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Abstract
The concept of surface area for flat shapes is often perceived as a challenging mathematical topic among elementary school students. In fact, the context of tourism can be integrated into the learning of geometry, for example, the topic of surface area. The objective of this study is to develop a learning trajectory that enhances problem-solving skills with respect to surface area problems in the context of Bukit Sulap, a tourism destination in Lubuklinggau City. The design research methodology, which included a validation study, was implemented in three stages: preparation and design, experimental teaching, and retrospective analysis. The subjects of this study were 27 elementary school students in Lubuklinggau City, Indonesia. The instruments utilized in this study included surface area problem solving task sheets, video recordings of in-depth interviews conducted during the learning process, field notes, and observation sheets. The findings of the study indicate that learning trajectories designed within the context of Bukit Sulap facilitate students' comprehension of problems, formulation of problem-solving strategies, implementation of these strategies, and interpretation of the results of problem-solving processes. The activities included in the learning trajectory are as follows: defining the contextual problem; self-review; designing a resolution plan; implementing the resolution plan; and establishing a mathematical model regarding surface area within the context used. Through the use of tourism as a context, students are expected to be able to solve surface area problems and learn the principles of surface area of flat shapes. This learning approach is an effective technique for improving problem-solving skills regarding surface area.
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References
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- Agusdianita, N., Widada, W., Afriani, N. H., Herawati, H., Herawaty, D., & Nugroho, K. U. Z. (2021). The exploration of the elementary geometry concepts based on tabot culture in Bengkulu. Journal of Physics: Conference Series, 1731, 1–11. https://doi.org/10.1088/1742-6596/1731/1/012054
- Andriani, D., Widada, W., Herawaty, D., Ardy, H., Nugroho, K. U. Z., Ma’rifah, N., Anggreni, D., & Anggoro, A. F. D. (2020). Understanding the number concepts through learning connected mathematics (CM): a local cultural approach. Universal Journal of Educational Research, 8(3), 1055–1061. https://doi.org/10.13189/ujer.2020.080340
- Anggoro, A. F. D., Haji, S., & Sumardi, H. (2022). Structural equation fit test of mathematical connection ability, mathematical reasoning, and mathematics problem-solving ability of junior high school students. International Journal of Trends in Mathematics Education Research, 5(1), 82–93. https://doi.org/10.33122/ijtmer.v5i1.117
- Anggoro, A. F. D., Hendriana, H., & Yuliani, A. (2023). Structural model between mathematical reasoning and mathematics problem-solving abilities of junior high school students. Journal of Honai Math, 6(1), 71–75. https://doi.org/10.30862/jhm.v6i1.405
- Anggoro, A. F. D., Widada, W., Umam, K., & Nugroho, Z. (2023). Mathematics study habits through an ethnomathematics approach and entrepreneurial behavior of mathematics education students. Wiyata Dharma: Jurnal Penelitian dan Evaluasi Pendidikan, 11(2), 144–152. https://doi.org/10.30738/wd.v11i2.16617
- Biswas, M., & Ferdausy, S. (2017). Role of emotional intelligence in solving problems in the private commercial banks of Bangladesh. The Comilla University Journal of Business Studies, 4(1), 51–66. https://www.researchgate.net/publication/331177962
- Bradshaw, Z., & Hazell, A. (2017). Developing problem-solving skills in mathematics: a lesson study. International Journal for Lesson and Learning Studies, 6(1), 32–44. https://doi.org/10.1108/IJLLS-09-2016-0032
- Druken, B. (2021). Four tasks to catalyze change: perimeter, area, surface area, and volume. CMC ComMuniCator, 45(3), 26–32. https://www.fullerton.edu/math/faculty/bdruken/articles/Druken2021CMCCatalyzingChangeGeometry.pdf
- Fitriyani, H., Widodo, S. A., & Hendroanto, A. (2018). Students’ geometric thinking based on van Hiele’s Theory. Infinity Journal of Mathematics Education, 7(1), 55–60. https://doi.org/10.22460/infinity.v7i1.p55-60
- Friansah, D., Zulkardi, Z., Susanti, E., & Nusantara, D. S. (2024). Hypothetical learning trajectory (HLT) design uses the context of climate change to train statistical literacy skills [in Bahasa]. SJME (Supremum Journal of Mathematics Education), 08(01), 59–71. https://doi.org/10.35706/sjme.v8i1.10440
- Frischkorn, G., & Schubert, A. L. (2018). Cognitive models in intelligence research: advantages and recommendations for their application. Journal of Intelligence, 6(3), 34. https://doi.org/10.3390/jintelligence6030034
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- Herawaty, D., Widada, W., Falaq, A., Anggoro, D., Dewarif, S., & Anggoro, T. (2021). Overcoming difficulties in understanding the linear equation system through the ethnomathematics approach in the COVID-19 pandemic. Advances in Social Science, Education and Humanities Research, 532, 129–137. https://doi.org/10.2991/assehr.k.210227.022
- Lubis, A. N. M. T., Widada, W., Herawaty, D., Nugroho, K. U. Z., & Anggoro, A. F. D. (2021). The ability to solve mathematical problems through realistic mathematics learning based on ethnomathematics. Journal of Physics: Conference Series, 1731(1), 012050. https://doi.org/10.1088/1742-6596/1731/1/012050
- Muslimahayati., Dasari, D., & Agustiani, R. (2020). Mathematical critical thinking ability of students with realistic mathematics learning innovations with ethnomathematics (PMRE). Journal of Physics: Conference Series, 1480(1), 012004. https://doi.org/10.1088/1742-6596/1480/1/012004
- NCTM. (2010). Principles and Standards for School Mathematics. Reston, VA: NCTM.
- Nugroho, K. U. Z., Widada, W., Herawaty, D., Tuzzahra, R., Panduwinata, B., & Sospolita, N. (2021). Abstraction ability of students about fractions through local cultural approaches. Advances in Social Science, Education, and Humanities Research, 532(1), 480-485. https://doi.org /10.2991/assehr.k.210227.082
- Nugroho, K. U. Z., Izwanto, E., Widada, W., Falaq, A., Anggoro, D., Herawaty, D., Jumri, R., Dewarif, S., & Aggoro, T. (2023). The relationship among self-efficacy, mathematical concepts understanding , creative thinking skills , mathematical problem-solving skills , and mathematics learning outcomes. EDUMATIKA: Jurnal Riset Pendidikan Matematika, 6(2), 118-132. https://doi.org/10.32939/ejrpm.v6i2.3169
- Nursyahidah, F., Albab, I. U., & Rubowo, M. R. (2023). Learning design of sphere using realistic mathematics education assisted by interactive video. Jurnal Pendidikan Matematika, 17(3), 297–312. https://doi.org/10.22342/jpm.17.3.20040.297-312
- Özcan, Z. Ç. (2016). The relationship between mathematical problem-solving skills and self-regulated learning through homework behaviours, motivation, and metacognition. International Journal of Mathematical Education in Science and Technology, 47(3), 408–420. https://doi.org/10.1080/0020739X.2015.1080313
- Plomp, T., & Nieveen, N. (2013). Educational Design Research: An Introduction. Enschede, The Netherlands: Netherlands Institute For Curriculum Development. https://ris.utwente.nl/ws/portalfiles/portal/14472302/Introduction_20to_20education_20design_20research.pdf
- Quiroz, S. M. R., Orrego, S. M. L., & López, C. M. J. (2015). Measurement of area and volume in an authentic context: an alternative learning experience through mathematical modelling. International Perspectives on the Teaching and Learning of Mathematical Modelling, (January), 229–240. https://doi.org/10.1007/978-3-319-18272-8_18
- Sembiring, R. K., Hadi, S., & Dolk, M. (2008). Reforming mathematics learning in Indonesian classrooms through RME. ZDM - International Journal on Mathematics Education, 40(6), 927–939. https://doi.org/10.1007/s11858-008-0125-9
- Sukasno, S., Zulkardi, Z., Putri, R. I. I., & Somakim, S. (2024). Students’ cognitive processes in understanding fractions through the tourist context. Jurnal Pendidikan Matematika 18(1), 27–38. http://doi.org//10.22342/jpm.v18i1.pp27-38
- Sukestiyarno, Y. L., Nugroho, K. U. Z., Sugiman, S., & Waluya, B. (2023). Learning trajectory of non-euclidean geometry through ethnomathematics learning approaches to improve spatial ability. Eurasia Journal of Mathematics, Science and Technology Education, 19(6), 1–17. https://doi.org/10.29333/ejmste/13269
- Syafriafdi, N., Fauzan, A., Arnawa, I. M., Anwar, S., & Widada, W. (2019). The tools of mathematics learning based on realistic mathematics education approach in elementary school to improve math abilities. Universal Journal of Educational Research, 7(7), 1532–1536. https://doi.org/10.13189/ujer.2019.070707
- Wedelin, D., Adawi, T., Jahan, T., & Andersson, S. (2015). Investigating and developing engineering students’ mathematical modelling and problem-solving skills. European Journal of Engineering Education, 40(5), 557–572. https://doi.org/10.1080/03043797.2014.987648
- Widada, W., Herawaty, D., Ma’rifah, N., & Yunita, D. (2019). Characteristics of students thinking in understanding geometry in learning ethnomathematics. International Journal of Scientific & Technology Research, 8(11), 3496–3503. http://www.ijstr.org/final-print/nov2019/Characteristics-Of-Students-Thinking-In-Understanding-Geometry-In-Learning-Ethnomathematics.pdf
- Widada, W., Nugroho, K. U. Z., Sari, W. P., & Pambudi, G. A. (2019). The ability of mathematical representation through realistic mathematics learning based on ethnomathematics. Journal of Physics: Conference Series, 1318(3), 012056. https://doi.org/10.1088/1742-6596/1179/1/012056
- Widada, W, Herawaty, D., Hudiria, I., Prakoso, Y. A., Anggraeni, Y. R., & Zaid, K. U. (2020). The understanding of the triangle in Lobachevsky Geometry through local culture. Journal of Physics: Conference Series, 1657(1), 012038. https://doi.org/10.1088/1742-6596/1657/1/012038
- Widada, W, Herawaty, D., Widiarti, Y., Aisyah, S., & Tuzzahra, R. (2020). The cognitive process of students in understanding the triangles in Geometry of Riemann through local content. Journal of Physics: Conference Series, 1657(1), 012033. https://doi.org/10.1088/1742-6596/1657/1/012033
- Widada, W., Herawaty, D., Andriyani, D. S., Marantika, R., Yanti, I. D., & Falaq D. A. A. (2020). The thinking process of students in understanding the concept of graphs during ethnomathematics learning. Journal of Physics: Conference Series, 1470(1). 012072. https://doi.org/10.1088/1742-6596/1470/1/012072
- Woodward, J., Beckmann, S., Driscoll, M., Herzig, P., Jitendra, A., Koedinger, K. R., & Ogbuehi, P. (2018). Improving Mathematical Problem-solving in Grades 4 Through 8. Institue of Education Sciences, 1–92. http://ies.ed.gov/ncee/wwc/publica-
- Zulkardi, Z., & Kohar, A. W. (2019). Designing PISA-like mathematics tasks in indonesia: experiences and challenges. Journal of Physics: Conference Series, 947(1), 012015. https://doi.org/10.1088/1742-6596/947/1/012015
- Zulkardi, Z., Putri, R. I. I., & Wijaya, A. (2020). Two decades of realistic mathematics education in indonesia. In International Reflections on the Netherlands Didactics of Mathematics, Visions on and Experiences with Realistic Mathematics Education (pp. 325–340) https://link.springer.com/chapter/10.1007/978-3-030-20223-1_18
References
Abadi, M. A. S., & Amir, M. F. (2022). Analysis of the elementary school students difficulties of in solving perimeter and area problems. JIPM (Jurnal Ilmiah Pendidikan Matematika), 10(2), 396. https://doi.org/10.25273/jipm.v10i2.11053
Agusdianita, N., Widada, W., Afriani, N. H., Herawati, H., Herawaty, D., & Nugroho, K. U. Z. (2021). The exploration of the elementary geometry concepts based on tabot culture in Bengkulu. Journal of Physics: Conference Series, 1731, 1–11. https://doi.org/10.1088/1742-6596/1731/1/012054
Andriani, D., Widada, W., Herawaty, D., Ardy, H., Nugroho, K. U. Z., Ma’rifah, N., Anggreni, D., & Anggoro, A. F. D. (2020). Understanding the number concepts through learning connected mathematics (CM): a local cultural approach. Universal Journal of Educational Research, 8(3), 1055–1061. https://doi.org/10.13189/ujer.2020.080340
Anggoro, A. F. D., Haji, S., & Sumardi, H. (2022). Structural equation fit test of mathematical connection ability, mathematical reasoning, and mathematics problem-solving ability of junior high school students. International Journal of Trends in Mathematics Education Research, 5(1), 82–93. https://doi.org/10.33122/ijtmer.v5i1.117
Anggoro, A. F. D., Hendriana, H., & Yuliani, A. (2023). Structural model between mathematical reasoning and mathematics problem-solving abilities of junior high school students. Journal of Honai Math, 6(1), 71–75. https://doi.org/10.30862/jhm.v6i1.405
Anggoro, A. F. D., Widada, W., Umam, K., & Nugroho, Z. (2023). Mathematics study habits through an ethnomathematics approach and entrepreneurial behavior of mathematics education students. Wiyata Dharma: Jurnal Penelitian dan Evaluasi Pendidikan, 11(2), 144–152. https://doi.org/10.30738/wd.v11i2.16617
Biswas, M., & Ferdausy, S. (2017). Role of emotional intelligence in solving problems in the private commercial banks of Bangladesh. The Comilla University Journal of Business Studies, 4(1), 51–66. https://www.researchgate.net/publication/331177962
Bradshaw, Z., & Hazell, A. (2017). Developing problem-solving skills in mathematics: a lesson study. International Journal for Lesson and Learning Studies, 6(1), 32–44. https://doi.org/10.1108/IJLLS-09-2016-0032
Druken, B. (2021). Four tasks to catalyze change: perimeter, area, surface area, and volume. CMC ComMuniCator, 45(3), 26–32. https://www.fullerton.edu/math/faculty/bdruken/articles/Druken2021CMCCatalyzingChangeGeometry.pdf
Fitriyani, H., Widodo, S. A., & Hendroanto, A. (2018). Students’ geometric thinking based on van Hiele’s Theory. Infinity Journal of Mathematics Education, 7(1), 55–60. https://doi.org/10.22460/infinity.v7i1.p55-60
Friansah, D., Zulkardi, Z., Susanti, E., & Nusantara, D. S. (2024). Hypothetical learning trajectory (HLT) design uses the context of climate change to train statistical literacy skills [in Bahasa]. SJME (Supremum Journal of Mathematics Education), 08(01), 59–71. https://doi.org/10.35706/sjme.v8i1.10440
Frischkorn, G., & Schubert, A. L. (2018). Cognitive models in intelligence research: advantages and recommendations for their application. Journal of Intelligence, 6(3), 34. https://doi.org/10.3390/jintelligence6030034
Herawaty, D., Widada, W., Sairan, I., Herdian, F., Nugroho, K. U. Z., & Falaq Dwi Anggoro, A. (2020). The cognitive process of extended trans students in understanding the real number system. Journal of Physics: Conference Series, 1470(1), 012070. https://doi.org/10.1088/1742-6596/1470/1/012070
Herawaty, D., Widada, W., Falaq, A., Anggoro, D., Dewarif, S., & Anggoro, T. (2021). Overcoming difficulties in understanding the linear equation system through the ethnomathematics approach in the COVID-19 pandemic. Advances in Social Science, Education and Humanities Research, 532, 129–137. https://doi.org/10.2991/assehr.k.210227.022
Lubis, A. N. M. T., Widada, W., Herawaty, D., Nugroho, K. U. Z., & Anggoro, A. F. D. (2021). The ability to solve mathematical problems through realistic mathematics learning based on ethnomathematics. Journal of Physics: Conference Series, 1731(1), 012050. https://doi.org/10.1088/1742-6596/1731/1/012050
Muslimahayati., Dasari, D., & Agustiani, R. (2020). Mathematical critical thinking ability of students with realistic mathematics learning innovations with ethnomathematics (PMRE). Journal of Physics: Conference Series, 1480(1), 012004. https://doi.org/10.1088/1742-6596/1480/1/012004
NCTM. (2010). Principles and Standards for School Mathematics. Reston, VA: NCTM.
Nugroho, K. U. Z., Widada, W., Herawaty, D., Tuzzahra, R., Panduwinata, B., & Sospolita, N. (2021). Abstraction ability of students about fractions through local cultural approaches. Advances in Social Science, Education, and Humanities Research, 532(1), 480-485. https://doi.org /10.2991/assehr.k.210227.082
Nugroho, K. U. Z., Izwanto, E., Widada, W., Falaq, A., Anggoro, D., Herawaty, D., Jumri, R., Dewarif, S., & Aggoro, T. (2023). The relationship among self-efficacy, mathematical concepts understanding , creative thinking skills , mathematical problem-solving skills , and mathematics learning outcomes. EDUMATIKA: Jurnal Riset Pendidikan Matematika, 6(2), 118-132. https://doi.org/10.32939/ejrpm.v6i2.3169
Nursyahidah, F., Albab, I. U., & Rubowo, M. R. (2023). Learning design of sphere using realistic mathematics education assisted by interactive video. Jurnal Pendidikan Matematika, 17(3), 297–312. https://doi.org/10.22342/jpm.17.3.20040.297-312
Özcan, Z. Ç. (2016). The relationship between mathematical problem-solving skills and self-regulated learning through homework behaviours, motivation, and metacognition. International Journal of Mathematical Education in Science and Technology, 47(3), 408–420. https://doi.org/10.1080/0020739X.2015.1080313
Plomp, T., & Nieveen, N. (2013). Educational Design Research: An Introduction. Enschede, The Netherlands: Netherlands Institute For Curriculum Development. https://ris.utwente.nl/ws/portalfiles/portal/14472302/Introduction_20to_20education_20design_20research.pdf
Quiroz, S. M. R., Orrego, S. M. L., & López, C. M. J. (2015). Measurement of area and volume in an authentic context: an alternative learning experience through mathematical modelling. International Perspectives on the Teaching and Learning of Mathematical Modelling, (January), 229–240. https://doi.org/10.1007/978-3-319-18272-8_18
Sembiring, R. K., Hadi, S., & Dolk, M. (2008). Reforming mathematics learning in Indonesian classrooms through RME. ZDM - International Journal on Mathematics Education, 40(6), 927–939. https://doi.org/10.1007/s11858-008-0125-9
Sukasno, S., Zulkardi, Z., Putri, R. I. I., & Somakim, S. (2024). Students’ cognitive processes in understanding fractions through the tourist context. Jurnal Pendidikan Matematika 18(1), 27–38. http://doi.org//10.22342/jpm.v18i1.pp27-38
Sukestiyarno, Y. L., Nugroho, K. U. Z., Sugiman, S., & Waluya, B. (2023). Learning trajectory of non-euclidean geometry through ethnomathematics learning approaches to improve spatial ability. Eurasia Journal of Mathematics, Science and Technology Education, 19(6), 1–17. https://doi.org/10.29333/ejmste/13269
Syafriafdi, N., Fauzan, A., Arnawa, I. M., Anwar, S., & Widada, W. (2019). The tools of mathematics learning based on realistic mathematics education approach in elementary school to improve math abilities. Universal Journal of Educational Research, 7(7), 1532–1536. https://doi.org/10.13189/ujer.2019.070707
Wedelin, D., Adawi, T., Jahan, T., & Andersson, S. (2015). Investigating and developing engineering students’ mathematical modelling and problem-solving skills. European Journal of Engineering Education, 40(5), 557–572. https://doi.org/10.1080/03043797.2014.987648
Widada, W., Herawaty, D., Ma’rifah, N., & Yunita, D. (2019). Characteristics of students thinking in understanding geometry in learning ethnomathematics. International Journal of Scientific & Technology Research, 8(11), 3496–3503. http://www.ijstr.org/final-print/nov2019/Characteristics-Of-Students-Thinking-In-Understanding-Geometry-In-Learning-Ethnomathematics.pdf
Widada, W., Nugroho, K. U. Z., Sari, W. P., & Pambudi, G. A. (2019). The ability of mathematical representation through realistic mathematics learning based on ethnomathematics. Journal of Physics: Conference Series, 1318(3), 012056. https://doi.org/10.1088/1742-6596/1179/1/012056
Widada, W, Herawaty, D., Hudiria, I., Prakoso, Y. A., Anggraeni, Y. R., & Zaid, K. U. (2020). The understanding of the triangle in Lobachevsky Geometry through local culture. Journal of Physics: Conference Series, 1657(1), 012038. https://doi.org/10.1088/1742-6596/1657/1/012038
Widada, W, Herawaty, D., Widiarti, Y., Aisyah, S., & Tuzzahra, R. (2020). The cognitive process of students in understanding the triangles in Geometry of Riemann through local content. Journal of Physics: Conference Series, 1657(1), 012033. https://doi.org/10.1088/1742-6596/1657/1/012033
Widada, W., Herawaty, D., Andriyani, D. S., Marantika, R., Yanti, I. D., & Falaq D. A. A. (2020). The thinking process of students in understanding the concept of graphs during ethnomathematics learning. Journal of Physics: Conference Series, 1470(1). 012072. https://doi.org/10.1088/1742-6596/1470/1/012072
Woodward, J., Beckmann, S., Driscoll, M., Herzig, P., Jitendra, A., Koedinger, K. R., & Ogbuehi, P. (2018). Improving Mathematical Problem-solving in Grades 4 Through 8. Institue of Education Sciences, 1–92. http://ies.ed.gov/ncee/wwc/publica-
Zulkardi, Z., & Kohar, A. W. (2019). Designing PISA-like mathematics tasks in indonesia: experiences and challenges. Journal of Physics: Conference Series, 947(1), 012015. https://doi.org/10.1088/1742-6596/947/1/012015
Zulkardi, Z., Putri, R. I. I., & Wijaya, A. (2020). Two decades of realistic mathematics education in indonesia. In International Reflections on the Netherlands Didactics of Mathematics, Visions on and Experiences with Realistic Mathematics Education (pp. 325–340) https://link.springer.com/chapter/10.1007/978-3-030-20223-1_18