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Abstract
This research aims to describe students' cognitive processes in understanding fractions through a tourist context. This research method is design research. The data collection technique is through tests and in-depth interviews. The results of this research show that student's cognitive process in understanding fractions through a tourism context is that students first understand the problems in the tourism context of Lake Air Gegas; then students create mathematical models based on context; third, students complete mathematical models based on context; the fourth student creates a solution to the context problem; Finally, students make mathematical conclusions. Through the tourism context, students can solve problems appropriately. The conclusion is that there are five stages of students' cognitive process in discovering the principle of multiplication of fractions, namely students understand the problem through a tourism context, create a mathematical model based on context, complete a mathematical model based on context, create a context problem solution, and end by making mathematical conclusions about the principle of Multiplication of Fractions. Therefore, it is recommended that mathematics teachers use the tourism context as a starting point for mathematics learning.
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References
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- 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
- Baiduri, Putri, O. R. U., & Alfani, I. (2021). Mathematics Connection Process of Students With Low Mathematical Ability in Solving Contextual Problems Based on Gender, 513, 549–555. https://doi.org/10.2991/assehr.k.201230.161
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- Hasbi, M., Lukito, A., Sulaiman, R., Muzaini, M., Negeri Surabaya, U., Lidah Wetan, K., & Lidah Wetan-Surabaya, J. (2019). Improving the Mathematical Connection Ability of Middle-School Students through Realistic Mathematics Approach. Journal of Mathematical Pedagogy, 1(1), 37–46. Retrieved from https://journal.unesa.ac.id/index.php/JOMP/article/view/7147
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- Hidayatullah, A., & Csíkos, C. (2022). Mathematics Related Belief System and Word Problem-Solving in the Indonesian Context. Eurasia Journal of Mathematics, Science and Technology Education, 18(4). https://doi.org/10.29333/ejmste/11902
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- Nurutami, A., Riyadi, R., & Subanti, S. (2020). Identification of Mathematical Literacy Students Level 2, 3, 4 of Pisa Task, (36), 423–426. https://doi.org/10.5220/0008523004230426
- Ozrecberoglu, N., Aydın, S., & Aydın, O. (2022). Students’ Skills In Solving Non-Routine Mathematical Problems. Education Quarterly Reviews, 5(2), 542–551. https://doi.org/10.31014/aior.1993.05.02.504
- Pant, V. (2019). Conceptual Understanding and Procedural Knowledge of Fractions : How to Learn and How to Teach, 17–35.
- Plomp, T., & Nieveen, N. (2013). Educational Design Research. Educational Design Research, (July), 1–206. https://doi.org/10.1007/978-1-4614-3185-5_11
- Salam, M., & Salim, S. (2020). Analysis of Mathematical Reasoning Ability (MRA) with the Discovery Learning Model in Gender issues. Journal of Educational Science and Technology (EST), 6(2), 137–150. https://doi.org/10.26858/est.v6i2.13211
- 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
- Tsaniya, N. P., Darta, D., & Fisher, D. (2022). Analysis of the Mathematical Ability of Junior High School Students in terms of the Extrovert-Introvert Personality Type. IndoMath: Indonesia Mathematics Education, 5(1), 63. https://doi.org/10.30738/indomath.v5i1.16
- Umbara, U., & Suryadi, D. (2019). Re-interpretation of mathematical literacy based on the teacher’s perspective. International Journal of Instruction, 12(4), 789–806. https://doi.org/10.29333/iji.2019.12450a
- Widada, W., Efendi, S., Herawaty, D., & Nugroho, K. U. Z. (2020). The genetic decomposition of students about infinite series through the ethnomathematics of Bengkulu , Indonesia. IOP Conf. Series: Journal of Physics: Conf. Series 1470 (2020) 012078, 1–9. https://doi.org/10.1088/1742-6596/1470/1/012078
- Widada, W., Herawaty, D., & Lubis, A. N. M. T. (2018). Realistic mathematics learning based on the ethnomathematics in Bengkulu to improve students’ cognitive level. Journal of Physics: Conference Series, 1088. https://doi.org/10.1088/1742-6596/1088/1/012028
- Widada, W., Herawaty, D., Lusiana, D., Afriani, N. H., Sospolita, N., Jumri, R., & Trinofita, B. (2020). How are the process of abstraction of the division of fraction numbers by elementary school students ? International Seminar on Applied Mathematics and Mathematics Education 2020 (2nd ISAMME 2020). Journal of Physics: Conference Series, 1657(012040), 1–7. https://doi.org/10.1088/1742-6596/1657/1/012040
- Widada, W., Herawaty, D., Pusvita, Y., Anggreni, D., Aripianti, R., & Panduwinata, B. (2020). Multiplication and division of integers through cultural approaches of playing dakon. International Seminar on Applied Mathematics and Mathematics Education 2020 (2nd ISAMME 2020), Journal of Physics: Conference Series, 1657(012030), 1–9. https://doi.org/10.1088/1742-6596/1657/1/01203
References
Amanat, A., & Reid, N. (2012). Understanding mathematics: Some key factors. European Journal of Educational Research, 1(3), 283–299. https://doi.org/10.12973/eu-jer.1.3.283
Ambarita, S. M., Asri, L., Agustina, A., Octavianty, D., & Zulkardi. (2018). Mathematical Modeling Skills on Solving PISA Problems. Journal of Physics: Conference Series, 1097(1). https://doi.org/10.1088/1742-6596/1097/1/012115
Andari, R. M., & Setianingsih, R. (2021). Students ’ Mathematical Literacy in Solving PISA Problem Using Indonesian Cultural Context, 6(1), 52–67.
Andriani, D., Widada, W., Herawaty, D., Ardy, H., Nugroho, K. U. Z., Ma’rifah, N., … 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
Baiduri, Putri, O. R. U., & Alfani, I. (2021). Mathematics Connection Process of Students With Low Mathematical Ability in Solving Contextual Problems Based on Gender, 513, 549–555. https://doi.org/10.2991/assehr.k.201230.161
Fritz, A., Ehlert, A., & Balzer, L. (2013). Development of mathematical concepts as basis for an elaborated mathematical understanding. South African Journal of Childhood Education, 3(1), 38–67.
Hasbi, M., Lukito, A., Sulaiman, R., Muzaini, M., Negeri Surabaya, U., Lidah Wetan, K., & Lidah Wetan-Surabaya, J. (2019). Improving the Mathematical Connection Ability of Middle-School Students through Realistic Mathematics Approach. Journal of Mathematical Pedagogy, 1(1), 37–46. Retrieved from https://journal.unesa.ac.id/index.php/JOMP/article/view/7147
Herawaty, D, Gusri, S. A., Saputra, R., Liana, E., & Aliza, F. (2019). The mathematics communication of students in learning based on ethnomathematics Rejang Lebong. Journal of Physics: Conference Series PAPER, 1318(012074), 1–8. https://doi.org/10.1088/1742-6596/1318/1/012074
Herawaty, D., Widada, W., Herdian, F., & Nugroho, K. U. Z. (2020). The cognitive process of extended trans students in understanding the real number system. IOP Conf. Series: Journal of Physics: Conf. Series 1470 (2020) 012070 Doi:10.1088/1742-6596/1470/1/012070, 1470, 1–6. https://doi.org/10.1088/1742-6596/1470/1/012070
Herawaty, D., Khrisnawati, D., Widada, W., & Mundana, P. (2020). The cognitive process of students in understanding the parallels axiom through ethnomathematics learning. IOP Conf. Series: Journal of Physics: Conf. Series 1470, 1–8. https://doi.org/10.1088/1742-6596/1470/1/012077
Hidayatullah, A., & Csíkos, C. (2022). Mathematics Related Belief System and Word Problem-Solving in the Indonesian Context. Eurasia Journal of Mathematics, Science and Technology Education, 18(4). https://doi.org/10.29333/ejmste/11902
Jailani, Retnawati, H., Apino, E., & Santoso, A. (2020). High school students’ difficulties in making mathematical connections when solving problems. International Journal of Learning, Teaching and Educational Research, 19(8), 255–277. https://doi.org/10.26803/ijlter.19.8.14
Lazić, B., Abramovich, S., Mrđa, M., & Romano, D. A. (2017). On the Teaching and Learning of Fractions through a Conceptual Generalization Approach. International Electronic Journal of Mathematics Education, 12(8), 749–767.
Listiawati, N., Sabon, S. S., Wibowo, S., & ... (2023). Analysis of implementing Realistic Mathematics Education principles to enhance mathematics competence of slow learner students. Journal on …, 14(4), 683–700. Retrieved from http://jme.ejournal.unsri.ac.id/index.php/jme/article/view/396
Nugroho, K. U. Z., Widada, W., & Herawaty, D. (2019). The Ability To Solve Mathematical Problems Through Youtube Based Ethnomathematics Learning. International Journal of Scientific & Technology Research, 8(10), 1232–1237.
Nurutami, A., Riyadi, R., & Subanti, S. (2020). Identification of Mathematical Literacy Students Level 2, 3, 4 of Pisa Task, (36), 423–426. https://doi.org/10.5220/0008523004230426
Ozrecberoglu, N., Aydın, S., & Aydın, O. (2022). Students’ Skills In Solving Non-Routine Mathematical Problems. Education Quarterly Reviews, 5(2), 542–551. https://doi.org/10.31014/aior.1993.05.02.504
Pant, V. (2019). Conceptual Understanding and Procedural Knowledge of Fractions : How to Learn and How to Teach, 17–35.
Plomp, T., & Nieveen, N. (2013). Educational Design Research. Educational Design Research, (July), 1–206. https://doi.org/10.1007/978-1-4614-3185-5_11
Salam, M., & Salim, S. (2020). Analysis of Mathematical Reasoning Ability (MRA) with the Discovery Learning Model in Gender issues. Journal of Educational Science and Technology (EST), 6(2), 137–150. https://doi.org/10.26858/est.v6i2.13211
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
Tsaniya, N. P., Darta, D., & Fisher, D. (2022). Analysis of the Mathematical Ability of Junior High School Students in terms of the Extrovert-Introvert Personality Type. IndoMath: Indonesia Mathematics Education, 5(1), 63. https://doi.org/10.30738/indomath.v5i1.16
Umbara, U., & Suryadi, D. (2019). Re-interpretation of mathematical literacy based on the teacher’s perspective. International Journal of Instruction, 12(4), 789–806. https://doi.org/10.29333/iji.2019.12450a
Widada, W., Efendi, S., Herawaty, D., & Nugroho, K. U. Z. (2020). The genetic decomposition of students about infinite series through the ethnomathematics of Bengkulu , Indonesia. IOP Conf. Series: Journal of Physics: Conf. Series 1470 (2020) 012078, 1–9. https://doi.org/10.1088/1742-6596/1470/1/012078
Widada, W., Herawaty, D., & Lubis, A. N. M. T. (2018). Realistic mathematics learning based on the ethnomathematics in Bengkulu to improve students’ cognitive level. Journal of Physics: Conference Series, 1088. https://doi.org/10.1088/1742-6596/1088/1/012028
Widada, W., Herawaty, D., Lusiana, D., Afriani, N. H., Sospolita, N., Jumri, R., & Trinofita, B. (2020). How are the process of abstraction of the division of fraction numbers by elementary school students ? International Seminar on Applied Mathematics and Mathematics Education 2020 (2nd ISAMME 2020). Journal of Physics: Conference Series, 1657(012040), 1–7. https://doi.org/10.1088/1742-6596/1657/1/012040
Widada, W., Herawaty, D., Pusvita, Y., Anggreni, D., Aripianti, R., & Panduwinata, B. (2020). Multiplication and division of integers through cultural approaches of playing dakon. International Seminar on Applied Mathematics and Mathematics Education 2020 (2nd ISAMME 2020), Journal of Physics: Conference Series, 1657(012030), 1–9. https://doi.org/10.1088/1742-6596/1657/1/01203