Trivium curriculum in Ethno-RME approach: An impactful insight from ethnomathematics and realistic mathematics education
DOI:
https://doi.org/10.29408/jel.v9i1.7262Keywords:
Ethno-RME, ethnomathematics, realistic mathematics education, trivium curriculumAbstract
In implementing Ethnomathematics-Realistic Mathematics Education (Ethno-RME), teaching mathematics correctly is needed through learning practices in teaching and learning activities. This pedagogical activity requires guidance in the form of a curriculum. So, the teacher can determine the ethnomathematics context as a starting point in teaching mathematics using Ethno-RME. Therefore, this paper focuses on constructing an Ethno-RME curriculum to guide teachers to apply Ethno-RME in their learning process. This research was collected data from a few relevant kinds of literature to build the Ethno-RME curriculum, such as literature about the D’Ambrosio trivium curriculum, the principles, and character of RME, and literature about the implementation of RME and Ethnomathematics in school. Then, the data were reviewed, criticized, and synthesized, which was done by integrating the ideas in the literature with the new ideas to form the new concept and formula for Ethno-RME curriculum. This study comprehensively explains the goal of Ethno-RME learning, Ethno-RME competencies, and the procedure of Ethno-RME learning. Its process consists of several steps: determining, exploring, processing, and finding mathematics in the ethnomathematics context. Furthermore, this procedure continues with conducting self-development models and critical reflection as an assessment.References
Acharya, B. R., Kshetree, M. P., Khanal, B., Panthi, R. K., & Belbase, S. (2021). Mathematics educators’ perspectives on cultural relevance of basic level mathematics in Nepal. Journal on Mathematics Education, 12(1), 17–48. https://doi.org/10.22342/jme.12.1.12955.17-48
Adam, S. (2004). Ethnomathematical ideas in the curriculum. Mathematics Education Research Journal, 16(2), 49–68. https://doi.org/10.1007/BF03217395
Brandt, A., & Chernoff, E. (2015). The importance of ethnomathematics in the math class. Ohio Journal of School Mathematics, 71(2015), 31–36.
Cobb, P. (1994). Constructivism in mathematics and science education. Educational researcher, 23(7), 4–4. https://doi.org/10.2307/1176932
D'Ambrosio, U. (1999). Literacy, matheracy, and technoracy: A trivium for today. Mathematical Thinking and Learning, 1(2), 131–153. https://doi.org/10.1207/s15327833mtl0102_3
D'Ambrosio, U. (2007). The role of mathematics in educational systems. ZDM - International Journal on Mathematics Education, 39(1–2), 173–181. https://doi.org/10.1007/s11858-006-0012-1
D'Ambrosio, U. (2016). An overview of the history of ethnomathematics. In M. Rosa, U. D'Ambrosio, D. C. Orey, L. Shirley, W. V. Alangui, P. Palhares, & M. E. Gavarrete (Eds.), Current and Future Perspectives of Ethnomathematics as a Program (pp. 5–10). Springer Nature. https://doi.org/10.1007/978-3-319-30120-4_2
D'Ambrosio, U., & D'Ambrosio, B. S. (2013). The role of ethnomathematics in curricular leadership in mathematics education. Journal of Mathematics Education at Teachers College, 4(1), 19–25. https://doi.org/10.7916/jmetc.v4i1.767
de Lange, J. (1987). Mathematics, insight and meaning. Utrecht University. http://www.fisme.science.uu.nl/wiki/index.php/Mathematics%2C_Insight_and_Meaning
de Lange, J. (1996). Using and applying mathematics in education. In International Handbook of Mathematics Education (pp. 49–97). Springer. https://doi.org/10.1007/978-94-009-1465-0_4
Dewey, J. (1993). 21. Why have progressive schools? In E. T. Weber (Ed.), America's Public Philosopher: Essays on Social Justice, Economics, Education, and the Future of Democracy (pp. 133–142). Columbia University Press. https://doi.org/10.7312/dewe19894-023
Dias, D., Costa, C., & Palhares, P. (2015). Ethnomathematics of the Southwestern Angola Nyaneka-Nkhumbi ethnic group and its application to mathematics education. Revista Latinoamericana de Etnomatemática: Perspectivas Socioculturales de La Educación Matemática, 8(1), 10–28. http://www.revista.etnomatematica.org/index.php/RLE/article/view/171
Doorman, M. (2016, 2016). What can mathematics education contribute to preparing students for our future society? Proceeding of 3rd International Conference on Research Implementation and Education of Mathematics and Science,
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, 11(2), 402–437. https://doi.org/10.16949/turkbilmat.688780
Farrell, T. S. C. (2012). Reflecting on reflective practice: (Re)Visiting Dewey and Schön. TESOL Journal, 3(1), 7–16. https://doi.org/10.1002/tesj.10
Ferreira, E. S. (1997). Etnomatemática: Uma proposta metodológica [Ethnomathematics: A methodological proposal]. MEM/USU.
Fonseca, M. D. C. F. R. (2010). Adult education and ethnomathematics: Appropriating results, methods, and principles. ZDM, 3(42), 361–369. https://doi.org/10.1007/s11858-010-0257-6
Fouze, A. Q., & Amit, M. (2018). Development of mathematical thinking through integration of ethnomathematics folklore game in math instruction. Eurasia Journal of Mathematics, Science and Technology Education, 14(2), 617–630. https://doi.org/10.12973/ejmste/80626
François, K. (2012). Ethnomathematics in a European context: Towards an enriched meaning of ethnomathematics. Journal of Mathematics and Culture, 6(1), 191–208.
François, K. (2016). Ethnomathematics as a human right. In Critical Mathematics Education: Theory, Praxis and Reality (pp. 187–198).
Freudenthal, H. (1986). Didactical phenomenology of mathematical structures (Vol. 1). Springer Science & Business Media.
Freudenthal, H. (2006). Revisiting mathematics education: China lectures (Vol. 9). Springer Science & Business Media.
Ghanizadeh, A. (2017). The interplay between reflective thinking, critical thinking, self-monitoring, and academic achievement in higher 185 education. Higher Education, 74(1), 101–114. https://doi.org/10.1007/s10734-016-0031-y
Ghanizadeh, A., Al-Hoorie, A. H., & Jahedizadeh, S. (2020). Higher order thinking skills in the language classroom: A concise guide. In Second Language Learning and Teaching (pp. 1–177). Springer. https://doi.org/10.1007/978-3-030-56711-8_1
Gravemeijer, K. (1994). Developing realistic mathematics education. CD-ß Press/Freudenthal Institute.
Gravemeijer, K. (2000). Realistic mathematics education. In Twilight Mathematics Education Staff & Students Seminar
Gravemeijer, 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
Larsen, S. (2018). Didactical phenomenology: The engine that drives realistic mathematics education. For the Learning of Mathematics, 38(3), 25–29.
Long, S., & Chik, Y. (2020). Fundamental applications of mathematics in agriculture and cultural heritage in daily life of Melanau Tellian, Mukah, Sarawak: An ethnomathematics review. Malaysian Journal of Social Sciences and Humanities (MJSSH), 5(11), 217–227. https://doi.org/10.47405/mjssh.v5i11.551
Massarwe, K., Verner, I., & Bshouty, D. (2013). Ethnomathematics and multi-cultural education: Analysis and construction of geometric ornaments. Journal of Mathematics and Culture, 53(9), 1689–1699.
Michelsen, C. (2006). Functions: A modelling tool in mathematics and science. ZDM, 38(3), 269–280. https://doi.org/10.1007/BF02652810
OECD. (2003). PISA 2003 – Learning for tomorrow’s world. OECD Publishing.
Orey, D. C. (2000). The ethnomathematics of the Sioux tipi and cone. In Mathematics Across Cultures (pp. 239–252). Springer. https://doi.org/10.1007/978-94-011-4301-1_13
Papadakis, S., Kalogiannakis, M., & Zaranis, N. (2021). Teaching mathematics with mobile devices and the realistic mathematical education (RME) approach in kindergarten. Advances in Mobile Learning Educational Research, 1(1), 5–18. https://doi.org/10.25082/AMLER.2021.01.002
Paroqi, L. L., Mursalin, M., & Marhami, M. (2020). The implementation of realistic mathematics education approach to improve students’ mathematical communication ability in statistics course. International Journal for Educational and Vocational Studies, 2(10), 879–889. https://doi.org/10.29103/ijevs.v2i10.3311
Pradhan, J. B. (2017). Mathematical ideas in Chundara culture: Unfolding a Nepalese teaching and learning system. In M. Rosa, L. Shirley, M. E. Gavarrete, & W. V. Alangui (Eds.), Ethnomathematics and Its Diverse Approaches for Mathematics Education (pp. 125–152). Springer. https://doi.org/10.1007/978-3-319-59220-6_6
Pradhan, J. B., & Sharma, T. (2021). Ethnomathematics research practices and its pedagogical implications: A Nepalese perspective. Journal of Mathematics and Culture, 15(1), 110–126.
Prahmana, R. C. I. (2012). Pendesainan pembelajaran operasi bilangan menggunakan permainan tradisional tepuk bergambar untuk siswa kelas III Sekolah Dasar (SD) [The design of number operations learning using the traditional illustrated pat game for grade III elementary school students] [Master Thesis, Universitas Sriwijaya].
Prahmana, R. C. I. (2022). Ethno-realistic mathematics education: The promising learning approach in the city of culture. SN Social Sciences, 2(12), 1–19. https://doi.org/10.1007/s43545-022-00571-w
Prahmana, R. C. I., & Istiandaru, A. (2021). Learning sets theory using shadow puppet: A study of javanese ethnomathematics. Mathematics, 9(22), 1–16. https://doi.org/10.3390/math9222938
Putra, E. C. S., & Mahmudah, F. N. (2021). The implementation of ethnomathematics based-learning for students. SJME (Supremum Journal of Mathematics Education), 5(2), 162–169. https://doi.org/10.35706/sjme.v5i2.4827
Risdiyanti, I., & Prahmana, R. C. I. (2018). Ethnomathematics: Exploration in Javanese culture. Journal of Physics: Conference Series, 943(1), 012032. https://doi.org/10.1088/1742-6596/943/1/012032
Risdiyanti, I., & Prahmana, R. C. I. (2021). Designing learning trajectory of set through the Indonesian shadow puppets and Mahabharata stories. Infinity Journal, 10(2), 331–348. https://doi.org/10.22460/infinity.v10i2.p331-348
Rosa, M., & Orey, D. C. (2007). Ethnomathematics: Cultural assertions and challenges towards pedagogical action. The Journal of Mathematics and Culture, 1(1), 57–78.
Rosa, M., & Orey, D. C. (2010). Culturally relevant pedagogy: An ethnomathematical approach. Springer International Publishing.
Rosa, M., & Orey, D. C. (2015). A trivium curriculum for mathematics based on literacy, matheracy, and technoracy: an ethnomathematics perspective. ZDM - International Journal on Mathematics Education, 47(4), 587–598. https://doi.org/10.1007/s11858-015-0688-1
Rubio, J. S. (2016). The ethnomathematics of the Kabihug tribe in Jose Panganiban, Camarines Norte, Philippines. Malaysian Journal of Mathematical Sciences, 10, 211–231.
Sitorus, 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
Skovsmose, O. (2019). Travelling through education. BRILL. https://doi.org/10.1163/9789087903626
Streefland, L. (1985). Search for the roots of ratio: Some thoughts on the long-term learning process (towards ... a theory). Educational Studies in Mathematics, 15(4), 327–348. https://doi.org/10.1007/bf00311111
Streefland, L. (1991). Fractions in realistic mathematics education: A paradigm of developmental research. Kluwer. https://doi.org/10.1007/978-94-011-3168-1
Streefland, L. (1994). The legacy of Hans Freudenthal. Springer Science & Business Media. https://doi.org/10.1007/978-94-017-3377-9
Tesfamicael, S. A. N., Ah, T., T, & G. (2021). Curriculum implications of using ethnomathematics to promote student learning in Ethiopia. Journal of Mathematics and Culture, 15(3), 85–123.
Tlonaen, M. A., & Deda, Y. N. (2021). Exploration ethnomathematics on traditional house Ume Kbubu in North Central Timor Districts. Journal of Physics: Conference Series, 1776(1), 012016. https://doi.org/10.1088/1742-6596/1776/1/012016
Torraco, R. J. (2005). Writing integrative literature reviews: Guidelines and examples. Human Resource Development Review, 4(3), 356–367. https://doi.org/10.1177/1534484305278283
Treffers, A. (1987). Integrated column arithmetic according to progressive schematisation. Educational Studies in Mathematics, 18(2), 125–145. https://doi.org/10.1007/BF00314723
Treffers, A. (1993). Wiskobas and Freudenthal realistic mathematics education. Educational Studies in Mathematics, 25(1), 89–108. https://doi.org/10.1007/BF01274104
Treffers, A. (2012). Three dimensions: A model of goal and theory description in mathematics instruction—The Wiskobas Project (Vol. 3). Springer Science & Business Media.
Tutak, F. A., Bondy, E., & Adams, T. L. (2011). Critical pedagogy for critical mathematics education. International Journal of Mathematical Education in Science and Technology, 42(1), 65–74. https://doi.org/10.1080/0020739X.2010.510221
van den Heuvel-Panhuizen, M. (2003). The didactical use of models in realistic mathematics education: An example from a longitudinal trajectory on percentage. Educational Studies in Mathematics, 54(1), 9–35. https://doi.org/10.1023/B:EDUC.0000005212.03219.dc
van den Heuvel-Panhuizen, M., & Drijvers, P. (2020). Realistic mathematics education. In S. Lerman (Ed.), Encyclopedia of Mathematics Education (pp. 713–717). Springer, Cham. https://doi.org/10.1007/978-3-030-15789-0_170
Webb, D. C., & Abels, M. (2011). Restrictions in algebra. In P. Drijvers (Ed.), Secondary Algebra Education: Revisiting Topics and Themes and Exploring the Unknown (pp. 101–118). SensePublishers. https://doi.org/10.1007/978-94-6091-334-1_5
Webb, D. C., Boswinkel, N., & Dekker, T. (2008). Beneath the tip of the iceberg: Using representations to support student understanding. Mathematics Teaching in the Middle School, 14(2), 110–113. https://doi.org/10.5951/MTMS.14.2.0110
Webb, D. C., Kooij, H., & Geist, M. R. (2011). Design research in the Netherlands: Introducing logarithms using realistic mathematics education. Journal of Mathematics Education at Teachers College, 2(1), 47–52. https://doi.org/10.7916/jmetc.v2i1.708
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(1), 012028. https://doi.org/10.1088/1742-6596/1088/1/012028
Wubbels, T., Korthagen, F., & Broekman, H. (1997). Preparing teachers for realistic mathematics education. Educational Studies in Mathematics, 32(1), 1–28. https://doi.org/10.1023/A:1002900522457
Zhang, C., Wijaya, T. T., Zhou, Y., Chen, J., & Ning, Y. (2021). Ethnomathematics values in temple of Heaven: An imperial sacrificial altar in Beijing, China. Journal of Physics: Conference Series, 2084(1), 012015. https://doi.org/10.1088/1742-6596/2084/1/012015
Zulkardi. (1999). How to design mathematics lessons based on the realistic approach? www.reocities.com/ratuilma/rme.html
Zulkardi. (2002). Developing a learning environment on realistic mathematics education for Indonesian student teachers [Ph.D. Thesis, University of Twente].
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish with the Jurnal Elemen agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under Creative Commons Attribution-ShareAlike 4.0 International License (CC BY-SA 4.0).
- Authors are able to enter into separate, additional contractual arrangements for the distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
Jurnal Elemen is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License
