Authors:
- Introduces learning space as a special case of knowledge space.
- Exposes theory and several applications of learning spaces and ancillary assessment procedures.
- Presents ALEKS as a practical application of learning spaces for an efficient web based learning environment.
- Includes supplementary material: sn.pub/extras
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Table of contents (18 chapters)
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Front Matter
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Back Matter
About this book
Learning spaces offer a rigorous mathematical foundation for practical systems of educational technology. Learning spaces generalize partially ordered sets and are special cases of knowledge spaces. The various structures are investigated from the standpoints of combinatorial properties and stochastic processes.
Leaning spaces have become the essential structures to be used in assessing students' competence of various topics. A practical example is offered by ALEKS, a Web-based, artificially intelligent assessment and learning system in mathematics and other scholarly fields. At the heart of ALEKS is an artificial intelligence engine that assesses each student individually and continously.
The book is of interest to mathematically oriented readers in education, computer science, engineering, and combinatorics at research and graduate levels. Numerous examples and exercises are included, together with an extensive bibliography.
Reviews
From the reviews:
“The book deals with the construction of knowledge spaces and learning spaces … . Thus, the creative mathematician will find material capable of entertaining him or her for some time. The practitioner may be interested in applications. … there is no doubt that reading and working with this book will be rewarding for the mathematician and useful for scientists from very different areas. In many aspects it has the potential to serve as a guideline to a new and theoretically better founded form of psychometry.” (Reinhard Suck, SIAM Review, Vol. 54 (2), 2012)
“This book is an enlarged second edition of the 1999 ‘Knowledge Spaces’ by the same authors. … The authors cover both deterministic and probabilistic models, justify their findings and give good examples and applications, such as pattern recognition and medical diagnosis. … We recommend it to doctoral and postdoctoral studies.” (George Stoica, Zentralblatt MATH, Vol. 1205, 2011)
Authors and Affiliations
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School of Social Sciences, Dept. Cognitive Sciences, University of California, Irvine, Irvine, USA
Jean-Claude Falmagne
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Dépt. Mathematique, Université Libre de Bruxelles, Bruxelles, Belgium
Jean-Paul Doignon
About the authors
Bibliographic Information
Book Title: Learning Spaces
Book Subtitle: Interdisciplinary Applied Mathematics
Authors: Jean-Claude Falmagne, Jean-Paul Doignon
DOI: https://doi.org/10.1007/978-3-642-01039-2
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2011
Hardcover ISBN: 978-3-642-01038-5Published: 14 September 2010
Softcover ISBN: 978-3-642-42277-5Published: 28 November 2014
eBook ISBN: 978-3-642-01039-2Published: 10 September 2010
Edition Number: 1
Number of Pages: XV, 417
Topics: Applications of Mathematics, Artificial Intelligence, Multimedia Information Systems, Math Applications in Computer Science, Computers and Education, Mathematics Education