entities that
denote the way learners can interact with the other entities of a learning situation - the dynamics
of the situation type.
To specify that a certain entity x (of content or dynamics) is part of the definition of a
situation 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 generalisation
and aggregation.
Objects are the units of content in situation types and represent the physical or conceptual
entities that are part of a learning situation. Objects are represented by n-place predicates, such
as in the two examples below taken from SAMPLE.
salad
ingredient(tomato)
To represent physical and conceptual aspects of complex phenomena in learning situations
the units provided by objects have to be combined in many different ways, according to the
roles that objects perform in relation to each other. This is represented in terms of relations
between 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 objects
might 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 useful
are: generalisations, that characterise is-a relations between sub-class entities and super-class
entities, and aggregations, that characterise part-of relations between component entities and
aggregate 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 of
events, and contexts of events.
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Apart from physical and conceptual entities, learning situations have at least one living
entity, the learner, and may have several others. These living entities interact with the physical
and conceptual entities, and with each other, by means of events. Each of these living entities
may have roles attributed to it in the learning situation, and there are a set of events that
characterise the actions involved in performing these roles. To define the potential events in a
situation type we use the notation event(a, e), where a is an agent and e is an event type. For
example:
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 type
represents the formal alphabet of that agent. In the above example, the role defined for the
learner in the situation type includes doing things like washing ingredients, and adding them to a
salad.
The conditions of activation of an event and the changes in a learning situation caused by
the 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 any
content entity and pa is the participation of x in the precondition or effect, which can assume the
values 1 or 0 to indicate whether x must hold or not to satisfy the precondition, or whether x will
hold or not in the effect. For instance:
pre(e, x, 1) means that the precondition for e is x
pre(e, x, 0) means that the precondition for e is not(x)
Preconditions and effects are particularly important to capture the circumstances involved
in 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 the
notion of context of an event, which we denote by context(e, x), where e is an event type and x
is a content entity that characterises a context for events of type e. As an example, suppose that
among the entities that are part of the content of learning situations in SAMPLE, there is this
book: book("Well balanced salads"), which may characterise a context for events of type addingredient-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 denotes
the 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 events
occur in situations. To denote the occurrence of events in situations we introduce the notation
occurs(e, a, s, t), where e is an event type, a is an agent, and (s, t) is the situation in which the
event 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. For
example, the following content entities may hold in the situations before and after the
occurrence 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 through
interactions, 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 that
must hold at the end of an event that occurs if the content entities that are preconditions for the
event hold at the beginning of that event. Table 1 presents the first two of these axioms. Other
two axioms (SD3 and SD4) are variations of SD-1 and SD-2 in which the value of the
participation 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)
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)
_____________________________________________________________________
SD-2:
The effect axioms allow us to infer the changes in content entities caused by the occurrence
of events in situations. However, they do not solve the general problem of determining the
content entities that hold in a certain situation. This is determined in our theory by taking into
consideration the histories of participation of content entities in the preconditions or effects of
events that have occurred, as described below.
As well as content entities that can hold in situations, actual preconditions and effects of
events 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 and
effects that hold at the beginning and at the end of an event e, with x being an instantiated
content entity and pa assuming 0 or 1. For example, some of the actual preconditions and effects
that 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 of
participation of content entities in the preconditions and effects of events that occur. These
histories are used in determining the content entities that hold in situations. In addition, we have
described earlier that the initial state of a situation type is given by the content of the situation
type defined using the formula define(x, s). Now, when the interaction in a situation type s
begins, events that occur give rise to histories of participation of content entities in
preconditions 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 must
take into consideration this initial definition of the situation type as well as the changes of
content 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 situation
development: SD-5 and SD-6, which refer to points of histories of content entities that hold in
situations, and SD-7, which allows to infer the content entities that hold in situations. These
axioms 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. A
course of interaction is defined in our theory by a sequence of situations and is denoted by
course(s1, t1, ..., sn, tn), where (s1, t1) and (sn, tn) are any two situations, which can possibly
be of the same type, and for which n>=2 and tn>t1. A particular case of a course of interaction
is the course of two situations course(s1, t1, s2, t2), which we will be using in the rest of this
paper.
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Table 2. Further axioms of situation development
_____________________________________________________________________
History axioms
SD-5:
SD-6:
define(pre(e, x, pa), s) occurs(e, a, s, t) in(pre(e, x, pa), s, t)
define(effect(e, x, pa), s) occurs(e, a, s, t) in(effect(e, x, pa), s, t+1)
State axiom

[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)
_____________________________________________________________________
SD-7:
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 of
interaction can overlap in many ways, and a situation can appear in more than one course of
interaction. As situations are a way of preserving the context of events that occur, courses of
interaction are a way of preserving the history of the interaction, which is essential to the
analysis 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 of
computational 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 the
work on computational theories of interaction and agency, as reported by Agre (1995), is to take
an 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 of
analysis that refer to interactions, whose definition requires research focused on the discovery of
structures in the world and of properties of interactions. To illustrate, Agre (1995) considers a
controller (the agent) of an oil refinery (the environment), with the general task of the agent
being the adjustment of certain devices in its environment so that a desired flow of oil is
sustained within the refinery. Given a proposed design for this controller, how can we know
whether it will work? The answer, it is argued, cannot rely only on an analysis of the controller
itself, and obviously, nor on an analysis of the plant in isolation. Instead, it is crucial to analyse
how the controller will interact with the plant.
Therefore, in order to understand an agent’s interaction with its environment this approach
focuses 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 in
the agent’s mind), rather than on the more classical AI approach of reasoning to recognise plans
that can be attributed to an agent.
Concerning human learners interacting in their learning environments, the interactional
perspective that is necessary to interpret learning phenomena, as we have discussed, requires
that we take the three aspects that characterise a learning interaction - context, activity, and
cognitive structures, and look for regularities in the ways these three aspects relate to each other
in interactions that are developed in learning processes.
In our model of learning situations, we have defined contexts of learning interactions as
types 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 these
contexts. In addition, we have defined a set of formal entities to denote aspects of the
interactions that are developed in these contexts when the potential activities defined in the
dynamics of a situation type actually occur. These three sets of formal entities: entities of
content, 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 patterns
of interaction, can be formally defined.
Therefore, the formalism introduced earlier for modelling structural information about
learning 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 higherorder regularities of interaction in learning situations.
Exploring the connections that are formed as learners interact in situations, among aspects
of interaction such as the context of activity, the nature of activity, and the cognitive states that
learners bring to activity, we have defined three types of patterns of interaction: patterns that
relate learner's actions to the situations in which they happen, patterns that relate learner's
cognitive states to the situations in which they hold, and patterns that capture relations between
situations. In the next sections we discuss these patterns and present some of their formal
definitions, 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 ways
by the content of the situation. Therefore, the nature of a learner's action in a situation is given
by the way it affects or is affected by the content of the situation. The different ways in which
this happens characterise different patterns of learner's actions in situations. Following the
discussion about the role of activity in learning, our definitions of these patterns intend to
capture the various ways in which meaning is constructed from acting in situations. Some of
these definitions, which correspond to learner's actions of utilising, generating, and accessing
entities in situations, are:
Definition (Utilising entities in situations) A learner a utilises an entity x through an event e in
a situation (s, t), iff the event e, defined in situation type s as part of the alphabet of the learner
a, occurs in (s, t), and x is a precondition of e that holds in (s, t), i. e. the participation of x in
the 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 following
entities 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 the
following 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 the
expressions (1), (2) and (3) above, we say that the learner utilises the ingredient lettuce by
washing it in the situation (salad-lab-a, 8), which is the same as saying that the following pattern
holds:
utilises(learner, ingredient(lettuce), wash-ingredient, salad-lab-a, 8)
Additionally, note that according to the expression (4) above, the learner also utilises in the
same event the notion of an ingredient lettuce being in a state of unwashed. In SAMPLE, some
of 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 transitions
of ingredients' states.
Definition (Generating entities in situations) A learner a generates an entity x through an
event e in a situation (s, t), iff the event e, defined in situation type s as part of the alphabet of
the 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 the
ingredient lettuce, the following entities hold in situation (salad-lab-a, 9):
in(effect(wash-ingredient, state(ingredient(lettuce), washed), 1), salad-lab-a, 9)
in(state(ingredient(lettuce), washed), salad-lab-a, 9)
(5)
Therefore, according to the definition of the pattern generates and according to the
expression (5) above, we say that the learner generates the notion of an ingredient lettuce being
in 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 ingredients
being in some sorts of states, the notions of an ingredient being part of a salad or dressing, and
the taste of a salad.
Here we can see how some limitations may be identified in learning environments such as
SAMPLE. Ingredients, which are the main building blocks in the salad preparation world for the
learner, 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 of
constructiveness, as we will discuss later.
Definition (Accessing entities in situations) A learner a accesses an entity x through an event e
in a situation (s, t), iff the learner a utilises the entity x in situation (s, t), and x is a precondition
of 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, the
contents of the salad or dressing being prepared, and characteristics of ingredients such as their
tastes or their current states.
Patterns of Learner's Cognitive States in Situations
According to constructivist views of learning, cognitive structures develop from acting in
situations. Therefore, some relevant cognitive structures may be developed from actions of
utilising, generating, or accessing entities in situations. These cognitive structures influence in
many ways the learner's view of the content and dynamics of subsequent situations. Following
the discussion about the role of cognitive structures in learning, our definitions of these patterns
are intended to capture the various ways in which entities of a situation are related to the
learner's previously formed cognitive structures. Some of these definitions, which correspond to
the 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 a
situation (s, t), iff the entity x holds in situation (s, t), and x has neither been utilised nor
generated 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 which
the following entity holds:
in(state(ingredient(lettuce), unwashed), salad-lab-a, 8)
Assuming that the entity state(ingredient(lettuce), unwashed) has neither been utilised nor
generated by the learner before, then according to the definition of the pattern new for content
entities, we say that the notion of an ingredient lettuce being in a state of unwashed is new for
the 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 a
situation (s, t), iff the entity x holds in situation (s, t), and x has been utilised or generated by the
learner 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 old
must be present in the situation, as denoted by the primitive in(x, s, t). This derives from the fact
that these patterns refer to cognitive states in relation to situations. Therefore, if an entity is not
new and is not present in a situation it does not characterise the kind of old that we are capturing
in 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 learning
occurs in situations that correspond to real life contexts and, therefore, requires multiple types of
situations where varied perspectives are portrayed and learners can explore various aspects of a
domain. As learners go from situation to situation, interacting in this kind of environment, they
are likely to connect through experience knowledge of different kinds, and these experiences
and the connections that derive from them will be influenced by the relations that exist between
entities of situations. The different ways in which entities of one situation may be related to
entities of another situation characterise different patterns of relations between situations.
Therefore, our definitions of these patterns are intended to capture the various ways in
which entities of one situation are related to entities of another situation. The patterns that we
have 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 with
respect to another situation. The specific patterns of each of these kinds correspond to the
different ways in which situations can share characteristics or have additional characteristics
with respect to other situations. The definition of one of these patterns is shown below (other
similar definitions are given in Akhras(1997)).
Definition (Sharing content entities) Two situations (s1, t1) and (s2, t2) share a content entity
x, 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 occurrence
of events when learners are engaged in interaction with the situation types of their learning
environments. As we have discussed earlier, the focus on the situations that develop when
events occur, rather than on the events alone, to account for the progression of the interaction
between 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 point
in the development of our formal account of interaction in the previous section, where a set of
patterns 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 the
interaction, which encompasses the process and structure by which aspects of interactions
developed 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 preserving
the history of the interaction.
Histories of interaction when preserved will embed information about particular ways in
which courses of interaction develop, according to the particular patterns of interaction that hold
in the situations of the course of interaction. These particular ways in which courses of
interaction develop will characterise regularities of a higher order than the patterns of interaction
as they will relate patterns of interaction that hold in different situations.
To model these regularities, our theory (that already encompasses formal entities to denote
the content and dynamics of situation types, aspects of situation development and patterns of
interaction) is now extended to include properties of courses of interaction, which are formal
entities that denote regularities of time-extended learning processes.
In order to model some of the process-related notions that are addressed by constructivist
learning approaches, we have defined four types of properties of courses of interaction:
cumulativeness, constructiveness, self-regulatedness, and reflectiveness. These properties are
defined in terms of patterns of interaction and of entities of situation type and of situation
development.
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 taken
from SAMPLE. Although the approach can be applied to any kind of course of interaction, the
properties that we have defined are based on courses of interaction involving only two
situations.
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 of
similar experiences in different contexts and involving different ways of looking at the
experiences may enable access to prior knowledge and the exploitation of similarities and
differences between the current and the previous experiences. Ultimately, this leads to a
cumulative process in which new meanings are added to elements of previous experiences and
current experiences are interpreted in the light of previous ones. Although cumulativeness alone
may 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 exhibits
when entities experienced by the learner in one situation are in some way revisited in a later
situation of the course of interaction. A particular way in which a course of interaction can be
cumulative is through a shared entity, which happens when the same entity is experienced in the
two situations of a course of interaction. Other ways may involve experiencing entities in the
two situations that are not the same but are in some ways related. Below we present the
definition of cumulativeness from a shared entity.
Definition (Cumulative with respect to a shared content entity) A course of interaction
course(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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System Intelligence in Constructivist Learning
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(saladlab-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 new
experiences in meaningful ways. In this process, not only is the knowledge associated with the
new experience constructed but also the learner's existent knowledge is sometimes reinterpreted in the light of the new experience. According to Shuell (1992), learning is
constructive in the sense that the new information that is perceived and interpreted by the
learner in a unique way must be elaborated and related to other information in order that it can
be learned.
Therefore, an essential feature of learning processes is the integration of aspects of new
learning experiences with the learner's existent knowledge. As the learner interacts in situations,
information from several sources, including previous experiences, must be elaborated and
combined in meaningful ways, so that the new information that is generated and interpreted by
the learner can be related to the learner's existent knowledge, which may also be re-interpreted
in the light of the new experience. Ultimately, this leads to a constructive process in which new
knowledge is generated and related to elements of previous experiences.
In our theory, constructiveness refers to the property that a course of interaction exhibits
when entities experienced by the learner in one situation are in some way related to new entities
that the learner generates in a later situation of the course of interaction. A particular way in
which a course of interaction can be constructive is from an event, which involves experiencing
an entity that is old for the learner, in one situation of a course of interaction, and further
generating a new entity, through an event that utilises the old entity, in another situation of the
course of interaction, which will then be constructive with respect to the new entity. This
definition is presented below. Other ways may involve generating a new entity that is connected
to the old entity in several other ways.
Definition (Constructive with respect to a content entity from an event) A course of interaction
course(s1, t1, s2, t2) is constructive with respect to a content entity x for a learner a, if the
learner 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 x
which 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(saladlab-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 property
holds:
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 and
constructiveness take not just the patterns utilises or generates (i.e. not just acting), but also
other patterns of interaction, relating acting to aspects of contexts and cognitive states involved
in action.
Property of Self-Regulatedness
As learners interact in situations they have to make decisions about what actions to take in order
to attain their goals or even to help in defining their goals. This requires an awareness of how
they are progressing in their learning experiences and an ability to regulate their involvement in
these experiences. In a constructivist view of learning, the activities that bring this awareness
and help in regulating the learner's actions are performed by the learner, and involve learners
regulating their actions based on several kinds of information that they obtain from their
interactions in situations. Ultimately, this leads to a self-regulated process in which aspects of
the 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 exhibits
when a learner's action performed in one situation is in some way evaluated by the learner in
another situation of the course of interaction, and this evaluation is taken into consideration to
guide the next learner's actions or change the effects of previous actions. The learner's actions
correspond to events that are part of the learner's alphabet and occur in situations. These events
have an associated context which represents the information that is relevant to evaluating the
corresponding actions. This information can be defined as part of the situation type and accessed
when needed or be generated by the learner in a dynamic evaluation. The different ways in
which this information is produced and used characterise different ways in which a course of
interaction can be self-regulated for a learner.
Among the many different ways in which a course of interaction can be self-regulated, we
have identified two main classes of self-regulatedness: self-regulatedness from access and selfregulatedness 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 another
situation of the course of interaction. The information accessed (or generated) is an evaluation
context for that action, and the course of interaction will then be self-regulated with respect to
the 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 the
event) A course of interaction course(s1, t1, s2, t2) is self-regulated with respect to generating a
content entity x through an event e and accessing a context c before the event, for a learner a, if
the learner a accesses the entity c that is an evaluation context for the event e, in (s1, t1), and
further generates the entity x in (s2, t2) through the event e, with t2-t1 being the time gap
between 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-a
for 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 of
interaction 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(saladlab-a, 26, salad-lab-a, 28) is self-regulated for the learner with respect to adding an ingredient
lettuce to a salad, in the context provided by the book "Well balanced salads", which means that
the 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 a
problem or to construct an artefact, reflection involves them being aware of the process by
which they are developing these activities, and to take this process as the object of their
thinking. According to Dewey (1933), quoted in (Ertmer and Newby, 1996), reflection involves
"reconstruction or reorganization of experience which adds to the meaning of experience and
which increases ability to direct the course of subsequent experience" (p.76). This reflective
activity 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 the
representation of that particular experience, or, as von Glasersfeld (1995) would prefer: the representation of the experience, as it involves the learner presenting again, or replaying, to
herself a past experience. In this process, the learner has to recollect what has taken place in the
experience 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 recollection
of information about an experience, is the evaluation. Based on this information the learner
evaluates the experience, focusing primarily on the process by which the course of interaction
has developed. This allows the learner to determine how effective her overall process was in
achieving 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 their
learning experiences focusing primarily on the overall process by which their interactions in
situations have developed.
In our theory, reflectiveness refers to the property that a course of interaction exhibits when
aspects of the learner's process of interaction in some situations are the objects of reflective
activities carried out by the learner in later situations of the course of interaction. Basic aspects
of the process of interaction are represented by the entities that denote the occurrence of events
and the presence of entities in situations. These entities are basic process entities and will
constitute the basic elements of other types of process entities defined in types of situations. For
example, a trace, which is a kind of process entity, can be generated as a sequence of event
occurrences, 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 of
situations of a course of interaction, and further accessing (or generating) an entity that contains
information about the process of interaction in those situations, in another situation of the course
of 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 content
entities that contain information about aspects of the process of interaction. Formally, a process
entity is a content entity that is related in some ways to an entity of situation development, such
as occurs( ) or in( ). Therefore, the two main types of process entities are: process entities
derived from collecting occurrences of events in situations, and process entities derived from
collecting states of situations or presences of entities in situations.
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Definition (Reflective from access with respect to occurrences) A course of interaction
course(s1, t1, s2, t2) is reflective with respect to a process entity x that collect occurrences of
events 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 type
salad-lab-a to show the sequence of events which occurred in the process of interaction with that
situation type, where t1 is the time of the first occurrence and tn is the time of the last
occurrence.
trace-salad(salad-lab-a, t1, tn)
Accessing this entity after developing the events that are collected in the trace will
characterise a reflective course of interaction.
The properties that we have discussed and defined above characterise regularities that may
happen in courses of interaction which denote particular ways in which learning processes can
be 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 further
properties. Our definitions could also be extended to adopt more complex models of these
properties, such as Winne and Hadwin's (1998) model of self-regulation, or the model of selfregulation 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 interaction
develop properties such as cumulativeness, constructiveness, self-regulatedness and
reflectiveness, when learning events that occur in the situations involved in these courses of
interaction lead to certain patterns of interaction that are relevant for the development of the
particular properties. Therefore, after a sequence of learning events, several patterns of
interaction hold in the situations where the learner had been interacting, and a set of properties
of courses of interaction hold as a consequence of these patterns. These patterns of interaction
and properties of courses of interaction that hold throughout the situations of the learning
process 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 several
situation types, and is about to engage in interaction with a further situation type. Each event
available 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 lead
to the development of courses of interaction that exhibit the same properties. Whether or not
possibilities for interactions entail possibilities for properties of courses of interaction will
depend on the state of the learning process.
Therefore, according to the characteristics of the events defined as part of the dynamics of
a given situation type, and according to the previous history of the learner's interaction with
other situation types, interaction in this new situation type may lead to the development of
particular patterns of interaction, and consequently, allow certain properties of courses of
interaction to hold. If a system can know in advance the possibilities offered by a situation type
for the development of these properties for a learning process that is in a certain state, then the
system can use this information to support its decision making concerning the kinds of situation
types that will be made available for the learner in the environment's space of interaction at a
particular time.
In order to allow an intelligent system to consider these possibilities in advance, we have
developed a formal account of possibilities for interactions and for time-extended processes of
interaction 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 learning
environment to reason about the features of situation types that afford the desired patterns of
interaction and properties of courses of interaction to be developed in the following events of a
learning process that is in a certain state.
Concerning interactions, a situation type may afford to a learner the development of
particular patterns of interaction. For example, a situation type s in which the following
definitions 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 of
the pattern generates). For another example: if an entity of a situation type is new to a learner
and there are ways in the situation type in which the learner can utilise this entity, which then
would become old for the learner (according to the definition of the pattern old), then we can
say that an affordance of this situation type to that learner is the possibility of developing the
pattern of interaction in which the referred entity is old for the learner. Of course, after this
event happens, i.e. the utilisation of the entity and it becoming old, the affordance will no longer
be 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 the
development of patterns of interaction such as the ones that we have defined earlier, a situation
type can also afford to a learner the development of courses of interaction that exhibit particular
properties. 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 following
patterns 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 now
developed situation (s, t), the holding of these patterns, according to the definition of
cumulativeness, 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 the
situation type s affords to the learner a, at a certain time greater than t1, the development of a
course of interaction that is cumulative with respect to the entity x.
Therefore, concerning time-extended processes, a situation type may afford to a learner the
development of courses of interaction that possess particular properties such as the ones that we
have defined in the previous section. Note that the way in which the affordance is relative to the
learner refers to relativeness to the whole process that the learner has gone through, and not only
to individual characteristics of the learner. In the example above, if the learner has not utilised
the entity x in any previous situation, the situation type s would not be able to afford
cumulativeness with respect to that entity at this time.
In our theory, we have identified two types of affordances of situation types: affordances
for patterns of interaction, which represent possibilities in situation types for the development
of patterns of learner's actions in situations, learner's cognitive states in situations, or relations
between situations, and affordances for properties of courses of interaction, which represent
possibilities 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 more
extended 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's
actions in situations, the situation type must contain types of events with the kinds of
preconditions and effects that allow the learner to utilise, generate, or access entities of the
content 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 a
generating an entity x through an event e, iff the event e is defined in situation type s as part of
the 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 situation
type 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 to
the 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, a
situation type must contain the kind of content and dynamics that allow a learner who is in a
certain cognitive state to develop the patterns in which entities of the situation type become new
or old to the learner, according to the definitions of these patterns presented before. Below we
present the definition of the affordance for the pattern new, in which these conditions are
formally stated.
Definition (Affords new content entities in situations) A situation type s affords to a learner a
an entity x being new at the current time tc or after, iff the entity x is defined or can be
generated in the situation type s, and x has not been utilised nor generated by the learner a in
any 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 as
unwashed, and no pattern of utilising or generating this ingredient state holds in previous
situations, then, according to the definition above, we say the situation type affords to the
learner, at the current time or after, the notion of an ingredient cabbage in a state of unwashed
being 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 interaction
that are cumulative, the situation type must afford to the learner the development of the kinds of
patterns of interaction that will lead to particular kinds of cumulativeness being developed,
according to the definitions of cumulativeness presented before. Below we present the definition
of one of these affordances.
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Definition (Affords cumulativeness with respect to a content entity) A situation type s affords
to a learner a the development of a course of interaction from situation (si, ti) that is cumulative
for the learner with respect to a content entity x, if the learner utilises x in (si, ti) or generates it
in (si, ti-1) and the situation type s affords to the learner a situation that shares the entity x with
situation (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 (saladlab-a, 8):
utilises(learner, ingredient(lettuce), wash-ingredient, salad-lab-a, 8)
In addition, suppose that the following affordances for patterns of interaction hold in
situation 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-b
affords 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 the
following 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's
action performed in one situation is in some way evaluated by the learner in another situation of
the course of interaction, and this evaluation is taken into consideration to guide the next
learner's actions or change the effects of previous actions. To afford to a learner the
development of courses of interaction that are self-regulated, a situation type must contain
particular content entities and afford to the learner the development of particular patterns of
interaction that will lead to particular kinds of self-regulatedness being developed. Below is one
definition.
Definition (Affords self-regulatedness with respect to a content entity from access to context
after the event) A situation type s affords to a learner a the development of a course of
interaction from situation (si, ti) that is self-regulated for the learner with respect to a content
entity x, which is generated through an event e, from access to an evaluation context c, if the
learner generates the entity x through the event e in (si, ti), and the entity c is defined in
situation type s as an evaluation context for e, and the situation type s affords to the learner
accessing 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 (saladlab-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 for
the 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 to
the learner the development of a course of interaction from situation (salad-lab-a, 4) that is selfregulated for the learner with respect to adding an ingredient lettuce to a salad, in the context
provided by the book "Well balanced salads", which is the same as saying that the following
affordance 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 implemented
INCENSE – an INtelligent Constructivist ENvironment for Software Engineering learning.
INCENSE is capable of analysing a time-extended process of interaction between a learner and
a set of software engineering situations provided by the environment, in terms of its
cumulativeness, constructiveness, self-regulatedness, and reflectiveness. It can then adapt the
space of interaction provided by the environment in order to make available to the learner the
types of situations that afford the development of further courses of interaction that lead to the
desired 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. The
general setting is a software engineering laboratory in which two main needs shall arise:
 Modelling a software engineering process
Which involves the learner constructing a model of a particular process of software
engineering, such as the process of software project planning, so that the model can be
applied 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 software
development
Which involves the learner using a model of a particular process of software
engineering, such as a model of the project planning process, as a basis for developing
the activities related to this particular process in a project of software development.
The situations of INCENSE correspond to particular cases in which modelling a software
engineering process, or applying a software engineering process model, or both, are needed. In
situations that involve modelling a software engineering process, the model created by the
learner 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 of
software 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 in
planning a software development project, the application is defined in terms of the model being
applied. Therefore, the learner's actions, instead of focusing on creating a model, would be
actions 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 in
terms 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 this
notion constructed, which was not given, to construct another notion (e.g. the particular activity
graph that is part of planning a particular project). This would correspond, in the salad design
situations of SAMPLE, to constructing the notion that a salad is made of ingredients, which is
given in SAMPLE, and then constructing the notion that a particular ingredient is part of a
particular salad.
Learning Situations of INCENSE
Software engineering situations of INCENSE have content and dynamics. The content includes
sources 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 of
information also include the details of the model being created in the situation or the application
being developed. Physically, these sources of information are archives that are presented in the
situations 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 project
planning; and the learner archives, which contain the information created by the learner during
her or his interaction with the situation.
The dynamics of INCENSE situations include a set of interaction events that can be
activated by the learner using the mouse and which activate procedures that correspond to the
several kinds of actions necessary to create models of software engineering processes, as shown
in Figure 1 (e.g. create-process, create-material, etc.), or to apply models of software
engineering processes. For example, to include the process "specify requirements" with result
"data flow diagram" in her model, the learner activates the procedure create-process, which
allows to add a process to the model, which is selected from a list of process-concepts, and then
activates 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 the
external view of INCENSE situations, as these characteristics are physically part of the
representation of the situation setting that appears in the screen and with which the learner
physically interacts. The formal, internal representation of these and other characteristics of the
content and dynamics of INCENSE situations is presented below, for the situation type modelrs2, 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 are
the sources of information for modelling the particular software engineering process, and two
sets of software engineering concepts: process concepts and information concepts. Process
concepts are used to create processes in the model. Information concepts are used to create
materials, results or contents in the model. Some of the objects of these kinds defined in modelrs2 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 support
modelling, with their preconditions, effects and associated contexts. To create processes in the
model 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 processconcepts 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 introduced
in 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 a
situation type for modelling the process of software project definition; model-rs1, which is a
situation 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 wish
to interact is made from the space of interaction, which contains a selection of situation types
that 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 characterise
a 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 developed
involving the content and dynamics of this situation type.
Formally, the events that occurred and the changes in the content of the situations
developed by the occurrence of these events are described in terms of the entities of situation
development 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 process
created. 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 1
occurs create_process
time 2
in process(specify requirements)
in part(trace_modelling(model_rs2, 2), occurs(create_process, model_rs2, 1))
occurs access_archive
time 3
occurs
create_material
time 4
in 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 5
occurs
create_result
time 6
in 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 generated
in the whole interaction (six steps). The fragment of the software engineering process model
constructed in these few events is shown in Figure 2.
In practical terms, what happened in these six steps of interaction is that the learner started
to create her or his model of the process of software requirements specification, whose partial
product is illustrated in Figure 2. This model fragment represents that the activity of specifying
the software requirements uses the description of the project scope as material and produces a
data flow diagram as result. In the course of this interaction, the learner has also accessed the
archive that contains information about how software requirements are analysed. Although this
archive contains information that helps the learner to build her or his own model, the meaning of
entities such as "project scope", "specify requirements", and "data flow diagram" has to be
constructed by the learner as she or he applies her or his model in other situations.
project
scope
specify
requirement s
dat a f low
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 been
developed, which correspond to the system's interpretation of the learner's interactions in the
situations. The procedures for doing this in INCENSE, implemented in prolog, follow quite
straightforward from the formal definitions of the patterns of interaction. An extract is presented
below.
After the learner A has interacted in situation S from Tm to Tn
For 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) holds
Otherwise, 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 example
concerning the patterns of learner's actions in situations (utilises, generates, and accesses) and
the patterns of cognitive states in situations (new and old). In the Figure, software engineering
concepts are represented by wiggly bubbles, processes by round bubbles, materials or results by
rectangles, and the arrows indicate input and output of learner's events.
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System Intelligence in Constructivist Learning
t im e 1
t im e 2
specif y
r equi remen t s
specif y
re quir ement s
ut il ises
ge nerat e s
new
Req uir ement s
analysis
n ew
accesses
t ime 4
t im e 3
Trace
p ro ject
scop e
specif y
r equi remen t s
ut il ises
new
ut ilises
> -- > -- > -- -
p ro ject
scop e
ne w
o ld
accesse s
gen erat e s
t im e 6
t im e 5
d at a flo w
d iagr am
ut ili ses
new
ut ilises
spe ci fy
r equ ireme nt s
d at a flo w
d iagr am
n ew
old
ge nerat e s
Figure 3. Patterns of interaction in the situation for modelling the process of requirements
specification
Analysing the Time-Extended Process of Interaction
Following the analysis of interaction, INCENSE proceeds with the analysis of courses of
interaction to determine the properties of cumulativeness, constructiveness, reflectiveness, and
self-regulatedness, which correspond to the system's interpretation of the time-extended process
of interaction developed. In reasoning about courses of interaction, INCENSE uses its
knowledge about properties of courses of interaction that we have formally described earlier to
obtain the properties that hold in a process of interaction. Table 4 shows some of the properties
developed from the interactions of our example.
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Akhras and Self
Table 4. Properties of courses of interaction in the situation for modelling the process of
requirements specification
_____________________________________________________________________
time 1  time 2
self-regulated with respect to process(specify requirements)
and context archive(Requirements analysis)
time 2  time 3
cumulative with respect to process(specify requirements)
time 3  time 4
constructive 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 6
constructive 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 of
learning events developed in the situation that the learner has just left, INCENSE analyses the
situation types that are part of the environment so that the affordances of these situations to the
learner can be determined. As we have discussed earlier, this is done taking into consideration
the interactions developed in the situations up to the current time and the possibilities of the new
situation types for the development of further interactions that lead to properties of
cumulativeness, constructiveness, self-regulatedness, and reflectiveness holding in the following
learning interactions. In Table 5 we show some of these affordances for situation type modelrs2. (Note that if an entity contains a variable, such as in the case of process(X), this variable is
bound 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 n
cumulative with respect to concept(specify requirements)
time 2  time n
cumulative with respect to process(specify requirements)
constructive with respect to relation(material(concept(Var), process(Var)))
time 3  time n
cumulative 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 n
constructive with respect to information(Var)
...
time 6  time n
self-regulated with respect to process(Var)
and context archive(Requirements development)
reflective with respect to trace_modelling
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System Intelligence in Constructivist Learning
In practical terms, what the analysis of affordances presented above tells the system is that
if, for example, model-rs2 is the next situation to be selected by the learner in the space of
interaction (in case it is there to be selected), then there are possibilities for cumulativeness with
respect 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 candidates
for the next space of interaction. In our example, we can see that all the four situation types
afford some of the desired properties of courses of interaction to be developed in the following
process. To sort this set of situation types in terms of their potential benefit for the learner we
have 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 selfregulations.
 Reflectiveness policy: consider situation types that afford reflections about entities that
have 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, are
summarised in Table 6. As the affordances for reflectiveness and self-regulatedness did not
change from one situation type to another due to the situation types of the example being all for
modelling and having similar mechanisms for self-regulation (access to similar archives), the
selection of situation types for the space of interaction in our example was based only on the
results of the analysis of affordances in relation to the policies concerning cumulativeness and
constructiveness, whose summary is shown in Table 6, in terms of the number of entities that
the situation types afford a first time cumulation and the number of entities that the situation
types afford construction.
Table 6. Summary of affordances
situation type
cumulativeness
constructiveness
model-pp2
model-rs1
model-rs2
model-d1
2
3
7
1
11
11
32
5
Therefore, following from the selection of the situation type model-rs2 in the first space of
interaction, which contained the situation types model-pp2 and model-rs2, and according to the
sequence of learning events developed in the situations derived from the situation type modelrs2, the next two situation types that are more likely to enable, for the learner, the development
of courses of interaction that exhibit the desired properties, are the situation types model-rs2 and
model-rs1. In practical terms this means that the objects and the possibilities for action that the
learner will encounter in the contexts provided by these two types of situations allow the
development of learning interactions that make connections with aspects of interactions
developed in previous situations and, therefore, help to ensure a continuing learning experience
that 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 which
two students used INCENSE, each one interacting individually for about thirty minutes with the
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Akhras and Self
system, producing courses of interaction that extended over fifty events, in which they had to
model a process of software engineering project planning. The main goal of this study was to
observe the development of properties of cumulativeness, constructiveness, self-regulatedness
and reflectiveness in more extended sequences of learning events developed by real students.
The results are summarised in the table below.
number of different entities cumulated
number of different entities constructed
number of different entities self-regulated
number of different entities reflected upon
student A
25
32
1
0
student B
8
22
9
0
Neither student developed reflective courses of interaction, which in INCENSE means that
the interaction traces were not accessed. Concerning the properties developed, the numbers
show that student A cumulated and constructed more than student B but spent less time selfregulating, which in INCENSE corresponds to accessing archives that contain information about
software engineering concepts. Following an analysis of affordances, the system might tend to
offer to student A situations that allow fewer new constructions and more self-regulation of the
constructions made before, while to student B the system might offer situations that allow more
new constructions.
CONCLUSION
In this paper we have argued that the change in perspective provided by constructivist views of
learning, in regard to the nature of knowledge, the way learners learn, and the way learning can
be promoted, rather than pointing to a move away from the idea of system intelligence in the
computational support to constructivist learning, points to a new kind of system intelligence that
is 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 of
learning.
Focusing on these issues, we have developed a set of formal mechanisms that support the
kinds of knowledge representation, reasoning, and decision making that are necessary in order
that a constructivist learning environment can develop an evaluation of learning with a focus on
the process rather than on the product of learning and can then use this evaluation in order to
adapt the environment to the learner needs, aiming for the development of further processes of
learning that possess certain desired properties rather than the acquisition of a target knowledge.
The whole approach was implemented in INCENSE, which is an intelligent learning
environment for software engineering learning that follows a constructivist perspective.
INCENSE is able to evaluate learning processes in terms of the four main properties that have
been put forward by constructivist theorists as conducive to learning: cumulativeness,
constructiveness, self-regulatedness, and reflectiveness. It is also able to adapt the learning
environment in a way that facilitates the occurrence of these properties in following courses of
interaction.
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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