Probabilistic thinking in prospective teachers from the use of TinkerPlots for simulation: Hat problem
Timur Koparan 1 * , Francisco Rodríguez-Alveal 2
More Detail
1 1Zonguldak Bulent Ecevit University, Eregli Faculty of Education, Turkey
2 Universidad del Bío-Bío, Facultad de Educación y Humanidades, Chillán, Chile
* Corresponding Author

Abstract

Solving real-life problems through mathematical modeling is one of the aims of modern mathematics curricula. For this reason, prospective mathematics teachers need to acquire modeling skills and use these skills in learning environments in terms of creating rich learning environments. With this study, it is aimed to examine the reflections of using a simulation on a problem involving uncertainty on the probabilistic thinking of prospective teachers. The activity includes an experimental review of the famous Hat problem. It was observed that the hat problem, which started as a puzzle, was linked to coding theory and reached the limit of mathematics, statistics, and computer science research. Research findings revealed that the simulation-supported learning environment not only contributes to prospective teachers' probabilistic thinking skills, but also offers the opportunity to experience different methods (such as working with real data, technology assisted learning, modeling) in teaching and learning mathematics. It has been concluded that simulations have a unique potential that other methods do not have in terms of gaining statistical thinking as well as problem solving and modeling skills. 

Keywords

References

  • Batanero, C. (2005). Significados de la probabilidad en la eduación secundaria [Meanings of probability in secondary education]. Revista Latinoamericana de Investigación en Matemática Educativa, 8(3), 247-264.
  • 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.
  • Batanero, C., & Godino, J. (2002). Estocástica y su Didáctica para Maestros [Stochastics and its Teaching for Teachers]. Proyecto Edumat-Maestros, Granada, Universidad de Granada. https://www.ugr.es/~jgodino/edumat-maestros/manual/6_Estocastica.pdf
  • Batanero, C., Arteaga, P., Serrano, L., & Ruiz, B. (2014). Prospective primary school teachers’ perception of randomness. In E. Chernoff & B. Sriraman (Eds.), Probabilistic thinking: Presenting plural perspectives (pp. 345–366). Springer.
  • Batanero, C., Biehler, R., Engel, J., Maxara, C., & Vogel, M. (2005). Simulation as a tool to bridge teachers’ probabilistic and pedagogical knowledge. Paper presented at the ICMI Study 15. Professional development of mathematics teachers. Aguas de Lindoia, Brazil, 2005.
  • Batanero, C., Chernoff, E.J., Engel, J., Lee, H.S., Sánchez E. (2016). Research on teaching and learning probability. In G. Kaiser (Ed.), Research on Teaching and Learning Probability. ICME-13 Topical Surveys. Springer. https://doi.org/10.1007/978-3-319-31625-3_1
  • Ben-Zvi, D. (2000). Towards understanding the role of technological tools in statistical learning. Mathematical Thinking and Learning, 2(1&2), 127-155. https://doi.org/10.1207/S15327833MTL0202_6
  • Ben-Zvi, D. (2002). Seventh grade students sense making of data and data representations. In B. Phillips (Ed.), Proceedings of the Sixth International Conference on Teaching of Statistics, Cape Town, South Africa. International Statistical Institute.
  • Biehler, R., & Maxara, C. (2007). Integration von stochastischer Simulation in den Stochastikunterricht mit Hilfe von Werkzeugsoftware [Integration of stochastic simulation in Stochastics lessons with the help of tool software.]. Der Mathematikunterricht, 53(3), 45-62.
  • Biehler, R., Frischemeier, D., & Podworny, S. (2017). Elementary preservice teachers' reasoning about modeling a “family factory” with Tinkerplots: A pilot study. Statistics Education Research Journal, 16, 244–286,
  • Borovcnik, M., & Kapadia, R (2009). Research and developments in probability education. International Electronic Journal of Mathematics, 4(3), 111-130. https://doi.org/10.29333/iejme/233
  • Carver, R., Everson, R., Gabrosek, J., Horton, N., Lock, R., Mocko, M., Rossman, A., Holmes, G., Velleman, P., Witmer, J., Wood, V. (2016). Guidelines for Assessment and Instruction in Statistics Education College Report 2016. https://core.ac.uk/download/pdf/217183737.pdf
  • Chance, B. L. (2002). Components of statistical thinking and implications for instruction and assessment. Journal of Statistics Education, 10, 1-18. https://doi.org/10.1080/10691898.2002.11910677
  • Chance, B., delMas, R., & Garfield, J. (2004). Reasoning about sampling distributions. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning and thinking (pp. 295-323). Kluwer Academic Publishers.
  • Chick, H. L., & Pierce, R. U. (2008). Teaching statistics at the primary school level: Beliefs, affordances, and pedagogical content knowledge. In C. Batanero, G. Burrill, C. Reading, & A. Rossman (Eds.), Proceedings of the ICMI study 18 and IASE round table conference (Vol. 1, pp. 1-6). International Commission on Mathematics Instruction and International Association for Statistical Education.
  • Çekmez, E. (2022). An example of the use of GeoGebra for simulation: Buffon’s needle problem, International Journal of Mathematical Education in Science and Technology. Advance online publication. https://doi.org/10.1080/0020739X.2022.2034063
  • de Montmort, P. R. (1708). Essay d'analyse sur les jeux de hazard [Analytical essay on games of chance]. Revue & augmentée de plusieurs Lettres.
  • delMas, R. C. (2002). Statistical literacy, reasoning, and learning: A commentary. Journal of Statistics Education, 10(3). www.amstat.org/publications/jse/v10n3/delmas_discussion.html
  • delMas, R. C., Garfield, J., & Chance, B. L. (1999). A model of classroom research in action: Developing simulation activities to improve students’ statistical reasoning. Journal of Statistics Education, 7(3).
  • Franklin, C., Kader, G., Mewborn, D. S., Moreno, J., Peck, R., Perry, M., & Scheaffer, R. (2007). Guidelines for assessment and instruction in statistics education (GAISE) report: A pre-K-12 curriculum framework. American Statistical Association. Retrieved from https://www.amstat.org/asa/files/pdfs/gaise/gaiseprek-12_full.pdf
  • Garfield, J., & Gal, I. (1999). Assessment and statistics education: Current challenges and directions. International Statistical Review, 67(1), 1-12. https://doi.org/10.1111/j.1751-5823.1999.tb00377.x
  • Garfield, J., delMas, R., & Zieffler, A. (2012). Developing statistical modelers and thinkers in an introductory, tertiary- level statistics course. ZDM, 44(7), 883-898. https://doi.org/10.1007/s11858-012-0447-5
  • Huerta, P.(2020). Hipótesis y conjeturas en el desarrollo del pensamiento estocástico: retos para su enseñanza y en la formación de profesores [Hypotheses and conjectures in the development of stochastic thinking: challenges for its teaching and teacher training]. Revista Latinoamericana de Investigación en Matemática Educativa, 23(1), 79-102. https://doi.org/10.12802/relime.20.2313.
  • Inzunza, S., & Rocha, E. (2021). Los datos y el azar en el currículo de educación básica y bachillerato en México: Reflexiones desde la perspectiva internacional [Data and chance in the basic education and high school curriculum in Mexico: Reflections from an international perspective]. Diálogos sobre educación. Temas actuales en investigación educativa, 12(23), 00027. https://doi.org/10.32870/dse.v0i23.717
  • Jones, G., Thornton, C., Langrall, C., Mooney, E., Perry, B., & Putt, I. (2000). A framework for characterizing children’s statistical thinking. Mathematical Thinking and Learning, 2(4), 269-307. https://doi.org/10.1207/S15327833MTL0204_3
  • Konold C., Harradine A., & Kazak S. (2007). Understanding distributions by modeling them. International Journal of Computers for Mathematical Learning, 12 (3), 217-230. https://doi.org/10.1007/s10758-007-9123-1
  • Konold, C. & Miller, C. (2004). TinkerPlots™ Dynamic Data Exploration. Key Curriculum Press.
  • Konold, C., & Kazak, S. (2008). Reconnecting data and chance. Technology Innovations in Statistics Education, 2(1), 1-37. https://doi.org/10.5070/T521000032
  • Koparan, T. (2019). Teaching game and simulation based probability. International Journal of Assessment Tools in Education, 6(2), 235-258. https://doi.org/10.21449/ijate.566563
  • Koparan, T. (2022a). The impact of a game and simulation based probability learning environment on the achievement and attitudes of prospective teachers. International Journal of Mathematical Education in Science and Technology, 53(9), 2319-2337. https://doi.org/10.1080/0020739X.2020.1868592
  • Koparan, T. (2022b). How does simulation contribute to prospective mathematics teachers’ learning experiences and results? Education Sciences 12(9), 624. https://doi.org/10.3390/educsci12090624
  • Koparan, T. & Taylan Koparan, E. (2019). Empirical Approaches to probability problems: An action research. European Journal of Education Studies, 5(10), 100-117. http://doi.org/10.5281/zenodo.2557521
  • 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. https://doi.org/10.13189/ujer.2015.031101
  • Koparan. T. (2015). Difficulties in learning and teaching statistics: teacher views. International Journal of Mathematical Education in Science and Technology, 46(1), 94-104. https://doi.org/10.1080/0020739X.2014.941425
  • Koparan. T. (2016a). 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. https://doi.org/10.1080/0020739X.2015.1070210
  • Koparan. T. (2016b). Using simulation as a problem solving method in dice problems. British Journal of Education, Society & Behavioural Science, 18(1), 1-16. https://doi.org/10.9734/BJESBS/2016/27611
  • Le, L. (2017). Assessing the development of students' statistical thinking: An exploratory study. Retrieved from the University of Minnesota Digital Conservancy. https://hdl.handle.net/11299/185599
  • Maxara, C., & Biehler, R. (2007). Constructing stochastic simulations with a computer tool students’ competencies and difficulties. Paper presented at Fifth Congress of the European Society for Research in Mathematics Education, 22 – 26 February 2007, Cyprus.
  • Merriam, S. B. (1998). Qualitative research and case study applications in education. Jossey-Bass.
  • Mooney, E. S. (2002). Development of a middle school statistical thinking framework. Submitted for publication. Mathematical Thinking and Learning, 4(1), 23-63. https://doi.org/10.1207/S15327833MTL0401_2
  • National Council of Teachers of Mathematics (NCTM) (2000). Principles and standards for school mathematics. Author.
  • Pfannkuch, M., & Wild, C. (2002). Statistical thinking models. Proceedings of the sixth International Conference on Teaching Statistics. South Africa: International Association for Statistical Education.
  • Prodromou, T. (2014). Developing a modelling approach to probability using computer-based simulations. In E. Chernoff & B. Sriraman (Eds.), Probabilistic thinking. Presenting multiple perspectives (pp. 417–439). Springer.
  • Rodríguez-Alveal, F., Díaz-Levicoy, D., & Vásquez Ortiz, C. (2018). Evaluación de la alfabetización probabilística del profesorado en formación y en activo [Evaluation of the probabilistic literacy of teachers in training and in active service]. Estudios Pedagógicos, 44(1), 135–156. https://doi.org/10.4067/S0718-07052018000100135
  • Rumsey, D. J. (2002). Discussion: Statistical literacy: Implications for teaching, research and practice. International Statistical Review, 70, 32–36.
  • Stohl, H. (2005). Probability in teacher education and development. In G. Jones (Ed.), Exploring probability in schools: Challenges for teaching and learning (pp. 345–366). Springer.
  • Wallman, K. K. (1993). Enhancing statistical literacy: Enriching our society. Journal of the American Statistical Association, 88, 1-8. https://doi.org/10.1080/01621459.1993.10594283
  • Yin, R. K. (2009). Case study research: Design and methods. Sage.
  • Zieffler, A., Justice, N., delMas, R., & Huberty, M. D. (2021). The use of algorithmic models to develop secondary teachers’ understanding of the statistical modeling process. Journal of Statistics and Data Science Education, 29(1), 131-147. https://doi.org/10.1080/26939169.2021.1900759

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.