Algebraic reasoning of high school students in solving inverse function problems: Viewed from mathematical resilience

Aflich Yusnita Fitrianna, Rizky Rosjanuardi, Sufyani Prabawanto

Abstract


Algebra is one of the essential branches of mathematics that often presents challenges for students, especially when faced with inverse function problems. This study aims to describe algebraic reasoning in solving inverse function problems from the perspective of students' mathematical resilience. This qualitative research uses a case study design involving 33 eleventh-grade students from a public high school in West Bandung Regency. The instruments used were a mathematical resilience scale and an algebraic reasoning test. Data analysis was conducted through data reduction, presentation, and conclusion drawing. The results showed that 15.15% of students had low resilience, 72.72% had moderate resilience, and 12.12% had high resilience. There were different characteristics in algebraic reasoning among students in these resilience categories. The implications indicate that targeted learning strategies can enhance algebraic reasoning, especially for moderate and low-resilience students.

Keywords


algebraic reasoning, high school students, inverse of function, mathematics resilience, qualitative research

Full Text:

PDF

References


M. Chirimbana, “The effect of a problem based learning approach on the teaching and learning of composition and inverses of functions in a foundation programme,” Ph.D. dissertation, Dept. Education, Stellenbosch University, 2014. [Online]. Available: https://scholar.sun.ac.za/items/90cf7d5f-de3d-4430-b6a7-7ad8fe2c3a16

L. Delastri, Purwanto, Subanji, and M. Muksar, “Students ’ conceptual understanding on inverse function concept,” in International Conference on Mathematics and Science Education, 2018. pp. 1-7, doi: 10.1088/1742-6596/1157/4/042075.

K. Chan and Y. Zhou, “Effects of cooperative learning with dynamic mathematics software (DMS) on learning inversely proportional functions,” Int. J. Emerg. Technol. Learn., vol. 15, no. 20, pp. 210–225, 2020.

M. Ikram, I. N. Parta, and H. Susanto, “Exploring the Potential Role of Reversible Reasoning: Cognitive Research on Inverse Function Problems in Mathematics,” J. Educ. Gift. Young Sci., vol. 8, no. 1, pp. 591–611, 2020.

D. Castillo, J. Carrión, C. Chamba, Y. Jiménez, M. J. Rodríguez-Álvarez, and V. Lakshminarayanan, “Teaching math: A review of effective teaching and learning strategies in higher education,”, vol. 1, no. 1, pp. 1-32, 2024, doi : 10.21203/rs.3.rs-4708199/v1.

S. A. Licorish, H. E. Owen, B. Daniel, and J. L. George, “Students’ perception of Kahoot!’s influence on teaching and learning,” Res. Pract. Technol. Enhanc. Learn., vol. 13, no. 1, pp. 1–23, 2018.

I. Bayazit and E. Gray, “Understanding Inverse functions: The relationship between teaching practice and student learning,” in Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, 2004, vol. 2, no. 1986, pp. 103–110.

T. Paoletti, “Reasoning about relationships between quantities to reorganize inverse function meanings: The case of arya,” J. Math. Behav., vol. 57, no. 1, pp. 1-24, 2020, doi: 10.1016/j.jmathb.2019.100741.

C. Kieran, “Algebraic thinking in the early grades: What is it,” Math. Educ., vol. 8, no. 1, pp. 139–151, 2004.

A. Twohill, “Algebraic reasoning in primary school: Developing a framework of growth points,” in Proceedings of the British Society for Research into Learning Mathematics, 2013, vol. 33, no. June, pp. 55–60.

D. W. Carraher, A. D. Schliemann, B. M. Brizuela, and D. Earnest, “Arithmetic and algebra in early mathematics education,” J. Res. Math. Educ., vol. 37, no. 2, pp. 87–115, 2006.

J. R. Lepak, J. L. W. Wernet, and R. A. Ayieko, “Capturing and characterizing students’ strategic algebraic reasoning through cognitively demanding tasks with focus on representations,” J. Math. Behav., vol. 50, no. 1, pp. 57–73, 2018, doi: 10.1016/j.jmathb.2018.01.003.

R. Even, “The inverse function: Prospective teachers’ use of ‘undoing,’” Int. J. Math. Educ. Sci. Technol., vol. 23, no. 4, pp. 557–562, 1992, doi: 10.1080/0020739X.1992.10715689.

J. Nolasco, “The struggle with inverse functions doing and undoing process,” California State University, 2018.

D.-D. Andrea, “Investigating student leaning and building the concept of inverse function,” The State University of New Jersey, 2011.

M. N. Hanifah and U. Fatmahanik, “Students’ learning difficulties in learning mathematics in view of mathematical resilience,” in Syekh Nurjati International Conference on Elementary Education, 2023, pp. 277–291, doi : 10.24235/sicee.v1i0.14631.

A. O. A. Awofala, “A validation of the mathematical resilience scale for twelfth graders through confirmatory factor analysis and its relationship with achievement in mathematics in Nigeria,” SN Soc. Sci., vol. 1, no. 8, pp. 1-17, 2021.

Johnston-Wilder and C. Lee, “Developing mathematical resilience,” in BERA Annual Conference 2010, University of Warwick, Sept. 1-4, 2010, pp. 1–16.

C. Lee and S. Johnston-Wilder, The Construct of Mathematical Resilience. Elsevier Inc : Belanda, 2017.

A. N. A. Hindi and I. Muthahharah, “Teacher’s perception of student’s mathematics learning difficulties,” Daya Mat. J. Inov. Pendidik. Mat., vol. 9, no. 1, pp. 170–177, 2021.

S. Rohmah, T. A. Kusmayadi, and L. Fitriana, “Problem solving ability of junior high school students viewed by mathematical resilience,” Univers. J. Educ. Res., vol. 8, no. 7, pp. 3026–3033, 2020.

M. A. Rudin and M. T. Budiarto, “MATHE dunesa,” J. Ilm. Pendidik. Mat., vol. 8, no. 2, pp. 232–237, 2019.

P. E. Kobandaha, Y. Fuad, and Masriya, “Algebraic reasoning of students with logical-mathematical intelligence and visual-spatial intelligence in solving algebraic problems,” Int. J. Trends Math. Educ. Res., vol. 2, no. 4, pp. 207–211, 2019, doi: 10.33122/ijtmer.v2i4.138.

N. Authary and Nazariah, “Pelevalan penalaran aljabar siswa dalam memecahkan masalah matematika berbasis taksonomi structure of the observed learning outcome (SOLO),” J. Numer., vol. 6, no. 2, pp. 274–282, 2019.

Rifdah and N. Priatna, “The relationship between mathematics resilience and mathematics communication skills,” in International Conference on Mathematics and Science Education, 2019, pp. 1-6, doi: 10.1088/1742-6596/1521/3/032037.

D. Attami, B. Budiyono, and D. Indriati, “The mathematical problem-solving ability of junior high school students based on their mathematical resilience,” in International Conference on Mathematics and Science Education, 2020, pp. 1-8, doi: 10.1088/1742-6596/1469/1/012152.

Laelasari, Darhim, and S. Prabawanto, “Analysis of students ’ mathematics resilience abilities on linear program material,” in MSCEIS, 2018, pp. 1-5, doi: 10.1088/1742-6596/1280/4/042005.

A. Haerani, K. Novianingsih, and Turmudi, “Analysis of students ’ errors in solving word problems viewed from mathematical resilience,” J. Teor. dan Apl. Mat., vol. 5, no. 1, pp. 246–253, 2021.

A. Suri and T. Herman, “How are the contributions of mathematics resilience for developing attitude rubric to assess mathematics learning ?,” in International Converence on Mathematics and Science Education, 2019, pp. 1-6, doi: 10.1088/1742-6596/1521/3/032055.

S. Arikunto, Prosedur Penelitian. Jakarta: Rineka Cipta, 2012.

N. H. Fitrah, N. Fatihah, and A. Madihie, “Resilience in mathematics , academic resilience , or mathematical resilience ?: An overview,” Univers. J. Educ. Res., vol. 8, pp. 34–39, 2020, doi: 10.13189/ujer.2020.081905




DOI: http://dx.doi.org/10.24042/ijsme.v7i2.21087

Refbacks

  • There are currently no refbacks.




Copyright (c) 2024 Unit Riset dan Publikasi Ilmiah FTK UIN Raden Intan Lampung

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Creative Commons License

Indonesian Journal of Science and Mathematics Education is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License