Application of Grey System Theory to Assessment of Computational Thinking Skills

Michael Gr. Voskoglou^1,

¹Department of Mathematical Sciences, Graduate T. E. I. of Western Greece, Patras, Greece

Cite this paper:
Michael Gr. Voskoglou. Application of Grey System Theory to Assessment of Computational Thinking Skills. American Journal of Applied Mathematics and Statistics. 2018; 6(6):253-261. doi: 10.12691/ajams-6-6-6

Abstract

Computational thinking is a kind of analytic thinking that synthesizes critical thinking and existing knowledge and applies them for solving complex real life and technological problems, designing systems, and understanding human behaviour, by drawing on fundamental principles of computer science. This involves frequently a degree of uncertainty and (or) the use of approximate data. On the other hand, a grey system is characterized by lack of adequate information about its components and (or) its function and the corresponding theory has found nowadays many applications to real life, science and engineering. In grey system theory the main tool for handling approximate data is the use of the grey numbers, which are indeterminate numbers defined with the help of the closed real intervals. In the present work grey numbers are used for evaluating computational thinking skills and examples are presented to illustrate our results. The outcomes of this new assessment method are compared to the corresponding outcomes of the classical method of calculating the GPA index and of a similar method developed in earlier works that uses as tools triangular fuzzy numbers instead of grey numbers.

Keywords:
Computational Thinking (CT) Case-Based Reasoning (CBR) Grey System (GS) Grey Numbers (GNs) Whitening Fuzzy Set (FS) Triangular Fuzzy Numbers (TFNs) Centre of Gravity (CoG) defuzzification technique assessment methods

This 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]	Balley, K. D., Sociology and the New Systems Theory: Toward a Theoretical Synthesis. New York: State of New York Press, 1994.
[2]	Voskoglou, M. Gr., Finite Markov Chain and Fuzzy Logic Assessment Models: Emerging Research and Opportunities, Columbia, SC, Createspace.com.-Amazon, 2017.
[3]	Voskoglou, M. Gr., Use of the Triangular Fuzzy Numbers for Student Assessment, American Journal of Applied Mathematics and Statistics, 3(4), 146-150, 2015.
[4]	Green, A. J. K. & Gillhooly, K., Problem solving, in Braisby, N. & Gelatly, A. (Eds.), Cognitive Psychology, Oxford University Press, Oxford, 2005.
[5]	Mc Peck, J. E., Critical thinking and education, Martin Robinson, Oxford, 1981.
[6]	Salomon, G. & Perkings, D., Rocky roads to transfer: Rethinking mechanisms of a neglected phenomenon, Educational Psychologist, 24, 113-142, 1989.
[7]	Mc Guinness, C., Teaching thinking: New signs for theories of cognition, Educational Psychology,, 13(3-4), 305-316, 1993
[8]	Papert, S., An exploration in the space of Mathematics Education, International Journal of Computers for Mathematics, 1(1), 95-123, 1996.
[9]	Wing, J. M., Computational thinking, Communications of the ACM, 49, 33-35, 2006.
[10]	Voskoglou, M.Gr. & Buckley, S., Problem Solving and Computers in a Learning Environment, Egyptian Computer Science Journal,, 36(4), 28-46, 2012.
[11]	Liu, J. & Wang, L., Computational Thinking in Discrete Mathematics, Proceedings of the IEEE 2nd International Workshop on Education Technology and Compute Science, pp. 413-416, 2010.
[12]	Kazimoglu, C., Kiernan, M., Bacon, L. & MacKinnon, L., Understanding Computational Thinking Before Programming: Developing Guidelines for the Design of Games to Learn Introductory Programming through Game-Play, International Journal of Game-Based Learning, 1(3), 30-52, 2011.
[13]	Voskoglou, M. Gr. & Salem A.-B.M., Analogy-Based and Case-Based Reasoning: Two Sides of the Same Coin, International Journal of Applications of Fuzzy Sets and Artificial Intelligence, 4, 7-18, 2014.
[14]	Klir, G. J. & Folger, T. A., Fuzzy Sets, Uncertainty and Information, Prentice-Hall, London, 1988.
[15]	Kaufmann, A. & Gupta, M., Introduction to Fuzzy Arithmetic, Van Nostrand Reinhold Company, New York, 1991.
[16]	Van Broekhoven, E. & De Baets, B., Fast and accurate centre of gravity defuzzification of fuzzy systems outputs defined on trapezoidal fuzzy partitions, Fuzzy Sets and Systems, 157(7), 904-918, 2006.
[17]	Zadeh, L.A., Fuzzy Sets, Information and Control, 8, 338-353, 1965.
[18]	Deng, J., Control Problems of Grey Systems, Systems and Control Letters, 288-294, 1982.
[19]	Deng, J., Introduction to Grey System Theory, The Journal of Grey System, 1, 1-24, 1989.
[20]	Liu, S. F. & Lin, Y. (Eds.), Advances in Grey System Research, Berlin-Heidelberg: Springer, 2010.
[21]	Moore, R.A., Kearfort, R.B. & Clood, M.J., Introduction to Interval Analysis, 2nd Printing, Philadelphia, SIAM, 1995.
[22]	Voskoglou, M. Gr., Solving Systems of Equations with Grey Data, International Journal of Applications of Fuzzy Sets and Artificial Intelligence, 8, 103-111, 2018.
[23]	Voskoglou, M. Gr., Solving Linear Programming Problems with Grey Data, Oriental Journal of Physical Sciences, 3(1), 17-23, 2018.
[24]	Voskoglou, M. Gr., Fuzzy Linear Programming, Egyptian Journal of Computer Science, 42(3), 1-14, 2018.