American Journal of Educational Research
ISSN (Print): 2327-6126 ISSN (Online): 2327-6150 Website: https://www.sciepub.com/journal/education Editor-in-chief: Ratko Pavlović
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American Journal of Educational Research. 2014, 2(12), 1144-1150
DOI: 10.12691/education-2-12-3
Open AccessArticle

A Trapezoidal Fuzzy Method for Assessing Students’ Mathematical Modeling Skills

Michael Gr. Voskoglou1,

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

Pub. Date: December 01, 2014

Cite this paper:
Michael Gr. Voskoglou. A Trapezoidal Fuzzy Method for Assessing Students’ Mathematical Modeling Skills. American Journal of Educational Research. 2014; 2(12):1144-1150. doi: 10.12691/education-2-12-3

Abstract

Fuzzy logic due to its nature of characterizing each case with multiple values offers a rich field of resources covering the assessment of situations characterized by a degree of vagueness and/or uncertainty. In this paper, we apply a new trapezoidal fuzzy assessment model (TRFAM) for measuring students’ mathematical modeling (MM) skills. TRFAM is actually a variation of the commonly used in fuzzy logic centre of gravity (COG) defuzzification technique, which we have properly adapted and utilized in earlier papers as an assessment model. Our COG and TRFAM models focus on students’ quality performance by assigning greater coefficients to the higher scores. A classroom experiment is also presented, illustrating our results in practice. Through this experiment the above two models are compared to each other and also with two traditional assessment methods based on principles of bivalent logic (the calculation of means and of the GPA index) and some useful conclusions are drawn.

Keywords:
mathematical modeling (MM) fuzzy sets and logic centre of gravity (COG) defuzzification technique trapezoidal fuzzy assessment model (TRFAM)

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References:

[1]  Asiala, M., et al., “A framework for research and curriculum development in undergraduate mathematics education”, Research in Collegiate Mathematics Education II, CBMS Issues in Mathematics Education, 6, 1-32, 1996.
 
[2]  Berry, J. and Davies, A., “Written reports, Mathematics Learning and Assessment: Sharing Innovative Practices”, in Haines, C. R. & Dunthornr (Eds.), London, Arnold, 1996.
 
[3]  Blomhψj, M. and Jensen, T. H., “Developing mathematical modelling competence: Conceptual clarification and educational planning”, Teaching Mathematics and its Applications, 22, 123-129, 2003.
 
[4]  Blum, W. & Leii, “How do students and teachers deal with modelling problems?’. In C. Chaines, P. Galbraith, W. Blum & S. Khan (Eds.): Mathematical Modelling (ICTMA 12): Education, Engineering and Economics, Chichester, Horwood Publishing, 222-231, 2007.
 
[5]  Edwards D. & Hamson M. J., Mathematical Modelling Skills, London, Macmillan, 1996.
 
[6]  “Grade Point Average Assessment”, available in the Web at: http://www.swinburne.edu.au/student-administration/assessment/gpa.html, visited October 15, 2014.
 
[7]  Greefrath, G., Modellieren lernen mitoffenen realitatsnahen Aufgaben, Koln, Aulis Verlag, 2007.
 
[8]  Haines, C. & Crouch, R., “Remarks on a Modelling Cycle and Interpretation of Behaviours’. In R.A. Lesh et al. (Eds.): Modelling Students’ Mathematical Modelling Competencies (ICTMA 13), 145-154, Springer, US, 2010
 
[9]  Klir, G. J. & Folger, T. A.., Fuzzy Sets, Uncertainty and Information, Prentice-Hall, London, 1988.
 
[10]  Lewandowski, G. et al., “Common sense computing (episode 3): Concurrency and concert tickets”, Proceedings of the Third International Workshop on Computing Education Research (ICER), 2007.
 
[11]  Pollack H. O., “The interaction between Mathematics and other school subjects”, New Trends in Mathematics Teaching, Volume IV, Paris: UNESKO, 1979.
 
[12]  Polya, G., “On learning, teaching and learning teaching”, American Mathematical Monthly, 70, 605-619, 1963.
 
[13]  Subbotin, I. Ya., Badkoobehi, H., Bilotckii, N. N., “Application of fuzzy logic to learning assessment”. Didactics of Mathematics: Problems and Investigations, 22, 38-41, 2004.
 
[14]  Subbotin, I. Ya., Voskoglou, M. Gr., “Fuzzy Models for Learning Assessment”, arXiv: 1410.4497 [math. OC], submitted on October 15, 2014.
 
[15]  van Broekhoven, E. & De Baets, B., “Fast and accurate centre of gravity defuzzification of fuzzy system outputs defined on trapezoidal fuzzy partitions”, Fuzzy Sets and Systems, 157 (7), 904-918.
 
[16]  Voskoglou, M. Gr. (1994), An application of Markov Chain to the process of modelling, International Journal of Mathematical Education in Science and Technology, 25 (4), 475-480, 2006.
 
[17]  Voskoglou, M. Gr., “A stochastic model for the modelling process”. In C. Chaines, P. Galbraith, W. Blum & S. Khan (Eds.): Mathematical Modelling (ICTMA 12): Education, Engineering and Economics, Chichester, Horwood Publishing, 149-157, 2007.
 
[18]  Voskoglou, M. Gr., Stochastic and fuzzy models in Mathematics Education, Artificial Intelligence and Management, Lambert Academic Publishing, Saarbrucken, Germany, 2011. For more details look at http://amzn.com./3846528218).
 
[19]  Voskoglou, M. Gr. & Buckley, S., “Problem Solving and Computers in a Learning Environment”, Egyptian Computer Science Journal, 36 (4), 28-46, 2012.
 
[20]  Voskoglou, M. Gr. & Subbotin, I. Ya., “Dealing with the Fuzziness of Human Reasoning”, International Journal of Applications of Fuzzy Sets and Artificial Intelligence, Vol. 3, 91-106, 2013.
 
[21]  Voskoglou, M. Gr., “Assessing the Players’ Performance in the Game of Bridge: A Fuzzy Logic Approach, American Journal of Applied Mathematics and Statistics, 2 (3), 115-120, 2014.
 
[22]  Weller, K. et al., “Student performance and attitudes in courses based on APOS theory and the ACE teaching style”. In A. Selden et al. (Eds.), Research in collegiate mathematics education V, 97- 13, Providence, RI, American Mathematical Society, 2003.
 
[23]  Wikipedia, “Trapezoid: Other properties”, available in the Web at: http://en.wikipedia.org/wiki/trapezoid#other_properties, visited on October 10, 2014.
 
[24]  Wikipedia, “Center of mass: A system of particles”, available in the Web at: http://en.wikipedia.org/wiki/Center_of_mass#A_system_of_particles, visited on October 10, 2014.
 
[25]  Yadav, A. et al., “Introducing Computational Thinking in Education Courses”, Proceedings of the 42nd ACM technical symposium on Computer Science Education 11, 465-470, March 9-12, 2011.