The Growth of Students' Function Limit Concepts Understanding in Solving Controversial Problems Based on Pirie Kieren's Theory

Susiswo Susiswo; Pradina Parameswari; Octavina Rizky Utami Putri; Harfin Lanya; Anita Dewi Utami; Tatik Retno Murniasih

doi:10.31764/jtam.v7i4.16835

The Growth of Students' Function Limit Concepts Understanding in Solving Controversial Problems Based on Pirie Kieren's Theory

Susiswo Susiswo, Pradina Parameswari, Octavina Rizky Utami Putri, Harfin Lanya, Anita Dewi Utami, Tatik Retno Murniasih

Abstract

Almost all students understand the limit of a function only up to an intuitive definition and have difficulty understanding the concept of a limit function formally. This study aims to describe the growth of student understanding of functions limit concept in solving controversial problems based on Pirie Kieren's theory. There were twelve Calculus class students in the short semester as participants. The students selected were those who had taken calculus courses. Students are given the task of solving controversial problems to understand the concept of limit functions. There was only one student who showed a growing understanding of the concept of the limit of a function and was interviewed for further exploration. This research is a qualitative descriptive research. Therefore, the researchers analyzed the results of students' work through data reduction, data presentation, and conclusion drawing. The result shows that through controversial problems, students' understanding grows to an inventising level. However, students did ‘fold back’ at the observing level. At this level, students look at or re-read their notebooks to recall previously owned concepts. For further research it is suggested that researchers can design a learning process that can help grow student understanding through controversial problems.

Keywords

The Growth; Understanding; Function Limit; Controversial Problem; Pirie Kieren Theory.

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References

Ahmadpour, F., Reid, D., & Reza Fadaee, M. (2019). Students’ Ways of Understanding a Proof. Mathematical Thinking and Learning, 21(2), 85–104. https://doi.org/10.1080/10986065.2019.1570833

Cohen, L., Manion, L., & Morrison, K. (2018). Research Methods in Education, Eighth Edition. Taylor & Francis Group.

Creswell, J. W., & Creswell, J. D. (2017). Research Design: Qualitative, Quantitative, and Mixed Methods Approaches. SAGE Publications.

Gokalp, N. D., & Bulut, S. (2018). A New Form of Understanding Maps: Multiple Representations with Pirie and Kieren Model of Understanding. International Journal of Innovation in Science and Mathematics Education, 26(6), 1–21.

Gulkilik, H., Moyer-Packenham, P. S., Ugurlu, H. H., & Yuruk, N. (2020). Characterizing the Growth of One Student’s Mathematical Understanding in a Multi-Representational Learning Environment. Journal of Mathematical Behavior, 58(December 2019), 100756. https://doi.org/10.1016/j.jmathb.2020.100756

Hiebert, J., & Carpenter, T. P. (1992). Learning and Teaching with Understanding. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 65–97). The National Council of Teachers of Mathematics, Inc. https://doi.org/10.5860/choice.30-2122

Martin, L. C., & Towers, J. (2016). Folding back, thickening and mathematical met-befores. Journal of Mathematical Behavior, 43, 89–97. https://doi.org/10.1016/j.jmathb.2016.07.002

Mueller, M., & Yankelewitz, D. (2014). Fallacious Argumentation in Student Reasoning: Are There Benefits? European Journal of Science and Mathematics Education, 2(1), 27–38. https://doi.org/10.30935/scimath/9398

Palha, S., Dekker, R., Gravemeijer, K., & van Hout-Wolters, B. (2013). Developing shift problems to foster geometrical proof and understanding. Journal of Mathematical Behavior, 32(2), 142–159. https://doi.org/10.1016/j.jmathb.2012.12.002

Patmaniar, Amin, S. M., & Sulaiman, R. (2021). Students’ Growing Understanding in Solving Mathematics Problems Based On Gender: Elaborating Folding Back. Journal on Mathematics Education, 12(3), 507–530. https://doi.org/10.22342/JME.12.3.14267.507-530

Pirie, S., & Kieren, T. (1994). Growth in Mathematical Understanding: How Can We Characterise It and How Can We Represent It? Educational Studies in Mathematics, 26(2–3), 165–190. https://doi.org/10.1007/BF01273662

Puspitasari, R. E., & Amir, M. F. (2020). A folding back analysis on elementary students ’ growth in mathematical understanding. 1(June), 1–16.

Putri, O. R. U., Susiswo, S., Hidayanto, E., & Slamet, S. (2023). Problem-solving : Growth of Students ’ Mathematical Understanding in Producing Original Solutions. 15(3).

Putri, R. A., & Susiswo. (2020). Analysis of layer of primitive knowing of high school students in linear function material: A study of application of student activity sheets based on Pirie Kieren theory. The 3rd International Conference on Mathematics and Sciences Education (ICoMSE) 2019, 2215. https://doi.org/10.1063/5.0000525

Rahayuningsih, S., Sa’dijah, C., Sukoriyanto, & Qohar, A. (2022). Exploring Students’ Understanding Layers in Solving Arithmagon Problems. Cakrawala Pendidikan, 41(1), 170–185. https://doi.org/10.21831/cp.v41i1.33837

Rosyadi, A. A. P., Sa’Dijah, C., Susiswo, & Rahardjo, S. (2022). High Order Thinking Skills: Can it Arise When a Prospective Teacher Solves a Controversial Mathematics Problem? Journal of Physics: Conference Series, 2157(1). https://doi.org/10.1088/1742-6596/2157/1/012038

Simic-Muller, K., Fernandes, A., & Felton-Koestler, M. D. (2015). “I Just Wouldn’t Want to Get as Deep Into It”: Preservice Teachers’ Beliefs about the Role of Controversial Topics in Mathematics Education. Journal of Urban Mathematics Education, 8(2), 53–86. https://doi.org/10.21423/jume-v8i2a259

Subanji, Rosyadi, A. A. P., & Emanuel, E. P. L. (2021). Levels of Controversial Reasoning of the Pre-Service Teachers To Solve Mathematical Problems. Journal of Southwest Jiaotong University, 56(4), 645–658. https://doi.org/10.35741/issn.0258-2724.56.4.55

Subanji, S., Nusantara, T., Sukoriyanto, S., & Atmaja, S. A. A. (2023). Student’s Creative Model in Solving Mathematics Controversial Problems. Jurnal Cakrawala Pendidikan, 42(2), 310–326. https://doi.org/10.21831/cp.v42i2.55979

Suryawan, I. P. P., Jana, P., Pujawan, I. G. N., Hartawan, I. G. N. Y., & Putri, P. E. W. (2023). Ethnomathematically Controversial Problem-Based Multimodal Approach in Terms of Students ’ Critical Thinking Ability. Pegem Journal of Education and Instruction, 13(3), 323–336. https://doi.org/10.47750/pegegog.1

Susiswo, Subanji, Chandra, T. D., Purwanto, & Sudirman. (2019). Folding back and pseudo-folding back of the student when solving the limit problem. Journal of Physics: Conference Series, 1227(1). https://doi.org/10.1088/1742-6596/1227/1/012014

Syafiqoh, N., Amin, S. M., & Siswono, T. Y. E. (2018). Analysis of Student’s Understanding of Exponential Concept: A Perspective of Pirie-Kieren Theory. Journal of Physics: Conference Series, 1108(1). https://doi.org/10.1088/1742-6596/1108/1/012022

Walida, S. El, Sa’dijah, C., Subanji, & Sisworo. (2022). A Portrait of Controversial Mathematics Problems and Students’ Metacognitive Awareness: A Case of Indonesia. Journal of Higher Education Theory and Practice, 22(12), 51–62. https://doi.org/10.33423/jhetp.v22i12.5462

Yang, Z., Yang, X., Wang, K., Zhang, Y., Pei, G., & Xu, B. (2021). The Emergence of Mathematical Understanding: Connecting to the Closest Superordinate and Convertible Concepts. Frontiers in Psychology, 12(November), 1–13. https://doi.org/10.3389/fpsyg.2021.525493

Yao, X. (2020). Characterizing Learners’ Growth of Geometric Understanding in Dynamic Geometry Environments: a Perspective of the Pirie–Kieren Theory. Digital Experiences in Mathematics Education, 6(3), 293–319. https://doi.org/10.1007/s40751-020-00069-1

Yao, X., & Manouchehri, A. (2020). Teacher Interventions for Advancing Students’ Mathematical Understanding. Education Sciences, 10(6), 1–21. https://doi.org/10.3390/educsci10060164

Yao, X., & Manouchehri, A. (2022). Folding Back in Students’ Construction of Mathematical Generalizations Within a Dynamic Geometry Environment. Mathematics Education Research Journal, 34(2), 241–268. https://doi.org/10.1007/s13394-020-00343-w

Yee, S. P., & Bostic, J. D. (2014). Developing a contextualization of students’ mathematical problem solving. Journal of Mathematical Behavior, 36, 1–19. https://doi.org/10.1016/j.jmathb.2014.08.002

DOI: https://doi.org/10.31764/jtam.v7i4.16835