Journal of Interactive Learning Research

Volume 11, Number 3/4 2000

Special Issue on Intelligent Systems/Tools in Training and Lifelong Learning


Contents


Intelligent Systems/Tools In Training and Lifelong Learning
Piet Kommers and Riichiro Mizzoguchiv 259

Lifelong Learning—More Than Training

Gerhard Fischer 265

Collaborative Innovation as a Process for Cognitive Development

Madhumita Bhattacharya and Ranajit Chatterjee 295

Learning at the Mental Gym: How to Get Mentally Fit for the Task You Have at Hand

Eshaa M. Alkhalifa and Helen Pain 313

Towards Adaptivity and Agility A Fractal view on Learning Environments

Sylvain Giroux, Richard Hotte, and Kim Dao 333

Learning-by-Judging: A Network Learning Environment Based on Peer Evaluation

Chuen-Tsai Sun 355

SmexWeb: An Adaptive Web-Based Hypermedia Teaching System

Florian Albrecht, Nora Koch, and Thomas Tiller 367

Formalization to Improve Lifelong Learning

Sylvie Ranwez, Torsten Leidig, and Michel Crampes 389

The GET-BITS Model of Intelligent Tutoring Systems

Vladan Devedzic, Ljubomir Jerinic, and Danijela Radovic 411

Micro-Robots Based Learning Environments for Continued Education in Small and Medium Enterprises (SMEs)

Pascal Leroux and Martial Vivet1 435

Arithmeticus: A DPS-Based Model for Arithmetical Competence

Joseph Klep 465

A Concept Model For Learning

R. Min, P. Kommers, H. Vos, and C. van Dijkum 485


Abstracts


Intelligent Systems/Tools In Training and Lifelong Learning

Piet Kommers

The University of Twente
PO Box 217, 7500 AE Enschede
The Netherlands

kommers@edte.utwente.nl

Riichiro Mizzoguchi

The Institute of Scientific and Industrial Research
Osaka University, 8-1 Mihogaoka, Ibaraki
Osaka, 567-0047, Japan

http://www.ei.sanken.osaka-u.ac.jp/

Learning is an active process clearly distinguished from simply being taught. Active involvement in learning helps learners build knowledge in their heads, which is one of the key issues advocated by constructivists. However, learners still need other kinds of help that instructivists might suggest. Not all learners can always be active. They sometimes meet an impasse they cannot resolve by themselves. What they need is not the extreme paradigms but a mild and friendly paradigm that enables them to be active when they want to and help and guide them when necessary. Such a paradigm needs sophisticated intelligence.

Media Technology for the Further Evolution of Learning Paradigms

Learning is a lifelong process where learners cannot always expect teachers around them. People need tools/systems to facilitate the learning. One of the problems there is adaptation to the changes of the environment, which requires evolutionary tools. In industrial settings, people are expected to catch up with the rapid technological development—that is the reason why training is so important in industries. Billions of dollars have been invested in employee training in industries each year. One of the serious problems is lack of trainers. Advanced training systems of high performance also require intelligence to partially mimic such trainers’ performance.

We have learned a lot about technology-based learning paradigms to date. They include:

In the evolution of the paradigms, we could see a direction that we were headed. It was a learner-centered, continued, network-supported, collaborative, and intelligent learning environment. This direction enjoys many of the characteristics of the paradigms we have seen thus far and compatible with most of them.

To learn more about such a new direction, we planned to have the special issue on

Intelligent Systems/Tools in Training and Lifelong Learning

Fifteen papers were submitted and ten of them were accepted together with one invited paper, namely the one by Gerhard Fisher.

The invited paper authored by Gerhard Fisher, Center for Lifelong Learning & Design (L3D), University of Colorado, USA, provides comprehensive views of lifelong learning based on thorough investigation of the current situation of training/learning and the conventional learning support paradigms. The paper provides theoretical foundation for learner-centered, authentic, situated, continued, domain-oriented, collaborative and open environment for learning/training based on constructivism and technology support. It declares a departure from institutional education/training. He also presents his activities along with his theories

The ten papers are classified into the following three categories:

An Architecture/System Based on Constructivism

1. Collaborative Innovation as a Process for Cognitive Development by Madhumita Bhattacharya, and Ranajit Chatterjee

2. Learning at the Mental Gym—How to Get Mentally Fit for the Task you Have at Hand by Eshaa M. Alkhalifa and Helen Pain

3. Towards Adaptivity and Agility—A Fractal View on Learning Environment by Sylvain Giroux, Richard Hotte, and Kim Dao

4. Learning by Judging: A Network Learning Environment Based on Peer Evaluation by Chuen-Tsai Sun

Innovative AI Technology Applications to Educational Systems

5. SmexWeb: An Adaptive Web-Based Hypermedia Teaching System by Florian Albrecht, Nora Koch, and Thomas Tiller

6. Pedagogical Ontology and Teaching Strategies: A New Formalization to Improve Lifelong Learning by Sylvie Ranwez, Torsten Leidig, and Michel Crampes

7. The GET-BITS Model of Intelligent Tutoring Systems by Vladan Devedzic, Ljubomir Jerinic, and Danijela Radovic

Report on Practical Experiences of Learning Environments

8. Micro-Robots Based Learning Environments for Continued Education in SMEs by Pascal Leroux and Martial Vivet

9. Arithmeticus: A DPS-based Model for Arithmetical Competence by Joseph Klep

A (Retro)Prospective Study of the Elementary Conceptual Model for Learning

10. An Attempt to Define a Proper Relations Scheme Between Instruction, Learning and to Establish the Dynamics of Learning in Relation to Modern Political Concepts as Study-Fairness by Rik Min, Piet Kommers, Hans Vos, and Cor van Dijkum

 

Those in the first category share a lot besides constructivism-based approach. All of them deal with collaborative learning and three of them assume Internet environments. Giving learners the initiative in the learning process, the systems/architectures exploit the capabilities of the Internet to enable collaboration beyond the limitation of distance. The common attitude towards learning support includes efforts in finding a best mixture of free exploration with highest initiative of a learner and an appropriate guidance from the environment. They have come up with two types of solutions to this problem: one is to put the learner in collaborative settings and the other is the introduction of guidance capability to the system.

After comprehensive investigation of the role of collaborative innovation, Madhumita Bhattacharya and Ranajit Chatterjee introduce several useful tools for goal-oriented collaborative discussion for innovation and designed a unified system. The unique features of their research include that they base the design rationale of the system on learning theories and that they come up with practical tools justified by the very basic consideration. Eshaa M. Alkhalifa and Helen Pain try to combine virtual reality environment with simulated players and intelligent tutoring to give a learner appropriate guidance keeping a situated learning environment. Chuen-Tsai Sun also employs group learning with peer evaluation through the Internet to realize the Delphi method. Collaboration with human and/or simulated agents give the learners motivation and active involvement in their learning process. These ideas also contribute to guiding learners and preventing them from being lost. To attain the same goal, Sylvain Giroux, Richard Hotte, and Kim Dao discuss an innovative idea of hypermedia-based navigation to realize high adaptivity and agility. A key idea here is to prepare a sophisticated multidimensional hyper-link mechanism that is adaptive to the context as well as to learner’s learning and cognitive styles. Although the system assumes a single learner paradigm, it succeeds in realizing a learning environment of a good mixture of free exploration and guided learning.

Articles in the second category are different from those discussed previously in that they are more enabling and technology-oriented. The common claim of the three includes artificial intelligence technology works well for adaptive tutoring/teaching to realize learning environments of stronger guidance that could compensate some negative aspects of free exploration in the huge information space. Two of them deal with web-based learning environment and the two of them discuss ontology as an innovative enabling technology. Florian Albrecht, Nora Koch, and Thomas Tiller discuss an Internet-based approach and propose an adaptive web-based tutoring system. They introduce Java applet to build learner model-based adaptive teaching in a web-based teaching. Sylvie Ranwez, Torsten Leidig, and Michel Crampes discuss a pedagogical ontology for dynamically composing web-based learning material. They put the adaptive navigation of hypermedia one step further to adaptive building of hypermedia as a learning material. Thus these two articles try to find a good solution of active behavior of the learning environment. Vladan Devedzic, Ljubomir Jerinic, and Danijela Radovic discuss a sophisticated model for building an ITS. Their main interests include reusable component-based architecture that is deeply related to ontology. Their contribution is based on amalgamation of software engineering and AI.

In the third section Pascal Leroux and Martial Vivet present a report on substantial activities in the real world, Small and Medium Enterprises: SMEs. It is about a year long practice of well-situated and continued training using micro-robots, which has a lot to learn about how the ideas have evolved.

Joost Klep describes the rationale and interactional consequences of his learning program Arithmeticus. MathMirror is its front end that allows a student to express calculations by manipulating mathematical objects. The manipulations are interpreted as partial solutions and are recorded with time annotations. Comparing these students’ expressions with solutions produced by Arithmeticus gives abundant information about the students’ work so it is possible to qualify solutions in terms of effectiveness, speed, degree of automation, and rote knowledge used . Those qualifications are based on students’ individual learning history. Arithmeticus and MathMirror offer a learning environment in which a child can develop his own strategies. There are no predefined expert solutions. A solution can be good or nicely related to a student’s learning history. The more strategies or facts he/she learns, the smarter Arithmeticus will be and the more smart solutions Arithmeticus will expect from the student.

In the fourth section Rik Min and his colleagues go back to the more traditional reductionism to find the most elementary mechanism in learning, regardless of the control aspects around the learner. This article may be seen as a provocation to the various learning paradigms such as cognitivism and environmentalism, not to speak of constructivism. In the era of “zapping” and “staccato” browsing through the information ocean on the World Wide Web (WWW or Web) however, this notion about short exposure time and Short Term Memory (STM) may need this almost forgotten analogon in order to understand the mechanism of the feedback regulation system.

If the completely free exploration is the primary key condition to implement constructivist’s ideas, then a set of books is the best solution. If the complete support of the learning process is necessary, on the other hand, ITS with stronger AI technology gives the best solution. No one believes, however, that either of both extremes is what we need. Appropriate stimuli should be given at appropriate timing to the learners to maintain motivation, to help them when they reach a deadlock, to let them reflect, and so forth. All learners cannot behave actively to explore the huge space continuously. They will definitely come across difficulties that need to be overcome by help. These are areas where AI technology might contribute.

One of the main issues here, however, is that all AI-based methods need modeling which is the key to enabling sophisticated and adaptive behaviors such as suggestion generation. Without modeling, what a system can do is to show hard-wired behavior (canned suggestion generation), which cannot be adaptive to the situation. The problem with modeling is that it does impose something negative on a constructivism approach, since it requires limitations of the target to model and such limitations might include learner’s cognitive state, learner’s behaviors, interactions among co-learners, and so forth. This has been one of the main reasons why many of the AI-based systems have not been completely compliant to the constructivist approach. Articles we have in this special issue try to overcome these difficulties. Although the evaluation is up to the readers, the article should be informative and thought provoking.

As we have browsed all the articles, what you will find in this special issue are comprehensive and theoretical articles, sophisticated techniques to realize the theories, and practical experiences in the industrial settings. The co-editors would like the readers to enjoy them.

Return to Contents


Lifelong Learning—More Than Training

Gerhard Fischer

Center for LifeLong Learning & Design (L3D)
Department of Computer Science and Institute of Cognitive Science
University of Colorado, Boulder, CO, USA

Wisdom is not a product of schooling, but the lifelong attempt to acquire it.—Einstein

Learning can no longer be dichotomized into a place and time to acquire knowledge (school) and a place and time to apply knowledge (the workplace). Today’s citizens are flooded with more information than they can handle, and tomorrow’s workers will need to know far more than any individual can retain.

Lifelong learning is an essential challenge for inventing the future of our societies; it is a necessity rather than a possibility or a luxury to be considered. Lifelong learning is more than adult education and/or training—it is a mindset and a habit for people to acquire. Lifelong learning creates the challenge to understand, explore, and support new essential dimensions of learning such as self-directed learning, learning on demand, collaborative learning, and organizational learning. These approaches need new media and innovative technologies to be adequately supported.

A theory of lifelong learning must investigate new frameworks to learning required by the profound and accelerating changes in the nature of work and education. These changes include: a) an increasing prevalence of “high-technology” jobs requiring support for learning on demand because coverage of all concepts is impossible; (b) the inevitability of change in the course of a professional lifetime, which necessitates lifelong learning; and (c) the deepening (and disquieting) division between the opportunities offered to the educated and to the uneducated.

This article explores conceptual frameworks and innovative computational environments to support lifelong learning. It also analyzes why training approaches need to be transcended and how this can be done.

Return to Contents


Collaborative Innovation as a Process for Cognitive Development

Madhumita Bhattacharya

Instructional Science Academic Group
National Institute of Education
Nanyang Technological University
Singapore

mitab@nie.edu.sg 

Ranajit Chatterjee

Department of Computational
Intelligence and System Science
Tokyo Institute of Technology
4259 Nagatsuta, Midori-ku,
Yokohama 226-8502 Japan

ranajit@cs.dis.titech.ac.jp

In this article we propose a methodology for collaborative innovation, which leads to cognitive development. Motivation for innovation could be an effective means for efficient and meaningful learning. Meaningful learning contributes to cognitive development. Therefore, in professional education the aim is to maintain the continuous cognitive development through lifelong learning.

Distributed cognition of people and artifacts are integrated during the process of collaborative innovation. This, in turn, enriches the individuals’ cognition, metacognitive abilities, techniques of interpersonal communication, and reflective thinking skills. A mechanism for the process of innovation is discussed to identify the possible stages of interaction for collaboration. The guidelines for interaction are identified to develop an intelligent support system. This support system guides participants in carrying out innovative activities. Based on participants’ personal portfolios, the network can be used to perform an intelligent compatibility search on the World Wide Web (Web) for locating companions for collaboration. The same tool can also be incorporated for other ontological searches in connection with the process of innovation such as suggesting possible problems to be explored and providing relevant information on available resources.

In this methodology, the main intention is to continue the cognitive development process where the innovative activities are used to sustain the motivation of the learner. Any other outcome from these innovative activities were considered incidental. In future work, we intend to develop a measure for assessing cognitive changes for providing periodic feedback to participants about their progress. An intelligent tool would be developed for periodic assessment and reporting cognitive changes to the participants to help in sustaining their motivation.

Return to Contents


Learning at the Mental Gym: How to Get Mentally Fit for the Task You Have at Hand

Eshaa M. Alkhalifa and Helen Pain

School of Artificial Intelligence
University of Edinburgh
80 South Bridge, Edinburgh EH1 1HN
Scotland

eshaaa&helen@dai.ed.ac.uk

Learning is as necessary a process for the psyche as is exercise for the body. It is an ongoing activity that takes place with every movement or word said. But at times we can control it by submitting ourselves to a controlled environment, which would bombard us with information that restructures our world model and how we deal with that particular aspect of life.

The theories that exist in learning are based on two alternative approaches: Constructionism versus Instructionism (Papert, 1990b). However, why should we have to choose between them when, in fact, we could take the best of both worlds by interleaving them (Lawler & Yazdani, 1997)? Or better still, why don’t we have both approaches simultaneously where the student is surrounded by a constructive Virtual Reality environment with a specific training target at hand, coupled with enough abstraction to enable him to react to positive as well as negative expertise (Minksy, 1994) through adaptation of thinking processes rather than just memorizing. This paper proposes an interactive Virtual Reality environment that allows learning to occur through virtual experience and experimentation.

Return to Contents


Towards Adaptivity and Agility A Fractal view on Learning Environments

Sylvain Giroux

Mediatech SRL
Città dell’innovazione
6a Strada Ovest
Loc. Macchiareddu,Uta (CA),
09010, Italy

giroux@mediatech.didael.it

Richard Hotte and Kim Dao

LICEF Research Center,
Télé-Université,
1001, Sherbrooke east,
Montreal, P.Q.,
Canada H2L 4L5

rhotte@teluq.uquebec.ca

Continuous education helps people cope with an ever changing labor market, while distance education reaches them where they are, keeping them at work. This article tackles the production of learning environments (LEs) on the World Wide Web (Web). The produced LEs can be adapted to a wide variety of learners. They are also agile and able to sustain the fast evolution of contents and technology. The resulting LEs are germane to fractals. Fractals are usually characterized by a self-similar structure which remains independent of changes in scale. First, we liken changes in scale to levels in LEs. Each level expresses a given viewpoint on knowledge. Second, self-similarity establishes a classification from which to derive a grammar. Third, texts and activities are highly fragmented. Fourth, the interfaces rely on the fractal structure to provide for “spatial” landmarks. The LEs are adaptive with respect to learners’ objectives, background and cognitive style and are agile with respect to their design, implementation, and maintenance. The fractal design and the underlying grammar set up the formal grounds required to code procedures that generate LEs, extend them, manage updates, and maintain the site.

Return to Contents


Learning-by-Judging: A Network Learning Environment Based on Peer Evaluation *

Chuen-Tsai Sun

Department of Computer and Information Science
National Chiao Tung University, Taiwan

ctsun@cis.nctu.edu.tw

The paradigms of science and engineering education have been evolving along the dimensions of theory, pedagogy, and technology. As network-based, computer-assisted learning is drawing more and more attention the past few years, promising learning theories such as constructive learning and collaborative learning have found new meaning and new ways of implementation in the new, network-based environment. In this article, we propose a learning environment in which a learning strategy, called Learning-by-Judging, can be realized to help constructive learning.

The proposed environment is a World Wide Web (Web) based system that supports learning strategies through design and peer evaluation. Samples designed by students are demonstrated in screen windows for others to evaluate by way of a network. A learning procedure includes several rounds of sample-design and mutual evaluation. The learning process is recorded and analyzed, and then the result is fed back to the students to achieve the goal of meta-cognition. We expect this approach to encourage students participating in instructional activities early and effectively.

We conducted a small-scale experiment in which color-matching was chosen as the design subject. We collected and analyzed users’ behavior patterns in a preliminary manner. We are improving the functionality and interface of the learning environment. We expect to conduct formal instructional experiments in the near future.

Return to Contents


SmexWeb: An Adaptive Web-Based Hypermedia Teaching System

Florian Albrecht, Nora Koch, and Thomas Tiller

Ludwig-Maximilians-University of Munich
Institute of Computer Science
Oettingenstr 67, 80538 München
Germany

florian@fast.de

{albrechf, kochn, tiller}@informatik.uni-muenchen.de

http://www.pst.informatik.uni-muenchen.de/~kochn

A computer learning system that aims at being efficient and gratifying has to adapt itself to the learner’s needs. SmexWeb (Student modelled exercising on the Web) (http://pst1.pst.informatik. uni-muenchen.de:8080/) as an adaptive hypermedia system offers advantageous features of the hypermedia paradigm. To take into account spatial and mental abilities of learners, various techniques have been developed in the field of adaptive hypermedia. All of them, adaptations of contents as well as all kinds of adaptive navigational support, are integrated into SmexWeb. While those techniques move the locus of control towards the system, all action still has to be taken by the user. SmexWeb extends the means of navigation further by taking navigation actions for the user based on its student model. By employing a technique called Passive Navigation, the level of the system’s activity can vary subtly and can be adjusted to the user’s learning preferenceses.

SmexWeb guarantees easy accessibility, as it is a web-based application that solely requires a standard web-browser. Partially bypassing HTTP as a stateless protocol, SmexWeb enables a higher amount of user-system interactivity than most web-based learning environments. The Java server resembles a classical ITS architecture; the modularity of the framework allows an easy instantiation for future SmexWeb applications. First tests of a SmexWeb application with students have shown that it is an easy-to-use and effective learning environment.

Return to Contents


Formalization to Improve Lifelong Learning

Sylvie Ranwez1, Torsten Leidig, and Michel Crampes

Laboratoire de Génie Informatique et Ingénierie de Production (LGI2P) EERIE-EMA
Parc Scientifique G. BESSE
30 035 NîMES Cedex 1, FRANCE

mcrampes@ensm-ales.fr, ranwezs@eerie.fr

http://www.eerie.fr/LGI2P/lgi2p.htm

European Applied Research Center
SAP AG - CEC Karlsruhe
Vincenz Prießnitz Str. 1
76131 KARLSRUHE Germany

Torsten.Leidig@sap-ag.de

 Utilizing the World Wide Web (Web) for delivering lifelong training services to individuals or communities raises great interest in intelligent methods for adaptive course curriculum building. People notice that it is insufficient to make training materials accessible by way of the browser. To satisfy learner requirements, the learning service has to give a highly customized and up-to-date view. Moreover, training is an interactive and collaborative process. The flow of the curriculum has to follow some didactic principles. Learners need to be guided through the training material according to these principles and their own preferences. A conventional hypertext system cannot provide this, mainly because the pedagogic semantics of the material are not “known” by the system.

This article presents a new approach for adaptive, computer-supported learning services within our Lifelong Learning project. This approach is based on a formalization of pedagogical knowledge, about learning material and learning processes, as well as the domain knowledge and a learner model. The goal of our research is to integrate efficient and reusable pedagogical knowledge representations into an adaptive learning system (and authoring tools). The article concentrates on the Didactic Planning obtained by various Pedagogical Strategies. Therefore, we focus on the strategy formalization using an expressive knowledge representation based on a dedicated learning ontology using conceptual graphs. The power of our approach for designing a new kind of adaptive learning system is demonstrated through examples of pedagogical strategies applied to course material.

Return to Contents


The GET-BITS Model of Intelligent Tutoring Systems

Vladan Devedzic

University of Belgrade, FON - School of Business Administration, Jove Ilica 154, 11000 Belgrade, Yugoslavia

devedzic@galeb.etf.bg.ac.yu

Ljubomir Jerinic

University of Novi Sad, Institute of Mathematics, Trg Dositeja Obradovica 4, 21000 Novi Sad, Yugoslavia

jerinic@uns.ns.ac.yu

Danijela Radovic

University of Kragujevac, Technical Faculty Cacak, Svetog Save 65, 32000 Cacak, Yugoslavia

danijela@emi.yu

This article describes an object-oriented model of intelligent tutoring systems (ITS), called GET-BITS. The article concentrates on class hierarchies and design of classes for knowledge representation in the GET-BITS model. Other models of intelligent tutoring systems used today, as well as the corresponding knowledge models, differ only to an extent. However, the design methodologies employed vary a lot and, sometimes, even remain blurred for the sake of the system functionality alone. Although using a shell or an authoring tool for developing intelligent tutoring systems brings more systematic design, it can also become a limiting factor if the shell/authoring tool doesn’t support a certain knowledge representation technique or design strategy that may be needed in a particular system. The GET-BITS model makes it possible to develop more flexible intelligent tutoring systems and the corresponding software development environments, significantly increasing their modularity and reusability. It is based on a number of design patterns and class libraries developed in order to support building of intelligent systems. Important parts of any ITS design process, like domain knowledge, pedagogical knowledge, student model, and explanation strategies, are all covered in the GET-BITS model. The advantages of the model are shown in the article by: (a) explicit discussion of several different aspects of the model, and (b) description of a GET-BITS-based intelligent tutoring system for teaching formal languages. The processes of computer-based tutoring and learning based on the GET-BITS model are much closer to human-based instruction. The model can be easily extended to cover the needs of specific tutoring systems. In addition, two extremely important issues are discussed from the GET-BITS perspective: the issue of ontologies in the area of intelligent tutoring systems, and the issue of software components in that area.

Return to Contents


Micro-Robots Based Learning Environments for Continued Education in Small and Medium Enterprises (SMEs)

Pascal Leroux AND Martial Vivet1

Laboratoire d’Informatique de l’Université du Maine
Institut d’Informatique Claude Chappe
Avenue Olivier Messiaen
72085 LE MANS Cedex 9
France

Pascal.Leroux@lium.univ-lemans.fr

Martial.Vivet@lium.univ-lemans.fr

One of the main problems in the Small and Medium Enterprises (SMEs) is the adaptation of their production process to keep their markets. The improvement of the process is often realized by the introduction of new technologies such as more fully automated machinery and computers. Therefore, training has been designed to prepare workers for the future by helping them use these new technologies.

 Since 1989, for training people in this context, we have developed learning environments and defined a pedagogical approach, called ATRIUM, which is based on the use of pedagogical micro-robots driven by computers. The micro-robotics activities aim at helping learners discover technology by handling, building, designing, and driving micro-robots through a project-based pedagogical approach. The role of the trainer is to set up and manage the activities of several learner groups (each group is composed of 2-3 persons). We have experimented with a first generation of learning environments using LOGO as the software to drive the micro-robots. Beyond the effectiveness of the approach, we observed that our environments created an overload for the trainers (we say over-appeal) because they had different roles to play. We chose to decrease the trainers’ over-appeal and improve their work by increasing the autonomy of the learner groups and by having a better interaction between the computer and the human actors. We have designed and developed pedagogical assistant software, called ROBOTEACH, which cooperates with learners during the micro-robotics activities and helps the trainers manage the sessions. ROBOTEACH is actually diffused and used in professional training in SMEs.

Return to Contents


Arithmeticus: A DPS-Based Model for Arithmetical Competence

Joseph Klep

Institute for Curriculum Development
Boulevard 1945 3, 7511 CA Enschede
P.O. Box 2041, 7500 CA Enschede, The Netherlands

J.Klep@slo.nl

http://www.slo.nl/network/engels.html

The Position of Arithmeticus Between other Student Models

Petrushin and Sinitsa (1990) offer a short classification of learner models. They distinguish between fixing and simulating models. Both kinds of models are based on a set of expert-rules. The learner model is a description of students behaviour related to that set of expert-rules.

Arithmeticus does not contain expert-rules in the field of mathematics, but meta-mathematical rules, telling which transitions are permitted in calulations or in argumentations. Using those rules, Arithmeticus can construct lines of arguments.

If a student has expressed his solution of a problem, Arithmeticus tries to realise (for itself) this expressed solution by constructing a fitting line of arguments (or algorithm). So, Arithmeticus offers a generic description of mathematical knowledge based on meta-mathematical rules. The kernel of Arithmeticus is not a psychological, but an epistemological, generic description of mathematics (arithmetics).

Return to Contents


A Concept Model for Learning

An attempt to define a proper relations scheme between instruction and learning, and to establish the dynamics of learning in relation to modern political concepts as study-fairness

R. Min, P. Kommers, H. Vos, and C. van Dijkum1

Educational Science and Technology
University of Twente
P.O. Box 217, 7500 AE Enschede
1 University of Utrecht
The Netherlands

min@edte.utente.nl,

kommers@edte.utwente.nl

vos@edte.utwente.nl

c.vandijkum@fsw.ruu.nl

For years, it has been attempted within educational science to establish the process of learning. A lot is known about instruction, but as to learning and acquiring knowledge and insight, we still know very little. A lot of research is conducted on methods of instruction, but very little on learning with learning tools. In this article, an attempt is made to do so. Discussions should then be: how can a learning process be turned into a model? And, how can learning be modeled? First, there should be a conceptual model with the basic entities and the relations between them. Recently, a committee of the Ministery of Education and Science introduced the political concept “study-fairness,” an extra reason to lay down the points of application of these concepts in a larger, meaningful context and an understandable model so that each concept can be applied in the overall learning process. In this article, we want to construct a clear and irrefutable model, an analogon, to describe the phenomenon of learning. This might, in the long run, help us identify the fundamentals of learning. We consider learning as a student activity, and instruction, on the other hand, as a relatively static condition. (Not to be confused with the traditional teacher role.)

Return to Contents