THE I-CON MODEL IN CONSTRUCTING MATHEMATICAL PROOF

Abdul Mujib, Firmansyah Firmansyah, Siti Shara Siagian, Devi Mathelinea

Abstract


Purpose-This research aims to analyze the role of the I-CON model in constructing mathematical proofs.

Methodology-The research used is qualitative with a grounded theory approach. Respondents were selected using a theoretical sampling approach, based explicitly on concepts that have been shown to relate to the theory being developed. Analysis data is obtained based on student test results, which are given to respondents, compiled into a new concept or theme, and then the desired subcategory.

Findings- The theory derived from this research is that, through the I-CON model, students can construct robust, precise, and valid mathematical proofs. The implementation of the I-CON model in the ability to construct mathematical proofs is (1) students can link facts with properties to interpret existing problems, (2) students can sequence valid proof steps, (3) students can use premises, definitions, and theorems related to statements to build a proof, (4) students can use appropriate arguments in the proof process, (5) Students have a systematic flow of thinking so that the proof steps are consistent, and (6) Students can interpret symbols mathematical and use precise mathematical communication language, which is obtained through learning the ICON model. Through learning the I-CON model, students can have the ability to understand various concepts, theorems, and definitions. They can make conjectures from statements given by interpreting them in detail. Implementing the Interpretation-Construction Design (I-CON) model in constructing mathematical proof produces six categories: Initial steps of proof, Flow of Proof, Related concepts, Arguments, Interpretation, and Language of Proof.

Significance-The results emphasize the importance of students constructing interpretations of real-world problem situations, discussion activities in building interpretations, reflecting, analyzing, and concluding interpretations that students construct as the primary focus of learning activities

Keywords


Learning Model; ICON-Model; Mathematical Proof

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References


Alon, U., Zilberstein, M., Levy, O., & Yahav, E. (2019). code2vec : Learning Distributed Representations of Code. Proceedings of the ACM on Programming Languages, 3(January), ISSN 2475-1421. https://doi.org/https://doi.org/10.1145/3290353

Ball, D. L., & Bass, H. (2003). Making Mathematics Reasonable in School. In A Research Companion to Principles and Standards for School Mathematics (Issue January 2003, pp. 27–44).

Black, J. B., & Mcclintock, R. O. (1996). An Interpretation Construction Approach to Constructivist Design Interpretation Construction ( ICON ) Design Model. In Constructivist Learning Environments: Case Studies in Instructional Design (Issue October, pp. 1–6).

Bond, M. (2020). Facilitating student engagement through the flipped learning approach in K-12 : A systematic review. Computers & Education, 151(10), 103–819. https://doi.org/10.1016/j.compedu.2020.103819

Hanna, G. (2020). Mathematical Proof, Argumentation, and Reasoning. In S. Lerman (Ed.), Encyclopedia of Mathematics Education. Springer. https://doi.org/10.4324/9780203825495

Harel, G., & Larry, S. (2007). Toward Comprehensive Perspectives on the Learning and Teaching of Proof. In Second handbook of research on mathematics teaching and learning: a project of the National Council of Teachers of Mathematics (Vol. 6179, Issue 619, pp. 1–60).

Haryadi, J., Mujib, A., & Siagian, S. S. (2024). Analysis of Student Image Concepts in Constructing Proof and Mathematical Communication in terms of Gender. International Journal of Multidisciplinary and Current Educational Research (IJMCER), 6(4), 103–109.

Jones, M., & Alony, I. (2011). Guiding the Use of Grounded Theory in Doctoral Studies – An Example from the Australian Film Industry. International Journal of Doctoral Studies, 6(1), 94–114.

Kingsdorf, S., & Krawec, J. (2014). Error Analysis of Mathematical Word Problem Solving Across Students with and without Learning Disabilities. Learning Disabilities Research & Practice, 29(2), 66–74.

Kurniawan, A., Jumadi, Kuswanto, H., & Syar, N. I. (2024). The 21st Century Education : A Systematic Literature Review Of Transforming Learning Methods To Foster Critical Thinking Skills Through Augmented Reality. Jurnal Eduscience (JES), 11(3), 601–622.

Lin, F. L., Yang, K. L., & Chen, C. Y. (2004). The features and relationships of reasoning, proving and understanding proof in number patterns. International Journal of Science and Mathematics Education, 2(2), 227–256. https://doi.org/10.1007/s10763-004-3413-z

Manurung, A. S., & Pappachan, P. (2025). The role of discovery learning in efforts to develop students’ critical thinking abilities. Journal of Education and Learning, 19(1), 46–53. https://doi.org/10.11591/edulearn.v19i1.21788

Methkal, Y. (2022). Role, need and benefits of mathematics in the development of society. Journal for the Mathematics Education and Teaching Practices, 3(1), 23–29.

Mutianingsih, N., Hadi, S., Prayitno, L. L., Sugandi, E., & Maftuh, M. S. (2025). Eksplorasi Konstruksi Bukti Matematis Mahasiswa Menyelesaikan Soal Graf Euler : Perspektif Toulmin. Jurnal Wahana Pendidikan, 12(1), 41–52.

Nugraha, T. H., & Pujiastuti, H. (2019). Analisis Kemampuan Komunikasi Matematis Siswa Berdasarkan Perbedaan Gender. Edumatica, 09(1), 1–7.

Prabandari, R. S., Nurhasanah, F., & Siswanto, S. (2024). Analyzing Student Creative Thinking with Wallas Theory. International Journal of Mathematics and Mathematics Education, 2(2), 114–127. https://doi.org/10.56855/ijmme.v2i2.1056

Rohid, N., Suryaman, S., & Rusmawati, R. D. (2019). Students’ Mathematical Communication Skills (MCS) in Solving Mathematics Problems: A Case in Indonesian Context. Anatolian Journal of Education, 4(2), 19–30. https://doi.org/10.29333/aje.2019.423a

Selden, A. (2003). Validations of Proofs Considered as Texts : Can Undergraduates Tell Whether an Argument Proves a Theorem ? Journal for Research in Mathematics Education, 34(1), 4–36.

Siagian, S. S., Mujib, A., & Zahari, C. L. (2022). Analisis Tingkat Kecemasan Matematika dalam Pembentukan Konsep Image Siswa. Paradikma: Jurnal Pendidikan Matematika, 15(1), 8–13. https://doi.org/10.24114/paradikma.v15i1.34569

Sianturi, T. Y. (2021). Kemampuan Representasi Dan Pemecahan Masalah Matematis Siswa Ditinjau Dari Tingkat Kecemasan Matematika. Universitas Pendidikan Indonesia.

Stylianides, G. J., Stylianides, A. J., & Moutsios, A. (2024). Proof and proving in school and university mathematics education research : a systematic review. ZDM – Mathematics Education, 56(1), 47–59. https://doi.org/10.1007/s11858-023-01518-y

Stylianou, D. A., Blanton, M. L., & Rotou, O. (2015). Undergraduate Students ’ Understanding of Proof : Relationships Between Proof Conceptions , Beliefs , and Classroom Experiences with Learning Proof. International Journal of Research in Undergraduate Mathematics Education, 1(1), 91–134. https://doi.org/10.1007/s40753-015-0003-0

Susanto, P. C., Yuntina, L., Saribanon, E., & Soehaditama, J. P. (2024). Qualitative Method Concepts : Literature Review , Focus Group Discussion , Ethnography and Grounded Theory. Siber Journal of Advanced Multidisiplinary (SJAM), 2(2), 262–275.

Suwanto, F. R., Tobondo, Y. V., & Riskiningtyas, L. (2017). Kemampuan Abstraksi dalam Pemodelan Matematika. Seminar Matematika Dan Pendidikan Matematika UNY, July, M–45.

Tsai, C. (2001). The interpretation construction design model for teaching science and its applications to Internet-based instruction in Taiwan. International Journal of Educational Development, 21(5), 401–415.

Ye, H., Liang, B., Ng, O. L., & Chai, C. S. (2023). Integration of computational thinking in K ‑ 12 mathematics education : a systematic review on CT ‑ based mathematics instruction and student learning. International Journal of STEM Education, 10(3), 1–26. https://doi.org/10.1186/s40594-023-00396-w

Zulkarnaen, R. (2018). Implementasi Interpretation-Construction Design Model Terhadap Kemampuan Siswa. KNPMP III, 24–32.




DOI: https://doi.org/10.36987/jes.v12i3.7240

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