Prospective teachers’ thinking through realistic mathematics education based emergent modeling in fractions


  • Ekasatya Aldila Afriansyah Department of Mathematics Education, Institut Pendidikan Indonesia, West Java
  • Turmudi Turmudi Department of Mathematics Education, Universitas Pendidikan Indonesia, West Java



descriptive qualitative, emergent modeling, model of, model for, prospective teachers, realistic mathematics education


The unconsciousness of a teacher in obtaining knowledge due to students can be known if the teacher was notified when he was a student. A student has an essential role in learning, and the teacher is responsible for supporting smooth learning. Students' problem-solving processes need to be found because each student's reasoning and ideas in solving problems are different. This study focuses on students' thinking processes using realistic mathematics education based on emergent modeling. In this study, the researcher is the teacher, and the student is the prospective teacher. The prospective teacher involved were students of the Institut Pendidikan Indonesia mathematics study program. Prospective teachers were selected as research subjects for as many as 74 people (11 males and 63 females) consisting of 3 classes. The research method uses descriptive qualitative. As learning activities progress, students get a kind of model that seems as solutions to solving problems given by the teacher. Various kinds of models emerged from various student ideas and ended with a mutually agreed for a model for. Through this study, a teacher can learn about student models in the learning process.


Abdulhameed, S., & Rashid, T. A. (2022). Child drawing development optimization algorithm based on child’s cognitive development. Arabian Journal for Science and Engineering, 47, 1337-1351.

Afriansyah, E. A., Puspitasari, N., Luritawaty, I. P., Mardiani, D., & Sundayana, R. (2019). The analysis of mathematics with ATLAS. ti. Journal of Physics: Conference Series, 1402(7), 077097.

Afriansyah, E. A. (2021). Realistic mathematics education berbasis emergent modeling untuk meningkatkan kemampuan berpikir kritis dan kreatif matematis serta curiosity mahasiswa calon guru [Realistic mathematics education based on emergent modeling to improve mathematical critical and creative thinking skills and the curiosity of prospective teacher students], [Unpublished doctoral dissertation]. Universitas Pendidikan Indonesia.

Afriansyah, E. A., & Arwadi, F. (2021). Learning trajectory of quadrilateral applying realistic mathematics education: Origami-based tasks. Mathematics Teaching Research Journal, 13(4), 42-78.

Afriansyah, E. A., Herman, T., Turmudi, & Dahlan, J. A. (2021, February). Critical thinking skills in mathematics. Journal of Physics: Conference Series, 1778(1), 012013.

Ardianingsih, A., Lusiyana, D., & Rahmatudin, J. (2019). Penerapan pembelajaran realistic mathematic education berbasis etnomatematika untuk meningkatkan HOTS matematik siswa [Application of realistic mathematics education based on ethnomathematics to increase students' math HOTS]. Mathline: Jurnal Matematika dan Pendidikan Matematika, 4(2), 148-161.

Awidi, I. T., & Paynter, M. (2019). The impact of a flipped classroom approach on student learning experience. Computers & Education, 128, 269-283.

Baier, F., Decker, A. T., Voss, T., Kleickmann, T., Klusmann, U., & Kunter, M. (2019). What makes a good teacher? The relative importance of mathematics teachers’ cognitive ability, personality, knowledge, beliefs, and motivation for instructional quality. British Journal of Educational Psychology, 89(4), 767-786.

Büscher, C., & Schnell, S. (2017). Students’ emergent modelling of statistical measures–a case study. Statistics Education Research Journal, 16(2), 144-162.

Cao, Y., Zhang, S., Chan, M. C. E., & Kang, Y. (2021). Post-pandemic reflections: lessons from Chinese mathematics teachers about online mathematics instruction. Asia Pacific Education Review, 22(2), 157-168.

Carroll, J. A., Wilson, E. E., Klimow, N., & Hill, K. (2018). Acts of teaching: How to teach writing: A text, a reader, a narrative. ABC-CLIO.

Danesi, M. (2018). The mathematical mind. In Ahmes’ Legacy (pp. 127-149). Springer.

diSessa, A. A. (2002). Students’ criteria for representational adequacy. In Gravemeijer, K., Lehrer, R., Oers, B., & Verschaffel, L., Symbolizing, modeling and tool use in mathematics education, (pp. 105-129). Springer., Dordrecht.

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.

Fredriksen, H. (2021). Exploring realistic mathematics education in a flipped classroom context at the tertiary level. International Journal of Science and Mathematics Education, 19(2), 377-396.

Freudenthal, H. (2006). Revisiting mathematics education: China lectures (Vol. 9). Springer Science & Business Media.

Gravemeijer, K. (1999). How emergent models may foster the constitution of formal mathematics. Mathematical thinking and learning, 1(2), 155-177.

Gravemeijer, K. (2002a). Preamble: From models to modeling. In Gravemeijer, K., Lehrer, R., Oers, B., & Verschaffel, L. (Eds.), Symbolizing, modeling and tool use in mathematics education (pp. 7-22). Springer, Dordrecht.

Gravemeijer, K. (2002b, July). Emergent modeling as the basis for an instructional sequence on data analysis. In Proceedings of the 6th International Conference on Teaching Statistics.

Gravemeijer, K., & Bakker, A. (2006, July). Design research and design heuristics in statistics education. In Proceedings of the Seventh International Conference on Teaching Statistics (pp. 1-6).

Gravemeijer, K. (2007). Emergent modeling and iterative processes of design and improvement in mathematics education. Recuperado enero, 30, 2009.

Hefendehl-Hebeker, L., vom Hofe, R., Büchter, A., Humenberger, H., Schulz, A., & Wartha, S. (2019). Subject-matter didactics. In Traditions in German-speaking mathematics education research (pp. 25-59). Springer.

Herman, T. (2018). Improving students’ mathematical representational ability through RME-based progressive mathematization. Journal of Physics: Conference Series, 948(1), 012038).

Huang, J., Liu, Q., Zheng, Y., Wu, L., Ding, Y., & Huang, L. (2021, August). Research on machine understanding math word problems: From the perspective of discourse comprehension models. In 2021 International Symposium on Educational Technology (ISET) (pp. 139-144). IEEE.

Johnson, E. (2013). Implications of realistic mathematics education for analyzing student learning. In Conference on research in undergraduate mathematics education, Denver, CO. 16_submission_106. pdf

Kaiser, G. (2020). Mathematical modelling and applications in education. Encyclopedia of mathematics education, 553-561.

Kieren, T. E. (2020). Rational and fractional numbers as mathematical and personal knowledge: Implications for curriculum and instruction. In Analysis of arithmetic for mathematics teaching (pp. 323-371). Routledge.

Kitchen, W. H. (2019). Wittgensteinian pedagogy for mathematics: Rule-following, and why it matters for mathematics teaching and learning. Exeter University.

Lehrer, R., & Pritchard, C. (2002). Symbolizing space into being. In Gravemeijer, K., Lehrer, R., Oers, B., & Verschaffel, L. (Eds.), Symbolizing, modeling and tool use in mathematics education (pp. 59-86). Springer, Dordrecht.

Mardiah, N., Permana, D., & Arnawa, I. M. (2021). The validity of hypothetical learning trajectory based on realistic mathematic education on function topics for grade X senior high school. Journal of Physics: Conference Series, 1742(1), 012005.

Marino, M. C. (2020). Critical code studies. MIT Press.

Mead, G. H. (1934). Mind, self and society (Vol. 111). University of Chicago Press.

Mead, G. H. (1938). The philosophy of the act, edited by Charles W. Morris et al. University of Chicago.

Meira, L. R. D. L. (2002). Mathematical representations as systems of notations-in-use. In Symbolizing, modeling and tool use in mathematics education (pp. 87-103). Springer, Dordrecht.

Nurfadilah, P., & Afriansyah, E. A. (2022). Analisis gesture matematis siswa dalam menyelesaikan soal open-ended [Analysis of students' mathematical gestures in solving open-ended problems]. Journal of Authentic Research on Mathematics Education (JARME), 4(1), 14-29.

O’Connor, C., & Michaels, S. (2019). Supporting teachers in taking up productive talk moves: The long road to professional learning at scale. International Journal of Educational Research, 97, 166-175.

Octizasari, G., & Haji, S. (2018). Penerapan model pembelajaran RME berbasis ethnomatematika untuk meningkatkan kemampuan pemecahan masalah mahasiswa calon guru pendidikan matematika FKIP universitas bengkulu [Application of the ethnomathematical-based RME learning model to improve problem solving ability of prospective students of mathematics education teachers FKIP university of bengkulu]. Jurnal Pendidikan Matematika (Jupitek), 1(1), 1-7.

Presmeg, N. (2002). Transitions in emergent modelling. In Gravemeijer, K., Lehrer, R., Oers, B., & Verschaffel, L. (Eds.), Symbolizing, Modelling, and Tool Use in Mathematics Education (pp 131-137). Kluwer Academic Publishers.

Riyanto, B., & Putri, R. I. I. (2017, December). Mathematical modeling in realistic mathematics education. Journal of Physics: Conference Series, 943(1), 012049.

Sarvita, L., & Syarifuddin, H. (2020, May). The developed hypothetical learning trajectory for integral topic based on realistic mathematics education. Journal of Physics: Conference Series, 1554(1), 012032.

Silinskas, G., & Kikas, E. (2019). Math homework: Parental help and children’s academic outcomes. Contemporary Educational Psychology, 59, 101784.

Sumirattana, S., Makanong, A., & Thipkong, S. (2017). Using realistic mathematics education and the DAPIC problem-solving process to enhance secondary school students' mathematical literacy. Kasetsart Journal of Social Sciences, 38(3), 307-315.

van Oers, B. (2002). Informal representations and their improvements. In Gravemeijer, K., Lehrer, R., Oers, B., & Verschaffel, L. (Eds.), Symbolizing, Modelling, and Tool Use in Mathematics Education (pp. 25-28). Springer, Dordrecht.

Vinner, S. (2018). The misconception fallacy, the pseudo-conceptual and the pseudo-analytical behaviors in mathematical contexts. In Mathematics, Education, and Other Endangered Species (pp. 23-52). Springer, Cham.

Walshaw, M. (2017). Understanding mathematical development through vygotsky. Research in Mathematics Education, 19(3), 293-309.

Wertsch, J. V. (1985). Vygotsky and the social formation of mind. Harvard University Press.

Wijaya, A. (2012). Pendidikan matematika realistik suatu alternatif pendekatan pembelajaran matematika [Realistic mathematics education is an alternative approach to learning mathematics]. Graha Ilmu.

Witha, T. S., Karjiyati, V., & Tarmizi, P. (2020). Pengaruh model RME berbasis etnomatematika terhadap kemampuan literasi matematika siswa kelas IV SD gugus 17 kota bengkulu [The influence of the ethnomathematical-based RME model on the mathematical literacy ability of fourth grade elementary school cluster 17 bengkulu city]. JURIDIKDAS: Jurnal Riset Pendidikan Dasar, 3(2), 136-143.




How to Cite

Afriansyah, E. A., & Turmudi, T. (2022). Prospective teachers’ thinking through realistic mathematics education based emergent modeling in fractions. Jurnal Elemen, 8(2), 605–618.




Similar Articles

<< < 5 6 7 8 9 10 11 12 13 14 > >> 

You may also start an advanced similarity search for this article.