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
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American Journal of Educational Research. 2021, 9(2), 85-90
DOI: 10.12691/education-9-2-6
Open AccessReview Article

Problem Solving and Mathematical Modelling

Michael Gr. Voskoglou1,

1Department of Mathematical Sciences, Graduate Technological Educational Institute of Western Greece, Patras, Greece

Pub. Date: February 26, 2021

Cite this paper:
Michael Gr. Voskoglou. Problem Solving and Mathematical Modelling. American Journal of Educational Research. 2021; 9(2):85-90. doi: 10.12691/education-9-2-6

Abstract

Problem solving is one of the most important components of the human cognition that affects for ages the progress of the human society. Mathematical modelling is a special type of problem solving concerning problems related to science or everyday life situations. The present study is a review of the most important results reported in the literature from the 1950’s until nowadays on problem solving and mathematical modelling from the scope of Education. Its real goal is that it presents in a systematic way and in a few pages only the results of many years research on the subject. This helps the reader to get a comprehensive idea about a very important topic belonging to the core of Mathematics Education, which is very useful to those wanting to study deeper the subject and get directions for further research in the area.

Keywords:
mathematics education problem solving mathematical modeling application-oriented teaching of mathematics

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References:

[1]  Polya, G., How I solve it: A new aspect of mathematical method. Princeton University Press: New Jersey, 1973.
 
[2]  Schoenfeld, A., The wild, wild, wild, wild world of problem solving: A review of sorts. For the Learning of Mathematics, 3, 40-47, 1983.
 
[3]  .Green, A.J.K.; Gillhooly, K., Problem Solving. In Cognitive Psychology, Braisby, N. and Gelatly, A. (Eds.); Oxford University Press: Oxford, 2005.
 
[4]  Martinez, M., What is metacognition? Teachers intuitively recognize the importance of metacognition, but may not be aware of its many dimensions. Phi Delta Kappan, 87(9), 696-714, 2007.
 
[5]  Polya G., How to solve it. Princeton Univ. Press: Princeton, 1945.
 
[6]  Polya G., Mathematics and Plausible Reasoning. Princeton Univ. Press: Princeton, 1954.
 
[7]  Polya G., Mathematical Discovery. Wiley and Sons: New York, 1962/65 (2 Vols.).
 
[8]  Schoenfeld, A., Teaching Problem Solving Skills. Amer. Math. Monthly, 87, 794-805, 1980.
 
[9]  Wright B. D., Solving measurement problems with the Rasch model. J. of Educational Measurement, 14(2), 97-116, 19767.
 
[10]  Schoenfeld, A., Measures of problem-solving performance and of problem-solving instruction. J. Res. Math. Educ., 13, 31-49, 1982.
 
[11]  Voskoglou, M. G.; Perdikaris, S. C., A Markov chain model in problem solving. Int. J. Math. Educ. Sci. Technol., 22, 909-914, 1991.
 
[12]  Voskoglou, M. G., A Fuzzy Model for Problem Solving. Turkish Journal of Fuzzy Systems, 3(1), 1-15, 2012.
 
[13]  Voskoglou, M. G., Finite Markov Chains and Fuzzy Logic Assessment Models. Amazon-Create Space Independent Publishing Platform: Columbia, SC, 2017.
 
[14]  Owen, E.; Sweller, J., Should problem solving be used as a learning device in Mathematics? J. for Research in Mathematics Education 20, 322-328, 1989.
 
[15]  Halpern, D., Thought and `knowledge: An introduction to critical thinking, Earlbaum: NJ, 4TH Edition, 2003.
 
[16]  Matlin, W.M., Cognition, Wiley & Sons: New York, 2005.
 
[17]  Carlson, M.P., Bloom, I., The cyclic nature of problem solving: An emergent multidimensional problem-solving framework Educational Studies in Mathematics, 58, 47-75, 2005.
 
[18]  Schoenfeld, A., How we think: A theory of goal-oriented decision making and its educational applications, Routledge: New York, 2010.
 
[19]  Voskoglou, M. G., Athanassopoulos, E. Statistical Thinking in Problem Solving, American Journal of Educational Research, 8(10), 754-761, 2020.
 
[20]  Papert, S. An exploration in the space of Mathematics Education. Int. J. of Computers for Mathematics, 1(1), 95-123, 1996.
 
[21]  Wing, J.M., Computational Thinking, Communications of the ACM, 49, 33-35, 2006.
 
[22]  Voskoglou, M.G.; Buckley, S., Problem Solving and Computers in a Learning Environment. Egyptian Computer Science Journal, 36(4), 28-46, 2012.
 
[23]  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, Int. J. of Game-Based Learning, 1(3), 30-52, 2011.
 
[24]  Voskoglou, M. G.; Salem, A.-B.M. Analogy Based and Case Based Reasoning: Two Sides of the Same Coin, Int. J. Appl. Fuzzy Sets Artif. Intell., 4, 5-51, 2014.
 
[25]  Voskoglou, M. G., Communities of Practice for Teaching and Learning Mathe3matics, American Journal of Educational Research, 7(6), 386-391, 2019.
 
[26]  Brown, S.I., Walters, M.I. The Art of Problem Posing, Erlbaum: Hillsdale, NJ, 1990.
 
[27]  Voskoglou, M. G., Problem-Solving from Polya to Nowadays: A Review and Future Perspectives. In Progress in Education, R.V. Nata (Ed.), Nova Science Publishers: NY, Vol. 22, Chapter 4, 65-82, 2011.
 
[28]  Voskoglou, M. G. Problem Solving in the Forthcoming Era of the Third Industrial Revolution, Int. J. Psychology Research, 10(4), 361-380, 2016.
 
[29]  Taha, H. A. Operations Research - An Introduction, Collier Macmillan: N.Y.-London, Second Edition, 1967.
 
[30]  Pollak H. O. The interaction between Mathematics and other school subjects, New Trends in Mathematics Teaching, Volume IV, Paris: UNESKO, 1979.
 
[31]  Haines, C.; Crouch, R. Remarks on a Modelling Cycle and Interpretation of Behaviours. In Modelling Students’ Mathematical Modelling Competencies (ICTMA 13), Lesh, R.A. et al. (Eds.), Springer: US, 145-154, Springer, 2010.
 
[32]  Voskoglou, M. G. A stochastic model for the modelling process. In Mathematical Modelling: Education, Engineering and Economics (ICTMA 12), Haines, C.; Galbraith, P.; Blum, W.; Khan, S. (Eds.), Horwood Publishing: Chichester, 149-157, 2007.
 
[33]  Galbraith, P.L.; Stillman, G., Assumptions and context: Pursuing their role in modeling activity. In Modelling and Mathematics Education: Applications in Science and Technology (ICTMA 9), Matos, J.F. et al. (Eds.), Horwood Publishing: Chichester, 300-310, 2001.
 
[34]  Borroneo Ferri, R. Modelling problems from a cognitive perspective. In Mathematical Modelling: Education, Engineering and Economics (ICTMA 12), Chaines, C.; Galbraith, P.; Blum, W.; Khan, S. (Eds.), Horwood Publishing: Chichester, 260-270, 2007.
 
[35]  Doer, H.M. What knowledge do teachers need for teaching mathematics through applications and modeling? In Modelling and Applications in Mathematics Education, Blum, W. et al. (Eds.), Springer: NY, 69-78, 2007.
 
[36]  Voskoglou, M. G. Use of total possibilistic uncertainty as a measure of students’ modeling capacities, Int. J. Mathematical Education in Science and Technology, 41(8), 1051-1060, 2010.
 
[37]  Voskoglou, M.G. The Application Orientated Teaching of Mathematics, Proceedings International Conference on Mathematics Education, 8-90, Svishtov, Bulgaria, 2005.
 
[38]  Voskoglou, M.G. Teaching Mathematics or Mathematical Modelling? An Answer to a Comment, ICTMA Newsletter, 8(1), 12-13, 2015.
 
[39]  Voskoglou, M. G. The use of mathematical modeling as a learning tool of mathematics, Quaderni di Ricerca in Didactica, 16, 53-60, 2006.
 
[40]  Voskoglou, M. G. Mathematical Modelling as a Teaching Method of Mathematics, Journal of Research in Innovative Teaching, 8(1), 35-50, 2015.
 
[41]  Edwards, D., Hamson, M., Guide to Mathematical Modelling. Macmillan: London, UK, Second Edition, 2001.
 
[42]  Samarskii, A.A., Mikhailov, A.P., Principles of Mathematical Modelling: Ideas, Methods, Examples. CRC Press (Taylor & Francis Group): Boca Raton, FL 2001.
 
[43]  Muthukrishna, M. and Henrinch, J., A problem in theory, Nature Human Behaviour, 3, 221-229, 2019.
 
[44]  Leikin R., How Can Cognitive Neuroscience Contribute to Mathematics Education? Bridging the Two Research Areas. In Kaiser G., Forgasz H., Graven M., Kuzniak A., Simmt E., Xu B. (Eds.), Invited Lectures from the 13th International Congress on Mathematical Education, ICME-13 Monographs, 2018.
 
[45]  Kuznetsova, E. and Matytcina, M., A multidimensional approach to training mathematics students at a university: improving the efficiency through the unity of social, psychological and pedagogical aspects, International Journal of Mathematical Education in Science and Technology, 49(3), 401-416, 2018.
 
[46]  Weber, K. and Leikin, R., Recent Advances in Research on Problem Solving and Problem Posing, in Gutierrez, A., Leber, G.C. and Boero, P. (Eds.), The Second Handbook of Research on the Psychology of Mathematics Education: The Journey Continues, Springer, pp. 353-382, 2016.
 
[47]  Kumar, M., A Study on Problem Solving Ability and Creativity among the Higher Secondary Students, Shanlax International Journal of Education, 8(21), 30-34, 2020.
 
[48]  Szado, Z.K., Kortesi, P., Guncaga, J. Szado, D. and Neag, R., Examples of Problem Solving Strategies in Mathematics Education Supporting the Sustainability of 21st Century Skills, Sustainability, 12, article 10113, 2020.