Statistical Thinking in Problem Solving

Michael Gr. Voskoglou^1, and Evangelos Athanassopoulos²

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

²Independent Researcher, Gastouni, Greece

Cite this paper:
Michael Gr. Voskoglou and Evangelos Athanassopoulos. Statistical Thinking in Problem Solving. American Journal of Educational Research. 2020; 8(10):754-761. doi: 10.12691/education-8-10-3

Abstract

This article studies the role of Statistical Thinking in Problem Solving., where the problem is considered with its wide meaning (not mathematical problems only). Particular emphasis is given to Bayesian Reasoning, whose importance in everyday life and science applications has been only recently fully recognized. Critical and Computational Thinking, the other two main modes of thinking used in Problem Solving, are also discussed and examples are presented illustrating our conclusions.

Keywords:
Problem Solving (PS) Critical Thinking (CrT) Statistical Thinking (ST) Computational Thinking (CT) Bayesian Reasoning Fuzzy Logic (FL)

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References:

[1]	Polya, G., How I solve it: A new aspect of mathematical method, New Jersey: Princeton University Press, 1973.
[2]	Schoenfeld, A., “The wild, wild, wild, wild world of problem solving: A review of sort”|, For the Learning of Mathematics, 3, 40-47, 1983.
[3]	Green, A. J. K. & Gillhooly, K., “Problem solving”, in Braisby, N. & Gelatly, A. (Eds.), Cognitive Psychology, 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]	Schuler, J. & Lipsch utz, S., Schaum’s Outline of Probability, 2nd Edition, McGraw Hill, NY, USA, 2010.
[6]	Jaynes, E.T., Probability Theory: The Logic of Science, 8th Printing, Cambridge University Press, UK, 2011.
[7]	Mumford, D., “The Dawning of the Age of Stochasticity”, in V. Amoid, M. Atiyah, P. Laxand & B. Mazur (Eds.), Mathematics: Frontiers and Perspectives, AMS, 197-218, 2000.
[8]	Kosko, B., Fuzzy Thinking: The New Science of Fuzzy Logic, Hyperion, NY, USA, 1993.
[9]	Zadeh, L.A., “Fuzzy Sets”, Information and Control, 8, 338-353, 1965.
[10]	Voskoglou, M.Gr., “Methods for Assessing Human-Machine Performance under Fuzzy Conditions”, Mathematics, 7, article 230, 2019.
[11]	Changingminds.org, “Full alphabetic list of Fallacies”, available online at: http://changingminds.org/disciplines/argument /fallacies/fallacies_alpha.htm (accessed on 23 June 2020)
[12]	Athanassopoulos, E. and Voskoglou, M.Gr., “Quantifying the Aristotle’s Fallacies”, Mathematics, 8, article 1399, 2020.
[13]	Voskoglou, M. Gr. & Buckley, S., “Problem Solving and Computers in a Learning Environment”, Egyptian Computer Science Journal, 36(4), 28-46, 2012.
[14]	Halpern, D., Thought and knowledge: An introduction to critical thinking, 4th edition, Mahwah, Earlbaum, NJ, USA, 2003.
[15]	Warburton, N., A little history of Philosophy, Yale University Press, USA, 2011.
[16]	Gardener, J. & Resnik, D., “The misuse of statistics, concepts, tools and a research agenda”, Accountability in Research: Policies and Quality Assurance, 9(2), 65-74, 2002.
[17]	Wason, P. C., “Self-contradictions, in Johnson-Laird”, P. N.; Wason, P. C. (Eds.), Thinking: Readings in cognitive science, Cambridge, Cambridge University Press, 1977.
[18]	Evans, J.St.B.T., Newstead, S. E., Byrne, R.M.J., Human Reasoning: The Psychology of Deduction, Psychology Press, East Sussex, UK, 1993.
[19]	Tversky, A., & Kahneman, D., Judgment under uncertainty: Heuristics and biases, Cambridge University Press, Cambridge, UK, 1982.
[20]	Aristidou, M., “Irrationality Re-Examined: A Few Comments on the Conjunction Fallacy”, Open Journal of Philosophy, 3(2), 329-336, 2013.
[21]	Papert, S., “An exploration in the space of Mathematics Education”, International Journal of Computers for Mathematics, 1(1), 95-123., 1996.
[22]	Wing, J. M., “Computational thinking”, Communications of the ACM, Vol.49, 33-35, 2006.
[23]	Liu, J. & Wang, L., “Computational Thinking in Discrete Mathematics”, IEEE 2nd International Workshop on Education Technology and Computer Science, 413-416, 2010.
[24]	Matlin, W. M., Cognition, Wiley & Sons, New York, 2005.
[25]	Mc Guinness, C., “Teaching thinking: New signs for theories of cognition”, Educational Psychology, 13(3-4), 305-316, 1993.
[26]	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.
[27]	Horgan, J., “Bayes’ Theorem: What is the Big Deal?”, available at http//:blogs.scientificamerican.com/cross-check/bayes-s-theorem-what-s-the-big-deal, 2015.
[28]	Athanassopoulos, E. & Voskoglou, M.Gr., “A Philosophical Treatise on the Connection of Scientific Reasoning with Fuzzy Logic”, Mathematics, 8, article 875, 2020.
[29]	Bertsch McGrayne, S., The Theory that would not die, Yale University Press, New Haven and London, 2012.
[30]	What do you think about machines that think?, available at http://edge.org/response-detail/26871, 2015.
[31]	Jeffreys, H., Scientific Inference, 3d Edition, Cambridge University Press, UK, 1973.
[32]	Stone, L.D., Keller, C.M., Kratzke, T.M. & Strumpfer, J.F., “Search for the Wreckage of the Air France Flight AF 447, Statistical Science, 29(1), 69-80, 2014.
[33]	Thrope, W.H, The origins and rise of ethology: The science of the natural behavior of animals, Praeger, London-NY, 1979.
[34]	Gingerich, O., TheEye of the Heaven - Ptolemy, Copernicus, Kepler, American Institute of Physics, NY, USA, 1993.
[35]	Singh, S., “Bing Bang - The Origin of the Universe”, Harper Perennian Publishers, NY, USA, 2005.