Knowledge space

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A knowledge space is a mathematical structure used to model the acquisition of knowledge in a knowledge area. For this purpose, the knowledge area is divided into learning units ( topics ). Know states (Knowledge States) are combinations of these units. With each learning unit, a knowledge state also includes its requirements. The knowledge structure consists of all these knowledge states. A learning space is a knowledge space with special properties.

Mathematically, a knowledge structure is therefore a set system that is ordered through the subset relationship. One speaks of a knowledge space if each of two states of knowledge also includes their union. Additional mathematical assumptions lead to particularly easily manageable knowledge spaces , which are then referred to as learning spaces .

history

The theory of knowledge spaces was developed in 1985 by the Californian psychologist Jean-Claude Falmagne in collaboration with the Belgian mathematician Jean-Paul Doignon . It was later expanded under the name of study rooms . Numerous scientists have dealt with the topic. B. a group around Dietrich Albert at the Knowledge Technologies Institute of the Technical University of Graz .

The theory of the knowledge spaces shows close parallels to the formal concept analysis , especially with regard to the algorithms.

method

In a knowledge or learning room, a field of knowledge is broken down into learning units according to didactic aspects and then a description of how these learning units build on one another. This helps to quickly determine a learner's level of knowledge with relatively few test questions. From the mastery of a learning unit it can be concluded that its prerequisites are also already understood. The amount of all learning units that a learner has mastered then describes his state of knowledge .

After a level of knowledge has been determined, the order structure also shows for which learning units that have not yet been mastered the level of knowledge determined is sufficient so that one of them can be successfully learned next. These learning units are external knowledge edge called (Outer Fringe).

application

In practical application, the learner is offered explanations and exercises from the outer edge of knowledge determined for him . In addition, it is repeatedly checked whether newly acquired knowledge is sustainable or whether it requires further practice.

Starting in 1994, Falmagne at the University of California, Irvine began developing the learning software " ALEKS " based on the theory of knowledge spaces . In 2013 it was sold to the American school book and educational publisher McGraw-Hill Education .

At TU Graz , applications are currently (as of 2017) being developed that are primarily aimed at students and teachers.

Individual evidence

  1. ↑ Jean-Paul Doignon, Jean-Claude Falmagne: Spaces for the assessment of knowledge . In: International Journal of Man-Machine Studies . tape 23 . Elsevier Ltd., 1985, pp. 175-196 , doi : 10.1016 / S0020-7373 (85) 80031-6 .
  2. ↑ Jean-Paul Doignon, Jean-Claude Falmagne: Knowledge Spaces . Springer-Verlag , Berlin Heidelberg 1999, ISBN 978-3-642-58625-5 .
  3. ^ Jean-Claude Falmagne, Jean-Paul Doignon: Learning Spaces - Interdisciplinary Applied Mathematics . Springer-Verlag , Berlin Heidelberg 2011, ISBN 978-3-642-01039-2 .
  4. ↑ Cord Hockemeyer: Bibliography on Knowledge Spaces maintained by Cord Hockemeyer. November 2, 2017, accessed November 2, 2017 .
  5. ^ Dietrich Albert: Dietrich Albert. Graz University of Technology , 2014, accessed on November 2, 2017 .
  6. ↑ a b Michael A. Bedek: LEA's BOX and weSPOT Two practical applications of knowledge spaces. Graz University of Technology , October 21, 2017, accessed on November 2, 2017 .
  7. ↑ Bernhard Ganter : Learning in Knowledge Spaces - A successful learning methodology with a mathematical basis. Ernst Schröder Center for Conceptual Knowledge Processing eV , October 21, 2017, accessed on October 28, 2017 .
  8. ↑ Heather Ashbach: Bridging the gap: Adaptive learning program developed at UCI supplements and reinforces math and science skills. UCI News, July 10, 2013, accessed October 28, 2017 .
  9. ^ McGraw-Hill Education Agrees to Acquire ALEKS Corporation, Developer of Adaptive Learning Technology for K-12 and Higher Education. Cision PR Newswire, June 20, 2013, accessed October 28, 2017 .
  10. ↑ Trial version of ALEKS. ALEKS, McGraw Hill, accessed October 28, 2017 .
  11. ↑ LEA's BOX - LEarning Analytics Toolbox. TU Graz, Knowledge Technologies Institute, Cognitive Science Section (CSS), 2014, accessed on November 16, 2017 (English).
  12. ↑ weSPOT - Working Environment with Social and Personal Open Tools for Inquiry. TU Graz, Knowledge Technologies Institute, Cognitive Science Section (CSS), 2014, accessed on November 16, 2017 (English).