American Journal of Applied Mathematics and Statistics
ISSN (Print): 2328-7306 ISSN (Online): 2328-7292 Website: https://www.sciepub.com/journal/ajams Editor-in-chief: Mohamed Seddeek
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American Journal of Applied Mathematics and Statistics. 2016, 4(6), 173-177
DOI: 10.12691/ajams-4-6-2
Open AccessArticle

An Absorbing Markov Chain Model for Problem-Solving

Michael Gr. Voskoglou1,

1Department of Mathematical Sciences, School of Technological Applications, Graduate Technological Educational Institute (T. E. I.) of Western Greece, Patras, Greece

Pub. Date: December 23, 2016

Cite this paper:
Michael Gr. Voskoglou. An Absorbing Markov Chain Model for Problem-Solving. American Journal of Applied Mathematics and Statistics. 2016; 4(6):173-177. doi: 10.12691/ajams-4-6-2

Abstract

In the present paper an absorbing Markov Chain model is developed for the description of the problem-solving process and through it a measure is obtained for problem-solving skills. Examples are also presented illustrating the model’s applicability in practice.

Keywords:
Problem-Solving (PS) Multidimensional PS Framework (MPSF) Finite Markov Chain (FMC) Absorbing Markov Chain (AMC) Transition Matrix Fundamental Matrix

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]  Bartholomew, D.J. (1973). Stochastic Models for Social Processes, J. Wiley and Sons, .
 
[2]  Carlson, M.P. & Bloom, I. (2005). The cyclic nature of problem solving: An emergent multidimensional problem-solving framework, Educational studies in Mathematics, 58, 45-75.
 
[3]  Kemeny, J. G. & Snell, J. L. (1963). Mathematical Models in the Social Sciences, Ginn and Company, New York, USA.
 
[4]  Kemeny, J. G. & Snell J. L. (1976). Finite Markov Chains, Springer - Verlag, New York, USA.
 
[5]  Morris, A. O. (1978). An Introduction to Linear Algebra, Van Nostrand Beinhold Company Ltd., Berkshire, England.
 
[6]  Polya, G. (1945). How to Solve it, Princeton University Press, Princeton.
 
[7]  Schoenfeld, A. (1980). Teaching Problem Solving skills, Amer. Math. Monthly, 87, 794-805.
 
[8]  Schoenfeld, A. (2010). How we think: A theory of goal-oriented decision making and its educational applications; Routledge: New York.
 
[9]  Suppes, P. & Atkinson, R. C. (1960). Markov Learning Models for Multiperson Interactions, Stanford University Press, Stanford-California, USA.
 
[10]  Voskoglou, M. Gr. & Perdikaris, S. C. (1991). A Markov chain model in problem- solving, International Journal of Mathematical Education in Science and. Technology, 22, 909-914.
 
[11]  Voskoglou, M. Gr. (2007). A stochastic model for the modelling process. In: Mathematical Modelling: Education, Engineering and Economics (ICTMA 12), Chaines, Chr., Galbraith, P., Blum W. and Khan, S. (Eds). 149-157, Horwood Publishing, Chichester, England.
 
[12]  Voskoglou, M. Gr. (2011). Problem-Solving from Polya to Nowadays: A review and Future Perspectives, in Nata, R. (Ed.). Progress in Education, Vol. 22, Chapter 4, 65-82, Nova Publishers, New York.
 
[13]  Voskoglou, M. Gr. (2011). Stochastic and Fuzzy Models in Mathematics Education, Artificial Intelligence and Management, Lambert Academic Publishing, Saarbrucken, Germany.
 
[14]  Voskoglou, M. Gr. (2015). Defuzzification of Fuzzy Numbers for Student Assessment, American Journal of Applied Mathematics and Statistics, 3(5), 206-210.
 
[15]  Voskoglou, M. Gr. (2016). Applications of Finite Markov Chain Models to Management, American Journal of Computational and Applied Mathematics, 6(1), 7-13.
 
[16]  Voskoglou, M. Gr. (2016). Problem Solving in our Knowledge Society and Future Perspectives, in K. Newton (Ed.). Problem-Solving: Challenges and Outcomes, Nova Publishers, Chapter 13, 243-258.