Recorder into an annotated exercise graph which is later used to trace the student’s steps through the problem solution.
Such a simple tool removes the necessity of programming domain pro- duction rules, that makes it more accessible to teachers. But since there is no automatic pattern matching that can combine any possible next step with any possible next but one step, all the alternative correct and incorrect solutions have to be hand-crafted by the author.
Each step can be annotated with one or more hints, which are ordered sequentially at runtime. Finally, so-called knowledge labels are attached to the links in the behavior graph to refer to the underlying domain concepts.
Studies have shown that the Pseudo Tutor system finds intelligent tutorial behavior equivalent to the production based Cognitive Tutor. Authoring both kinds of systems is comparably time consuming.
The recorded behavior graphs, used for building Pseudo Tutors, can be also used to guide the development and testing of a cognitive model for use in a Cognitive Tutor, as described in [Aleven et al., 2006]. However, Pseudo Tutors do not remove the necessity to program domain production rules. The behavior graphs just help to explore the cognitive model of the domain and can be used as unit tests for the domain model.
A collection of tools for authoring Cognitive Tutors includes a number of further components, assisting building the Cognitive Tutors as well as external editor for editing Jess rules for the cognitive model.
CTAT tools have also been used for a machine learning approach to rule creation, using the Simulated Student - a machine learning agent [Matsuda et al., 2005]. This agent analyses the sample behavior graphs pro- duced by the human tutor and infers production rules. The Simulated Student agent is integrated into the CTAT tools, so that the authors can test the generated production rules by letting Simulated Student solve the new problems. Advanced authors can then manually modify the generated Jess rules, if desired.
2.4
The ActiveMath Learning Environment
The web based interactive learning environment ActiveMath is an intelli- gent tutoring system that supports advanced outer and inner feedback loops. Figure 2.4 shows the coarse architecture of ActiveMath.
30 CHAPTER 2. BACKGROUND AND RELATED WORK CAS Tutorial Component Student Model Knowledge Base Exercise Subsystem Client Presen tation Engine Search Index Books V iews External Diagnosis Systems
Figure 2.4: Coarse architecture of ActiveMath
One of the major features of ActiveMath is adaptivity. The Tutorial Component of ActiveMath, responsible for the adaptation in the outer loop, is capable of automatic course generation and presentation which is adapted to the learner’s goals, the given learning scenario and other indivi- dual parameters of the learner, as presented in [Ullrich, 2008] and in [Ullrich and Melis, 2009].
The Tutorial Component actively communicates with the ActiveMath Student Model, gathering information about the learner’s progress and mak- ing conclusions about his current knowledge mastery.
An important feature of the ActiveMath’s Student Model is that it dynamically extracts relations and metadata from the content ontology and makes use of their semantics. This metadata, together with the diagnosis of the student actions in interactive exercises, enables the Student Model to estimate the student’s competencies. This way the Student Model of ActiveMath is not bound to any concrete domain, but can work with any domain, that can be ”loaded” into the system. For more information on the Student Model of ActiveMath see [Faulhaber and Melis, 2008].
The Exercise Subsystem of ActiveMath implements the inner loop and provides the Student Model with evidence about learning progress,
2.4. THE ACTIVEMATH LEARNING ENVIRONMENT 31 based upon the diagnosis of learning events in interactive exercises.
Early versions of ActiveMath provided only hand-crafted interactive exercises, which lacked deep diagnosis of the learners’ actions and provided the Student Model only with a flag feedback.
This thesis shows how we enriched ActiveMath with intelligent reason- ing tools in multiple domains and provided a framework for reusable tutorial strategies for the inner loop.
Among other advantages of the ActiveMath Exercise Subsystem, is the possibility to create hybrid, partially authored and partially generated exercises. This allows for more control of the exercise design by the author or teacher, letting the automatic intelligent tools assist and not control the tutoring process. The author or teacher can reuse the automatic existing tutorial strategies or devise his own strategies manually.
The authored part of the ActiveMath exercise is similar to the behavior graph of CTAT. This graph is, however, more compact than the graph pro- duced by CTAT. Some of the alternative steps of the learner can be evaluated by a CAS, and hence all the semantically equivalent steps of the learner can be collapsed into one. Each step is annotated with some relations to domain concepts, which is similar to the knowledge labels in CTAT. However, in Ac- tiveMath the exercise steps are annotated with more educational metadata such as difficulty, competency and others, as described in Section 3.3. Such annotation provides a basis for application of different tutorial strategies, as we show later in this thesis.
We make use of domain reasoner systems connected to the ActiveMath as Web-services, and use a generic format for educational queries and seman- tic Web broker for distributing these queries. Thus, we offer a web service architecture that can be connected to multiple interoperable domain reason- ing services.
This gives us the unique possibility of semi-automatically creating cross- domain exercises, that use several domain reasoners simultaneously.
The framework for tutorial strategies of ActiveMath seems to fulfill the requirements of educationalists and cognitive psychologists as demonstrated in several research projects, see, e.g. [Tsovaltzi et al., 2009] for the ALOE project, [Eichelmann et al., 2008] for the ATuF project, and [Polushkina, 2009] for the MAPS MOSSAIC project. Many more strategies were built for the needs of teachers in schools and universities where ActiveMath exercises are used for teaching different mathematical subjects.
32 CHAPTER 2. BACKGROUND AND RELATED WORK strategies, such as Eon and REDEEM, ActiveMath allows human tutors to customize the automated strategies and locally overwrite them or manually tune their parameters. This is decided because in many cases teachers wish to have custom strategies, which are statically attached to the tasks within exercises.
Also, generic automatic tutorial strategies that model the tutorial process in various domains, are insensitive to the needed values of parameters when applied to a concrete task. In comparison, an experienced tutor will always have some rough estimate on the average values of such parameters, e.g. the maximal number of trials or hint levels sensible for the current task. In case of an adaptive strategy, the values of strategy parameters may change dynamically, as the strategy continuously adapts to the learner.