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Abstract
This study explores how integrating Mobile Math Trails within the Problem-Based Learning (PBL) model can effectively support numeracy learning. This research was conducted using a design research method with an exploratory approach focused on the design experiment stage. The study involved eighth-grade students from SMP N 39 Semarang. Data was collected through observation, questionnaires, portfolios of students’ work, and interviews. The findings show that Mobile Math Trails-supported learning using PBL model can be an alternative numeracy reinforcement learning. The tasks design students explore around the school environment refers to numeracy indicators with specific content, context, and cognitive levels. The features embedded within the Mobile Math Trails application assist students in the problem-solving process. The tasks designed within the application foster a direct link between mathematical concepts and real-world scenarios within the school environment, thereby necessitating students' reasoning skills. Active student involvement is crucial in this learning, as collaboration among peers is essential for generating optimal learning experiences. Moreover, the learning steps outlined in the research necessitate students' physical engagement. Future studies could explore the application of numeracy reinforcement learning facilitated by Mobile Math Trails in diverse environments.
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Copyright (c) 2024 Nazzun Sholikha Nurin, Iwan Junaedi, Adi Nur Cahyono
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References
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- Barbosa, A., & Vale, I. (2023). Mobile Math Trails: An experience in Teacher Training with Mathcitymap. Acta Scientiae, 25(6), 157–182. https://doi.org/10.17648/acta.scientiae.7597
- Barbosa, A., Vale, I., Jablonski, S., & Ludwig, M. (2022). Walking through algebraic thinking with theme-based (mobile) math trails. Education Sciences, 12(5). https://doi.org/10.3390/educsci12050346
- Barlovits, S., Caldeira, A., Fesakis, G., Jablonski, S., Koutsomanoli Filippaki, D., Lázaro, C., Ludwig, M., Mammana, M. F., Moura, A., Oehler, D. X. K., Recio, T., Taranto, E., & Volika, S. (2022). Adaptive, Synchronous, and Mobile Online Education: Developing the ASYMPTOTE Learning Environment. Mathematics, 10(10), 1–36. https://doi.org/10.3390/math10101628
- Begum, S., Flowers, N., Tan, K., Carpenter, D. M. H., & Moser, K. (2021). Promoting literacy and numeracy among middle school students: Exploring the mediating role of self-efficacy and gender differences. International Journal of Educational Research, 106, 101722. https://doi.org/10.1016/j.ijer.2020.101722
- Botty, H. M. R. H., Shahrill, M., Jaidin, J. H., Li, H. C., & Chong, M. S. F. (2016). The implementation of problem-based learning (PBL) in a year 9 mathematics classroom: A study in Brunei Darussalam. International Research in Education, 4(2), 34-47. https://doi.org/10.5296/ire.v4i2.9466
- Buchori, A., & Puspitasari, G. D. (2023). Development of mathematics learning media assisted by the mathcitymap to improve students’ critical thinking skills. Journal of Higher Education Theory and Practice, 23(10), 187–197. https://doi.org/10.33423/jhetp.v23i10.6193
- Cahyono, Adi Nur, & Ludwig, M. (2018). Teaching and learning mathematics around the city supported by the use of digital technology. Eurasia Journal of Mathematics, Science and Technology Education, 15(1), 1-8. https://doi.org/10.29333/ejmste/99514
- Cahyono, Adi Nur, 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. https://doi.org/10.22342/jme.11.2.10729.181-192
- Civil, M., & Hunter, R. (2015). Participation of non-dominant students in argumentation in the mathematics classroom. Intercultural Education, 26(4), 296–312. https://doi.org/10.1080/14675986.2015.1071755
- Chen, C. H., Shih, C. C., & Law, V. (2020). The effects of competition in digital game-based learning (DGBL): a meta-analysis. Educational Technology Research and Development, 68(4), 1855–1873. https://doi.org/10.1007/s11423-020-09794-1
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- Firdaus, H. P. E., As’ari, A. R., Sukoriyanto, & Muksar, M. (2023). Originality versus non-originality problem seeking. Journal of Higher Education Theory and Practice, 23(9), 266–279. https://doi.org/10.33423/jhetp.v23i9.6147
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- Indonesia. Ministry of Education and Culture. (2020). Development design of minimum competency assessment questions [in Bahasa].
- Jablonski, S., Matthias, L., & Zender, J. (2018, September 5-7). Task quality vs. task quantity. A dialog-based review system to ensure a certain quality of tasks the MathCityMap web community [Paper presentation]. Proceedings of the Fifth ERME Topic Conference (ETC 5) on Mathematics Education in the Digital Age (MEDA), Copenhagen, Denmark. https://mathcitymap.eu/id/publikasi/?cp=3#
- Jain, P., & Rogers, M. (2019). Numeracy as critical thinking. Adults Learning Mathematics: An International Journal, 14(1), 23–33. https://alm-online.net/wp-content/uploads/2019/10/almij_141_october2019.pdf
- Kang, H. (2017). Preservice teachers’ learning to plan intellectually challenging tasks. Journal of Teacher Education, 68(1), 55–68. https://doi.org/10.1177/0022487116676313
- Ke, F. (2014). An implementation of design-based learning through creating educational computer games: A case study on mathematics learning during design and computing. Computers & education, 73, 26-39. https://doi.org/10.1016/j.compedu.2013.12.010
- Kelly, O., Buckley, K., Lieberman, L.J., & Arndt, K. (2022). Universal design for learning - A framework for inclusion in outdoor learning. Journal of Outdoor and Environmental Education, 25, 75–89. https://doi.org/10.1007/s42322-022-00096-z
- König, J., Krepf, M., Bremerich-Vos, A., & Buchholtz, C. (2021). Meeting cognitive demands of lesson planning: Introducing the code-plan model to describe and analyze teachers’ planning competence. The Teacher Educator, 56(4), 466–487. https://doi.org/10.1080/08878730.2021.1938324
- Larmann, P., Barlovits, S., & Ludwig, M. (2022, September 13-16). Synchronous distance learning with mcm@home: A case study on digital learning environments [Paper presentation]. Proceedings of the 15th International Conference on Technology in Mathematics Teaching (ICTMT 15), Copenhagen, Denmark. https://doi.org/https://doi.org/10.7146/aul.452
- Laššová, K., & Rumanová, L. (2023). Engaging STEM learning experience of spatial ability through activities with using math trail. Mathematics, 11(11). https://doi.org/10.3390/math11112541
- Ludwig, M., & Jesberg, J. (2015). Using mobile technology to provide outdoor modelling tasks-The MathCityMap-Project. Procedia-Social and Behavioral Sciences, 191, 2776-2781. https://doi.org/10.1016/j.sbspro.2015.04.517
- Maqtary, N., Mohsen, A., & Bechkoum, K. (2019). Group formation techniques in computer-supported collaborative learning: A systematic literature review. Technology, Knowledge and Learning, 24(2), 169–190. https://doi.org/10.1007/s10758-017-9332-1
- Nugraha, A. A., Rizal, N., & Cahyono, A. N. (2023). Mathematical modelling ability in outdoor learning with mobile math trails. International Journal on Emerging Mathematics Education, 7(1), 1. https://doi.org/10.12928/ijeme.v7i1.24771
- Nurin, N. S., Junaedi, I., & Cahyono, A. N. (2023). Designing math trails-based hypothetical learning trajectory to promote students’ numeracy skill [Paper presentation]. International Conference on Science, Education and Technology, Semarang, Indonesia. https://proceeding.unnes.ac.id/ISET/article/view/2475
- Pambudi, D. S., Sunardi, S., & Sugiarti, T. (2022). Learning mathematics using a collaborative rme approach in the indoor and outdoor classrooms to improve students’ mathematical connection ability. Jurnal Pendidikan Matematika, 16(3), 303–324. https://doi.org/10.22342/jpm.16.3.17883.303-324
- Perienen, A. (2019). Frameworks for ict integration in mathematics education - a teacher’s perspective. Eurasia Journal of Mathematics, Science and Technology Education, 16(6), 1–12. https://doi.org/10.29333/EJMSTE/7803
- Purnomo, H., Sa’dijah, C., Hidayanto, E., Sisworo, Permadi, H., & Anwar, L. (2022). Development of instrument numeracy skills test of minimum competency assessment (mca) in Indonesia. International Journal of Instruction, 15(3), 635–648. https://doi.org/10.29333/iji.2022.15335a
- Setiyani, Waluya, S. B., Sukestiyarno, Y. L., Cahyono, A. N., & Santi, D. P. D. (2024). Assessing numeracy skills on flat shapes and scaffolding forms in junior high school. International Journal of Evaluation and Research in Education, 13(1), 422–432. https://doi.org/10.11591/ijere.v13i1.25186
- Sholikhah, B. U., & Cahyono, A. N. (2021). Augmented reality student worksheets for learning mathematics during the COVID-19 pandemic [Paper presentation]. 247th ECD Meeting, Montreal, Canada. https://doi.org/10.1088/1742-6596/1918/4/042063
- Støren, L. A., Lundetræ, K., & Børing, P. (2018). Country differences in numeracy skills: how do they vary by job characteristics and education levels? International Journal of Lifelong Education, 37(5), 578–597. https://doi.org/10.1080/02601370.2018.1554718
- Taranto, E., Jablonski, S., Recio, T., Mercat, C., Cunha, E., Lázaro, C., Ludwig, M., & Mammana, M. F. (2021). Professional Development in Mathematics Education—Evaluation of a MOOC on Outdoor Mathematics. Mathematics, 9(22). https://doi.org/10.3390/math9222975
References
Ayotte-Beaudet, J. P., Berrigan, F., Deschamps, A., L’Heureux, K., Beaudry, M. C., & Turcotte, S. (2023). K-11 teachers’ school-based outdoor education practices in the province of Québec, Canada: from local initiatives to a grassroots movement. Journal of Adventure Education and Outdoor Learning, 24(2), 334–347. https://doi.org/10.1080/14729679.2022.2164787
Bakker, A. (2018). Design research in education: A practical guide for early career researchers. Routledge.
Barbosa, A., & Vale, I. (2023). Mobile Math Trails: An experience in Teacher Training with Mathcitymap. Acta Scientiae, 25(6), 157–182. https://doi.org/10.17648/acta.scientiae.7597
Barbosa, A., Vale, I., Jablonski, S., & Ludwig, M. (2022). Walking through algebraic thinking with theme-based (mobile) math trails. Education Sciences, 12(5). https://doi.org/10.3390/educsci12050346
Barlovits, S., Caldeira, A., Fesakis, G., Jablonski, S., Koutsomanoli Filippaki, D., Lázaro, C., Ludwig, M., Mammana, M. F., Moura, A., Oehler, D. X. K., Recio, T., Taranto, E., & Volika, S. (2022). Adaptive, Synchronous, and Mobile Online Education: Developing the ASYMPTOTE Learning Environment. Mathematics, 10(10), 1–36. https://doi.org/10.3390/math10101628
Begum, S., Flowers, N., Tan, K., Carpenter, D. M. H., & Moser, K. (2021). Promoting literacy and numeracy among middle school students: Exploring the mediating role of self-efficacy and gender differences. International Journal of Educational Research, 106, 101722. https://doi.org/10.1016/j.ijer.2020.101722
Botty, H. M. R. H., Shahrill, M., Jaidin, J. H., Li, H. C., & Chong, M. S. F. (2016). The implementation of problem-based learning (PBL) in a year 9 mathematics classroom: A study in Brunei Darussalam. International Research in Education, 4(2), 34-47. https://doi.org/10.5296/ire.v4i2.9466
Buchori, A., & Puspitasari, G. D. (2023). Development of mathematics learning media assisted by the mathcitymap to improve students’ critical thinking skills. Journal of Higher Education Theory and Practice, 23(10), 187–197. https://doi.org/10.33423/jhetp.v23i10.6193
Cahyono, Adi Nur, & Ludwig, M. (2018). Teaching and learning mathematics around the city supported by the use of digital technology. Eurasia Journal of Mathematics, Science and Technology Education, 15(1), 1-8. https://doi.org/10.29333/ejmste/99514
Cahyono, Adi Nur, 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. https://doi.org/10.22342/jme.11.2.10729.181-192
Civil, M., & Hunter, R. (2015). Participation of non-dominant students in argumentation in the mathematics classroom. Intercultural Education, 26(4), 296–312. https://doi.org/10.1080/14675986.2015.1071755
Chen, C. H., Shih, C. C., & Law, V. (2020). The effects of competition in digital game-based learning (DGBL): a meta-analysis. Educational Technology Research and Development, 68(4), 1855–1873. https://doi.org/10.1007/s11423-020-09794-1
Dalim, S. F., Syed Aris, S. R., Hoon, T. S., Nadzri, F. A., Deni, S. M., Yahya, N., & Si, E. M. (2023). Framework for numeracy and digital skills attributes in higher education. Research in Social Sciences and Technology, 8(3), 16–35. https://doi.org/10.46303/ressat.2023.18
Firdaus, H. P. E., As’ari, A. R., Sukoriyanto, & Muksar, M. (2023). Originality versus non-originality problem seeking. Journal of Higher Education Theory and Practice, 23(9), 266–279. https://doi.org/10.33423/jhetp.v23i9.6147
Geiger, V., Goos, M., & Forgasz, H. (2015). A rich interpretation of numeracy for the 21st century: A survey of the state of the field. ZDM, 47(4), 531–548. https://doi.org/10.1007/s11858-015-0708-1
Hakim, A. R., Kartono, Wardono, & Cahyono, A. N. (2022). Elementary students’ mathematical literacy in solving realistic mathematics through math trail activities [Paper presentation]. International Conference on Science, Education, and Technology, Semarang, Indonesia. https://proceeding.unnes.ac.id/ISET/article/view/1730
Indonesia. Ministry of Education and Culture. (2017). Numeracy literacy support materials [in Bahasa].
Indonesia. Ministry of Education and Culture. (2020). Development design of minimum competency assessment questions [in Bahasa].
Jablonski, S., Matthias, L., & Zender, J. (2018, September 5-7). Task quality vs. task quantity. A dialog-based review system to ensure a certain quality of tasks the MathCityMap web community [Paper presentation]. Proceedings of the Fifth ERME Topic Conference (ETC 5) on Mathematics Education in the Digital Age (MEDA), Copenhagen, Denmark. https://mathcitymap.eu/id/publikasi/?cp=3#
Jain, P., & Rogers, M. (2019). Numeracy as critical thinking. Adults Learning Mathematics: An International Journal, 14(1), 23–33. https://alm-online.net/wp-content/uploads/2019/10/almij_141_october2019.pdf
Kang, H. (2017). Preservice teachers’ learning to plan intellectually challenging tasks. Journal of Teacher Education, 68(1), 55–68. https://doi.org/10.1177/0022487116676313
Ke, F. (2014). An implementation of design-based learning through creating educational computer games: A case study on mathematics learning during design and computing. Computers & education, 73, 26-39. https://doi.org/10.1016/j.compedu.2013.12.010
Kelly, O., Buckley, K., Lieberman, L.J., & Arndt, K. (2022). Universal design for learning - A framework for inclusion in outdoor learning. Journal of Outdoor and Environmental Education, 25, 75–89. https://doi.org/10.1007/s42322-022-00096-z
König, J., Krepf, M., Bremerich-Vos, A., & Buchholtz, C. (2021). Meeting cognitive demands of lesson planning: Introducing the code-plan model to describe and analyze teachers’ planning competence. The Teacher Educator, 56(4), 466–487. https://doi.org/10.1080/08878730.2021.1938324
Larmann, P., Barlovits, S., & Ludwig, M. (2022, September 13-16). Synchronous distance learning with mcm@home: A case study on digital learning environments [Paper presentation]. Proceedings of the 15th International Conference on Technology in Mathematics Teaching (ICTMT 15), Copenhagen, Denmark. https://doi.org/https://doi.org/10.7146/aul.452
Laššová, K., & Rumanová, L. (2023). Engaging STEM learning experience of spatial ability through activities with using math trail. Mathematics, 11(11). https://doi.org/10.3390/math11112541
Ludwig, M., & Jesberg, J. (2015). Using mobile technology to provide outdoor modelling tasks-The MathCityMap-Project. Procedia-Social and Behavioral Sciences, 191, 2776-2781. https://doi.org/10.1016/j.sbspro.2015.04.517
Maqtary, N., Mohsen, A., & Bechkoum, K. (2019). Group formation techniques in computer-supported collaborative learning: A systematic literature review. Technology, Knowledge and Learning, 24(2), 169–190. https://doi.org/10.1007/s10758-017-9332-1
Nugraha, A. A., Rizal, N., & Cahyono, A. N. (2023). Mathematical modelling ability in outdoor learning with mobile math trails. International Journal on Emerging Mathematics Education, 7(1), 1. https://doi.org/10.12928/ijeme.v7i1.24771
Nurin, N. S., Junaedi, I., & Cahyono, A. N. (2023). Designing math trails-based hypothetical learning trajectory to promote students’ numeracy skill [Paper presentation]. International Conference on Science, Education and Technology, Semarang, Indonesia. https://proceeding.unnes.ac.id/ISET/article/view/2475
Pambudi, D. S., Sunardi, S., & Sugiarti, T. (2022). Learning mathematics using a collaborative rme approach in the indoor and outdoor classrooms to improve students’ mathematical connection ability. Jurnal Pendidikan Matematika, 16(3), 303–324. https://doi.org/10.22342/jpm.16.3.17883.303-324
Perienen, A. (2019). Frameworks for ict integration in mathematics education - a teacher’s perspective. Eurasia Journal of Mathematics, Science and Technology Education, 16(6), 1–12. https://doi.org/10.29333/EJMSTE/7803
Purnomo, H., Sa’dijah, C., Hidayanto, E., Sisworo, Permadi, H., & Anwar, L. (2022). Development of instrument numeracy skills test of minimum competency assessment (mca) in Indonesia. International Journal of Instruction, 15(3), 635–648. https://doi.org/10.29333/iji.2022.15335a
Setiyani, Waluya, S. B., Sukestiyarno, Y. L., Cahyono, A. N., & Santi, D. P. D. (2024). Assessing numeracy skills on flat shapes and scaffolding forms in junior high school. International Journal of Evaluation and Research in Education, 13(1), 422–432. https://doi.org/10.11591/ijere.v13i1.25186
Sholikhah, B. U., & Cahyono, A. N. (2021). Augmented reality student worksheets for learning mathematics during the COVID-19 pandemic [Paper presentation]. 247th ECD Meeting, Montreal, Canada. https://doi.org/10.1088/1742-6596/1918/4/042063
Støren, L. A., Lundetræ, K., & Børing, P. (2018). Country differences in numeracy skills: how do they vary by job characteristics and education levels? International Journal of Lifelong Education, 37(5), 578–597. https://doi.org/10.1080/02601370.2018.1554718
Taranto, E., Jablonski, S., Recio, T., Mercat, C., Cunha, E., Lázaro, C., Ludwig, M., & Mammana, M. F. (2021). Professional Development in Mathematics Education—Evaluation of a MOOC on Outdoor Mathematics. Mathematics, 9(22). https://doi.org/10.3390/math9222975