Analisis Kesalahan Mahasiswa dalam Menyusun Flowchart Metode Posisi Palsu Berdasarkan Teori Rittle-Johnson dan Alibali

Khadijah; Usman Mulbar

doi:10.46918/equals.v8i2.3015

Authors

Khadijah Universitas Negeri Makassar https://orcid.org/0000-0003-4376-7511
Usman Mulbar Universitas Negeri Makassar

DOI:

https://doi.org/10.46918/equals.v8i2.3015

Keywords:

Error analysis, Conceptual knowledge, Procedural knowledge, Flowchart

Abstract

This study aims to describe students’ errors in implementing the False Position Method algorithm using the PHP programming language through the Computational Thinking–Error Analysis Framework (CT–EAF) approach. A descriptive qualitative design was employed by analyzing students’ final projects consisting of algorithm documentation and executable code. The analysis involved data reduction, error classification, and interpretation based on computational thinking dimensions and mathematical error categories. The findings indicate that students encountered various difficulties in translating mathematical concepts into computational structures and in evaluating the accuracy of iterative results. Most errors were related to challenges in abstracting the mathematical formula of the False Position Method into program logic, as well as limited reflection and debugging of computational outcomes. Errors in abstraction mainly involved incorrect operators, parentheses, or formula translation of the False Position Method, while evaluation errors were related to the omission of numerical convergence criteria ∣f(c)∣<ε or|Δc|<ε. The integration of CT–EAF provided a comprehensive perspective on the relationship between students’ algorithmic thinking processes and the types of conceptual and procedural errors they made. This study highlights the importance of strengthening computational thinking and algorithmic literacy in numerical methods learning. The CT–EAF approach serves as an effective framework for guiding students to connect mathematical concepts with computational logic, fostering a learning process that emphasizes both conceptual understanding and algorithmic reasoning rather than mere computational outcomes.

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References

Araujo, A. L., Oliveira, E. A., & Ramos, R. (2022). Integrating computational thinking into numerical methods: Effects on engineering students’ learning. Computer Applications in Engineering Education, 30(3), 875–890. https://doi.org/10.1002/cae.22562

Atkinson, K. E., & Han, W. (2009). Elementary Numerical Analysis: A Unified Approach (3rd ed.). John Wiley & Sons.

Burden, R. L., Faires, J. D., & Burden, A. M. (2016). Numerical Analysis (10th ed.). Cengage Learning.

Chapra, S. C., & Canale, R. P. (2015). Numerical Methods for Engineers (7th ed.). McGraw-Hill Education.

Cohen, L., Manion, L., & Morrison, K. (2018). Research Methods in Education (8th ed.). Routledge.

Creswell, J. W., & Poth, C. N. (2018). Qualitative Inquiry and Research Design: Choosing among Five Approaches (4th ed.). SAGE Publications.

Dorner, C., Lichtenberger, T., & Fritzlar, T. (2025). Revealing the nature of mathematical procedural knowledge: The role of explicit error correction. International Journal of Mathematical Education in Science and Technology. https://doi.org/10.1080/0020739X.2024.2445666

Fitriyani, F., Suriyah, S., & Rochmah, L. (2023). Developing computational thinking through algorithmic problem-solving in numerical methods learning. International Journal of Emerging Technologies in Learning (IJET), 18(3), 120–134. https://doi.org/10.3991/ijet.v18i03.39205

Hurrell, D. (2021). Conceptual and procedural knowledge in mathematics: The role of teachers. Australian Journal of Teacher Education, 46(1), 34–50. https://doi.org/10.14221/ajte.2021v46n1.3

Mardapi, D. (2017). Pengukuran, Penilaian, dan Evaluasi Pendidikan. Parama Publishing.

Mhlolo, M. K. (2018). Students’ mathematical errors and misconceptions in higher education: A systematic review. Journal of Education and Practice, 9(32), 15–22.

Miles, M. B., Huberman, A. M., & Saldaña, J. (2014). Qualitative Data Analysis: A Methods Sourcebook (3rd ed.). SAGE Publications.

Nurafni, R., & Suyitno, A. (2022). Profil kemampuan algoritmik mahasiswa pada pembelajaran metode numerik berbasis pemrograman. Jurnal Riset Pendidikan Matematika, 9(2), 132–145.

Rittle-Johnson, B., & Alibali, M. W. (1999). Conceptual and procedural knowledge of mathematics: Does one lead to the other? Journal of Educational Psychology, 91(1), 175–189. https://doi.org/10.1037/0022-0663.91.1.175

Rittle-Johnson, B., & Schneider, M. (2015). Developing conceptual and procedural knowledge of mathematics. In R. Cohen Kadosh & A. Dowker (Eds.), Oxford Handbook of Numerical Cognition (pp. 1102–1118). Oxford University Press. https://doi.org/10.1093/oxfordhb/9780199642342.013.014

Rittle-Johnson, B., Siegler, R. S., & Alibali, M. W. (2001). Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of Educational Psychology, 93(2), 346–362. https://doi.org/10.1037/0022-0663.93.2.346

Shute, V. J., Sun, C., & Asbell-Clarke, J. (2017). Demystifying Computational Thinking. Educational Research Review, 22, 74–100.

Sutamrin, S., & Khadijah, K. (2021). Analisis Kemampuan Berpikir Kritis dalam Project Based Learning Aljabar Elementer. EQUALS: Jurnal Ilmiah Pendidikan Matematika, 4(1), 28–41. https://doi.org/10.46918/equals.v4i1.892

Weintrop, D., Beheshti, E., Horn, & Al, M. et. (2016). Defining computational thinking for mathematics and science. Journal of Science Education and Technology, 25, 127–147. https://link.springer.com/article/10.1007/s10956-015-9581-5?utm_source=chatgpt.com#citeas

Weintrop, D., Beheshti, E., Horn, M., Orton, K., Jona, K., Trouille, L., & Wilensky, U. (2016). Defining Computational Thinking for Mathematics and Science Classrooms. Journal of Science Education and Technology, 25(1), 127–147.

Wing, J. M. (2006). Computational Thinking. Communications of the ACM, 49(3), 33–35.