The Effects of Mathematical Modelling in Mathematics Teaching of Linear, Quadratic and Logarithmic Functions
This study aims to acquaint high school students with the process of modelling in mathematics teaching. The research lasted 5 weeks with a group of (N.
- Pub. date: December 15, 2021
- Pages: 129-144
- 728 Downloads
- 853 Views
- 0 Citations
This study aims to acquaint high school students with the process of modelling in mathematics teaching. The research lasted 5 weeks with a group of (N=36) high school students of Zenica-Doboj Canton (Bosnia and Herzegovina). Students had an opportunity to learn about functions and their properties, and subsequently about mathematical modelling with linear, quadratic, and logarithmic functions. Examples in the research were related to real-world phenomena and processes. The problems were composed of the following subtasks: creating or testing a model, explaining the results, finding the domain and range, and critical thinking about the model. The research identifies the importance of mathematical modelling in teaching. The results display a positive impact of such an approach on students, their thinking, attitude towards teaching, understanding of the materials, motivation and examination scores. The experiences that both students and teachers may have in a mathematical modelling framework could be extremely important for the academic success. A control group of 36 students took the final exam as well. The students of the experimental group got much better results than the students of the control group. Indeed, learning through mathematical modelling has been shown to contribute to all the aspects of students' expected development.
applied mathematics critical thinking mathematics education mathematical modelling modelling
Keywords: Applied mathematics, critical thinking, mathematics education, mathematical modelling, modelling.
0
References
Apatić, D. (2016). Modeliranje [Modelling] [Graduation thesis, University of Osijek]. Nacionalni repozitorij završnih i diplomskih radova ZIR. https://zir.nsk.hr/islandora/object/mathos%3A70
Bikić, N., Maričić, S. M., & Pikula, M. (2016). The effects of differentiation of content in problem-solving in learning geometry in secondary school. Eurasia Journal of Mathematics, Science and Technology Education, 12(11), 2783-2795. https://doi.org/10.12973/eurasia.2016.02304a
Blum, W. (1993). Mathematical modelling in mathematics education and instruction. In T. Breiteig, I. Huntley & G. Kaiser-Messmer (Eds.), Teaching and learning mathematics in context (pp. 3-14). Ellis Horwood Limited.
Blum, W., & Borromeo Ferri, R. (2009). Mathematical modelling: Can I be taught and learn? Journal of Mathematical Modeling and Application, 1(1), 45–58. https://bit.ly/3ri9BXo
Blum, W., & Leiβ, D. (2007). How do students and teachers deal with modelling problems? In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling: Education, engineering and economics (pp. 222–231). Woodhead Publishing Limited. https://doi.org/10.1533/9780857099419.5.221
Carlson, M. A., Wickstrom, M. H., Burroughs, E. A., & Fulton, E. W. (2016). A case for mathematical modelling in the elementary school classroom. In C. R. Hirsch (Ed.), Mathematical modelling and modelling mathematics (pp. 121-129). National Council of Teachers of Mathematics.
Çelik, H. C. (2017). Mathematical modelling research in Turkey: A content analysis study. Educational Research and Reviews, 12(1), 19-27. https://doi.org/10.5897/ERR2016.3077
Cevikbas, M., Kaiser, G., & Schukajlow, S. (2021). A systematic literature review of the current discussion on mathematical modeling competencies: State-of-the-art developments in conceptualizing, measuring, and fostering. Educational Studies in Mathematics. https://doi.org/10.1007/s10649-021-10104-6
Drijvers, P. (2013). Digital technology in mathematics education: Why it works (or doesn't). PNA, 8(1), 1-20. https://doi.org/10.1007/978-3-319-17187-6_8
Frejd, P. (2020). Teachers’ possibilities to generate science capital for modelling. In G. A. Stillman, G. Kaiser, & C. E. Lampen (Eds.), Mathematical modelling education and sense-making (pp. 39–49). Springer. https://doi.org/10.1007/978-3-030-37673-4_4
Frejd, P., & Ärlebäck, J. B. (2011). First results from a study investigating Swedish upper secondary students’ mathematical modelling competencies. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling. International perspectives on the teaching and learning of mathematical modelling (Vol. 1, pp 407-416). Springer. https://doi.org/10.1007/978-94-007-0910-2_40
Galbraith, P., & Holton, D. (2018). Mathematical Modelling: A guidebook for teachers and teams. Australian Council for Educational Research (ACER).
Garfunkel, S. A., Montgomery, M., Consortium for mathematics and its applications (U.S.), & National Council of Teachers of Mathematics. (2016). GAIMME: Guidelines for assessment and instruction in mathematical modeling education. COMAP, Incorporated
Gusić, J. (2011). Matematičko modeliranje u srednjoj školi [Mathematical modelling in high school]. Poučak, 12(45). 48-61. https://hrcak.srce.hr/103846
Hankeln, C. (2020). Validating with the use of dynamic geometry software. In G. A. Stillman, G. Kaiser, & C. E. Lampen (Eds.), Mathematical modelling education and sense-making (pp. 277–286). Springer. https://doi.org/10.1007/978-3-030-37673-4_24
Hernández, M. L., Levy, R., Felton-Koestler, M. D., & Zbiek, R. M. (2016). Mathematical modeling in the high school curriculum. Mathematics Teacher: Learning and Teaching Pk–12, 110(5), 336–342. https://doi.org/10.5951/mathteacher.110.5.0336
Kaiser, G., Blum, W., Ferri, B. R., & Stillman, G. (2011). Trends in teaching and learning of mathematical modelling: ICTMA14 (International perspectives on the teaching and learning of mathematical modelling, vol 1) (2011th ed.). Springer. https://doi.org/10.1007/978-94-007-0910-2_1
Marković, Z. (2011). Matematičko modelovanje u matematičkom obrazovanju [Mathematical modelling in mathematical education]. Istraživanje matematičkog obrazovanja, 3(4), 35–50.
Molina-Toro, J. F., Rendón-Mesa, P. A., & Villa-Ochoa, J. A. (2019). Research trends in digital technologies and modeling in mathematics education. Eurasia Journal of Mathematics, Science and Technology Education, 15(8), em1736. https://doi.org/10.29333/ejmste/108438
Niss, M., Blum, W., & Galbraith, P. (2007). Introduction. In W. Blum, P. Galbraith, H. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (pp. 3-32). Springer. https://doi.org/10.1007/s11858-007-0070-z
Perrenet, J., & Zwaneveld, B. (2012). The many faces of the mathematical modeling cycle. Journal of Mathematical Modelling and Application, 1(6), 3-21.
Riyanto, B., Zulkardi, Z., Putri, R. I. I., & Darmawijoyo, D. (2019). Senior high school mathematics learning through mathematics modelling approach. Journal on Mathematics Education, 10(3), 425–444. https://doi.org/10.22342/jme.10.3.8746.425-444
Rosa, M., Orey, D. C., & de Oliveira Cortes, D. P. (2020). Resignifying function concept: a mixed methods study to understand the contributions of the dialogic approach of ethnomodelling. In G. A. Stillman, G. Kaiser, & C. E. Lampen (Eds.), Mathematical modelling education and sense-making (pp. 107–116). Springer. https://doi.org/10.1007/978-3-030-37673-4_10
Sakinah, A. R., Hiltrimartin, C., Hartono, Y., & Indaryanti. (2020). High school students’ mathematical modelling skills in problem-based learning (PBL). Journal of Physics: Conference Series, 1480(2020), 012041. https://doi.org/10.1088/1742-6596/1480/1/012041
Vargas-Alejo, V., & Cristóbal-Escalante, C. (2014). Teacher’s ways of thinking about students’ mathematical learning when they implement problem solving activities. Journal of Mathematical Modelling and Application, 1(9), 41-48.
Vitoria, L., Ramli, M., Johar, R., & Mawarpury, M. (2021). A review of mathematical modelling in educational research in Indonesia. Journal of Physics: Conference Series, 1882(2021), 012145. https://doi.org/10.1088/1742-6596/1882/1/012145
Vos, P., Hernandez-Martinez, P., & Frejd, P. (2019). Connections of science capital and the teaching and learning of mathematical modelling: An introduction. In G. A. Stillman, G. Kaiser, & C. E. Lampen (Eds.), Mathematical modelling education and sense-making (pp. 33–38). Springer. https://doi.org/10.1007/978-3-030-37673-4_9
Zeytun, A. S., Cetinkaya, B., & Erbas, A. K. (2017). Understanding prospective teachers’ mathematical modeling processes in the context of a mathematical modeling course. Eurasia Journal of Mathematics Science and Technology Education, 13(3), 691–722. https://doi.org/10.12973/eurasia.2017.00639a
Zlokapa, B. (2012). Matematičko modelovanje u obrazovanju - problemi i prednosti [Mathematical modelling in education - problems and advantages]. Istraživanje Matematičkog Obrazovanja, 8(1), 33-42.