Analisis Pengetahuan Konseptual dan Prosedural Mahasiswa Calon Guru Sekolah Dasar Pada Bilangan Rasional

Authors

  • Rita Novita Universitas Pendidikan Indonesia-UPI Universitas Bina Bangsa Getsempena-UBBG PUI-PT PUSBANGDDRINDO, Bandung, Indonesia, Indonesia
  • Tatang Herman Universitas Pendidikan Indonesia, Indonesia
  • Didi Suryadi Universitas Pendidikan Indonesia PUI-PT PUSBANGDDRINDO, Bandung, Indonesia, Indonesia
  • Dadan Dasari Universitas Pendidikan Indonesia, Indonesia
  • Mulia Putra Universitas Bina Bangsa Getsempena, Indonesia
  • Rahmat Fitra Universitas Bina Bangsa Getsempena, Indonesia

DOI:

https://doi.org/10.33603/jnpm.v6i2.7056

Abstract

Penelitian ini bertujuan untuk mendeskripsikan pemahaman bilangan rasional mahasiswa calon guru sekolah dasar yang berkaitan dengan pengetahuan procedural dan konseptual. Metode kualitatif deskriptif digunakan dalam penelitian ini untuk mencapai tujuan yang telah ditetapkan. Penelitian ini melibatkan 102 mahasiswa pendidikan guru sekolah dasar tahun kedua pada dua perguruan tinggi swasta di Aceh, Indonesia. Pengumpulan data dilakukan dengan menggunakna tes tertulis yang berkaitan dengan bilangan rasional. Analisis data dilakukan secara deskripstif dengan cara mereduksi data, menyajikan data, dan menarik kesimpulan. Hasil penelitian menunjukkan bahwa pengetahuan mahasiswa calon guru sekolah dasar baik pengetahuan procedural dan konseptual pada bilangan rasional masih sangat terbatas. Secara kategorisasi, pengetahuan procedural mahasiswa tergolong dalam level moderate (70,05%) sedangkan pengetahuan konseptual (50,36%) masih berada pada level rendah. Berbagai bentuk miskonsepsi dan kesulitan (epistemological obstacles) masih dialami oleh mahasiswa dalam menyelesaikan masalah terkait dengan kedua pengetahuan ini. Interpretasi bilangan rasional dalam representasi pecahan dan decimal perlu menjadi focus dalam ruang kuliah matematika pada program Pendidikan guru sekolah dasar. Selain itu, penelitian ini juga mendukung penguatan pengetahuan konseptual melebihi pengetahuan procedural ditekankan pada mahasiswa calon guru sekolah dasar.

Author Biographies

Rita Novita, Universitas Pendidikan Indonesia-UPI Universitas Bina Bangsa Getsempena-UBBG PUI-PT PUSBANGDDRINDO, Bandung, Indonesia

Associate Professor of Mathematics Education Program in Universitas Bina Bangsa Getsempena

Tatang Herman, Universitas Pendidikan Indonesia

Full Professor of Mathematics Education Program in Universitas Pendidikan Indonesia

Didi Suryadi, Universitas Pendidikan Indonesia PUI-PT PUSBANGDDRINDO, Bandung, Indonesia

Full Professor of Mathematics Education Program in Universitas Pendidikan Indonesia

Dadan Dasari, Universitas Pendidikan Indonesia

Associate Professor of Mathematics Education Program in Universitas Pendidikan Indonesia

Mulia Putra, Universitas Bina Bangsa Getsempena

Assistant Professor of Mathematics Education Program in Universitas Bina Bangsa Getsempena

Rahmat Fitra, Universitas Bina Bangsa Getsempena

Assistant Professor of Mathematics Education Program in Universitas Bina Bangsa Getsempena

References

Anderson, L. W., Krathwohl, D. R., Airasian, P. W., Cruikshank, K. A., Mayer, R. E., Pintrich, P. R., Tathas, J., & Wittrock, M. C. (2011). A taxonomy for learning, teaching, and assessing: A revision of Bloom’s taxonomy of educational objectives. Addison Wesley Longman, Inc.

Adeniyi, C. ., Ogundele, L. ., & Odetola, C. . (2014). Teacher Quality Factors as Determinant of Students ’ Achievement in Mathematics. Jounal of Education and Practice, 5(37), 1–6.

Ayebale, L., Habaasa, G., & Tweheyo, S. (2020). Factors affecting students’ achievement in mathematics in secondary schools in developing countries: A rapid systematic. Statistical Journal of the IAOS, 36(S1), S73–S76. https://doi.org/10.3233/sji-200713

Baker, W., Czarnocha, B., Dias, O., Doyle, K., & Kennis, J. R. (2012). Procedural and conceptual knowledge: Adults reviewing fractions. ALM International Journal, 7(2), 39–65. https://bit.ly/37kgjnI

Baroody, A. J., Feil, Y., & Johnson, A. R. (2007). An alternative reconceptualization of procedural and conceptual knowledge. Journal for Research in Mathematics Education, 38(2), 115–131. https://doi.org/10.2307/30034952

Brousseau, G. (2002). Theory of Didactical Situations in Mathematics (N. Balacheff, M. Cooper, Warfield, R. Sutherland, & Virginia (eds.)). Kluwer Academic Publishers.

Creswell, J. W., & Poth, C. N. (2017). Qualitative inquiry and research design: choosing among five approaches (4th ed.). SAGE Publications Inc.

Forgues, H. L., Tian, J., & Siegler, R. (2015). Why is learning fraction and decimal arithmetic so difficult? Developmental Review, 38(1), 201–221. https://doi.org/10.1016/j.dr.2015.07.008

Fraenkel, J. R., Wallen, N. E., & Hyun, H. H. (2012). How to design and evaluate research in education. McGraw-Hill.

Freudenthal, H. (2002). Didactical phenomenology of mathematical structures. Kluwer Academic Publishers.

Fuentes, S. Q., Bloom, M. A., & Peace, H. (2014). Teaching Science and Mathematics: Preservice Teachers’ Perceptions of Knowledge Needs. Journal of College Science Teaching, 43(3), 30–35. https://doi.org/DOI:10.2505/4/jcst14_043_03_30

Ghazali, N. H. C., & Zakaria, E. (2011). Students ’ procedural and conceptual understanding of mathematics. Australian Journal of Basic and Applied Sciences, 5(7), 684–691. https://bit.ly/35jzA8e

Hiebert, J. (1986). Conceptual and procedural knowledge: The case of mathematics. Lawrence Erlbaum Associates, Inc.

Hill, H. C., Rowan, B., & Ball, D. L. (2005). for Teaching on Student Achievement. 42(2), 371–406.

Hurrell, D. (2021). Conceptual knowledge or procedural knowledge or conceptual knowledge and procedural knowledge: Why the conjunction is important to teachers. Australian Journal of Teacher Education, 46(2), 57–71. https://doi.org/10.14221/ajte.2021v46n2.4

Indonesia Ministry of National Education. (2007). Standar kualifikasi akademik dan kompetensi guru [Standards of academic qualification and teacher competence]. BSNP. https://bit.ly/3oubpKt

Indonesia Ministry of National Education and Culture. (2016). Kompetensi inti dan kompetensi dasar pelajaran pada kurikulum 2013 pada pendidikan dasar dan menengah [Core and basic competencies of lessons in the 2013 curriculum for elementary and secondary level]. Kemendikbud. https://bit.ly/333V1cg

Khashan, D. K. H. (2014). Conceptual and Procedural Knowledge of Rational Numbers for Riyadh Elementary School Teachers. Journal of Education and Human Development, 3(4), 181–197. https://doi.org/10.15640/jehd.v3n4a17

Kilpatrick, J. (2001). Understanding Mathematical Literacy : The Contribution of Research Source Springer. Educational Studies in Mathematics, 47(1), 101–116.

Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics (M. L. S. Committee (ed.)). National Research Council. https://bit.ly/3KRAQ1q

Lawshe, C. H. (1975). A quantitative approach to content validityâ€.Personnel Psychology. Personnel Psychology, 28, 563–575. https://doi.org/10.1111/j.1744-6570.1975.tb01393.x

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. https://doi.org/10.29333/iejme/646

Mahir, N. (2009). Conceptual and procedural performance of undergraduate students in integration. International Journal of Mathematical Education in Science and Technology, 40(2), 201–211. https://doi.org/10.1080/00207390802213591

Manandhar, N. K., Pant, B. P., & Dawadi, S. D. (2022). Conceptual and procedural knowledge of students of nepal in algebra: A mixed method study. Contemporary Mathematics and Science Education, 3(1), ep22005. https://doi.org/10.30935/conmaths/11723

Musser, G. L., Burger, W. F., & Peterson, B. E. (2011). Mathematics for elementary teachers: A contemporary approach (9th ed.). John Wiley & Sons, Inc.

National Council of Teachers of Mathematics. (2014). Principles to action:ensuring mathematical succes for all. NCTM.

National Council of Teachers of Mathematics. (2015). NCTM CAEP mathematics content for elementary mathematics specialist addendum to the NCTM CAEP standards 2012 (Issue 2012). https://bit.ly/3snggye

Novita, R., Herman, T., Suryadi, D., Dasari, D., & Putra, M. (2022). How Pre-Service Elementary Teachers Deal with Mathematical Literacy Problems? A Case Study. Advances in Social Science, Education and Humanities Research, 627, 135–143. https://doi.org/10.2991/ASSEHR.K.211229.022

Obersteiner, A., Reiss, K., Dooren, W. van, & Hoof, J. van. (2019). Understanding rational numbers – Obstacles for learners with and without mathematical learning difficulties. In A. Fritz, V. Geraldi, & P. Rasanen (Eds.), International handbook of mathematical learning difficulties (pp. 581–594). Springer. https://doi.org/10.1007/978-3-319-97148-3_34

Pitta-Pantazi, D. (2014). Number teaching and learning. In S. Lerman, E. B. Sriraman, Y. Jablonka, M. Shimizu, R. Artigue, R. Even, Jorgensen, & M. Graven (Eds.), Encyclopedia of mathematics education (pp. 470–476). Springer. https://doi.org/10.1007/978-94-007-4978-8

Radiusman, R., & Simanjuntak, M. (2021). Analisis Kesalahan Mahasiswa Calon Guru Sekolah Dasar dalam Menyelesaikan Soal Pembuktian Aljabar. JNPM (Jurnal Nasional Pendidikan Matematika), 5(1), 149. https://doi.org/10.33603/jnpm.v5i1.4336

Rahmadani, Nurlaelah, E., Herman, T., & Anaguna, N. (2019). Exploration of Primary School Teacher Students’ Understanding in Fraction Concept. Journal of Physics: Conference Series, 1211(1). https://doi.org/10.1088/1742-6596/1211/1/012060

Rittle-Johnson, B., Fyfe, E. R., & Loehr, A. M. (2016). Improving conceptual and procedural knowledge: The impact of instructional content within a mathematics lesson. British Journal of Educational Psychology, 86(4), 576–591. https://doi.org/10.1111/bjep.12124

Rittle-johnson, B., & Schneider, M. (2015). Developing conceptual and procedural knowledge of mathematics. In R. C. Kadosh & A. Dowker (Eds.), The Oxford Handbook of Numerical Cognition (pp. 1118–1134). Oxford University Press. https://doi.org/10.1093/oxfordhb/9780199642342.013.014

Rittle-Johnson, B., Schneider, M., & Star, J. R. (2015). Not a one-way street: Bidirectional relations between procedural and conceptual knowledge of mathematics. Educational Psychology Review, 27(4), 587–597. https://doi.org/10.1007/s10648-015-9302-x

Rittle-Johnson, B., & Siegler, R. S. (1998). The relation between conceptual and procedural knowledge in learning mathematics: A review. In C. Donlan (Ed.), The Development of Mathematical Skills (pp. 75–110). Psycology Press. https://doi.org/10.4324/9781315784755-6

Schoenfeld, A. H. (2002). Making Mathematics Work for All Children: Issues of Standards, Testing, and Equity. Educational Researcher, 31(1), 13–25. https://doi.org/10.3102/0013189X031001013

Shulman, L. (1987). Knowledge and Teaching:Foundations of the New Reform. Harvard Educational Review, 57(1), 1–23. https://doi.org/10.17763/haer.57.1.j463w79r56455411

Shulman, L. S. (1986). Those Who Understand: Knowledge Growth in Teaching. Educational Researcher, 15(2), 4–14.

Siegler, R. (2017). Build It and They Will Come. In D. C. Geary, D. B. Berch, R. J. Ochsendorf, & K. M. Koepke (Eds.), Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts. Elsevier Inc. https://doi.org/10.1016/B978-0-12-805086-6/00019-9

Siegler, R., & Pyke, A. A. (2013). Developmental and individual differences in understanding of fractions. Developmental Psychology, 49(10), 1994–2004. https://doi.org/10.1037/a0031200

Suryadi, D. (2019). Landasan Filosofis Penelitian Desain Didaktis (DDR) (Tim Gapura Press (ed.)). Gapura Press.

Tirosh, D., Tsamir, P., & Hershkovitz, S. (2013). Insights into children’s intuitions of addition, subtraction, multiplication and division. In A. Cockburn & G. Littler (Eds.), Mathematical Misconceptions: A Guide for Primary Teachers (pp. 54–70). SAGE Publications Ltd. https://doi.org/10.4135/9781446269121.n5

Vygotsky, L. (1986). Thought and language (2nd ed.). MA: MIT Press.

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. http://dro.deakin.edu.au/view/DU:30048398

Wijaya, A. (2017). The relationships between Indonesian fourth graders’ difficulties in fractions and the opportunity to learn fractions: A snapshot of TIMSS results. International Journal of Instruction, 10(4), 221–236. https://doi.org/10.12973/iji.2017.10413a

Downloads

Published

2022-06-30

Issue

Vol. 6 No. 2 (2022)

Section

Artikel

Citation Check

License

Penulis yang menerbitkan karyanya ke jurnal ini setuju dengan persyaratan berikut:

Penulis menyerahkan hak cipta dan memberikan hak penerbitan pertama kepada jurnal, dengan karya yang secara serentak dilisensikan di bawah Lisensi: Creative Commons Attribution - Share Alike 4.0 Internasional License yang memungkinkan orang lain membagikan karya dengan pengakuan penerbitan awal dan kepenulisan karya di jurnal ini.