Analysis of junior high school students’ algebraic reasoning abilities in solving problems viewed from the perspective of Adversity Quotient (AQ)

Fima Hayu Ning  Diyah; Ali  Shodikin

doi:10.31004/riggs.v5i1.7263

Authors

Fima Hayu Ning Diyah Universitas Negeri Surabaya
Ali Shodikin

DOI:

https://doi.org/10.31004/riggs.v5i1.7263

Keywords:

Algebraic Reasoning, Adversity Quotient, Problem Solving, Junior High School Students

Abstract

This study is motivated by the relatively low algebraic abilities of Indonesian students, particularly in transforming contextual problems into formal mathematical representations, as highlighted in recent mathematics education findings . Beyond cognitive factors, students’ success in overcoming such difficulties is strongly influenced by their mental resilience, known as Adversity Quotient (AQ). Therefore, this research aims to describe junior high school students’ algebraic reasoning abilities in problem-solving from the perspective of AQ. A descriptive qualitative approach was employed, involving three ninth-grade students representing each AQ category: climber, camper, and quitter. The subjects were selected through stratified purposive sampling based on the results of the Adversity Response Profile (ARP) questionnaire. Data were collected using written algebraic reasoning tasks integrating social arithmetic and two-variable linear inequalities, as well as in-depth semi-structured interviews. Data analysis followed the Miles, Huberman, and Saldaña model, including data condensation, data display, and conclusion drawing. The findings indicate significant differences in algebraic reasoning across AQ types. Climber students successfully demonstrated all stages of algebraic reasoning—pattern seeking, pattern recognition, and generalization—supported by persistence and adaptive strategies. Camper students showed adequate ability in identifying and recognizing patterns but were limited in formal representation and generalization. In contrast, quitter students experienced substantial difficulties at almost all stages, reflecting low persistence. These results confirm that AQ plays a crucial role in shaping students’ algebraic reasoning and problem-solving performance.

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References

OECD, PISA 2022 Results (Volume I): The State of Learning and Equity in Education. Paris, France: OECD Publishing, 2023, doi: 10.1787/53f23881-en.

C. S. Ayal and Y. S. Kusuma, “The enhancement of mathematical reasoning ability of junior high school students by applying mind mapping strategy,” Journal of Education and Practice, vol. 7, no. 25, pp. 50–58, 2016.

National Council of Teachers of Mathematics, Principles and Standards for School Mathematics. Reston, VA, USA: NCTM, 2000.

Ontario Ministry of Education, Paying Attention to Algebraic Reasoning: Support Document for Paying Attention to Mathematics Education. Toronto, ON, Canada: Queen’s Printer for Ontario, 2013.

C. Kieran, “Learning and teaching of algebra at the middle school through college levels,” in Second Handbook of Research on Mathematics Teaching and Learning, F. K. Lester Jr., Ed. Charlotte, NC, USA: National Council of Teachers of Mathematics, 2007, pp. 707–762.

K. Stacey and H. Chick, “The future of the teaching and learning of algebra: The 12th ICMI study,” in Third International Handbook of Mathematics Education, K. Clements and L. R. Ellerton, Eds. Dordrecht, Netherlands: Springer, 2004, pp. 535–571.

A. Jupri and P. H. M. Drijvers, “Student difficulties in mathematizing word problems in algebra,” Eurasia Journal of Mathematics, Science and Technology Education, vol. 12, no. 9, pp. 2481–2502, 2016, doi: 10.12973/eurasia.2016.1299a.

P. P. Sari and D. A. Lestari, “Analisis kesulitan siswa SMP dalam menyelesaikan soal cerita pada materi sistem persamaan linear dua variabel,” Jurnal Cendekia: Jurnal Pendidikan Matematika, vol. 4, no. 1, pp. 286–293, 2020, doi: 10.31004/cendekia.v4i1.181.

M. Ario and Suhendra, “Kesulitan siswa dalam menyelesaikan soal cerita aljabar,” AKSIOMA: Jurnal Program Studi Pendidikan Matematika, vol. 14, no. 2, pp. 458–472, 2025, doi: 10.24127/ajpm.v14i2.12440.

L. Radford, “Gestures, speech, and the upsurge of significations: A semiotic analysis of students’ algebraic activity,” Educational Studies in Mathematics, vol. 53, no. 2, pp. 101–125, 2003.

D. Glassmeyer and R. Edwards, “The role of algebraic reasoning in building conceptual knowledge,” The Mathematics Enthusiast, vol. 14, no. 1–3, pp. 579–606, 2017.

J. Mason, “Expressing generality and roots of algebra,” in Approaches to Algebra, N. Bednarz, C. Kieran, and L. Lee, Eds. Dordrecht, Netherlands: Kluwer Academic Publishers, 1996, pp. 65–86.

J. J. Kaput, “Teaching and learning a new algebra,” in Mathematics Classrooms that Promote Understanding, E. Fennema and T. A. Romberg, Eds. Washington, DC, USA: Lawrence Erlbaum Associates, 1999, pp. 133–155.

P. G. Stoltz, Adversity Quotient: Turning Obstacles into Opportunities. New York, NY, USA: John Wiley & Sons, 2000.

P. A. Setyaningrum and E. B. Rahaju, “Penalaran aljabar siswa SMP dalam menyelesaikan masalah SPLDV ditinjau dari gaya kognitif visualizer dan verbalizer,” MATHEdunesia: Jurnal Ilmiah Pendidikan Matematika, vol. 10, no. 1, pp. 79–94, 2021, doi: 10.26740/mathedunesa.v10n1.p79-94.

S. K. Dewi and R. Setianingsih, “Penalaran aljabar siswa sekolah menengah pertama dalam menyelesaikan soal open-ended ditinjau dari adversity quotient,” MATHEdunesia, vol. 14, no. 2, pp. 370–387, 2025, doi: 10.26740/mathedunesa.v14n2.p370-387.

M. L. Blanton and J. J. Kaput, “Characterizing a classroom practice that promotes algebraic reasoning,” Journal for Research in Mathematics Education, vol. 36, no. 5, pp. 412–446, 2005.

L. R. Ilmi and Abdussakir, “Analysis of students’ algebraic reasoning levels in solving PISA model problems in view of adversity quotient,” Journal of Physics: Conference Series, vol. 1200, no. 1, p. 012015, 2024, doi: 10.1088/1742-6596/1200/1/012015.

K. Herbert and R. H. Brown, “Patterns as tools for algebraic reasoning,” Teaching Children Mathematics, vol. 3, no. 6, pp. 340–345, 1997.

G. Polya, How to Solve It: A New Aspect of Mathematical Method, 2nd ed. Princeton, NJ, USA: Princeton University Press, 1973.

P. Andriani, “Penalaran aljabar dalam pembelajaran matematika,” Beta: Jurnal Tadris Matematika, vol. 8, no. 1, pp. 1–13, 2015.

E. Azhar, Y. Saputra, and I. Nuriadin, “Eksplorasi kemampuan pemecahan masalah matematis siswa pada materi perbandingan berdasarkan kemampuan matematika,” AKSIOMA: Jurnal Program Studi Pendidikan Matematika, vol. 10, no. 4, pp. 2129–2144, 2021, doi: 10.24127/ajpm.v10i4.3767.

L. Anwar, C. Sa’dijah, W. Murtafiah, and M. Huljannah, “Adversity quotient of Indonesian prospective mathematics teachers in solving geometry higher-order thinking skills problems,” Journal on Mathematics Education, vol. 15, no. 1, pp. 125–144, 2024, doi: 10.22342/jme.v15i1.pp79-98.

H. N. Rahmah and Masduki, “Pre-service mathematics teachers’ algebraic thinking in solving mathematics problems based on adversity quotient,” Prima: Jurnal Pendidikan Matematika, vol. 8, no. 1, pp. 156–168, 2023.

I. N. Sanit, S. Subanji, and I. M. Sulandra, “Profil penalaran aljabaris siswa dalam memecahkan masalah matematika ditinjau dari adversity quotient,” Jurnal Pendidikan: Teori, Penelitian, dan Pengembangan, vol. 4, no. 9, pp. 1213–1221, 2019, doi: 10.17977/jptpp.v4i9.12711.

M. B. Miles, A. M. Huberman, and J. Saldaña, Qualitative Data Analysis: A Methods Sourcebook, 3rd ed. Thousand Oaks, CA, USA: SAGE Publications, 2014.

M. L. A. Hidayah, A. Mashuri, and A. D. Rahmawati, “Analisis kemampuan berpikir aljabar siswa ditinjau dari adversity quotient (AQ),” Jurnal Jendela Matematika, vol. 2, no. 1, pp. 67–74, 2024, doi: 10.57008/jjm.v2i01.681.

F. X. D. Purwosetiyono et al., “Kemampuan penalaran siswa SMP dalam menyelesaikan soal literasi matematika pada tipe AQ,” Enggang: Jurnal Pendidikan, Bahasa, Sastra, Seni, dan Budaya, vol. 3, no. 1, 2025, doi: 10.37304/enggang.v3i1.8576.