American Journal of Educational Research
ISSN (Print): 2327-6126 ISSN (Online): 2327-6150 Website: http://www.sciepub.com/journal/education Editor-in-chief: Ratko Pavlović
Open Access
Journal Browser
Go
American Journal of Educational Research. 2016, 4(5), 397-403
DOI: 10.12691/education-4-5-6
Open AccessArticle

An Application of the Generalized Rectangular Fuzzy Model to Critical Thinking Assessment

Igor Ya. Subbotin1, and Michael Gr. Voskoglou2

1National University, Department of Mathematics and Natural Sciences, Los Angeles, California, USA

2Graduate Technological Educational Institute (T. E. I.) of Western Greece, Department of Applied Mathematics, Patras, Greece

Pub. Date: April 15, 2016

Cite this paper:
Igor Ya. Subbotin and Michael Gr. Voskoglou. An Application of the Generalized Rectangular Fuzzy Model to Critical Thinking Assessment. American Journal of Educational Research. 2016; 4(5):397-403. doi: 10.12691/education-4-5-6

Abstract

The authors apply the Generalized Rectangular Model (GRM) for assessing students’ critical thinking skills. GRM is a variation of the center of gravity (COG) defuzzification technique. The COG technique was properly adapted and used several times in the past by the present authors as an assessment method, called here the Rectangular Model (RM). The central idea of the GRM is the “movement” to the left of the rectangles appearing in the membership function’s graph of the RM, thus making the adjacent rectangles to share common parts. This treatment reflects better than RM the ambiguous assessment cases of student scores being at the boundaries between two successive assessment grades (e.g. something like 84-85% being at the boundaries between A and B) and therefore belonging to the common parts of the above rectangles. In fact, in GRM, assuming that these scores belong to both of the successive assessment grades, we consider twice the common parts of the rectangles for calculating the COG of the level’s section lying between the resulting graph and the OX axis. Our results are illustrated on the data of a classroom application performed in one of the Los Angeles Unified District High Schools and connecting the students CT skills with their language competencies.

Keywords:
Fuzzy Logic COG Defuzzification Technique Fuzzy Assessment Methods Rectangular Model (RM) Generalized Rectangular Model (GRM)

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]  Critical thinking, retrieved on February 12, 2013 from: http://dictionary.reference.com/browse/criticalthinking .
 
[2]  Klir, G. J. & Folger, T. A. (1988), Fuzzy Sets, Uncertainty and Information, Prentice-Hall, London.
 
[3]  McPeck, J. (1992) Thoughts on subject specificity. In S. Norris (Ed.), The generalizability of critical thinking (pp. 198–205), New York: Teachers College Press.
 
[4]  Paul, R. (1982), Teaching critical thinking in the strong sense: A focus on self-deception, world views and a dialectical mode of analysis, Informal Logic Newsletter, 4(2), 2-7.
 
[5]  Subbotin, I. Ya., Badkoobehi, H., Bilotckii, N. N. (2004), Application of fuzzy logic to learning assessment, Didactics of Mathematics: Problems and Investigations, 22, 38-41.
 
[6]  Subbotin, I. Ya, Voskoglou, M. Gr. (2011), Applications of fuzzy logic to Case-Based Reasoning, International Journal of Applications of Fuzzy Sets and Artificial Intelligence, 1, 7-18.
 
[7]  Subbotin, I. Ya., Bilotskii, N. N. (2014), Triangular fuzzy logic model for learning assessment, Didactics of Mathematics: Problems and Investigations, 41, 84-88.
 
[8]  Subbotin, I. Ya, Voskoglou, M. Gr. (2014), Language, mathematics and critical thinking: The cross influence and cross enrichment, Didactics of Mathematics: Problems and Investigations, 41, 89- 94.
 
[9]  Subbotin, I. Ya, Voskoglou, M. Gr. (2014), A Triangular Fuzzy Model for Assessing Critical Thinking Skills, International Journal of Applications of Fuzzy Sets and Artificial Intelligence, 4, 173-186.
 
[10]  Subbotin, I. Ya. (2014), Trapezoidal Fuzzy Logic Model for Learning Assessment, arXiv 1407.0823[math..GM],.
 
[11]  Subbotin, I. Ya, Voskoglou, M. Gr. (2014), Fuzzy Assessment Methods, Universal Journal of Applied Mathematics, 2(9), 305-311.
 
[12]  Subbotin, I. Ya. (2015), On Generalized Rectangular Fuzzy Model for Assessment, Global Journal of Mathematics, 2(1), 65- 70
 
[13]  van Broekhoven, E. & De Baets, B. (2006). Fast and accurate centre of gravity defuzzification of fuzzy system outputs defined on trapezoidal fuzzy partitions, Fuzzy Sets and Systems, 157(7), 904-918.
 
[14]  Voskoglou, M. Gr. (1999), An Application of Fuzzy Sets to the Process of Learning, Heuristics and Didactics of Exact Sciences, 10, 9-13.
 
[15]  Voskoglou, M. Gr. (2009), Transition across levels in the process of learning: A fuzzy Model, International Journal of Modelling and Application, Univ. Blumenau, Brazil, 1, 37-44.
 
[16]  Voskoglou, M. Gr. (2012), A Study on Fuzzy Systems, American Journal of Computational and Applied Mathematics,
 
[17]  Voskoglou, M. Gr., Subbotin, I. Ya. (2013) Dealing with the fuzziness of human reasoning, International Journal of Applications of Fuzzy Sets and Artificial Intelligence, 3, 91- 106.
 
[18]  Voskoglou, M. Gr. (2014), Assessing the players’ performance in the game of Bridge, American Journal of Applied Mathematics and Statistics, 2(3), 115-120.
 
[19]  Voskoglou, M. Gr. (2014), A Trapezoidal Fuzzy Method for Assessing Students Mathematical Modelling Skills, American Journal of Educational Research, 2(12), 1144-1159.
 
[20]  Voskoglou, M. Gr. (2015), Fuzzy Logic in the APOS/ACE Instructional Treatment of Mathematics, American Journal of Educational Research,, 3(3), 330-339.
 
[21]  Voskoglou, M. Gr. (2015), Subbotin, I. Ya., Application of the Triangular Assessmen5t Model to Assessment of Analogical Reasoninng Skills, American Journal of Applied Mathematics and Statistics, 3(1), 1-6.
 
[22]  Wikipedia (2014), Center of mass: A system of particles. Retrieved on October 10, 2014 from http://en.wikipedia.org/wiki/Center_of_mass#A_system_of_particles.