Mathematical Modelling Ability in Outdoor Learning with Mobile Math Trails

Adam Arya Nugraha, Nur Rizal, Adi Nur Cahyono


The aim of this study is to describe how outdoor learning with mobile math trails can support students' mathematical modelling ability. The method used is design research with three phases, namely preparation and design, teaching experiment, and retrospective analysis. This study was conducted at junior high school involving 32 students. The Hypothetical Learning Trajectory (HLT) was designed and learning activities that include several math trails tasks were created, then students run the activity. Data were collected by observation, interviews, tests, and worksheets. The findings indicate that the learning activity that has been implemented can support students’ mathematical modelling ability. The learning activity can provide opportunities for students to engage in meaningful mathematical modelling activities in accordance with mathematical modelling indicators. The study identified a link between HLT as learning design and mathematical modelling activities in learning process. In addition, it was found that students' mathematical modelling ability had improved.


mathematical modelling; outdoor learning; math trail; mobile math trail; design research

Full Text:



Ahsan, M. G. K., Miftahudin, & Cahyono, A. N. (2020). Designing augmented reality-based mathematics mobile apps for outdoor mathematics learning. Journal of Physics: Conference Series.

Bakker, A. (2018). Design Research in Education: A Practical Guide for Early Career Researchers. In Design Research in Education (1st ed.). Routledge.

Barbosa, A., & Vale, I. (2016). Math Trails: Meaningful Mathematics Outside the Classroom With Pre-Service Teachers. Journal of the European Teacher Education Network, 11(135), 63–72.

Barbosa, A., & Vale, I. (2020). Math Trails through Digital Technology: An Experience with Pre-Service Teachers. Research on Outdoor STEM Education in the Digital Age. Proceedings of the ROSETA Online Conference, 47–54.

Barlovits, S., & Ludwig, M. (2020). Mobile-Supported Outdoor Learning in Math Class: Draft of an Efficacy Study about the MathCityMap App. Research on Outdoor STEM Education in the Digital Age. Proceedings of the ROSETA Online Conference, 55–62.

Cahyono, A. N., & Ludwig, M. (2017). Examining motivation in mobile app-supported math trail environments. 10th Congress of European Research in Mathematics Education (CERME 10).

Cahyono, A. N., & Ludwig, M. (2018). Exploring mathematics outside the classroom with the help of GPS-enabled mobile phone application. Journal of Physics: Conference Series.

Cahyono, A. N., & Ludwig, M. (2019). Teaching and Learning Mathematics around the City Supported by the Use of Digital Technology. EURASIA Journal of Mathematics, Science and Technology Education, 15(1).

Cahyono, A. N., & Miftahudin. (2018). Mobile technology in a mathematics trail program: how does it works? Unnes Journal of Mathematics Education, 7(1), 24–30.

Cahyono, A. N., Sukestiyarno, Y. L., Asikin, M., Miftahudin, Ahsan, M. G. K., & Ludwig, M. (2020). Learning Mathematical Modelling with Augmented Reality Mobile Math Trails Program: How Can It Work? Journal on Mathematics Education, 11(2), 181–192.

Dawn, N. K. E. (2018). Towards a professional development framework for mathematical modelling: the case of singapore teachers. ZDM - Mathematics Education, 50(1–2), 287–300.

Drijvers, P., Kodde-Buitenhuis, H., & Doorman, M. (2019). Assessing mathematical thinking as part of curriculum reform in the Netherlands. Educational Studies in Mathematics, 102(3), 435–456.

Druken, B., & Frazin, S. (2018). Modeling with Math Trails. Ohio Journal of School Mathematics, 79(1), 43–53.

Gurjanow, I., & Ludwig, M. (2017). Gamifying Math Trails with the MathCityMap app: Impact of Points and Leaderboard on Intrinsic Motivation. Proceedings of the 13th International Conference on Technology in Mathematics Teaching (ICTMT 13), 105–122.

Ismaya, B. F., Cahyono, A. N., & Mariani, S. (2018). Kemampuan Penalaran Matematika dengan Math Trail Project berbantuan MathCityMap. Seminar Nasional Pendidikan Matematika Ahmad Dahlan, 17–26.

Jablonski, S., & Ludwig, M. (2020). Development of an Intensive Study Programme on Outdoor Mathematics Teaching with Digital Tools. Research on Outdoor STEM Education in the Digital Age. Proceedings of the ROSETA Online Conference.

Jablonski, S., Ludwig, M., & Zender, J. (2018). Task quality vs. task quantity. A dialog-based review system to ensure a certain quality of tasks the MathCityMap web community. Proceedings of the 5th ERME, 115–122.

Kaiser, G. (2007). Modelling and Modelling Competencies in School. In Mathematical Modelling: Education, Engineering and Economics (pp. 110–119). Woodhead Publishing Limited.

Khusna, H., & Ulfah, S. (2021). Kemampuan Pemodelan Matematis dalam Menyelesaikan Soal Matematika Kontekstual. Mosharafa: Jurnal Pendidikan Matematika, 10(1), 153–164.

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).

OECD. (n.d.). Education GPS - Indonesia - Student performance (PISA 2018). Retrieved July 9, 2022, from

OECD. (2017). PISA 2015 Assessment and Analytical Framework: Science, Reading, Mathematic, Financial Literacy and Collaborative Problem Solving, revised edition. In OECD Publishing.

OECD. (2019). PISA 2018 Assessment and Analytical Framework. In OECD Publishing.

Orey, D. C., & Rosa, M. (2018). Developing a mathematical modelling course in a virtual learning environment. ZDM - Mathematics Education, 50(1–2), 173–185.

Otte, C. R., Bølling, M., Elsborg, P., Nielsen, G., & Bentsen, P. (2019). Teaching maths outside the classroom: does it make a difference? Educational Research, 61(1), 38–52.

Pambudi, D. S. (2022). The Effect of Outdoor Learning Method on Elementary Students Motivation and Achievement in Geometry. International Journal of Instruction, 15(1), 747–764.

Pambudi, W. A. S., Zaenuri, & Kharisudin, I. (2021). Kemampuan Penalaran Dan Representasi Matematis Siswa Dengan Model Pembelajaran MiC Berbasis Etnomatematika. Pedagogi: Jurnal Penelitian Pendidikan, 8(2), 87–100.

Prahmana, R. C. I. (2017). Design Research (Teori dan Implementasinya: Suatu Pengantar). Rajawali Pers.

Santi, E. E. (2017). Pembelajaran Matematika Melalui Pemodelan. Seminar Nasional Pendidikan Berkemajuan Dan Menggembirakan, 2, 493–498.

Suparlan. (2019). Teori Konstruktivisme Dalam Pembelajaran. Islamika: Jurnal Keislaman Dan Ilmu Pendidikan, 1(2).

Tong, D. H., Loc, N. P., Uyen, B. P., & Giang, L. T. (2019). Developing the Competency of Mathematical Modelling: A Case Study of Teaching the Cosine and Sine Theorems. International Journal of Learning, Teaching and Educational Research, 18(11), 18–37.

Wardono, & Mariani, S. (2018). The analysis of mathematics literacy on PMRI learning with media schoology of junior high school students. Journal of Physics: Conference Series.



Copyright (c) 2023 Adam Arya Nugraha, Nur Rizal, Adi Nur Cahyono

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

International Journal on Emerging Mathematics Education
Kampus 2 Universitas Ahmad Dahlan
Jalan Pramuka No. 42, Pandeyan, Umbulharjo, Yogyakarta - 55161
Telp. (0274) 563515, ext. 4902; Fax. (0274) 564604

p-ISSN: 2549-4996 | e-ISSN: 2548-5806

This work is licensed under a Creative Commons Attribution 4.0 International License

View IJEME's Stats