Pengetahuan Didaktika Calon Guru Sekolah Dasar tentang Pecahan Ditinjau dari Teori Antropologi Didaktik
DOI:
https://doi.org/10.29408/jel.v6i2.2056Keywords:
fractions, mathematical knowledge, didactical knowledge, anthropological theory of the didacticAbstract
Prospective elementary teachers (PET) are required to have sufficient mathematical and didactic knowledge about fractions, but many of them have difficulties explaining various concepts of fractions to students. Given the importance of prospective teachers’ knowledge of fractions, this study aims to investigate further the didactic knowledge of PETs’ didactic knowledge of fractions. Their knowledge is seen from their ability to construct contextual tasks about fractions based on number sense, problem-solving, mathematical literacy, and problem posing. PETs’ didactical knowledge is analyzed based on the anthropological theory of the didactic. This research method is qualitative with an internet-based research approach. The subjects of this study consist of 38 PsETs from a teacher education institution in Pekanbaru, Riau, Indonesia. The results of this study indicate that PsETs’ didactic knowledge of fractions is inappropriate, especially in the aspect of constructing contextual tasks about the division of fractions by fractions. PsETs tend to present the type of task associated with simple fraction operations and techniques in the form of standard algorithms. This study also indicates that PsETs’ theoretical knowledge is still limited to informal knowledge to support standard algorithms.
References
Alenazi, A. (2017). Examining middle school pre-service teachers’ knowledge of fraction division interpretations. International Journal of Mathematics Education in Science and Technology, 47(5), 696–716. https://doi.org/10.1080/0020739X.2015.1083127.
Austin, P., Carbone, R. E., & Webb, P. (2011). Prospective primary school teachers’ attempts to pose acceptable word problems on the addition of fractions: Some insights from south africa and the united states of america. African Journal of Research in Mathematics, Science and Technology Education, 15(2), 168–178. https://doi.org/10.1080/10288457.2011.10740710.
Bosch, M., & Gascón, J. (2006). Twenty-five years of the didactic transposition. ICMI Bulletin, 58, 51–65.
Brousseau, G. (2002). Theory of didactical situation. New York: Kluwer Academic Publisher.
Castro-RodrÃguez, E., Pitta-Pantazi, D., Rico, L., & Gómez, P. (2016). Prospective teachers’ understanding of the multiplicative part-whole relationship of fraction. Educational Studies in Mathematics, 92(1), 129–146. https://doi.org/10.1007/s10649-015-9673-4.
Charalambous, C. Y., & Pitta-Pantazi, D. (2007). Drawing on a theoretical model to study students’ understandings of fractions. Educational Studies in Mathematics, 64(3), 293–316. https://doi.org/10.1007/s10649-006-9036-2.
Chevallard, Y. (2006). Steps towards a new epistemology in mathematics education. In M. Bosch (Ed.), Proceedings of the IV Congress of the European Society for Research in Mathematics Education (pp. 21–30). Grenoble: La Pensée Sauvage.
Cohan, L., Manion, L., & Morrison, K. (2007). Research methods in education (Sixth Edit). London: Routledge. https://doi.org/10.4324/9780203029053.
Depaepe, F., Torbeyns, J., Vermeersch, N., Janssens, D., Janssen, R., Kelchtermans, G., … Van Dooren, W. (2015). Teachers’ content and pedagogical content knowledge on rational numbers: A comparison of prospective elementary and lower secondary school teachers. Teaching and Teacher Education, 47, 82–92. https://doi.org/10.1016/j.tate.2014.12.009.
Dixon, J. K., Andreasen, J. B., Avila, C. L., Bawatneh, Z., Deichert, D. L., Howse, T. D., & Turner, M. S. (2014). Redefining the whole: common errors in elementary preservice teachers’ self-authored word problems for fraction subtraction. Investigations in Mathematics Learning, 7(1), 1–22. https://doi.org/10.1080/24727466.2014.11790336.
Durmus, S. (2005). Identifying pre-service elementary school teachers’ conceptualization levels of rational numbers. Educational Sciences: Theory & Practice, 5(2), 659–666.
Durrand-Guerrier, V., Winsløw, C., & Yoshida, H. (2010). A model of mathematics teacher knowledge and a comparative study in Denmark, France and Japan. ANNALES de DIDACTIQUE et de SCIENCES COGNITIVES, 15, 147–172.
Freudenthal, H. (1991). Revisiting mathematics education: China lecturers. Dordrecht: Kluwer Academic Publishers.
Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371–406. https://doi.org/10.3102/00028312042002371.
Johar, R., Patahuddin, S. M., & Widjaja, W. (2017). Linking pre-service teachers’ questioning and students’ strategies in solving contextual problems: A case study in Indonesia and the Netherlands. The Mathematics Enthusiast, 14(1–3), 101–128. https://doi.org/10.1242/dmm.009688.
Liu, C., Xin, Z., & Li, X. (2011). The development of chinese students’ understanding of the concept of fractions from fifth to eighth grade. Journal of Mathematics Education, 4(2), 17–34. Retrieved from http://educationforatoz.com/images/Liu_Xin_Li.pdf
Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ.: Lawrence Erlbaum Associates.
Newton, K. J. (2008). An extensive analysis of preservice elementary teachers’ knowledge of fractions. American Educational Research Journal, 45(4), 1080–1110. https://doi.org/10.3102/0002831208320851.
Putra, Z. H. (2016). Pengetahuan mahasiswa pedidikan guru sekolah dasar dalam merepresentasikan operasi pecahan dengan model persegi panjang. Jurnal Elemen, 2(1), 1–13. https://doi.org/10.29408/jel.v2i1.174.
Putra, Z. H. (2018). A praxeological analysis of pre-service elementary teachers’ knowledge of rational numbers. Recherches En Didactique Des Mathematiques, 38(3), 315–364.
Putra, Z. H. (2019a). Elementary teachers’ knowledge on fraction multiplication: An anthropological theory of the didactic approach. Journal of Teaching and Learning in Elementary Education, 2(1), 47–52. https://doi.org/10.33578/jtlee.v2i1.6964.
Putra, Z. H. (2019b). Praxeological change and the density of rational numbers: The case of pre-service teachers in Denmark and Indonesia. Eurasia Journal of Mathematics, Science and Technology Education, 15(5). https://doi.org/10.29333/ejmste/105867.
Rasmussen, K. (2016). Lesson study in prospective mathematics teacher education: didactic and paradidactic technology in the post-lesson reflection. Journal of Mathematics Teacher Education, 19(4), 301–324. https://doi.org/10.1007/s10857-015-9299-6.
Siegler, R. S., & Lortie-Forgues, H. (2017). Hard lessons: Why rational number arithmetic is so difficult for so many people. Current Directions in Psychological Science, 26(4), 346–351. https://doi.org/10.1177/0963721417700129.
Thanheiser, E., Moss, M., Browning, C. A., Garza-kling, G., & Watanabe, T. (2010). Developing mathematical content knowledge for teaching elementary school mathematics. IUMPST: The Journal, 1, 1–13.
Toluk-Uçar, Z. (2009). Developing pre-service teachers understanding of fractions through problem posing. Teaching and Teacher Education, 25(1), 166–175. https://doi.org/10.1016/j.tate.2008.08.003.
Van Dooren, W., Lehtinen, E., & Verschaffel, L. (2015). Unraveling the gap between natural and rational numbers. Learning and Instruction, 37, 1–4. https://doi.org/10.1016/j.learninstruc.2015.01.001.
van Steenbrugge, H., Lesage, E., Valcke, M., & Desoete, A. (2014). Preservice elementary school teachers’ knowledge of fractions: A mirror of students’ knowledge? Journal of Curriculum Studies, 46(1), 138–161. https://doi.org/10.1080/00220272.2013.839003.
Widjaja, W., Stacey, K., & Steinle, V. (2008). Misconceptions about density of decimals: Insights from Indonesian pre-service teachers’ work. Journal for Science and Mathematics Education in Southeast Asia, 31(2), 117–131.
Wijayanti, D., & Winsløw, C. (2017). Mathematical practice in textbooks analysis: Praxeological reference models, the case of proportion. Journal of Research in Mathematics Education, 6(3), 307–330. https://doi.org/10.17583/redimat.2017.2078.
Winsløw, C., & Durand-Guerrier, V. (2007). Education of lower secondary mathematics teachers in Denmark and France. Nordic Studies in Mathematics Education, 12(2), 5–32.
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