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Abstract
Traditional Indonesian dances can serve as meaningful contexts for mathematics instruction, yet this potential remains underutilized in many classrooms, including in West Nusa Tenggara. This study aims to design a learning trajectory for integer operations by integrating Sagele dance, which features rhythmic forward and backward movements suitable for representing positive and negative numbers. Employing a design research methodology, data were collected through video recordings, field notes, questionnaires, and classroom observations. The study followed three key phases: preliminary design, design experiment, and retrospective analysis. The resulting trajectory consists of three learning activities: (1) exploring free movement in Sagele dance to emphasize directional shifts; (2) combining directional changes to illustrate integer operations; and (3) formalizing these concepts through number line models corresponding to the dance movements. Findings show that integrating the Sagele dance helped students transition from informal to formal mathematical thinking, supporting both conceptual understanding and character development, such as respect for cultural heritage. The cultural contextualization also enhanced student engagement and supported the internalization of abstract operations. This research offers a replicable model for incorporating ethnomathematics into classroom practice. While limited in scope and sample size, the study highlights the promise of culturally grounded learning trajectories in mathematics education and calls for broader application in future research.
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Copyright (c) 2025 Intan Dwi Hastuti, Yuni Mariyati, Sutarto
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References
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- Bakker, A. (2019). Design research in education: A practical guide for early career researchers. Routledge. https://doi.org/10.4324/9780203701010
- Cavanagh, T., Chen, B., Lahcen, R., & Paradiso, J. (2020). Constructing a design framework and pedagogical approach for adaptive learning in higher education: A practitioner's perspective. The International Review of Research in Open and Distributed Learning, 21(1), 172-196. https://doi.org/10.19173/irrodl.v21i1.4557
- Dominikus, W. (2023). Ethnomathematics at the traditional house of mbaru niang wae rebo, manggarai. https://doi.org/10.4108/eai.21-10-2022.2329709
- Ergene, Ö., ERGENE, B. Ç., & Yazıcı, E. Z. (2020). Ethnomathematics activities: reflections from the design and implementation process. Turkish Journal of Computer and Mathematics Education (TURCOMAT). https://doi.org/10.16949/turkbilmat.688780
- Eshaq, H. (2023). The effect of using STEM education on students’ mathematics achievement. Journal of Pedagogical Research. https://doi.org/10.33902/jpr.202423476
- Fuadiah, N., Suryadi, D., & Turmudi, T. (2019). Teaching and learning activities in classroom and their impact on student misunderstanding: A case study on negative integers. International Journal of Instruction, 12(1), 407-424. https://doi.org/10.29333/iji.2019.12127a
- Gravemeijer, K. P. E. (2004). Local Instruction Theories as Means of Support for teachers in Reform Mathematics Education. Mathematical Thinking and Learning, 6(2), 105-128. https://doi.org/10.1207/s15327833mtl0602_3
- Gravemeijer, K. (2020). A socio-constructivist elaboration of realistic mathematics education. https://doi.org/10.1007/978-3-030-33824-4_12
- Gravemeijer, K., & Cobb, P. (2006). Design research from a learning design perspective. In Akker, Jan van den., Gravemeijer, Koeno., McKenney, Susan., & Nieeven, Nienke. (Ed.), Educational Design Research (pp. 29–63). Routledge. https://doi.org/10.4324/9780203088364-12
- Hastuti, I. D., Surahmat, Sutarto, & Dafik. (2020). The effect of guided inquiry learning in improving metacognitive skill of elementary school students. International Journal of Instruction, 13(4), 315–330. https://doi.org/10.29333/iji.2020.13420a
- Hernandez, A., & Burrows, K. (2021). Implementing culturally relevant teaching in the classroom. Open Journal of Leadership, 10(4), 338–363. https://doi.org/10.4236/ojl.2021.104020
- Hidayatullah, A. (2023). Exploring students’ mathematical beliefs: Gender, grade, and culture differences. Journal on Efficiency and Responsibility in Education and Science, 16(3), 186-195. https://doi.org/10.7160/eriesj.2023.160303
- Ilma, I. (2024). Improving creative thinking skills and learning motivation through ethnomathematics-based interactive multimedia: An experimental study in primary school. Multidisciplinary Science Journal, 6(8), 2024141. https://doi.org/10.31893/multiscience.2024141
- Kafyulilo, A., & Fisser, P. (2019). Developing TPACK in science and mathematics teacher education in Tanzania: A proof of concept study. https://doi.org/10.1007/978-3-030-20062-6_8
- Karunanayaka, S., & Naidu, S. (2017). A design-based approach to support and nurture open educational practices. Asian Association of Open Universities Journal, 12(1), 1-20. https://doi.org/10.1108/aaouj-01-2017-0010
- Khalid, M., & Embong, Z. (2020). Sources and possible causes of errors and misconceptions in operations of integers. International Electronic Journal of Mathematics Education, 15(2), em0568. https://doi.org/10.29333/iejme/6265IEJME+1Home+1
- Kusuma, A. B., Hanum, F., Abadi, A. M., & Ahmad, A. (2024). Exploration of ethnomathematics research in Indonesia 2010-2023. Infinity Journal, 13(2), 393-412. https://doi.org/10.22460/infinity.v13i2.p393-412
- Laamena, C., & Laurens, T. (2021). Development of integer number learning devices using moluccas local wisdom. Eduma Mathematics Education Learning and Teaching, 10(1), 60. https://doi.org/10.24235/eduma.v10i1.8163
- Muslimin, M., Putri, R., Zulkardi, Z., & Aisyah, N. (2020). Learning integers with realistic mathematics education approach based on Islamic values. Journal on Mathematics Education, 11(3), 363–384. https://doi.org/10.22342/jme.11.3.11721.363-384
- Naidoo, J. (2021). Integrating indigenous knowledge and culturally based activities in South African mathematics classrooms. African Journal of Teacher Education, 10(2), 17-36. https://doi.org/10.21083/ajote.v10i2.6686
- National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston, VA: Author. Retrieved from https://www.nctm.org/standards/
- Nur, A., Kartono, K., Zaenuri, Z., & Rochmad, R. (2022). The learning trajectory construction of elementary school students in solving integer word problems. Participatory Educational Research, 9(1), 404-424. https://doi.org/10.17275/per.22.22.9.1
- Nuraida, I., & Amam, A. (2019). Hypothetical learning trajectory in realistic mathematics education to improve the mathematical communication of junior high school students. Infinity Journal, 8(2), 247. https://doi.org/10.22460/infinity.v8i2.p247-258
- Nursyahidah, F., Saputro, B., & Albab, I. (2021). The learning trajectory of sphere using megono gunungan tradition context. International Journal on Emerging Mathematics Education, 5(2), 69. https://doi.org/10.12928/ijeme.v5i2.18313
- Paliwal, V., & Baroody, A. J. (2020). Fostering the learning of subtraction concepts and the subtraction-as-addition reasoning strategy. Early Childhood Research Quarterly, 51, 403–415. https://doi.org/10.1016/j.ecresq.2019.05.008
- Permana, N. (2023). Improving students’ mathematics learning outcomes through Sundanese ethnomathematics: A systematic literature review. abjme, 1(1), 11-21. https://doi.org/10.61553/abjme.v1i1.12
- Prahmana, R. (2017). The role of research-based learning to enhance students’ research and academic writing skills. Journal of Education and Learning (EduLearn), 11(3), 351-366. https://doi.org/10.11591/edulearn.v11i3.5871
- Retnawati, H., Djidu, H., Kartianom, K., Apino, E., & Anazifa, R. (2018). Teachers’ knowledge about higher-order thinking skills and its learning strategy. Problems of Education in the 21st Century, 76(2), 215-230. https://doi.org/10.33225/pec/18.76.215
- Ramadhani, R., Prahmana, R. C. I., Soeharto, & Saleh, A. (2024). Integrating traditional food and technology in statistical learning: A learning trajectory. Journal on Mathematics Education, 15(4), 1277–1310. https://doi.org/10.22342/jme.v15i4.pp1277-1310
- Risdiyanti, I., & Indra Prahmana, R. C. (2020). The learning trajectory of number pattern learning using barathayudha war stories and uno stacko. Journal on Mathematics Education, 11(1), 157–166. https://doi.org/10.22342/jme.11.1.10225.157-166
- Risdiyanti, I., Prahmana, R. C. I., & Shahrill, M. (2019). The learning trajectory of social arithmetic using an indonesian traditional game. Elementary Education Online, 18(4), 2094–2108. https://doi.org/10.17051/ilkonline.2019.639439
- Santri, D., Hartono, Y., & Somakim, S. (2019). Mathematical modeling for learning algebraic operation. Journal of Education and Learning (EduLearn), 13(2), 201-211. https://doi.org/10.11591/edulearn.v13i2.8996
- Simamora, R., & Saragih, S. (2018). Improving students’ mathematical problem-solving ability and self-efficacy through guided discovery learning in local culture context. International Electronic Journal of Mathematics Education, 14(1). https://doi.org/10.12973/iejme/3966
- Sutarto, Muzaki, A., Hastuti, I. D., Fujiaturrahman, S., & Untu, Z. (2022). Development of an Ethnomathematics-Based e-Module to Improve Students’ Metacognitive Ability in 3D Geometry Topic. International Journal of Interactive Mobile Technologies, 16(3), 32–46. https://doi.org/10.3991/IJIM.V16I03.24949
- Syaifuddin, T., Nurlaela, L., & P, S. (2021). Contextual teaching and learning (CTL) model to students improve learning outcome at senior high school of model terpadu Bojonegoro. Ijorer International Journal of Recent Educational Research, 2(5), 528-535. https://doi.org/10.46245/ijorer.v2i5.143
- Turgut, M., Tanışlı, D., & Köse, N. (2021). A mathematics teacher educator’s feedback affecting teachers’ design of hypothetical learning trajectories for teaching patterns. International Journal for Mathematics Teaching and Learning, 22(2), 33-54. https://doi.org/10.4256/ijmtl.v22i2.382
- Utami, A., Sa’dijah, C., Subanji, S., & Irawati, S. (2018). Six levels of indonesian primary school students’ mental model in comprehending the concept of integer. International Journal of Instruction, 11(4), 29-44. https://doi.org/10.12973/iji.2018.1143a
- Verawati, N. (2024). Raising the issue of local wisdom in science learning and its impact on increasing students' scientific literacy. IJETE, 1(1), 42. https://doi.org/10.33394/ijete.v1i1.10881
- Wibawa, K. A., Payadnya, I. P. A. A., Yasa, I. G. U., & Prahmana, R. C. I. (2022). The learning trajectory of entrepreneurship arithmetic content using a traditional market. Mathematics Teaching Research Journal, 14(3), 144–169. https://eric.ed.gov/?id=EJ1361579
References
Andriani, D., Widada, W., Herawaty, D., Ardy, H., Nugroho, K., & Ma’rifah, N. (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
Bakker, A. (2019). Design research in education: A practical guide for early career researchers. Routledge. https://doi.org/10.4324/9780203701010
Cavanagh, T., Chen, B., Lahcen, R., & Paradiso, J. (2020). Constructing a design framework and pedagogical approach for adaptive learning in higher education: A practitioner's perspective. The International Review of Research in Open and Distributed Learning, 21(1), 172-196. https://doi.org/10.19173/irrodl.v21i1.4557
Dominikus, W. (2023). Ethnomathematics at the traditional house of mbaru niang wae rebo, manggarai. https://doi.org/10.4108/eai.21-10-2022.2329709
Ergene, Ö., ERGENE, B. Ç., & Yazıcı, E. Z. (2020). Ethnomathematics activities: reflections from the design and implementation process. Turkish Journal of Computer and Mathematics Education (TURCOMAT). https://doi.org/10.16949/turkbilmat.688780
Eshaq, H. (2023). The effect of using STEM education on students’ mathematics achievement. Journal of Pedagogical Research. https://doi.org/10.33902/jpr.202423476
Fuadiah, N., Suryadi, D., & Turmudi, T. (2019). Teaching and learning activities in classroom and their impact on student misunderstanding: A case study on negative integers. International Journal of Instruction, 12(1), 407-424. https://doi.org/10.29333/iji.2019.12127a
Gravemeijer, K. P. E. (2004). Local Instruction Theories as Means of Support for teachers in Reform Mathematics Education. Mathematical Thinking and Learning, 6(2), 105-128. https://doi.org/10.1207/s15327833mtl0602_3
Gravemeijer, K. (2020). A socio-constructivist elaboration of realistic mathematics education. https://doi.org/10.1007/978-3-030-33824-4_12
Gravemeijer, K., & Cobb, P. (2006). Design research from a learning design perspective. In Akker, Jan van den., Gravemeijer, Koeno., McKenney, Susan., & Nieeven, Nienke. (Ed.), Educational Design Research (pp. 29–63). Routledge. https://doi.org/10.4324/9780203088364-12
Hastuti, I. D., Surahmat, Sutarto, & Dafik. (2020). The effect of guided inquiry learning in improving metacognitive skill of elementary school students. International Journal of Instruction, 13(4), 315–330. https://doi.org/10.29333/iji.2020.13420a
Hernandez, A., & Burrows, K. (2021). Implementing culturally relevant teaching in the classroom. Open Journal of Leadership, 10(4), 338–363. https://doi.org/10.4236/ojl.2021.104020
Hidayatullah, A. (2023). Exploring students’ mathematical beliefs: Gender, grade, and culture differences. Journal on Efficiency and Responsibility in Education and Science, 16(3), 186-195. https://doi.org/10.7160/eriesj.2023.160303
Ilma, I. (2024). Improving creative thinking skills and learning motivation through ethnomathematics-based interactive multimedia: An experimental study in primary school. Multidisciplinary Science Journal, 6(8), 2024141. https://doi.org/10.31893/multiscience.2024141
Kafyulilo, A., & Fisser, P. (2019). Developing TPACK in science and mathematics teacher education in Tanzania: A proof of concept study. https://doi.org/10.1007/978-3-030-20062-6_8
Karunanayaka, S., & Naidu, S. (2017). A design-based approach to support and nurture open educational practices. Asian Association of Open Universities Journal, 12(1), 1-20. https://doi.org/10.1108/aaouj-01-2017-0010
Khalid, M., & Embong, Z. (2020). Sources and possible causes of errors and misconceptions in operations of integers. International Electronic Journal of Mathematics Education, 15(2), em0568. https://doi.org/10.29333/iejme/6265IEJME+1Home+1
Kusuma, A. B., Hanum, F., Abadi, A. M., & Ahmad, A. (2024). Exploration of ethnomathematics research in Indonesia 2010-2023. Infinity Journal, 13(2), 393-412. https://doi.org/10.22460/infinity.v13i2.p393-412
Laamena, C., & Laurens, T. (2021). Development of integer number learning devices using moluccas local wisdom. Eduma Mathematics Education Learning and Teaching, 10(1), 60. https://doi.org/10.24235/eduma.v10i1.8163
Muslimin, M., Putri, R., Zulkardi, Z., & Aisyah, N. (2020). Learning integers with realistic mathematics education approach based on Islamic values. Journal on Mathematics Education, 11(3), 363–384. https://doi.org/10.22342/jme.11.3.11721.363-384
Naidoo, J. (2021). Integrating indigenous knowledge and culturally based activities in South African mathematics classrooms. African Journal of Teacher Education, 10(2), 17-36. https://doi.org/10.21083/ajote.v10i2.6686
National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston, VA: Author. Retrieved from https://www.nctm.org/standards/
Nur, A., Kartono, K., Zaenuri, Z., & Rochmad, R. (2022). The learning trajectory construction of elementary school students in solving integer word problems. Participatory Educational Research, 9(1), 404-424. https://doi.org/10.17275/per.22.22.9.1
Nuraida, I., & Amam, A. (2019). Hypothetical learning trajectory in realistic mathematics education to improve the mathematical communication of junior high school students. Infinity Journal, 8(2), 247. https://doi.org/10.22460/infinity.v8i2.p247-258
Nursyahidah, F., Saputro, B., & Albab, I. (2021). The learning trajectory of sphere using megono gunungan tradition context. International Journal on Emerging Mathematics Education, 5(2), 69. https://doi.org/10.12928/ijeme.v5i2.18313
Paliwal, V., & Baroody, A. J. (2020). Fostering the learning of subtraction concepts and the subtraction-as-addition reasoning strategy. Early Childhood Research Quarterly, 51, 403–415. https://doi.org/10.1016/j.ecresq.2019.05.008
Permana, N. (2023). Improving students’ mathematics learning outcomes through Sundanese ethnomathematics: A systematic literature review. abjme, 1(1), 11-21. https://doi.org/10.61553/abjme.v1i1.12
Prahmana, R. (2017). The role of research-based learning to enhance students’ research and academic writing skills. Journal of Education and Learning (EduLearn), 11(3), 351-366. https://doi.org/10.11591/edulearn.v11i3.5871
Retnawati, H., Djidu, H., Kartianom, K., Apino, E., & Anazifa, R. (2018). Teachers’ knowledge about higher-order thinking skills and its learning strategy. Problems of Education in the 21st Century, 76(2), 215-230. https://doi.org/10.33225/pec/18.76.215
Ramadhani, R., Prahmana, R. C. I., Soeharto, & Saleh, A. (2024). Integrating traditional food and technology in statistical learning: A learning trajectory. Journal on Mathematics Education, 15(4), 1277–1310. https://doi.org/10.22342/jme.v15i4.pp1277-1310
Risdiyanti, I., & Indra Prahmana, R. C. (2020). The learning trajectory of number pattern learning using barathayudha war stories and uno stacko. Journal on Mathematics Education, 11(1), 157–166. https://doi.org/10.22342/jme.11.1.10225.157-166
Risdiyanti, I., Prahmana, R. C. I., & Shahrill, M. (2019). The learning trajectory of social arithmetic using an indonesian traditional game. Elementary Education Online, 18(4), 2094–2108. https://doi.org/10.17051/ilkonline.2019.639439
Santri, D., Hartono, Y., & Somakim, S. (2019). Mathematical modeling for learning algebraic operation. Journal of Education and Learning (EduLearn), 13(2), 201-211. https://doi.org/10.11591/edulearn.v13i2.8996
Simamora, R., & Saragih, S. (2018). Improving students’ mathematical problem-solving ability and self-efficacy through guided discovery learning in local culture context. International Electronic Journal of Mathematics Education, 14(1). https://doi.org/10.12973/iejme/3966
Sutarto, Muzaki, A., Hastuti, I. D., Fujiaturrahman, S., & Untu, Z. (2022). Development of an Ethnomathematics-Based e-Module to Improve Students’ Metacognitive Ability in 3D Geometry Topic. International Journal of Interactive Mobile Technologies, 16(3), 32–46. https://doi.org/10.3991/IJIM.V16I03.24949
Syaifuddin, T., Nurlaela, L., & P, S. (2021). Contextual teaching and learning (CTL) model to students improve learning outcome at senior high school of model terpadu Bojonegoro. Ijorer International Journal of Recent Educational Research, 2(5), 528-535. https://doi.org/10.46245/ijorer.v2i5.143
Turgut, M., Tanışlı, D., & Köse, N. (2021). A mathematics teacher educator’s feedback affecting teachers’ design of hypothetical learning trajectories for teaching patterns. International Journal for Mathematics Teaching and Learning, 22(2), 33-54. https://doi.org/10.4256/ijmtl.v22i2.382
Utami, A., Sa’dijah, C., Subanji, S., & Irawati, S. (2018). Six levels of indonesian primary school students’ mental model in comprehending the concept of integer. International Journal of Instruction, 11(4), 29-44. https://doi.org/10.12973/iji.2018.1143a
Verawati, N. (2024). Raising the issue of local wisdom in science learning and its impact on increasing students' scientific literacy. IJETE, 1(1), 42. https://doi.org/10.33394/ijete.v1i1.10881
Wibawa, K. A., Payadnya, I. P. A. A., Yasa, I. G. U., & Prahmana, R. C. I. (2022). The learning trajectory of entrepreneurship arithmetic content using a traditional market. Mathematics Teaching Research Journal, 14(3), 144–169. https://eric.ed.gov/?id=EJ1361579