Jurnal Riset Pendidikan Matematika
Keywords
Creative thinking, mathematical induction, procedural fluency
Document Type
Article
Abstract
Creativity in performing mathematics proof was assumed to be directed by the procedural fluency. This article examines the procedural fluency in proof based on the students' creative thinking level of mathematics. Subjects were selected pusposively to join the test and interview as the main instruments. Of the 36 students who took the test, 5 students were selected appropriate at each level of creative thinking skills to be followed with interviews.. The data were analyzed following data condensation, data presentation, and conclusion withdrawal as suggested by Miles, Huberman, and Saldana (2014). The results showed that very creative, creative, and quite creative students could demonstrate procedural fluency because they could use mathematical induction proof procedures correctly and modify the procedure in the correct rules although less creative students lacked completeness in performing mathematical induction proof procedures. Students of the lower creativity groups had less procedural fluency because they were unlikely to understand the use of mathematical induction proof procedures and found difficulties to apply mathematical induction proof procedures properly or even no attempt was made to modify procedures to solve problems.
Page Range
22-35
Issue
1
Volume
9
Digital Object Identifier (DOI)
10.21831/jrpm.v9i1.43987
Source
https://journal.uny.ac.id/index.php/jrpm/article/view/43987
Recommended Citation
Annurwanda, P., & Friantini, R. N. (2022). Mathematical induction proofing: Procedural fluency reviewed from the creative thinking level of mathematics students. Jurnal Riset Pendidikan Matematika, 9(1), 22-35. https://doi.org/10.21831/jrpm.v9i1.43987
References
Ashkenazi, Y., & Itzkovitch, E. (2014). Proof by Mathematical Induction. International Journal of Innovation and Research in Education, 1(3), 186–190. https://doi.org/10.1201/9781003082927-4
Bagay, M. C., Eugenio, W. A., Soriano, M. V. C., & Bautista, R. G. (2021). Project MC 2 : Raising Students ’ Procedural Fluency along Concepts of Forces and Motion. Journal of Innovations in Teaching and Learning, 1(July), 1–5. https://doi.org/10.12691/jitl-1-2-10
Bautista, R. G. (2013). The students’ procedural fluency and written-mathematical explanation on constructed response tasks in physics. Journal of Technology and Science Education, 3(1), 49–56.
Cartwright, K. (2018). Exploring mathematical fluency: teachers’ conceptions and descriptions of students. Making Waves, Opening Spaces (Proceedings of the 41st Annual Conference of the Mathematics Education Group of Australasia), 202–209.
Dogan, H. (2016). Mathematical Induction : Deductive Logic Perspective. European Journal of Science and Mathematics Education, 4(3), 315–330. https://doi.org/https://doi.org/10.30935/scimath/9473
Friantini, R. N. (2014). Proses Berpikir Mahasiswa Pendidikan Matematika dalam Pemecahan Masalah Pembuktian. Universitas Sebelas Maret.
Graven, M., & Stott, D. (2012). Conceptualising Procedural Fluency as A Spectrum of Proficiency. Proceedings of 18th Annual National Congress of the Association for Mathematical Education of South Africa (AMESA), June, 146–156.
Imamoglu, Y., & Yontar Togrol, A. (2010). Freshmen and Senior Teaching Science and Mathematics Students’ Proving Patterns and Conceptualizations of the Nature and Role of Proof in School Mathematics. International Journal for Cross-Disciplinary Subjects in Education, 1(2), 79–87. https://doi.org/10.20533/ijcdse.2042.6364.2010.0011
Inayah, S., Septian, A., & Fazrianto, R. (2020). Student Procedural Fluency in Numerical Method Subjects. Desimal: Jurnal Matematika, 3(1), 53–64. https://doi.org/10.24042/djm
Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding It Up: Helping Children Learn Mathematics. In D. of B. and S. S. and Education. Mathematics Learning Study Committee, Center for Education (Ed.), National Research Council. National Academy Press.
Kusuma Dewi, I. L., Waluya, S. B., Rachmad, & Firmasari, S. (2020). Adaptive Reasoning and Procedural Fluency in Three-Dimensional. Journal of Physics: Conference Series, 1511(1), 1–7. https://doi.org/10.1088/1742-6596/1511/1/012101
Kusuma, I. A., & Retnowati, E. (2021). Designs of Faded-Example to Increase Problem Solving Skills and Procedural Fluency in Algebraic Division. Journal of Physics: Conference Series, 1806(1), 1–7. https://doi.org/10.1088/1742-6596/1806/1/012109
Lince, R. (2016). Creative Thinking Ability to Increase Student Mathematical of Junior High School by Applying Models Numbered Heads Together. Journal of Education and Practice, 7(6), 206–212.
Maharani, H. R. (2014). CREATIVE THINKING IN MATHEMATICS : ARE WE ABLE TO SOLVE MATHEMATICAL PROBLEMS IN A VARIETY OF WAY. International
Conference on Mathematics, Science, and Education 2014, 2014(Icmse), 120–125.
Moleong, L. J. (2018). Metodologi Penelitian Kualitatif (Cetakan ke).
NCTM. (2014). Procedural fluency in mathematics. National Council of Teachers of Mathematics.
Sirmaci, N. (2012). Knowledge level of undergraduate students of mathematics teaching on proof methods. Global Advance Research Journals, 1(6), 118–123.
Siswono, T. Y. E. (2011). Level of Student’s Creative Thinking in Classroom Mathematics.
Educational Research and Reviews, 6(7), 548–553.
Sugiyono. (2010). Metode Penelitian Pendidikan: Pendekatan Kuantitatif, Kualitatif, dan R&D. Alfa Beta.
Švecová, V., Rumanová, L., & Pavlovičová, G. (2014). Support of Pupil’s Creative Thinking in Mathematical Education. Procedia - Social and Behavioral Sciences, 116, 1715–1719. https://doi.org/10.1016/j.sbspro.2014.01.461
Utomo, D. P., & Huda, M. (2020). Pemahaman Relasional Analisis Proses Pembuktian Menggunakan Induksi Matematika (Bildung).
Winata, R., Friantini, R. N., Annurwanda, P., Annur, M. F., & Permata, J. I. (2020). The arguments of mathematics education students to solve proof problems. AIP Conference Proceedings, 2268(September). https://doi.org/10.1063/5.0026049
Wladis, C. (2019). The complex relationship between conceptual understanding and procedural fluency in developmental algebra in college. Proceedings of the Forty-First Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education.
Yayuk, E., Purwanto, As’Ari, A. R., & Subanji. (2020). Primary school students’ creative thinking skills in mathematics problem solving. European Journal of Educational Research, 9(3), 1281–1295. https://doi.org/10.12973/eu-jer.9.3.1281
Zakaria, E., & Zaini, N. (2009). Conceptual and Procedural Knowledge of Rational Numbers in Trainee Teachers. European Journal of Social Sciences, 9(2), 202–217.