=Paper=
{{Paper
|id=Vol-381/paper-5
|storemode=property
|title=Revisiting Pedagogic Strategies for Supporting Students' Learning in Mathematical Microworlds
|pdfUrl=https://ceur-ws.org/Vol-381/paper04.pdf
|volume=Vol-381
}}
==Revisiting Pedagogic Strategies for Supporting Students' Learning in Mathematical Microworlds==
https://ceur-ws.org/Vol-381/paper04.pdf
Revisiting pedagogic strategies for supporting
students’ learning in Mathematical Microworlds.
Devolving teachers’ role to an ‘intelligent’ facilitator.
Manolis Mavrikis, Eirini Geraniou, Richard Noss and Celia Hoyles
London Knowledge Lab, Institute of Education, University of London,
23-29 Emerald Street, London, WC1N 3QS, UK
{m.mavrikis,e.geraniou,r.noss,c.hoyles}@ioe.ac.uk
Abstract. This paper presents categories of pedagogic strategies for
helping students during mathematical explorations in microworlds, that
take into account the constructivist theory of learning. We illustate the
strategies using examples from empirical data supported by other re-
search in the field. As precursor to designing intelligent support for ex-
ploratory learning environments we discuss ways to operationalise these
strategies in order to delegate some of the teacher’s responsibilities to
what we call an intelligent computer-based facilitator.
Key words: microworlds, pedagogic strategies
1 Introduction
The Migen project1 is developing a technical and pedagogical environment to
assist students with mathematical generalisations (see [1, 2]). Its core consists
of a microworld. Mathematical microworlds belong to a particular genre of ex-
ploratory learning environments (ELEs) that allow students to explore not only
the structure of accessible objects in the environment, but also construct their
own objects and explore the mathematical relationships between and within the
objects, as well as the representations that make them accessible [3, 4]. From
this perspective they are a generalisation of other ELEs which normally allow
the learner only to explore the effects of different variables on a particular model
(for a review of other types of ELEs -such as simulation environments- see [5]).
A substantial body of research shows that although students may be able to
use the tools available in microworlds (or in other exploratory environments), in
order to ensure that students’ interaction are effective and meaningful there is a
need for significant pedagogic support (see [5],[6, p70-71],[7]) from teachers. To
preserve the essence of exploratory learning environment, research suggests that
the role of the teacher should be that of a ‘competent guide’ [8], a ‘facilitator’ [9]
who, apart from structuring activities and promoting the appropriate learning
atmosphere, recognises the need for students’ autonomy and responsibility, di-
rects their attention accordingly, and can help them organise their environment
and plan and monitor their work.
1
http://www.migen.org. Funded jointly by the ESRC and the EPSRC through the
Technology Enhanced Learning Phase of the TLRP (RES-139-25-0381).
2 M. Mavrikis, E. Geraniou, R. Noss and C. Hoyles
This role is difficult to achieve in a normal classroom and therefore, teachers
often revert to their role as a transmitter of knowledge into a set of ‘empty vessels’
[9]. We envisage that some of the teacher’s responsibilities could be delegated to
an intelligent system which could support either the student directly or provide
information to teachers, helping them in their role as facilitators. We believe the
second option is particularly relevant and timely.
Along with other methods, principled approaches for developing intelligent
support can be based on observation of human tutors and students as well as rele-
vant theories of learning [10]. The constructivist theory of learning is particularly
relevant since it has been transformed through constructionism to a strategy for
learning, particularly applicable in microwords [11]. However, despite the fact
that previous research has recognised the need for more explicit research on
how students learn when interacting with microworlds and on appropriate types
of teacher interventions, relatively few attempts (e.g., [12]) investigate specific
strategies and ways to support students’ learning from a constructivist perspec-
tive in general. Fewer still (e.g., [7, 9]) are focused specifically on microworlds.
This paper presents pedagogic strategies for helping students during their
exploration in microworlds as a precursor to designing intelligent support. In
particular, Section 2 provides a brief description of the teacher’s role, shaped
by our understanding of our collaborating teachers, and taking into account
previous research in the field and the constructivist theory of learning. Section
3 presents an initial framework of pedagogic strategies, drawing examples from
empirical data supported by research literature. Section 4, provides suggestions
for operationalising our framework at a level of detail that would allow devolving
some of the teacher’s responsibilities to an intelligent computer-based facilitator.
2 Teacher’s role as a guide and facilitator
In microworlds, understandings are, at least partly, generated during interactions
with the system, rather than having to precede them. Although the design of the
microworld and the guidance provided by structuring activities should, ideally,
enable students to connect their actions and the relationships embedded in the
microworld, with the mathematical principles or ideas that a teacher would like
them to construct, inevitably they often need explicit support. The teacher’s
role as facilitator of this process is indispensable.
A helpful way of understanding this role, in general, is interpreting it as
having to be sensitive to the learner’s attention, but also to the way they are
attending [13], as well as their preferred strategies for solving a problem [12].
More specifically, in microworlds, a key challenge for teachers is to support ex-
ploration that is goal-oriented and which aligns with the teachers’ agenda (see
the ‘play paradox’ notion in [6] and other classroom vignettes in [7, 9]). In addi-
tion, expert teachers rarely assume the role only of an authority that judges the
quality of responses. On the contrary, they create situations where students can
reflect on their own responses and strategies. Additionally, the teacher promotes
motivation and supports the collaboration between students, not only through
the design of the activity but during the activity itself.
Pedagogic strategies for supporting students’ learning in microworlds. 3
3 Pedagogic strategies for student support in microworlds
The brief account of teachers’ role in Section 2 is the starting point for devel-
oping a set of categories of pedagogic strategies and teacher interventions (see
Table 1). This is based on our previous work for Logo [9] and dynamic geometry
environments (DGEs) [14] and is supported and adapted in the light of empirical
data from early prototype microworlds developed for the MiGen project [2].
1. Supporting processes of mathematical exploration
• Supporting students to set and work towards explicit goals.
• Directing students’ attention.
• Helping students organise their working environment.
• Provoking cognitive conflict.
• Encouraging alternative solutions.
2. Supporting reflection
3. Promoting motivation
4. Supporting collaboration
Table 1. A framework of pedagogic strategies for student support
These pedagogic strategies, discussed explicitly in the following sections, pro-
vide an initial framework for modelling teacher’s role. Section 4 revisits them
providing details and suggestions for designing a computer-based facilitator.
3.1 Supporting processes of mathematical exploration.
Adhering to their role as facilitators, teachers can support the processes of math-
ematical exploration by helping students set and monitor their goals, by directing
their attention appropriately, by helping them reflect on their actions and the
microworld’s visual feedback, and by provoking cognitive conflicts that demon-
strate the limitation of students’ approach. In addition, teachers can help stu-
dents reflect on their solutions and finally allow them, if not encourage them, to
come up with more alternative solutions. These are briefly discussed below.
Supporting students to set and work towards explicit goals. The im-
portance of directing students’ goals during mathematical exploration was men-
tioned already. Regardless of who sets activity goals the effective teacher’s role is
to orient students to work on well-defined investigations [6, 7] (e.g. “Investigate
the relationship between these two shapes”). However, a difficulty that students
face when solving problems in general is a tendency to lose sight of their overall
goal. As emphasised in [13], attention is usually caught up by current actions
which are sometimes only intermediate towards a goal. In microworlds, and par-
ticularly where interaction is via direct manipulation, some actions may not be
directly relevant to the mathematical aspects that are being explored, yet nec-
essary in order to reach a goal. This loss on focus on the goal is often observed
in our studies with the MiGen tools and in previous research with DGEs and
Logo. For students who are facing difficulties, teachers provide a reminder of
their goals trying to re-establish it: “What were you trying to do?”, “Do you
4 M. Mavrikis, E. Geraniou, R. Noss and C. Hoyles
remember the question?”. Often simple questions like these, even if they are not
answered, can orient students back towards their goal.
Another way of helping students is to provide specific prompts that can guide
them towards their goal. Before providing help, effective teachers establish the
goal students are trying to achieve and try to adopt their way of thinking rather
than the ‘correct’ one. In other words, the teacher needs to maintain a subtle
balance between solving problems for students (or providing the way to solve a
problem) and, leaving students on their own and unable to proceed if stuck.
Directing students’ attention. In order to direct students’ attention, teachers
first try to determine of what they are not yet aware, then find ways to prompt
them without giving the answers away [13]. For example, if they suspect that a
student has not noticed certain facts they may ask a question to direct students’
attention to this fact (e.g. “Did you notice what happens when you resized the
circle?”). Questions like this help students to start noticing invariants or other
details which are important towards their investigation.
In most cases, empirical data and other research (e.g., [12]) suggest that par-
ticularly expert teachers tend not to intervene if students’ attention seems to be
directed towards something that teachers believe is useful. If however, students
insist on looking or manipulating unnecessary elements of their construction
(e.g., dealing with relationships or properties that are not meaningful), teachers
eventually intervene by providing hints towards more constructive aspects to
be perceived. Finally, sometimes procedural mistakes can be scaffolded, or even
ignored [12] in favour of directing students’ attention to more important issues.
Helping students organise their working environment. Related to the
strategies mentioned above are interventions that teachers make, targeted specif-
ically to helping students organise their working environment, either in order to
work effectively towards a specific goal or in order to help them become aware of
relationships between objects. For example, they may suggest a specific action
(e.g.“Why don’t you make a [certain shape]”), or ask students to change the
location of a shape, its properties or delete unnecessary shapes.
The effectiveness of this strategy is supported by the fact that students who
cope better with activities, are very good at organising their environment and
take specific actions targeted towards their goal. Usually they find ways to place
shapes in ways that support their perception and avoid cluttering their interface.
Provoking cognitive conflicts. As mentioned in the Introduction, in mi-
croworlds students often have to be explicit about the relationships they recog-
nise. For example, in DGEs relationships and shape properties must be made
explicit if this shape is constructed and not simply drawn. Teachers employ
student-assigned relationships to create a cognitive conflict and help students
become aware of the lack of explicit relationships. A typical intervention is pro-
viding a counter-example. Another strategy, in DGEs, is “messing-up” [15] which
challenges students to generalise a construction by dragging a point to check if
its properties (e.g., an intersection point) remain invariant when the variable
aspects change. Although the exact technique is usually activity-specific, the
strategy is general and has been used effectively in other tasks (e.g., [1]) .
Pedagogic strategies for supporting students’ learning in microworlds. 5
Encouraging alternative solutions. Teachers who realise the importance of
encouraging students’ autonomy and responsibility over their learning, allow a
margin for different solutions to emerge even if it is not evident from the be-
ginning that an approach will be effective [12]. In microworlds and in activities
where there are multiple ways to approach a construction, it is surprising how
often students come up with innovative, valid, approaches that were not antic-
ipated in advance. Following a constructivist perspective, it is more desirable,
to let students choose their own way. Of course not all of them are elegant or
demonstrate perfectly the mathematical ideas that the teacher intended. The
teachers’ role then is to guide students to reflect on the limitations (or advan-
tages) of their approach, compared to other approaches that are, for example,
more efficient, more understandable, etc.
3.2 Supporting Reflection
Reflection is important in the process of learning as well as a critical meta-
cognitive skill. When students are working on a task, teachers usually remind
them of actions, strategies or even their own previous prompts. This eventually
supports students’ autonomy to become able to evaluate their own mistakes and
progress. To ensure students have not only reached their goals, but also gained
knowledge at the end of an activity, studies of human tutors suggest that they
often give help both during and after a student’s performance [16]. In addition,
even in the cases where mistakes are ignored or rectified, it is unlikely that a
teacher would proceed without a reflective discussion at the end of the session.
In microworlds, and particularly in activities with multiple solutions, an explicit
phase of reflection is important. Although students may have started recognising
some relationships, internalising them and perceiving the concepts that underpin
them in order to use them in subsequent activities requires explicit reflection,
and articulation by teacher and students.
3.3 Promoting Motivation
Although motivation is usually supported by the overall task-design which should
provide an intrinsic motivation and incentive for engagement, expert teachers
sense when students are in need of praise or encouragement and provide these
by employing several strategies. The right incentive and appropriate praise even
for the smallest achievement or effort that students exerts, usually have a positive
effect on their attitude towards learning and further progress. Similarly, constant
encouragement and support are important.
3.4 Supporting Collaboration
Apart from promoting a collaboration culture in classroom through appropri-
ately designed activities, the teacher needs to foster students’ collaboration and
to facilitate discussion, encourage questioning and, depending on the overall
task, help students set challenges to each other. The difficulty for the teacher in
a classroom is to monitor all the groups of students and be able to change the
group dynamics (e.g., if one student is dominating the discussion). In addition,
empirical data reveal another strategy where teachers dynamically allocate com-
petent students who have completed their tasks as ‘helpers’ for other students.
6 M. Mavrikis, E. Geraniou, R. Noss and C. Hoyles
4 Discussion - Suggestions for Intelligent Support
Each pedagogic strategy and the interventions discussed in Section 3 require in
depth discussion to be operationalised to the level of detail that would allow its
implementation for intelligent support. Although we presented these strategies
as ways of helping students directly, we acknowledge that some of them involve
a significant amount of uncertain information that an intelligent system cannot
always deal with. In what follows we provide brief suggestions on how aspects of
the teacher’s role might be devolved to an intelligent computer-based facilitator.
4.1 On supporting students to set and work towards explicit goals.
Section 3 highlighted the importance of helping students set and prioritise their
goals, but also the need to identify what the students’ current goals and inten-
tions are, before providing any help. The issue of support for students’ goals has
been targeted in intelligent simulation environments [5] where students’ goals
are determined or, at least, inferred, by letting them choose a specific assign-
ment from the environment. Since the goal of this assignment is known to the
system, it can offer more contextualised support. Something similar could be
achieved in microworlds. For example in [14] students work in a prototype in-
telligent DGE and select specific tasks and goals. This enables the system to
provide support and direct students’ attention according to predetermined rules
that are described by the activity designer.
In relation to secondary goals (within an activity) we can draw again on
an example from simulation environments. For example, the system presented
in [17], is designed to allow students to define and keep track of the hypothesis
they want to test in an explicit way. Although, ideally, this would require natural
language processing capabilities, providing possible goals and hypotheses in the
form of multiple choice questions or dropdown menus can provide an effective
scaffold for students and is not necessarily restricting, especially if different goals
can be chosen. A similar technique has been used in SHERLOCK [18] to help the
learner’s planning during a diagnostic problem-solving process by choosing their
next step from a menu of actions. This provides a window to their intentions
but also opportunities for metacognitive scaffolding.
4.2 On directing students’ attention
Modelling the structure of attention Directing students’ attention appro-
priately (or informing teachers about issues related to it) requires inferring stu-
dents’ current goals. In addition, it is important to be aware of the different ways
of attending [13] since they determine the kind of help that can be provided to
the student. A useful framework for modelling the different ways of attending
is provided in [13] and is referred to as, the ‘structure of attention’. With this
as a starting point and adapting it for microworlds we can distinguish three
intertwined but subtly different layers of attention. The first can be referred
to as exploring-manipulating and involves students spending time in arbitrary
object constructions and manipulation, usually at the beginning of the activity,
Pedagogic strategies for supporting students’ learning in microworlds. 7
followed by inspection of properties and more specific construction steps. The
role of an intelligent system, when students are still exploring, could be to direct
their attention appropriately (e.g., by flagging details they may be missing) or
to detect (and inform teachers) whether they are having difficulties and are fail-
ing to explore important aspects. The next layer of attention has been referred
to as “getting-a-sense-of ” [13, 6] and involves actions that demonstrate that the
student is starting to discern details and recognise important relationships be-
tween the concepts involved in a task. In the final layer of attention students
are perceiving general properties or concepts. It involves students’ employing the
relationships embedded in the microworld as the basis for their reasoning and is
usually manifested across different activities.
A window on the students’ object of attention Because of the nature
of microworlds it is often the case that students create and interact with many
objects in their attempts to get a sense of what they are being asked to do. This
introduces noise for an intelligent system. However, it is possible to make some
inferences about the object of students’ attention. For example, during studies on
students-tutors interactions in a setup where tutors could observe students’ work-
ing environments only from a remote location [19], mouse movements, button
clicks and other interactions helped tutors infer the object of students’ attention.
Their inferences can be emulated to help the computer-based facilitator be aware
of what students are attending to. Empirical data from students interacting with
the exploratory tools developed for MiGen suggest that direct manipulation of
objects and inspection of properties can provide substantial information to allow
an intelligent system to infer the object of students’ attention.
The difficulty the system faces is similar to the one a teacher faces when
approaching students who request help in a classroom and does not have a de-
tailed context of their preceding work. A teacher would establish which object
students are attending to by asking them directly. It is not too bold to imagine
that when the system lacks knowledge about the object of students’ attention
and before being able to help them, it could require a particular interaction such
as highlighting the object they are attending to. In particular, the microworld
can be designed in a way that ensures an increased ‘bandwidth’ (see [20]). For
example, instead of displaying all available information at once, the microworld
can be designed so as students’ interactions are less ambiguous providing evi-
dence for what they are attending to. Examples of such a design for a prototype
microworld for generalisation for the MiGen project are presented in [2].
4.3 On helping students organise their working environment
In Section 3.1 we mentioned the value of supporting students perceptions by
helping them organise their work space. Although the ways to help them achieve
this are situation-specific, assuming that the task is known to the system, there
are prompts that the system can give or actions it can take to help students
directly or through the teacher. Also, for different domains there will be general
principles that can be used for supporting students. For example, cognitive psy-
chology principles for the way humans organise perceptual stimuli, were useful in
8 M. Mavrikis, E. Geraniou, R. Noss and C. Hoyles
designing intelligent support for DGEs [14]. Based on these, an intelligent com-
ponent provides hints for bringing related objects close, for avoiding or trying
to make their size really small or large, and in general helps students reorganise
the locations of objects in order for their attention to be directed to appropri-
ate places. In addition, we mentioned that competent students avoid cluttering
their interface and that teachers employ similar strategies to help students. The
computer-based facilitator could inform teachers about students who seem to
have difficulties organising their environment.
4.4 On provoking cognitive conflict
Using strategies adapted from human tutors, it is possible to devolve this as-
pect of teachers’ support to a computer-based facilitator. Apart from providing
automatically-generated counter-examples, a system can also take actions that
would demonstrate to students limitations of their approach. One example is the
aforementioned “messing-up” strategy that can be easily automated (examples
of intelligent support using this strategy are presented in [21]).
4.5 On providing support for multiple and innovative solutions
Activities in microworlds usually expect students to come up with a construction
with explicit relationships and properties and therefore, by observing if these
relationships and properties are present, it may be easier than in others contexts
(e.g., solving procedural algrebraic problems) to support multiple and innovative
solutions. This could enable the system to determine students’ plans or strategies
and help either the teacher or the student directly, by providing notifications of
unpredictable or innovative strategies, or by suggesting appropriate next steps
employing students’ preferred strategies as envisaged in [12]. Some ideas of how
this could be achieved using case-based reasoning are presented in [21]. Also, in
[22] an approach based on Hidden Markov Models is presented that could be
used to allow freedom to learners and cater for innovative solutions.
4.6 On supporting reflection
An intelligent system could support the teacher’s responsibilities (see 3.2) and
automatically generate or propose activities that give students the opportunity
to reflect on their actions or important parts of an activity. Students’ proficiency
to perceive important concepts and use them in other situations can be ‘assessed’
by designing activities that expect knowledge acquired in previous activities to
be re-used. The computer-based facilitator can then observe if students are using
their previous understandings or, as they often tend to: reinvent the wheel.
4.7 On promoting motivation
In the field of Artificial Intelligence in Education (AIEd) there have been at-
tempts (and some success) to detect and adapt to aspects of students’ affective
and motivational characteristics. However, in certain cases it may be difficult
and inappropriate for a computer-based tutor to respond or adapt to students’
affective characteristics. Assuming that adequate intrinsic motivation is provided
Pedagogic strategies for supporting students’ learning in microworlds. 9
from the activities and the overall environment, intelligent support can be lim-
ited (but still very useful) in communicating to the teacher diagnoses of students’
motivational states. AIEd research suggests that it is possible to detect factors
such as confidence and effort [19] as well as off-task behaviour [23]. The latter
could be particularly useful in microworlds, where students tend to ‘play’ in
quite a few occasions. The teacher’s presence is necessary to decide when and
whether this should end. With appropriate prompts and good management skills
teachers with their authority could bring students back on-task, something that
may be difficult for a system to achieve easily.
4.8 On supporting collaboration
There is a substantial amount of research on computer-supported collaborative
learning. Here we would like to emphasise only the need to support the teacher
during classroom sessions with students collaborating in groups. A computer-
based facilitator can notify the teacher about students who finish part of the
tasks so as they can help others, or provide information about the dynamics of
different groups (e.g. dominating students), suggestions about more productive
groupings, or even intervene to help maintain a balance so as to ensure that the
positive effect of collaboration is achieved.
5 Further research
The strategies presented here need to be operationalised further before imple-
menting appropriate intelligent support in microworlds. Studies with low com-
munication bandwidth between teachers and students (such as the ones pre-
sented in [19, 24]), especially if designed to promote interventions that take into
account constructivist principles (such as the teaching experiments described in
[12]) can help in deriving more information on the effectiveness of such strategies
and specific ways of implementing them. Although the exact approach and some
of the prompts will be, inevitably, activity-specific, a general framework such
as the one presented here, could allow activity designers or teachers to specify,
for different activities, which responsibilities they would like to devolve to an
intelligent computer-based facilitator and how it could help them fulfill them.
References
1. Geraniou, E., Mavrikis, M., Hoyles, C., Noss, R.: Towards a constructionist ap-
proach to mathematical generalisation. In: Proceeding of the British Society for
Research into Learning Mathematics. Volume 28. (June 2008)
2. Pearce, D., Mavrikis, M., Geraniou, E., Gutierrez, S.: Issues in the design of an en-
vironment to support the learning of mathematical generalisation. In: Proceedings
of Third European Conference on Technology Enhanced Learning. (2008)
3. Thompson, P.W.: Mathematical microworlds and intelligent computer-assisted
instruction. In: Artificial intelligence and instruction: Applications and methods,
Boston, MA, USA, Addison-Wesley Longman Publishing Co., Inc. (1987) 83–109
4. Hoyles, C.: Microworlds/schoolworlds : The transformation of an innovation. In
Keitel, C., Ruthven, K., eds.: Learning from computers : mathematics education
and technology. Berlin : Springer-Verlag (1993) 1–17
10 M. Mavrikis, E. Geraniou, R. Noss and C. Hoyles
5. de van Jong, T., Joolingen, W.: Discovery learning with computer simulations of
conceptual domains. Review of Educational Research 68 (1998) 179–201
6. Noss, R., Hoyles, C.: Windows on mathematical meanings: Learning cultures and
computers. Dordrecht: Kluwer (1996)
7. Kynigos, C.: Insights into pupils’ and teachers’ activities in pupil-controlled
problem-solving situations. In: Information Technology and Mathematics Prob-
lem Solving: Research in Contexts of Practice. Springer Verlag (1992) 219–238
8. Leron, U.: Logo today: Vision and reality. Computing Research 12 (1985) 26–32
9. Hoyles, C., Sutherland, R.: Logo Mathematics in the Classroom. Routledge (1989)
10. du Boulay, B., Luckin, R.: Modelling human teaching tactics and strategies for
tutoring systems. International Journal of AIEd 12 (2001) 235–256
11. Harel, I., Papert, S.: Constructionism. Ablex Publishing Corporation (1991)
12. Lesh, R., Kelly, A.E.: A constructivist model for redesigning AI tutors in mathe-
matics. In Laborde, J., ed.: Intelligent learning environments: The case of geometry.
New York:Springer Verlag (1996)
13. Mason, J.: Being mathematical with & in front of learners: Attention, aware-
ness, and attitude as sources of differences between teacher educators, teachers &
learners. In Wood, T. & Jaworski, B., ed.: International handbook of mathematics
teacher education. Volume 4. Sense Publishers, Rotterdam, the Netherlands (2008)
14. Mavrikis, M.: Improving the effectiveness of interactive open learning environ-
ments. In: 3rd Hellenic Conference on Artificial Intelligence (SETN) - proceedings
companion volume. (2004) 260–269
15. Healy, L., Hoelzl, R., Hoyles, C., Noss, R.: Messing up. Micromath 10 (1994)
16. Katz, S., Connelly, J., Allbritton, D.: Going beyond the problem given: How human
tutors use post-solution discussions to support transfer. International Journal of
Artificial Intelligence in Education 13 (2003) 79–116
17. Veermans, K., Joolingen, W., de van Jong, T.: Promoting self-directed learning
in simulation based discovery learning environments through intelligent support.
Interactive learning environments 8 (2000) 257–277
18. Lesgold, A., Lajole, S., Bunzo, M., Eggan, G.: Sherlock: A coached practice envi-
ronment for an electronics troubleshooting job. In Larkin, J., Chabay, R., Scheftic,
C., eds.: Computer assisted instruction and ITS. Hillsdale N.J: LEA (1988)
19. Porayska-Pomsta, K., Mavrikis, M., Pain, H.: Diagnosing and acting on student
affect: the tutors perspective. UMUAI 18 (2008) 125–173
20. VanLehn, K.: Student modeling. In Polson, M., Richardson, J., eds.: Foundations
of Intelligent Tutoring Systems. Hillsdale, NJ: Erlbaum (1988) 55–78
21. Cocea, M., Magoulas, G., Gutierrez, S.: The challenge of intelligent support in
exploratory learning environments: A study of the scenarios. In: Proceedings of
the 1st Internation Workshop in Intelligent Support for Exploratory Environments
held in conjunction with ECTEL-08. (2008)
22. Stamper, J., Barnes, T., Croy, M.: Extracting student models for intelligent tutor-
ing systems. AAAI 2007 (2007) 1900–1901
23. Baker, R., Corbett, A., Koedinger, K., Wagner, A.: Off-task behavior in the cogni-
tive tutor classroom: When students ”game the system”. In: Proceedings of ACM
CHI 2004: Computer-Human Interaction. (2004) 383–390
24. Tsovaltzi, D., Rummel, N., Pinkwart, N., Scheuer, O., Harrer, A., Braun, I.,
McLaren, B.: Cochemex: Supporting conceptual chemistry learning via computer-
mediated collaboration scripts. In: Proceedings of the Third European Conference
on Technology Enhanced Learning (ECTEL-08). (September 2008)