Teaching and learning process for mathematization activities: The case of solving maximum and minimum problems

Al Jupri(1*), Dian Usdiyana(2), Ririn Sispiyati(3)

(1) Department of Mathematics Education, Universitas Pendidikan Indonesia,
(2) Department of Mathematics Education, Universitas Pendidikan Indonesia
(3) Department of Mathematics Education, Universitas Pendidikan Indonesia
(*) Corresponding Author

Abstract

One of the topics within the course of Essential Concepts in School Mathematics (ECSM) for prospective mathematics teachers concerns maximum and minimum problems. This type of problems requires mathematization, i.e., the activity of transforming a problem into a symbolic mathematics problem and of reorganizing within the mathematical system, in the solution process. This research aims to investigate the implementation of the learning and teaching process of the ECSM course that strengthen prospective mathematics teachers’  conceptual understanding and problem solving abilities through mathematization activities. To reach this aim, this qualitative study was conducted through an observation of the learning and teaching process, including the formative written assessment, for the case of maximum and minimum problems, involving 19 students of mathematics education program. The results of this study revealed that the learning and teaching process is implemented by emphasizing the use of a deductive approach. The written assessment showed students’ strategies and difficulties in dealing with maximum and minimum problems. Main difficulties included constructing visual representations and mathematical models in the mathematization processes. It can be concluded that the learning and teaching processes of the ECSM course need to be improved so as to develop better conceptual understanding and problem solving abilities through mathematization activities.

Keywords

Mathematization, quadratic functions, prospective mathematics teachers, maximum and minimum problems, Realistic Mathematics Education

Full Text:

PDF

References

Bahri, S., Abrar, A. I. P., & Angriani, A. D. (2017). Perbandingan metode deduktif dengan induktif terhadap hasil belajar matematika ditinjau dari motivasi belajar siswa. MaPan: Jurnal Matematika dan Pembelajaran, 5(2), 201-215. https://doi.org/10.24252/mapan.v5n2a4

Bukova-Güzel, E. (2011). An examination of pre-service mathematics teachers’ approaches to construct and solve mathematical modelling problems. Teaching Mathematics and its Applications: An International Journal of the IMA, 30(1), 19-36. https://doi.org/10.1093/teamat/hrq015

Chapman, O. (2006). Classroom practices for context of mathematics word problems. Educational Studies in Mathematics, 62(2), 211-230. http://doi.org/10.1007/s10649-006-7834-1

De Lange, J. (2006). Mathematical literacy for living from OECD-PISA perspective. Tsukuba Journal of Educational Study in Mathematics. Vol. 25. Special Issue on The APEC-TSUKUBA International Conference "Innovative Teaching Mathematics through Lesson Study" (pp. 13-35). Tokyo, Japan: University of Tsukuba. Retrieved from http://www.human.tsukuba.ac.jp/~mathedu/2503

Doorman, L. M., & Gravemeijer, K. P. E. (2009). Emergent modeling: Discrete graphs to support the understanding of change and velocity. ZDM, 41(1-2), 199-211. https://doi.org/10.1007/s11858-008-0130-z

Freudenthal, H. (1991). Revisiting mathematics education: China lectures. Dordrecht: Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47202-3

Gravemeijer, K., & Doorman, M. (1999). Context problems in realistic mathematics education: A calculus course as an example. Educational studies in mathematics, 39(1), 111-129. https://doi.org/10.1023/A:1003749919816

Jupri, A., & Drijvers, P. (2016). Student difficulties in mathematizing word problems in algebra. Eurasia Journal of Mathematics, Science, and Technology Education, 12(9), 2481-2502. https://doi.org/10.12973/eurasia.2016.1299a

Jupri, A., & Syaodih, E. (2016). Between formal and informal thinking: The use of algebra for solving geometry problems from the perspective of Van Hiele theory. Jurnal Pengajaran Matematika dan Ilmu Pengetahuan Alam, 21(2), 1-7. https://doi.org/10.18269/jpmipa.v21i2.817

Jupri, A. (2017). From geometry to algebra and vice versa: Realistic mathematics education principles for analyzing geometry tasks. In AIP Conference Proceedings (Vol. 1830, No. 1, pp. 050001-1-05001-5). AIPPublishing. https://doi.org/10.1063/1.4980938

Jupri, A., & Herman, T. (2017). Theory and practice of mathematics teacher education: An explorative study at the department of mathematics education, Indonesia University of Education. In Proceedings ofInternational Conference on Mathematics and Science Education.Atlantis Press. https://doi.org/10.2991/icmsed-16.2017.38

Jupri, A., & Rosjanuardi, R. (2020). An investigation of master student understanding on mathematical literacy problems. Jurnal Gantang, 5(1), 1-7. https://doi.org/10.31629/jg.v5i1.1828

Malambo, P. (2020). Pre-service mathematics teachers’ nature of understanding of the tangent function. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 5(2), 105-118. https://doi.org/10.23917/jramathedu.v5i2.10638

Marbán, J. M., & Sintema, E. J. (2020). Pre-service secondary teachers’ knowledge of the function concept: A cluster analysis approach. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 5(1), 38-53. https://doi.org/10.23917/jramathedu.v5i1.9703

Ndemo, Z., Zindi, F., & Mtetwa, D. (2017). Mathematics undergraduate student teachers' conceptions of guided inductive and deductive teaching approaches. Journal of Curriculum and Teaching, 6(2), 75-83. https://doi.org/10.5430/jct.v6n2p75

Osana, H. P., & Royea, D. A. (2011). Obstacles and challenges in preservice teachers’ explorations with fractions: A view from a small-scale intervention study. The Journal of Mathematical Behavior, 30(4), 333-352. https://doi.org/10.1016/j.jmathb.2011.07.001

Polya, G. (1945). How to solve it: A new aspect of mathematical method. Princeton University Press. https://doi.org/10.2307/j.ctvc773pk

Prince, M.J., & Felder, R.M. (2006). Inductive teaching and learning methods: Definitions, comparisons, and research bases. Journal of Engineering Education, 95(2), 123-138. https://doi.org/10.1002/j.2168-9830.2006.tb00884.x

Ramsden, P. (1987). Improving teaching and learning in higher education: the case for a relational perspective. Studies in Higher Education, 12(3), 275-286. https://dx.doi.org/10.1080/03075078712331378062

Rizta, A., & Antari, L. (2019). Tingkat mathematics anxiety pada mahasiswa calon guru matematika. Jurnal Pendidikan Matematika, 13(1), 9-20. https://doi.org/10.22342/jpm.13.1.6827.9-20

Treffers, A. (1987). Three dimensions. A model of goal and theory description in mathematics instruction-The Wiskobas project. Dordrecht, the Netherlands: Kluwer Academic Publishers. https://doi.org/10.1007/978-94-009-3707-9

Van den Heuvel-Panhuizen, M. (2003). The didactical use of models in realistic mathematics education: An example from a longitudinal trajectory on percentage. Educational studies in Mathematics, 54(1), 9-35. http://doi.org/10.1023/B:EDUC.0000005212.03219.dc

Van den Heuvel-Panhuizen, M., & Drijvers, P. (2020). Realistic Mathematics Education. In: Lerman S. (eds) Encyclopedia of Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-15789-0_170

Verschaffel, L., Schukajlow, S., Star, J., & Van Dooren, W. (2020). Word problems in mathematics education: a survey. ZDM Mathematics Education, 52, 1–16. http://doi.org/10.1007/s11858-020-01130-4

Wardani, S., & Kusuma, I. W. (2020). Comparison of learning in inductive and deductive approach to increase student’s conceptual understanding based on international standard curriculum. Jurnal Pendidikan IPA Indonesia, 9(1), 70-78. https://doi.org/10.15294/jpii.v9i1.21155

Yilmaz, S., & Tekin-Dede, A. (2016). Mathematization competencies of pre-service elementary mathematics teachers in the mathematical modelling process. International Journal of Education in Mathematics, Science and Technology, 4(4), 284-298. https://doi.org/10.18404/ijemst.39145

DOI: 10.23917/jramathedu.v6i2.13263

Article Metrics

Abstract view(s): 724 time(s)
PDF: 525 time(s)

Refbacks

  • There are currently no refbacks.