Perseverance in mathematical reasoning of climber students solving linear equations in one variable
DOI:
https://doi.org/10.29408/jel.v12i2.33592Keywords:
adversity quotient, climber, linear equation, mathematical reasoning, one variable, perceveranceAbstract
Research on mathematical reasoning has increasingly recognized perseverance as more than "not giving up"; it requires maintaining coherent reasoning when facing obstacles. However, micro-level analysis linking perseverance episodes to Adversity Quotient (AQ) dimensions remains limited, particularly in linear equation-in-one-variable contexts. The study used a descriptive qualitative approach, a single-case qualitative study that examined one climber-type student (selected via ARP questionnaire from 32 eighth graders) solving Linear Equation on Linear Variable (LEOV) tasks. Data included observations, semi-structured interviews, and written work, analyzed using Miles and Huberman's framework with source triangulation. The results show that Climber (AA) students illustrate strong Perseverance in Mathematical Reasoning (PiMR) through three integrated behaviors: (1) exploring multiple solution strategies and verifying results (Control–Endurance); (2) reflecting on errors and adapting approaches (Ownership–Reach); and (3) maintaining goal focus while revising strategies (Endurance–Control). These findings imply that mathematics instruction should systematically scaffold productive struggle, validation practices, and self-regulation to develop reasoning-specific perseverance, not merely task persistence.
References
Anggraini, N., Utomo, D. P., & Azmi, R. D. (2023). Analysis of student errors in solving minimum competency assessment problems based on Kastolan theory. Kalamatika Jurnal Pendidikan Matematika, 8(1), 1–10. https://doi.org/10.22236/kalamatika.vol8no1.2023pp1-10
Anwar, L., Sa’dijah, C., Murtafiah, W., & Huljannah, M. (2024). Adversity quotient of Indonesian prospective mathematics teachers in solving geometry higher-order thinking skills problems. Journal on Mathematics Education, 15(1), 79–98. https://doi.org/10.22342/jme.v15i1.pp79-98
Barnes, A. (2019). Perseverance in mathematical reasoning: The role of children’s conative focus in the productive interplay between cognition and affect. Research in Mathematics Education, 21(3), 271–294. https://doi.org/10.1080/14794802.2019.1590229
Barnes, A. (2021). Enjoyment in learning mathematics: Its role as a potential barrier to children’s perseverance in mathematical reasoning. Educational Studies in Mathematics, 106(1), 45–63. https://doi.org/10.1007/s10649-020-09992-x
Charolina, S., & Suhendra, S. (2025). Profile of students’ mathematical problem-solving ability in view of adversity quotient. Range Jurnal Pendidikan Matematika, 7(1), 298–313. https://doi.org/10.32938/jpm.v7i1.9445
Chong, M. S. F., Shahrill, M., & Li, H.-C. (2019). The integration of a problem-solving framework for Brunei high school mathematics curriculum in increasing student’s affective competency. Journal on Mathematics Education, 10(2), 215–228. https://doi.org/10.22342/jme.10.2.7265.215-228
Dewanti, S. S. (2018). Profil berpikir kritis mahasiswa PGMI dalam memecahkan masalah matematika dasar [Critical thinking profiles of PGMI students in solving basic mathematical problems]. Matematika dan Pembelajaran, 6(1), 11–22. https://doi.org/10.33477/mp.v6i1.451
Eraky, A., Лейкин, Р., & Hadad, B. (2022). Relationships between general giftedness, expertise in mathematics, and mathematical creativity that associated with pattern generalization tasks in different representations. Asian Journal for Mathematics Education, 1(1), 36–51. https://doi.org/10.1177/27527263221093427
Eriksson, H., & Sumpter, L. (2021). Algebraic and fractional thinking in collective mathematical reasoning. Educational Studies in Mathematics, 108(3), 473–491. https://doi.org/10.1007/s10649-021-10044-1
Fernández-León, A., Izquierdo, J. M. G., & Toscano, R. (2021). A case study on how primary-school in-service teachers conjecture and prove: An approach from the mathematical community. Journal on Mathematics Education, 12(1), 49–72. https://doi.org/10.22342/jme.12.1.12800.49-72
Fudin, M. I., Cahyono, H., & Putri, O. R. U. (2022). Analysis of the visual to verbal mathematical representation process for junior high school students in solving HOTS questions in terms of adversity quotient. Mathematics Education Journal, 6(2), 195–203. https://doi.org/10.22219/mej.v6i2.23047
Fukawa-Connelly, T., Klein, V., Silverman, J., & Shumar, W. (2018). An online professional development model to support teachers’ abilities to examine student work and thinking. Mathematics Teacher Educator, 6(2), 39–51. https://doi.org/10.5951/mathteaceduc.6.2.0039
Hadi, S. (2025). Mathematical reasoning: How Students learn mathematics? Journal on Mathematics Education, 16(3), 937–954. https://doi.org/10.22342/jme.v16i3.pp937-954
Hasanah, N., Buchori, A., Prasetyowati, D., & Nursyahidah, F. (2019). Efektivitas model pembelajaran relating, experiencing, applying, cooperating, transferring (REACT) dan reciprocal teaching berbantuan game edukasi [The effectiveness of the relating, experiencing, applying, cooperating, and transferring (REACT) learning model and reciprocal teaching supported by educational games]. Pythagoras Jurnal Pendidikan Matematika, 14(1), 92–101. https://doi.org/10.21831/pg.v14i1.17157
Heck, D. J., Tarr, J. E., Hollebrands, K., Walker, E. N., Berry, R. Q., Baltzley, P. C., Rasmussen, C., & King, K. (2012). Reporting research for practitioners: Proposed guidelines. Journal for Research in Mathematics Education, 43(2), 126–143. https://doi.org/10.5951/jresematheduc.43.2.0126
Hendriana, H., Johanto, T., & Sumarmo, U. (2018). The role of problem-based learning to improve students’ mathematical problem-solving ability and self confidence. Journal on Mathematics Education, 9(2), 291–299. https://doi.org/10.22342/jme.9.2.5394.291-300
Hidayah, I. R., Sa’dijah, C., Anwar, L., Yerizon, Y., & Arnawa, I. M. (2024). Empowering students’ numeracy skills: mathematics teachers’ perceptions regarding the effectiveness and challenges of indonesian national curriculum and the programs – A mixed method Study. Infinity Journal, 14(1), 163–188. https://doi.org/10.22460/infinity.v14i1.p163-188
Hidayat, W., Wahyudin, W., & Prabawanto, S. (2018). The mathematical argumentation ability and adversity quotient (AQ) of pre-service mathematics teacher. Journal on Mathematics Education, 9(2), 239–248. https://doi.org/10.22342/jme.9.2.5385.239-248
Hundeland, P. S., Carlsen, M., & Erfjord, I. (2020). Qualities of mathematical discourses in kindergartens. ZDM, 52(4), 691–702. https://doi.org/10.1007/s11858-020-01146-w
Kinanti, M. A. H., Sujadi, İ., Indriati, D., & Kuncoro, K. S. (2023). Examining students’ cognitive processes in solving algebraic numeracy problems: A phenomenology study. Jurnal Elemen, 9(2), 494–508. https://doi.org/10.29408/jel.v9i2.13266
Martino, P. D. (2018). Pupils’ view of problems: The evolution from kindergarten to the end of primary school. Educational Studies in Mathematics, 100(3), 291–307. https://doi.org/10.1007/s10649-018-9850-3
Miles, M., Huberman, A., & Saldana, J. (2014). Qualitative data analysis (3rd ed.). SAGE Publications, Inc.
Napitupulu, E. E., Suryadi, D., & Kusumah, Y. S. (2016). Cultivating upper secondary students’ mathematical reasoning ability and attitude towards mathematics through problem-based learning. Journal on Mathematics Education, 7(2), 117–128. https://doi.org/10.22342/jme.7.2.3542.117-128
Nur, A. S., Kartono, K., Zaenuri, Z., & Rochmad, R. (2022). The lateral thinking processes in solving mathematical word problems reviewed at adversity quotient and reflective cognitive style. Infinity Journal, 11(2), 223–236. https://doi.org/10.22460/infinity.v11i2.p223-236
OECD. (2023). PISA 2022. In D. Lewalter, J. Diedrich, F. Goldhammer, O. Köller, & K. Reiss (Eds.), PISA: Vol. I. Waxmann Verlag GmbH. https://doi.org/10.31244/9783830998488
Pradini, W. (2019). Analisis kesalahan siswa dalam menyelesaikan soal cerita persamaan linear dua variabel [Analysis of students’ errors in solving word problems involving linear equations with two variables]. Pythagoras: Jurnal Pendidikan Matematika, 14(1), 33–45. https://doi.org/10.21831/pg.v14i1.21481
Rasyid, A. N., Rohati, R., & Kumalasari, A. (2025). Analisis perseverance in mathematical reasoning (PiMR) siswa dengan tipe AQ camper pada materi persamaan linear satu variabel (PLSV) [Analysis of perseverance in mathematical reasoning (PiMR) among students with the “camper” AQ type when studying single-variable linear equations (PLSV)]. Kognitif: Jurnal Riset HOTS Pendidikan Matematika, 5(2), 923–934. https://doi.org/10.51574/kognitif.v5i2.3088
Richit, A., Ponte, J. P. d., & Quaresma, M. (2021). Aprendizagens profissionais de professores evidenciadas em pesquisas sobre estudos de aula [Teachers’ professional learning as evidenced in research on classroom studies]. Bolema Boletim De Educação Matemática, 35(70), 1107–1137. https://doi.org/10.1590/1980-4415v35n70a26
Säfström, A. I., Lithner, J., Palm, T., Palmberg, B., Sidenvall, J., Andersson, C., Boström, E., & Granberg, C. (2024). Developing a diagnostic framework for primary and secondary students’ reasoning difficulties during mathematical problem solving. Educational Studies in Mathematics, 115(2), 125–149. https://doi.org/10.1007/s10649-023-10278-1
Stoltz, P. G. (1997). Adversity quotient: Turning obstacles into opportunity. John Wiley & Sons.
Syamsyiah, Z. M., & Handayani, I. (2023). Analysis of numerical literacy ability of junior high school students in view of adversity quotient and gender. Edumatica | Jurnal Pendidikan Matematika, 13(02), 136–151. https://doi.org/10.22437/edumatica.v13i02.26353
Tampa, A., Layly, S., Helmi, H., & Alimuddin, N. F. (2022). The students’ numerical literacy ability in junior high schools. Kreano Jurnal Matematika Kreatif-Inovatif, 13(2), 269–282. https://doi.org/10.15294/kreano.v13i2.37541
Warshauer, H. K. (2014). Productive struggle in middle school mathematics classrooms. Journal of Mathematics Teacher Education, 18(4), 375–400. https://doi.org/10.1007/s10857-014-9286-3
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 Ade Kumalasari, Rohati Rohati, Sri Winarni, Marlina Marlina, Annisa Nur Rasyid
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Authors who publish with the Jurnal Elemen agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under Creative Commons Attribution-ShareAlike 4.0 International License (CC BY-SA 4.0).
- Authors are able to enter into separate, additional contractual arrangements for the distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
Jurnal Elemen is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License
