Proceedings of the workshop "Adaptive Systems and User Modeling on the World Wide Web",
Sixth International Conference on User Modeling, Chia Laguna, Sardinia, 2-5 June 1997

AST: Adaptive WWW-Courseware for Statistics

Marcus Specht, Gerhard Weber, Stephan Heitmeyer, Volker Schöch
Department of Psychology, University of Trier
Trier, Germany
Phone: +49-651-201-2975
Fax: +49-651-201-2955
e-mail: {specht | weber | stephan | schoech}

Abstract: In this paper we describe the Adaptive Statistics Tutor (AST), an adaptive courseware on the WWW. AST is based on a conceptual model of the domain of introductory statistics and uses the programmable WWW-server CL-HTTP (Mallery, 1994) to generate individualized courseware. The system monitors the interactions of learners with the learning materials in the course. Besides texts there are examples, so-called interactive playgrounds, and tests. The information gathered by the monitoring of the system is used to build up a probabilistic learner model. The learner model stores information about all interactions, their success, and individual instantiations of playgrounds. Learners can explore the curriculum or get recommendations by AST for each next best unit and learning material to work with depending on their previous interactions. Additionally, we have just begun to integrate cooperative modules in AST. Learners can ask and answer questions to other learners or the tutor and join discussion groups on any sections of the curriculum.

A knowledge based architecture for individualized learning on the WWW

Psychological models often mention three sources of knowledge competent teachers use. First, the teacher is an expert in the subject matter (e.g., he/she knows about the concepts of the domain and their interrelation, is able to criticise solutions of problems, answer questions, give examples, and far more). Second, teachers know how to teach something (e.g., they use strategies to teach a concept, they know when to use a certain teaching material or presentational method). Third, teachers build a model of the students' knowledge. This allows teachers to adapt their teaching methods to different students or groups of learners. Accordingly, our proposed architecture consists of three main modules:

In the domain expert module, the concepts of the domain, their interrelations and dependencies are described. Basically, the knowledge base is built on a conceptual network with different types of units which are lessons, sections, subsections, and concepts. Several types of information are associated with each concept. These are different kinds of text (introduction, several stages of teachtexts, summary), examples, demonstrations, playgrounds, and tests. Besides, each unit has prerequisites (units that the student should be familiar with before working on the unit), and consequences (possible outcomes and effects on other units). The tests and prerequisites are weighted according to their importance for a unit.

The pedagogical expert module contains pedagogical strategies and diagnostic knowledge. Teachers follow different strategies to teach different types of concepts. Teaching strategies in this sense are comparable to the teaching rules in Vassileva (1994). For example, when teaching statistics, introducing the arithmetic mean can easily be done with a text, a formula, some tasks, or an interactive playground. In contrast to that, it is very hard to "explain" a more abstract concept like different scale levels with just a text or a formula. For introducing scale levels it would be much easier to start with concrete examples and then go on with a more abstract text definition or a formula. Such different strategies in the sense of a certain sequence of learning materials are defined in the teaching strategies. The system has a default strategy for each concept type and teachers can specify a preferred strategy for each concept if needed. Moreover, rules are defined with each strategy which allow the system to adaptively choose a teaching strategy depending on critical learner features and on the class of the taught concept.

One problem with learning environments on the WWW is the reduced bandwidth of information. Due to the fact that a student loads a text page hardly anything can be inferred about the actual knowledge of the student. Integrating interactive tests in a WWW learning environment is one more valid way of getting information about the learner's knowledge. The diagnostic component stores the knowledge about several types of tests and how they have to be generated and evaluated similar to Nkambou and Gauthier's pedagogical resources (Nkambou & Gauthier, 1996). Each test in the test base can be connected to multiple concepts, rated on difficulty and on relevance for a concept. Depending on the difficulty and the relevance of a test, a student's solution has different impacts on the learner model.

The learner model stores the preferred settings of a learner and the domain units a learner worked on. A learned unit has information about the materials a learner has used and how successful he/she worked on the material (e.g., if tests are solved correctly, if the playground estimations were good or to what extent teachtexts were requested). Every action of a student has consequences for updating the learner model depending on the involved learning material and the previous experiences of a student. By accumulative information (Specht & Weber, 1996) stored with a learned unit a probabilistic conceptual overlay model for representing the student's domain knowledge is built up. The probabilistic overlay model can be used for several adaptive methods like adaptive sequencing, mastery learning, and adaptive testing (e.g., giving additional tests or teachtexts after wrong test solutions), or adaptive annotation (Weber & Specht, 1997).

Learner modeling in AST

New learners in AST are asked about their background, preferences, and goals in an introductory questionaire. Learners can specify preferred learning materials and can select a preferred learning strategy like learning by example, reading texts, or learning by doing. Besides learners can specify the level of detail for texts. Teachtexts for a concept can be displayed on three levels, from basic information to very detailed with expert hints. Furthermore an introductory statistics test is used for initializing the learner model. Every interaction with the system has an impact on the learner model in AST. The impact depends on the learning material involved and on parameters of the material:

Teachtexts: With every concept in AST a teachtext with three levels of detail is defined. The first level contains only basic information about a concept. The second level explains some concepts used in the first stage in more detail and the third stage gives detailed information and advanced hints. Depending on the detail level a student requests, the confidence value for the taught concept is increased.

Interactive Playgrounds in AST consist of shockwave plugins, and interactive html-forms (e.g., a spreadsheet simulation in which the learner can request data analysis and watch the computation stepwise in a formula filling up with the computed values). Request and usage of interactive html-forms increase the confidence value of a concept and are stored as a learning episode with the concept.

Examples can be requested only one by one. This is necessary to identify the examples a learner actually looks at. Displaying all examples for a concept at once would not allow any inference about how many of the examples a learner actually looked at. Requesting examples increases the confidence value of a concept.

Tests are the most important feedback for updating the model in AST. Four different types of tests are currently implemented: Yes-or-no-tests, multiple-choice tests, forced-choice tests, gap-filling tests and free-form tests. Every test has a general value for difficulty, and the relevance for the tested concept can be specified. Depending on the difficulty and the relevance the confidence value in the probabilistic learner model is increased. Besides the type of the learning material the last interaction with a concept, and the percentage of correct tests is taken into account for updating the confidence value of a concept. Based on the confidence values in the probabilistic learner model, adaptive navigation support, adaptive sequencing, and adaptive testing are implemented in AST.

Adaptivity in AST

Adaptive Navigation Support

Navigation in AST is supported through adaptive annotation of hyperlinks. With each hyperlink a colored ball is shown, which holds some information about the state of this link. A green ball stands for a recommended link, an orange ball means that the navigation to this concept is ok, and a red ball stands for a link the students lacks prerequisites for. Furthermore there are hooks for mastered concepts and white balls for infered concepts.

Adaptive sequencing

In AST, learners can start to work on the curriculum whereever they want. When a student selects a section the system checks if a he/she lacks any prerequisite knowledge to work on this unit and presents tests for lacking prerequisites. If a learner is not able to solve the given tests, AST recommends to work on the prerequisites first. Besides students can always ask for the next best unit in the curriculum. From any given point in the curriculum, AST can compute the next best unit depending on the probabilistic overlay model of a learner and the prerequisites of possible next units. The algorithm for computing the next best unit first filters possible alternatives by lacking prerequisites and then by the confidence and weight of fulfilled prerequisites. The unit with the most important prerequisites being most confident to the learner is chosen.

Adaptive testing

Each test in the AST test base is linked to one or multiple concepts with a specific weight of relevance and has a value for general difficulty. Depending on these two values, the user model is updated when a test is solved by a student. Difficult tests with a high relevance have the strongest impact on the confidence value of the tested unit. If a learning threshold of a unit is surpassed, the system infers that the unit and its prerequisites are known to the learner.

Adaptation of the default teaching strategy

Basically, AST has a default teaching strategy for each unit which can be specialized by the teacher. In the introductory questionaire, some information about the learner's preferred learning style is captured and the system monitors which combinations and sequences of learning materials are requested frequently by a learner. For example, when a student often requests the introduction, then looks for some examples, and then jumps directly to the tests, the system adapts to this learning strategy by presenting the links to the learning materials in this order. This is similar to approaches by Lindner (1995) for adapting module sequences in working environments to individual working styles and methods in intelligent agents. The adaptation to a preferred learning style takes into account the learner's success with the style. Strategies in which the learner shows a sufficient result in the final tests are rated as successful. Repeated occurence raises the confidence value of the style, and when exceeding a certain threshold the learning strategy is taken as the defualt strategy for the learner.


In this paper we sketched an architecture for adaptable and adaptive learning environments for the WWW. Integrating a domain expert, an interface expert, and a pedagogical expert into this architecture allows several adaptive and adaptable methods to be implemented. More advanced adaptive methods like individual cognitive diagnose of problem solutions or explanation of examples, of course require more elaborated approaches of learner modeling as implemented in ELM-ART (Weber & Specht, 1997). However, even with the architecture proposed here, a lot of advanced adaptive techniques can be realized. AST will be evaluated in summer at the University of Trier with students of introductory statistics.


Lindner, H. G. (1995). Ein Prototyp zur adaptiven Beratungsunterstützung des Versicherungsverkaufs. In U. Malinowsky (Eds.), Proceedings of Workshop Adaptivität und Benutzermodellierung in Interaktiven Softwaresystemen,. München: Siemens AG.

Mallery, J. C. (1994). A Common LISP hypermedia server. Proceedings of the First International Conference on the World-Wide Web (pp.

Nkambou, R. & Gauthier, G. (1996). Use of WWW resources by an intelligent tutoring system. In P. Carlson & F. Makedon (Eds.), Proceedings of ED-MEDIA'96 - World conference on educational multimedia and hypermedia (pp. 527-532). Charlottesville: AACE.

Specht, M. & Weber, G. (1996). Episodic adaptation in learning environments. In P. Brna, A. Paiva, & J. Self (Eds.), Proceedings of EuroAIED (European Conference on Artificial Intelligence in Education) (pp. 171-176)

Vassileva, J. (1994). A practical architecture for user modeling in a hypermedia-based information system. Proceedings of 4-th International Conference on User Modeling (pp. 115-120). Hyannis, MA: MITRE.

Weber, G. & Specht, M. (1997). User Modeling and Adaptive Navigation Support in WWW-Based Tutoring Systems.In Anthony Jameson, Cecile Paris, and Carlo Tasso (Eds.) User Modeling: Proceedings of sixth International Conference on User Modeling (pp 290-300). Springer, Wien New York.