Investigating preservice secondary mathematics teachers' skills in posing realistic mathematics tasks
DOI:
https://doi.org/10.29408/jel.v10i3.25607Keywords:
preservice mathematics teachers, Problem Posing, realistic mathematics tasksAbstract
Mathematics tasks situated in realistic situations play a central role in developing and applying mathematical knowledge. However, mathematics educators face difficulties in designing realistic mathematics tasks. This study was conducted to gain deeper insights into the characteristics of mathematical problems that underprepared preservice secondary mathematics teachers pose. This study examined 32 preservice secondary mathematics teachers' problem-posing skills based on three problem-posing situations: structured problem-posing, semi-structured problem-posing, and free problem-posing. As the context of the participants, they did not have learning experiences in designing realistic mathematics tasks. In evaluating the preservice teachers' works, the researchers used several evaluation criteria, namely the compatibility of the problem with the mathematical principles, plausibility and sufficiency of information, the problem text, level of context authenticity, cognitive demand, and the correctness of the solution. The results revealed that most preservice teachers posed problems with the first-order level of context use and low cognitive demand. Additionally, many of them encountered difficulties when attempting to solve the problem. The findings of this study were expected to serve as a basis for developing a curriculum for pedagogic and mathematics courses in teacher education.
References
Bonotto, C. (2013). Artifacts as sources for problem-posing activities. Educational Studies in Mathematics, 83(1), 37–55. https://doi.org/10.1007/s10649-012-9441-7
Brookhart, S. M. (2010). How to assess higher-order thinking skills in your classroom. ASCD.
Chan, C. M. E. (2013). Initial perspectives of teacher professional development on mathematical modelling in Singapore: Conceptions of mathematical modelling. In S. G, K. G, B. W, & Brown J (Eds.), Teaching Mathematical Modelling: Connecting to Research and Practice (pp. 405–413). Springer. https://doi.org/10.1007/978-94-007-6540-5_34
Chen, L., Van Dooren, W., Chen, Q., & Verschaffel, L. (2011). An investigation on Chinese teachers' realistic problem posing and problem solving ability and beliefs. International Journal of Science and Mathematics Education, 9(4), 919–948. https://doi.org/10.1007/s10763-010-9259-7
Chen, L., Van Dooren, W., & Verschaffel, L. (2015). Enhancing the development of Chinese fifth-graders' problem-posing and problem-solving abilities, beliefs, and attitudes: A design experiment. In Mathematical Problem Posing (pp. 309–329). Springer New York. https://doi.org/10.1007/978-1-4614-6258-3_15
Crespo, S., & Harper, F. k. (2020). Learning to pose collaborative mathematics problems with secondary prospective teachers. International Journal of Educational Research, 102(May), 101430. https://doi.org/10.1016/j.ijer.2019.05.003
Downton, A. (2013). Problem Posing: A Possible Pathway to Mathematical Modelling. In International Perspectives on the Teaching and Learning of Mathematical Modelling (pp. 527–536). https://doi.org/10.1007/978-94-007-6540-5_45
Freudenthal, H. (1991). Revisiting mathematics education: China lectures. Kluwer Academic Publishers.
Hartmann, L. M., Krawitz, J., & Schukajlow, S. (2021). Create your own problem! When given descriptions of real-world situations, do students pose and solve modelling problems? ZDM - Mathematics Education, 53(4), 919–935. https://doi.org/10.1007/s11858-021-01224-7
Kohar, A. W., Wardani, A. K., & Fachrudin, A. D. (2019). Profiling context-based mathematics tasks developed by novice PISA-like task designers. Journal of Physics: Conference Series, 1200(1), 012014. https://doi.org/10.1088/1742-6596/1200/1/012014
Kramarski, B., Mevarech, Z. R., & Arami, M. (2002). The effects of metacognitive instruction on solving mathematical authentic tasks. Educational Studies in Mathematics, 49, 225–250. https://doi.org/https://doi.org/10.1023/A:1016282811724
Lee, N. H. (2013). Initial perspectives of teacher professional development on mathematical modelling in Singapore: Problem Posing and Task Design. In S. G, K. G, B. W, & B. J (Eds.), International Perspectives on the Teaching and Learning of Mathematical Modelling (pp. 415–425). Springer. https://doi.org/10.1007/978-94-007-6540-5_35
Li, Y., & Schoenfeld, A. H. (2019). Problematizing teaching and learning mathematics as "given" in STEM education. International Journal of STEM Education, 6(1). Springer. https://doi.org/10.1186/s40594-019-0197-9
Moore, K. C. (2012). Coherence, quantitative reasoning, and the trigonometry of students. In R. L. Mayes & L. Hatfield (Eds.), Quantitative reasoning and mathematical modeling: A driver for STEM integrated education and teaching in context (pp. 75–92). University of Wyoming.
Olteanu, C. (2017). Reflection-for-action and the choice or design of examples in the teaching of mathematics. Mathematics Education Research Journal, 29(3), 349–367. https://doi.org/10.1007/s13394-017-0211-9
Rosen, K. H. (2019). Discrete Mathematics and Its Applications (8th ed.). McGraw-Hill Education.
Salgado, F. (2016). Developing a theoretical framework for classifying levels of context use for mathematical problems. Mathematics Education Research Group of Australasia. In B. White, M. Chinnappan, & S. Trenholm (Eds.), Proceedings of the 39th annual conference of the Mathematics Education Research Group of Australasia (pp. 110–117). MERGA.
Şengül, S., & Katranci, Y. (2015). Free problem posing cases of prospective mathematics teachers: Difficulties and solutions. Procedia - Social and Behavioral Sciences, 174(262), 1983–1990. https://doi.org/10.1016/j.sbspro.2015.01.864
Sevinc, S., & Lesh, R. (2021). Preservice mathematics teachers' conceptions of mathematically rich and contextually realistic problems. Journal of Mathematics Teacher Education, 0123456789. https://doi.org/10.1007/s10857-021-09512-5
Silber, S., & Cai, J. (2021). Exploring underprepared undergraduate students' mathematical problem posing. ZDM - Mathematics Education, 53(4), 877–889. https://doi.org/10.1007/s11858-021-01272-z
Siswono, T. Y. E., Kohar, A. W., Hartono, S., & Rosyidi, A. H. (2018). An innovative training model for supporting in-service teachers' understanding on problem-solving knowledge for teaching. Proceedings of the 8th ICMI-East Asia Regional Conference on Mathematics Education, 321–332.
Stacey, K. (2015). The real world and the mathematical world. In K. Stacey & R. Turner (Eds.), Assessing Mathematical Literacy (pp. 57–84). Springer International Publishing. https://doi.org/10.1007/978-3-319-10121-7_3
Stoyanova, E. N., & Ellerton, N. F. (1996). A framework for research into students' problem posing in school mathematics. In P. Clarkson (Ed.), Technology in mathematics education (pp. 518–525). Mathematics Education Research Group of Australia.
van den Heuvel-Panhuizen, M. (2005). The role of contexts in assessments problems in mathematics. For the Learning of Mathematics, 25(2), 2–9.
van den Heuvel-Panhuizen, M., & Drijvers, P. (2020). Realistic mathematics education. In S. Lerman (Ed.), Encyclopedia of Mathematics Education (Vol. 4, Issue 3, pp. 713–717). Springer International Publishing. https://doi.org/10.1007/978-3-030-15789-0_170
Wijaya, A., van den Heuvel-Panhuizen, M., & Doorman, M. (2015). Opportunity-to-learn context-based tasks provided by mathematics textbooks. Educational Studies in Mathematics, 89(1), 41–65. https://doi.org/10.1007/s10649-015-9595-1
Wijaya, A., Van den Heuvel-Panhuizen, M., Doorman, M., & Veldhuis, M. (2018). Opportunity-to-learn to solve context-based mathematics tasks and students' performance in solving these tasks - Lessons from Indonesia. Eurasia Journal of Mathematics, Science and Technology Education, 14(10), em1598. https://doi.org/10.29333/ejmste/93420
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