Contextualizing Mathematics in Tugu Yogyakarta: A Case Study on Students' Numerical and Visual Estimation Skills
Keywords:
Abstract
This research explores the impact of ethno-RME on students' thinking processes in solving decimal number operations in Tugu Yogyakarta, Indonesia. The study involved 32 grade 4 students and used three data collection techniques: task provision, cognitive interviews, and documentation. The qualitative data was analyzed using cross-sectional data and focus group discussions (FGD). The study results show that students' thinking process for completing ethno-RME-based mathematics tasks can be divided into two strategies. The first strategy is numerical estimation, where students who use this strategy focus on the numerical information available in each problem. The second strategy is visual estimation, where students who use this strategy focus on constructing a flat shape as closely as possible to the actual shape of the Tugu Yogyakarta. There is a rich context of sociocultural values that can be used to build students' character and ethics when utilizing science, especially mathematics.
Downloads
References
Adler, K., Salanterä, S., & Zumstein-Shaha, M. (2019). Focus group interviews in child, youth, and parent research: an integrative literature review. International Journal of Qualitative Methods, 18. https://doi.org/10.1177/1609406919887274
Google Scholar CrossrefAgustyaningrum, Abadi, A. M., Sari, R. N., & Mahmudi, A. (2018). An analysis of students’ error in solving abstract algebra tasks. IOP Conf. Series: Journal of Physics: Conf. Series, 4(2), 13–25. https://doi.org/10.1088/1742-6596/1097/1/012118
Google Scholar CrossrefAl-saleem, R. M., Al-Hilali, B. M., & Abboud, I. K. (2020). Mathematical representation of color spaces and its role in communication systems. Journal of Applied Mathematics, 2020 (7), 1–7. https://doi.org/10.1155/2020/4640175
Google Scholar CrossrefAndrews, P., Sunde, P. B., Nosrati, M., Petersson, J., Rosenqvist, E., Sayers, J., & Xenofontos, C. (2021). Computational estimation and mathematics education: a narrative literature review. Journal of Mathematics Education, 14(1), 6–27. https://doi.org/10.26711/007577152790061
Google Scholar CrossrefBarata, M., & Pinto, P. R. (2019). Representations of thompson groups from cuntz algebras. Journal of Mathematical Analysis and Applications, 478(1), 212–228. https://doi.org/10.1016/j.jmaa.2019.05.028
Google Scholar CrossrefBaškarada, S. (2014). Qualitative case study guidelines. In The Qualitative Report (Vol. 19). http://ssrn.com/abstract=2559424http://www.nova.edu/ssss/QR/QR19/baskarada24.pdf. https://doi.org/10.46743/2160-3715/2014.1008
Google Scholar CrossrefBennett, A., Burton, L., & Nelson, T. (2011). Mathematics for elementary teachers: a conceptual approach (9th ed.). McGraw-Hill Science.
Google Scholar CrossrefBikić, N., Maričić, S. M., & Pikula, M. (2016). The effects of differentiation of content in problem-solving in learning geometry in secondary school. Eurasia Journal of Mathematics, Science and Technology Education, 5(2), 15–23. https://doi.org/10.12973/eurasia.2016.02304a
Google Scholar CrossrefBonotto, C. (2005). How informal out-of-school mathematics can help students make sense of formal in-school mathematics: the case of multiplying by decimal numbers. Mathematical Thinking and Learning, 7(4), 313–344. https://doi.org/10.1207/s15327833mtl0704_3
Google Scholar CrossrefBrumbaugh, D. K., Moch, P. L., & Wilkinson, M. (2005). Mathematics content for elementary teachers (1st ed.). Lawrence Erlbaum Associates. https://doi.org/10.4324/9781410611345
Google Scholar CrossrefCesaria, A., Fitri, D. Y., & Rahmat, W. (2022). Ethnomathematic exploration based on realistic mathematics education (rme) in the traditional game “lore”. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 11(2). https://doi.org/10.24127/ajpm.v11i2.4958
Google Scholar CrossrefCharitas, R., Prahmana, I., Arnal-palacián, M., & Risdiyanti, I. (2023). Trivium curriculum in Ethno-RME approach: an impactful insight from ethnomathematics and realistic mathematics education. Jurnal Elemen, 9(January), 298–316. https://doi.org/10.29408/jel.v9i1.7262
Google Scholar CrossrefD’Ambrosio, U. (2007). The role of mathematics in educational systems. ZDM - International Journal on Mathematics Education, 39(1), 173–181 https://doi.org/10.1007/s11858-006-0012-1
Google Scholar CrossrefD’Ambrosio, U. (2018). Etnomatemática, justiça social e sustentabilidade. Estudos Avancados, 32(94), 189–204. https://doi.org/10.1590/s0103-40142018.3294.0014
Google Scholar CrossrefDe Walle, J. A. Van, Karp, K. S., & Bay-Williams, J. M. (2016). Elementary and middle school mathematics: teaching developmentally (9th ed.). Pearson Education Limited.
Google Scholar CrossrefDeliyianni, E., Gagatsis, A., Elia, I., & Panaoura, A. (2016). Representational flexibility and problem-solving ability in fraction and decimal number addition: a structural model. International Journal of Science and Mathematics Education, 17(2), 342–367. https://doi.org/10.1007/s10763-015-9625-6
Google Scholar CrossrefDen Heuvel-Panhuizen, M. Van, & Drijvers, P. (2014). Realistic mathematics education. In Encyclopedia of Mathematics Education (pp. 521–525). Springer Netherlands. https://doi.org/10.1007/978-94-007-4978-8_170
Google Scholar CrossrefFredriksen, 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. https://doi.org/10.1007/s10763-020-10053-1
Google Scholar CrossrefGarderen, D. Van, & Montague, M. (2003). Visual-spatial representation, mathematical problem solving, and students of varying abilities. Learning Disabilities Research and Practice, 18(4), 246–254. https://doi.org/10.1111/1540-5826.00079
Google Scholar CrossrefGoncharov, S., Milius, S., Schröder, L., Tsampas, S., & Urbat, H. (2023). Towards a higher-order mathematical operational semantics. Proceedings of the ACM on Programming Languages, 7(POPL), 632–658. https://doi.org/10.1145/3571215
Google Scholar CrossrefGravemeijer, K., & Terwel, J. (2000). Hans Freudenthal: a mathematician on didactics and curriculum theory. Journal of Curriculum Studies, 32(6), 777–796. https://doi.org/10.1080/00220270050167170
Google Scholar CrossrefHarrang, C. E. (2018). Painting poppies: on the relationship between concrete and metaphorical thinking. In Absolute Truth and Unbearable Psychic Pain (pp. 83–100). Routledge. https://doi.org/10.4324/9780429471544-6
Google Scholar CrossrefHsiao, G. C., & Kleinman, R. E. (1997). Mathematical foundations for error estimation in numerical solutions of integral equations in electromagnetics. IEEE Transactions on Antennas and Propagation, 45(3), 316–328. https://doi.org/10.1109/8.558648
Google Scholar CrossrefHyun, C. C., Tukiran, M., Wijayanti, L. M., Asbari, M., Purwanto, A., & Santoso, P. B. (2020). piaget versus vygotsky: implikasi pendidikan antara persamaan dan perbedaan. Journal of Engineering and Management Science Research (JIEMAR), 1(2), 286–293. https://journals.indexcopernicus.com/search/article?articleId=2661032
Google Scholar CrossrefKamid, Rusdi, M., Fitaloka, O., Basuki, F. R., & Anwar, K. (2020). Mathematical communication skills based on cognitive styles and gender. International Journal of Evaluation and Research in Education, 9(4), 847–856. https://doi.org/10.11591/ijere.v9i4.20497
Google Scholar CrossrefKing, A. (2014). Mathematical explorations: freshwater scarcity a proportional representation. NCTM, 20(3), 152–157. https://doi.org/10.5951/mathteacmiddscho.20.3.0178
Google Scholar CrossrefKosko, K. W., & Gao, Y. (2017). Mathematical communication in state standards before the common core. Educational Policy, 31(3), 275–302. https://doi.org/10.1177/0895904815595723
Google Scholar CrossrefLee, C. Y., & Chen, M. P. (2010). Taiwanese junior high school students’ mathematics attitudes and perceptions towards virtual manipulatives. British Journal of Educational Technology, 41(2). https://doi.org/10.1111/j.1467-8535.2008.00877.x
Google Scholar CrossrefLisesi, Ç. K. M. T. A. (2017). Examining the problem solving skills and the strategies used by high school students in solving non-routine problems. E-International Journal of Educational Research, 8(2), 91–114. https://doi.org/10.19160/ijer.321075
Google Scholar CrossrefMaulyda, M. A., Rahmatih, A. N., Gunawan, Hidayati, V. R., & Erfan, M. (2020). Retroactive thinking interference of grade vi students: a study on the topics of pisa literacy lessons. Journal of Physics: Conference Series, 1471(Maret), 1–7. https://doi.org/10.1088/1742-6596/1471/1/012037
Google Scholar CrossrefMenduni-Bortoloti, R., & Perovano, A. P. (2018). Production of mathematical texts: the communication between teacher and children. Educação Matemática Debate, 2(6), 229–241. https://doi.org/10.24116/emd25266136v2n62018a01
Google Scholar CrossrefNembhard, D. (2000). Experiential learning and forgetting for manual and cognitive tasks. International Journal of Industrial Ergonomics, 25(4), 315–326. https://doi.org/10.1016/S0169-8141(99)00021-9
Google Scholar CrossrefNing, X., Liu, Y., Miao, J. L., & Li, W. L. (2024). Enhancing the potentials of the focus group discussion – engaging frequently neglected but essential situational factors for analyzing data. International Journal of Qualitative Methods , 23. https://doi.org/10.1177/16094069241306332
Google Scholar CrossrefPansak, K., Supap, W., & Klin-eam, C. (2019). The develpoment of grade 10 students’ mathematical communication, and presentation ability using scaffolding learning in the topic of real number. Journal of Education, Mahasarakham University, 13(2), 32 – 44.
Google Scholar CrossrefPatel, S., & Pathak, H. (2022). A mathematical framework for link failure time estimation in MANETs. Engineering Science and Technology, an International Journal, 25, 100984. https://doi.org/10.1016/j.jestch.2021.04.003
Google Scholar CrossrefPrahmana, R. C. I. (2021). When culture meets mathematics as a starting point in learning mathematics. Ics, 19(2). https://www.facebook.com/International-Study-Group-on-Ethnomathematics -
Google Scholar CrossrefPrahmana, R. C. I. (2022). Ethno realistic mathematics education: the promising learning approach in the city of culture. SN Social Sciences, 1–19. https://doi.org/10.1007/s43545-022-00571-w
Google Scholar CrossrefPrahmana, R. C. I., Arnal-Palacián, M., Risdiyanti, I., & Ramadhani, R. (2023). Trivium curriculum in Ethno-RME approach: An impactful insight from ethnomathematics and realistic mathematics education. Jurnal Elemen, 9(1), 298–316. https://doi.org/10.29408/jel.v9i1.7262
Google Scholar CrossrefPurniati, T., Turmudi, Juandi, D., & Suhaedi, D. (2022). Ethnomathematics study: learning geometry in the mosque ornaments. International Journal on Advanced Science, Engineering and Information Technology, 12(5), 2096–2104. https://doi.org/10.18517/ijaseit.12.5.17063
Google Scholar CrossrefReys, R. E., Reys, B. J., Nohda, N., Ishida, J., Yoshikawa, S., & Shimizu, K. (1991). Computational estimation performance and strategies used by fifth-and eighth-grade japanese students. Source: Journal for Research in Mathematics Education, 22(1), 39–58. http://www.jstor.orgURL:http://www.jstor.org/stable/749553http://www.jstor.org/stable/749553?seq=1&cid=pdf-reference#references_tab_contents . https://doi.org/10.5951/jresematheduc.22.1.0039
Google Scholar CrossrefReys, R. E., Rogers, A., Cooke, A., Ewing, B., Robson, K., & Bennett, S. (2017). Helping children learn mathematics (2nd ed.).
Google Scholar CrossrefRobert, H., Michael, M., James, D. R., & Sharon, E. S. (2001). Instructional media and technologies for learning (7th ed.). PEARSON.
Google Scholar CrossrefRosa, M. (2017). Ethnomodelling as the mathematization of cultural practices. International Perspectives on the Teaching and Learning of Mathematical Modelling, pp. 153–162. https://doi.org/10.1007/978-3-319-62968-1_13
Google Scholar CrossrefSafi, F., & Desai, S. (2017). Promoting mathematical connections using three-dimensional manipulatives. NCTM, 22(8), 101–111. https://doi.org/10.5951/mathteacmiddscho.22.8.0488
Google Scholar CrossrefSarama, J., & Clements, D. H. (2009). “Concrete’”computer manipulatives in mathematics education. Child Development Perspectives, 3(3), 145–150. https://doi.org/10.1111/j.1750-8606.2009.00095.x
Google Scholar CrossrefSchneider, M., Grabner, R. H., & Paetsch, J. (2009). Mental number line, number line estimation, and mathematical achievement: Their interrelations in grades 5 and 6. Journal of Educational Psychology, 101(2), 359–372. https://doi.org/10.1037/a0013840
Google Scholar CrossrefSitorus, J., & Masrayati. (2016). Students’ creative thinking process stages: implementation of realistic mathematics education. Thinking Skills and Creativity, 22, 111–120. https://doi.org/10.1016/j.tsc.2016.09.007
Google Scholar CrossrefSlavin, R. E. (2018). Educational psychology. In Psychological Bulletin (Vol. 25, Issue 7). Pearson. https://doi.org/10.1037/h0074121
Google Scholar CrossrefSmit, R., Hess, K., Bachmann, P., Blum, V., & Birri, T. (2019). What happens after the intervention? results from teacher professional development in employing mathematical reasoning tasks and a supporting rubric. Frontiers in Education, 3(1), 1–12. https://doi.org/10.3389/feduc.2018.00113v
Google Scholar CrossrefSudarma, I. K., Wayan, A. I., & Yuda, I. (2022). Improving children’ s cognitive ability through information processing theory-based digital content. International Journal of Elementary Education, 6(1), 118–126.
Google Scholar CrossrefThe National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. The National Council of Teachers of Mathematics, Inc.
Google Scholar CrossrefTong, D. H., Uyen, B. P., & Quoc, N. V. A. (2021). The improvement of 10th students’ mathematical communication skills through learning ellipse topics. Heliyon, 7(11), e08282. https://doi.org/10.1016/j.heliyon.2021.e08282
Google Scholar CrossrefTurner, E. E., Aguirre, J., McDuffie, A. R., & Foote, M. Q. (2019). Jumping into modeling: elementary mathematical modeling with school and community contexts. Proceedings of the 41st Annual Meeting of PME-NA.
Google Scholar CrossrefUtami, L. F., Pramudya, I., & Slamet, I. (2020). Students’ mathematical communication skills in terms of concrete and abstract sequential thinking styles. Al-Jabar: Jurnal Pendidikan Matematika, 11(2), 371–381. https://doi.org/10.24042/ajpm.v11i2.7486
Google Scholar CrossrefValencia-Vallejo, N., López-Vargas, O., & Sanabria-Rodríguez, L. (2019). Effect of a metacognitive scaffolding on self-efficacy, metacognition, and achievement in e-learning environments. Knowledge Management and E-Learning, 11(1), 1–19. https://doi.org/10.34105/j.kmel.2019.11.001
Google Scholar CrossrefWang, Y. Q., & Siegler, R. S. (2013). Representations of and translation between common fractions and decimal fractions. Chinese Science Bulletin, 5(2), 123–146. https://doi.org/10.1007/s11434-013-6035-4
Google Scholar CrossrefWilkinson, L. C., Bailey, A. L., & Maher, C. A. (2018). Students’ mathematical reasoning , communication , and language representations : a video-narrative analysis. Ecnu Review Of Education, 1(3), 1–22. https://doi.org/10.30926/ecnuroe2018010301
Google Scholar CrossrefWright, R. J. (2013). Assessing early numeracy: Significance, trends, nomenclature, context, key topics, learning framework and assessment tasks. South African Journal of Childhood Education, 3(2), 20–34. https://doi.org/10.4102/sajce.v3i2.38
Google Scholar CrossrefYang, S., Kabir, M. H., & Hoque, M. R. (2016). Mathematical modeling of smart space for context-aware system: linear algebraic representation of state-space method based approach. Hindawi Publishing Corporation Mathematical Problems in Engineering, 8(1), 1–8. https://doi.org/10.1155/2016/8325054
Google Scholar CrossrefYin, R. K. (2013). Validity and generalization in future case study evaluations. Evaluation, 19(3), 321–332. https://doi.org/10.1177/1356389013497081
Google Scholar CrossrefZahri, M., Budayas, İ. K., & Lukito, A. (2021). Analysis of students’ mathematical communication ability in solving mathematical problems. Journal for the Education of Gifted Young Scientists, 9(3), 277–282. https://doi.org/10.17478/jegys.819995
Google Scholar CrossrefPublished
Metrics
Almetric
Dimensions
Issue
Section
License
Copyright (c) 2025 Nawang Sulistyani, Mohammad Archi Maulyda, Sugiman Sugiman, Yoppy Wahyu Purnomo

This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors retain copyright and grant the journal the right of first publication but allow anyone to share: (unload, , reprint, distribute and/or copy) and adapt (remix, transform reuse, modify,) for any proposition, even commercial, always quoting the original source.