This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Automata for the Assessment of Knowledge
May/June 2001 (vol. 13 no. 3)
pp. 451-461

Abstract—The results of this paper can be applied to construct efficient algorithms for the adaptive assessment of the students' knowledge. The problem of knowledge assessment is a special case of the problem of assessing the state of a system. These results are obtained suggesting a new assessment algorithm whose formal equivalence to previously suggested assessment algorithms is proven. A simulation study illustrates the vast improvements of efficiency with the new algorithm.

[1] J.-P. Doignon and J.-C. Falmagne, “Spaces for the Assessment of Knowledge,” Int'l J. Man-Machine Studies, vol. 23, pp. 175–196, 1985.
[2] J.-P. Doignon and J.-C. Falmagne, Knowledge Spaces. Berlin: Springer-Verlag, 1999.
[3] J.-C. Falmagne and J.-P. Doignon, “A Markovian Procedure for Assessing the State of a System,” J. Math. Psychology, vol. 32, pp. 232–258, 1988.
[4] M. Schrepp, “A Generalization of Knowledge Space Theory to Problems with More than Two Answer Alternatives,” J. Math. Psychology, vol. 41, pp. 237–243, 1997.
[5] K. Baumunk and C.E. Dowling, “Validity of Spaces for Assessing Knowledge about Fractions,” J. Math. Psychology, vol. 41, pp. 99–105, 1997.
[6] J.-C. Falmagne and J.-P. Doignon, “A Class of Stochastic Procedures for the Assessment of Knowledge,” British J. Math. and Statistical Psychology, vol. 41, pp. 1–23, 1988.
[7] J. Carroll and D. Long, Theory of Finite Automata. Englewood Cliffs, N.J.: Prentice Hall, 1989.
[8] J.E. Hopcroft and J.D. Ullman, Introduction to Automata Theory, Languages and Computation. Addison-Wesley, Apr. 1979.
[9] E. Degreef, J.-P. Doignon, A. Ducamp, and J.-C. Falmagne, “Languages for the Assessment of Knowledge,” J. Math. Psychology, vol. 30, pp. 243–256, 1986.
[10] J.-P. Doignon, “Probabilistic Assessment of Knowledge,” Knowledge Structures, D. Albert, ed., pp. 1–56, 1994.
[11] C.E. Dowling, C. Hockemeyer, and A.H. Ludwig, “Adaptive Assessment and Training Using the Neighbourhood of Knowledge States,” Intelligent Tutoring Systems, C. Frasson, G. Gauthier, and A. Lesgold, eds., pp. 578–586, 1996.
[12] O. Ore, Theory of Graphs. Providence, R.I.: AMS Colloquium Publications, Am. Math. Soc., 1962.
[13] G. Birkhoff, Lattice Theory. Am. Math. Soc. Colloquium Publication, Am. Math. Soc., third ed., 1967.

Index Terms:
Knowledge assessment, deterministic finite automaton, knowledge space, knowledge state, assessment language.
Citation:
Cornelia E. Dowling, Cord Hockemeyer, "Automata for the Assessment of Knowledge," IEEE Transactions on Knowledge and Data Engineering, vol. 13, no. 3, pp. 451-461, May-June 2001, doi:10.1109/69.929902
Usage of this product signifies your acceptance of the Terms of Use.