Timur Koparan, Ezgi Taylan Koparan


The purpose of this study is to explain the modelling and modelling process problems which require probability thinking ability by using simulations in an instructional way. For that purpose, action research was performed with 46 prospective mathematics teachers who were university students in Turkey. The simulation based activities executed in this study are based on Look, Think and Act cycle in Stringer’s action research. Two open ended popular probability problems (Cereal Box and Birthday Problems) were asked to the prospective mathematics teachers. The responses about each problem are analyzed and presented in tables with percentage and frequency. When the data were investigated, it was seen that the prospective teachers gave the wrong answers or did not answer the questions. Since the aim of the study is to adopt experimental rather than theoretical approaches in the solutions of the problems, the focus was on creating simulation models for problems, doing experiments, visualisation of the results and calculation processes. Then, experimental and theoretical solutions were compared. Thus, the relations and models which help to understand the theoretical solutions of probability problems by using experimental data were proposed. Moreover, the study also sheds light on the questions of how to use the TinkerPlots in order to increase the comprehension of students and how to integrate the technology into probability teaching. In this case, it is thought that the study will be beneficial to researchers, teachers and students alike.


Article visualizations:

Hit counter



teaching probability, simulation, experimental probability, theoretical probability, action research

Full Text:



National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. Reston, VA: National Council of Teachers of Mathematics.

Koparan. T. (2015). Difficulties in Learning and Teaching Statistics: Teacher Views. International Journal of Mathematical Education in Science and Technology. 46(1), 94-104.

Ben-Zvi, D. and Garfield, J. (2004). The Challenge of Developing Statistical Literacy, Reasoning, and Thinking, Kluwer Academic Publishers.

Koparan. T. Kaleli Yılmaz. G. (2015). The Effect of Simulation-Based Learning on Prospective Teachers’ Inference Skills in Teaching Probability. Universal Journal of Educational Research, 3(11), 775 -786.

Batanero, C., Henry, M., & Parzysz, B. (2005). The nature of chance and probability. In G.A. Jones (Ed.) Exploring probability in school: Challenges for teaching and learning, (pp. 15-37). Netherlands: Kluwer.

Borovcnik, M., & Kapadia, R (2009). Research and developments in probability education. International Electronic Journal of Mathematics, 4(3). www.iejme.com/032009/IEJME_p00_introd_E.pdf

Gürbüz, R. (2008). Olasılık Konusunun Öğretiminde Kullanılabilecek Bilgisayar Destekli Bir Materyal. Mehmet Akif Ersoy Üniversitesi Eğitim Fakültesi Dergisi, 8(15), 41-52.

Mills, J. (2002). Using computer simulation methods to teach statistics: A review of the literature. Journal of Statistics Education, 10(1). www.amstat.org/publications/jse/v10n1/mills.html

GAISE (2005). Guidelines for assessment and instruction in statistics education (GAISE) report: A curriculum framework for PreK-12 statistics education. The American Statistical Association (ASA). http://www.amstat.org/education/gaise

Koparan. T. (2016). The Effect on Prospective Teachers of The Learning Environment Supported by Dynamic Statistics Software. International Journal of Mathematical Education in Science and Technology, 47(2), 276-290.

Batanero, C., & Diaz, C. (2007). Probabilidad, grado de creencia y proceso de aprendizaje [Probability, degrees of belief and the learning process]. XIII Jornadas Nacionales de Enseñanza y Aprendizaje de las Matemáticas. Granada.

Konold C., Harradine A., Kazak S. (2007). Understanding distributions by modeling them. International Journal of Computers for Mathematical Learning. 12(3), 217-230.

Maxara C, Biehler R. Constructing stochastic simulations with a computer tool students’ competencies and difficulties. In Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education; 2007. www.ermeweb.free.fr/CERME%205/WG5/5_Maxara.pdf

Batanero C., Biehler R., Carmen Maxara C., Engel J. and Vogel M. (2005). Using Simulation to Bridge Teachers´ Content and Pedagogical Knowledge in Probability. In 15th ICMI Study Conference: The Professional Education and Development of Teachers of Mathematics.

Bogdan, R.C., & Biklen, S.K. (1998). Qualitative research for education: An introduction to theory and methods (3rd ed.). Boston: Allyn and Bacon.

Johnson, A.P. (2002). A short guide to action research. Boston: Allyn & Bacon.

Mills, G.E (2003). Action research: a guide for the teacher researcher (2nd ed.), New Jersey: Merrill Prentice Hall, 2003.

Fraenkel, J.R., & Wallen, N.E. (2003). How to design and evaluate research in education (5th Ed.). New York: Mac Graw Hill, Inc.

Cohen, L., & Manion L. (1996). Research methods in education. (4. edition). NewYork: Routledge.

Kemmis, S., & McTaggart, R. (1982). The Action Research Planner. Victoria: Deakin University Press.

Loftus, J. (1999). An action research enquiry into the marketing of an established first school in its transition to full primary status. Unpublished doctoral dissertation, University of Kingston, England.

Robson, J. (1993). Real World Research: A Resource for Social Scientists and Practitioner Researchers, Oxford: Blackwells.

Stringer E.T. (2007). Action Research (Third Edition). London: Sage Publications.

Konold, C. & Miller, C. (2004). TinkerPlots™ Dynamic Data Exploration 1.0. Emeryville, CA.: Key Curriculum Press.

Travers, K.J. (1981). Using Monte Carlo methods to teach probability and statistics. In A.P. Shulte & J.R. Smart (Eds.), Teaching statistics and probability. Reston VA: National Council of Teachers of Mathematics.

Garfield, J., & Ben-Zvi, D. (2008). Chapter 7: Learning to reason about statistical models and modeling. In J. Garfield & D. Ben-Zvi, Developing students statistical reasoning (pp.143-163). Dordrecht, The Netherlands: Springer.

DOI: http://dx.doi.org/10.46827/ejes.v0i0.2250


  • There are currently no refbacks.

Copyright (c) 2019 Timur Koparan, Ezgi Taylan Koparan

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Copyright © 2015-2022. European Journal of Education Studies (ISSN 2501 - 1111) is a registered trademark of Open Access Publishing Group. All rights reserved.

This journal is a serial publication uniquely identified by an International Standard Serial Number (ISSN) serial number certificate issued by Romanian National Library (Biblioteca Nationala a Romaniei). All the research works are uniquely identified by a CrossRef DOI digital object identifier supplied by indexing and repository platforms. All authors who send their manuscripts to this journal and whose articles are published on this journal retain full copyright of their articles. All the research works published on this journal are meeting the Open Access Publishing requirements and can be freely accessed, shared, modified, distributed and used in educational, commercial and non-commercial purposes under a Creative Commons Attribution 4.0 International License (CC BY 4.0).