The Assessment of Knowledge, in Theory and in Practice

Adaptations from a book and many scholarly articles are presented. It reviews the main ideas of a novel theory for the assessment of a student's knowledge in a topic and gives details on a practical implementation in the form of a software system available on the Internet. The basic concept of the theory is the 'knowledge state,' which is the complete set of problems that an individual is capable of solving in a particular topic, such as elementary algebra. The task of the assessor consists in uncovering the particular state of the student being assessed. Even though the number of knowledge states for a topic may exceed several hundred thousand, these large numbers are well within the capacity of current home or school computers. The result of an assessment consists in two short lists of problems, which may be labelled: 'what the student can do' and 'what the student is ready to learn'. In the most important applications of the theory, these two lists specify the exact knowledge state of the individual being assessed.

[1]  Jean-Claude Falmagne,et al.  Spaces for the Assessment of Knowledge , 1985, Int. J. Man Mach. Stud..

[2]  Mathieu Koppen.  The Construction of Knowledge Spaces by Querying Experts , 1994 .

[3]  Jean-Paul Doignon,et al.  A Markovian procedure for assessing the state of a system , 1988 .

[4]  K. Pearson,et al.  The Life, Letters and Labours of Francis Galton , 1931, Nature.

[5]  Jean-Claude Falmagne,et al.  Knowledge spaces , 1998 .

[6]  Ki Hang Kim.  Measurement theory with applications to decision-making, utility and the social sciences: Fred S. Robert Reading, MA 01867: Addison-Wesley, 1979. $24.50 , 1981 .

[7]  C. Dowling.  On the irredundant generation of knowledge spaces , 1993 .

[8]  Cornelia E. Dowling.  Applying the basis of a knowledge space for controlling the questioning of an expert , 1993 .

[9]  John B. Black,et al.  Knowledge Structures , 1986 .

[10]  Suck.  A Dimension-Related Metric on the Lattice of Knowledge Spaces. , 1999, Journal of mathematical psychology.

[11]  W. Trotter,et al.  Combinatorics and Partially Ordered Sets: Dimension Theory , 1992 .

[12]  G. Birkhoff.  Rings of sets , 1937 .

[13]  Jürgen Heller,et al.  A formal framework for characterizing querying algorithms , 2004 .

[14]  F. Roberts.  Measurement Theory with Applications to Decisionmaking, Utility, and the Social Sciences: Measurement Theory , 1984 .

[15]  Dietrich Albert,et al.  Knowledge Spaces: Theories, Empirical Research, and Applications , 1998 .

[16]  Gerhard H. Fischer,et al.  "Contributions to Mathematical Psychology, Psychometrics, and Methodology" , 1993 .

[17]  Mathieu Koppen,et al.  Extracting human expertise for constructing knowledge spaces: an algorithm , 1993 .

[18]  Jean-Paul Doignon,et al.  A class of stochastic procedures for the assessment of knowledge. , 1988 .

[19]  Reinhold Suck.  The Basis of a Knowledge Space and a Generalized Interval Order , 1999, Electron. Notes Discret. Math..

[20]  Hans-Hermann Bock,et al.  Data Analysis and Information Systems , 1996 .

[21]  Rudolf Wille,et al.  Knowledge Spaces and Formal Concept Analysis , 1996 .